Univariate and Dynamic Multivariate Analysis of Functional MRI Data 
 
by 
 
Hao Jia 
 
 
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Doctor of Philosophy 
 
Auburn, Alabama 
May 4, 2014 
 
 
 
 
Keywords: Functional MRI, Awake animal imaging, Functional connectivity, Effective 
connectivity, Clustering, Support vector machine 
 
 
Copyright 2014 by Hao Jia 
 
 
Approved by 
 
Gopikrishna Deshpande, Chair, Assistant Professor, Department of Electrical & Computer 
Engineering 
Thomas Denney, Director, Auburn University MRI Research Center 
Jeffrey Katz, Alumni Professor, Department of Psychology Auburn University 
Prathima Agrawal, Professor, Department of Electrical & Computer Engineering 
  
ii 
 
Abstract 
 
 
Functional magnetic resonance imaging (fMRI) has been increasingly used in the past decade 
for inferring brain function in both healthy and clinical populations. In this dissertation, we 
demonstrate fMRI data analysis strategies using both univariate and multivariate models. We 
demonstrate the utility of mass univariate general linear regression models in a novel context 
wherein we analyzed fMRI data of conscious dogs to investigate their olfactory system at the 
cognitive level. We investigated the modulation of olfactory related activity in the canine brain 
as a function of odorant concentration and dogs? consciousness state (lightly anesthetized or fully 
conscious). Besides, we conducted experiments with zinc nanoparticles added to the odorant to 
investigate their enhancement effect on olfactory perception, with pure odorant and odorant + 
gold nanoparticles as control conditions. The major finding was that olfactory bulb and piriform 
lobes were commonly activated in both awake and anesthetized dogs, while the frontal cortex 
and cerebellum were activated mainly in conscious dogs. Comparison of responses to low and 
high odorant concentrations showed differences in both the intensity and spatial extent of 
activation in the olfactory bulb, piriform lobes, cerebellum, and frontal cortex. Zinc nanoparticles 
conspicuously enhanced activations of olfactory bulb and olfactory cortex for anesthetized dogs 
and frontal areas for conscious dogs, compared to pure odorant and odorant + gold nanoparticles. 
On the other hand, multivariate regression models of fMRI data were employed to investigate 
connectivity between different regions of the brain. We used human resting state fMRI data to 
calculate four types of connectivities: static & dynamic functional connectivity (FC), and static 
iii 
 
& dynamic effective connectivity (EC). For dynamic connectivities, we used adaptive 
evolutionary clustering algorithm to cluster brain network states, correlated FCs with behavioral 
metrics, and linked EC network patterns to real world functionalities. We found several major 
patterns of brains states alternating with each other in a quasi-stable way, featuring the default 
mode network (DMN) in FC patterns and temporal-parietal-frontal interactions in EC patterns. 
Also, connectivity dynamics were testified to have more power in explaining behavior as 
compared to the static counterparts. Finally, connectivity dynamics were compared with 
connectivity statics with an application to classify patients with post-traumatic stress disorder 
(PTSD) and healthy individuals. We found that the temporal variability of connectivities had 
more sensitivity in predicting the diagnostic label of a novel subject than connectivity statics. 
 
  
iv 
 
Acknowledgments 
 
 
 I would like to thank my advisor, Dr. Gopikrishna Deshpande, for his prominent 
instructiveness in analyzing data, great patience in reviewing and modifying manuscripts, 
sparkling ideas and exquisite insight in trouble shooting during data processing. I would like to 
thank Oleg Pustovyy, Paul Waggoner, Ronald Beyers, John Schumacher, Chester Wildey, Jay 
Barrett, Edward Morrison, Nouha Salibi, Thomas Denney and Vitaly Vodyanoy for their 
cooperation and great help in conducting dog fMRI experiments, especially Ronald Beyers for 
his guidance in operating fMRI scans and Vitaly Vodyanoy for providing in vitro data of electro-
olfactogram measurement and suggestions on analysis of dog fMRI data about zinc nanoparticles? 
effect. Next, I would like to thank my friends in MRI center for their great help and 
encouragement, especially Pruthviraj Kyathanahally and Karthik Sreenivasan for help in 
software troubleshooting. Also, I would like to thank Prof. Xiaoping Hu for his precious 
feedback on projects about human data. For projects in Chapter 2 and Chapter 3, I acknowledge 
funding support from Auburn University Intramural Level-3 research grant from the Office of 
the Vice President for Research, Auburn University, and support by the Defense Advanced 
Research Projects Agency (government grant/contract number W911QX-13-C-0123). For 
project in Chapter 4, data were provided by the Human Connectome Project, WU-Minn 
Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657). 
 
  
v 
 
Table of Contents 
 
 
Abstract ......................................................................................................................................... ii 
Acknowledgments........................................................................................................................ iv 
List of Tables ................................................................................................................................ x 
List of Figures ............................................................................................................................. xii 
Chapter 1 Introduction .................................................................................................................. 1 
 1.1MRI & Functional MRI .................................................................................................... 1 
 1.2 FMRI Data Preprocessing ................................................................................................ 6 
1.2.1 Slice Timing Correction ........................................................................................... 7 
1.2.2 Realignment & Reslice ............................................................................................ 7 
1.2.3 Coregistration & Normalization ............................................................................... 8 
1.2.4 Temporal Filtering ................................................................................................... 8 
1.2.5 White Matter and Cerebrospinal Fluid Signal Removal .......................................... 9 
1.2.6 Spatial Smoothing .................................................................................................... 9 
 1.3 Organization of This Dissertation .................................................................................. 10 
Chapter 2 Univariate Analysis: Functional MRI of the Olfactory System in Conscious Dogs .. 12 
2.1 Introduction .................................................................................................................... 12 
2.2 Material and Methods .................................................................................................... 16 
2.2.1 Overview of the Dog FMRI Olfactory Imaging System ........................................ 16 
2.2.2 Dog Training and Preparation ................................................................................ 18 
vi 
 
2.2.3 Olfactory Stimulus Device ..................................................................................... 21 
2.2.4 Optical Head Motion Tracking .............................................................................. 26 
2.2.5 Stimulation Paradigm ............................................................................................. 28 
2.2.6 Data Acquisition..................................................................................................... 29 
2.2.7 Image Processing ................................................................................................... 30 
2.2.8 General Linear Modeling and Statistical Testing................................................... 32 
2.3 Results ............................................................................................................................ 35 
2.3.1 Spatial Normalization............................................................................................. 35 
2.3.2 Low and High Odor Concentration in Anesthetized and Conscious Dogs ............ 37 
2.3.3 Parametric Modulation of BOLD Signal by Odor Concentration ......................... 43 
2.3.4 Effect of Motion ..................................................................................................... 48 
2.4 Discussion ...................................................................................................................... 52 
Chapter 3 Univariate Analysis: Enhancement of Odor-induced Activity in the Canine Brain by 
 Zinc Nanoparticles: A Functional MRI Study in Conscious Dogs ............................ 60 
3.1 Introduction .................................................................................................................... 60 
3.2 Material and Methods .................................................................................................... 64 
3.2.1 Dog Preparation ..................................................................................................... 64 
3.2.2 Odorants ................................................................................................................. 65 
3.2.3 Dog FMRI Olfactory Imaging System ................................................................... 66 
3.2.4 Data Acquisition..................................................................................................... 67 
3.2.5 Experimental Paradigm .......................................................................................... 68 
3.2.6 Post Processing ...................................................................................................... 69 
3.3 Results ............................................................................................................................ 70 
3.4 Discussion ...................................................................................................................... 86 
vii 
 
Chapter 4 Dynamic Multivariate Analysis: Behavioral Relevance of the Dynamics of Functional 
 Brain Connectome ...................................................................................................... 93 
4.1 Introduction .................................................................................................................... 93 
4.2 Materials and Methods ................................................................................................... 99 
4.2.1 Data Acquisition and Pre-processing ..................................................................... 99 
4.2.2 Behavioural and Individual Difference Measures ................................................ 100 
4.2.3 Dynamic Functional Connectivity Model ............................................................ 100 
4.2.4 Clustering ............................................................................................................. 102 
4.2.5 Behavioral Relevance of Dynamic FC ................................................................. 119 
4.3 Results .......................................................................................................................... 111 
4.3.1 Simulation ............................................................................................................ 111 
4.3.2 Application to Experimental Resting State FMRI Data from HCP ..................... 115 
4.4 Discussion .................................................................................................................... 133 
Chapter 5 Dynamic Multivariate Analysis: Finite Number of Directional Brain Network 
Configurations Revealed from Time-Varying Connectivity Assessment of Resting 
 State FMRI ............................................................................................................... 139 
5.1 Introduction .................................................................................................................. 139 
5.2 Material and Methods .................................................................................................. 143 
5.2.1 Data Acquisition and Pre-processing ................................................................... 143 
5.2.2 Dynamic Effective Connectivity Model .............................................................. 144 
5.2.3 Clustering ............................................................................................................. 147 
5.2.4 Potential Correlates with Real World Functionalities .......................................... 153 
5.2.5 Simulation Setup .................................................................................................. 154 
5.3 Results .......................................................................................................................... 155 
5.3.1 Simulation Result ................................................................................................. 155 
viii 
 
5.3.2 Experimental Data Result .................................................................................... 158 
5.4 Discussion .................................................................................................................... 169 
Chapter 6 Dynamic Multivariate Analysis: Dynamic Brain Connectivity Is a Better Predictor of 
 PTSD than Static Connectivity................................................................................. 172 
6.1 Introduction .................................................................................................................. 172 
6.2 Material and Methods .................................................................................................. 174 
6.2.1 Data Acquisition and Preprocessing .................................................................... 174 
6.2.2 Static and Dynamic Effective Connectivity ......................................................... 175 
6.2.3 Static and Dynamic Functional Connectivity ...................................................... 177 
6.2.4 RCE-SVM Classification ..................................................................................... 178 
6.3 Results .......................................................................................................................... 182 
6.4 Discussion .................................................................................................................... 192 
Chapter 7 Conclusion ................................................................................................................ 198 
Chapter 8 Information on Published and Submitted Papers ..................................................... 200 
Bibliography ............................................................................................................................. 202 
Appendix A ............................................................................................................................... 217 
A.1 Selection of Sliding Window Length Range .............................................................. 217 
A.2 190 ROI Version of CC200 Atlas: Anatomical Labels and MNI Co-ordinates ......... 218 
A.3 Description of Behavioral Measures Employed in This Work ................................... 223 
A.4 Paths with Most and Least MTSTs ............................................................................. 226 
A.5 Regions with Top and Bottom 20% rMTST and rCFP ............................................... 228 
A.6 Paths with MTSTs Significantly Correlating with Selected Behavioral Measures .... 230 
A.7 Schematic of Distance Measure Calculation in Second Level Clustering .................. 235 
A.8 An Illustrative Example of the Calculation of Metrics: MTST, SDTST, CFP ........... 236 
ix 
 
Appendix B ............................................................................................................................... 238 
  
x 
 
List of Tables 
 
 
Table 2.1 ..................................................................................................................................... 41 
Table 2.2  .................................................................................................................................... 42 
Table 2.3  .................................................................................................................................... 42 
Table 2.4 ..................................................................................................................................... 43 
Table 2.5  .................................................................................................................................... 45 
Table 2.6  .................................................................................................................................... 46 
Table 3.1  .................................................................................................................................... 78 
Table 3.2  .................................................................................................................................... 79 
Table 3.3  .................................................................................................................................... 79 
Table 3.4  .................................................................................................................................... 80 
Table 3.5  .................................................................................................................................... 80 
Table 3.6  .................................................................................................................................... 80 
Table 3.7  .................................................................................................................................... 84 
Table 4.1  .................................................................................................................................. 119 
Table 5.1  .................................................................................................................................. 159 
Table 5.2  .................................................................................................................................. 169 
Table A1 ................................................................................................................................... 218 
Table A2 ................................................................................................................................... 223 
Table B1  ................................................................................................................................... 238 
xi 
 
Table B2  ................................................................................................................................... 240 
 
  
xii 
 
List of Figures 
 
 
Figure 1.1 ...................................................................................................................................... 2 
Figure 1.2 ...................................................................................................................................... 6 
Figure 2.1 .................................................................................................................................... 16 
Figure 2.2 .................................................................................................................................... 17 
Figure 2.3 .................................................................................................................................... 18 
Figure 2.4 .................................................................................................................................... 24 
Figure 2.5 .................................................................................................................................... 25 
Figure 2.6 .................................................................................................................................... 26 
Figure 2.7 .................................................................................................................................... 32 
Figure 2.8 .................................................................................................................................... 36 
Figure 2.9 .................................................................................................................................... 39 
Figure 2.10 .................................................................................................................................. 41 
Figure 2.11 .................................................................................................................................. 45 
Figure 2.12 .................................................................................................................................. 47 
Figure 2.13 .................................................................................................................................. 48 
Figure 2.14 .................................................................................................................................. 50 
Figure 2.15 .................................................................................................................................. 52 
Figure 3.1 .................................................................................................................................... 63 
Figure 3.2 .................................................................................................................................... 66 
xiii 
 
Figure 3.3 .................................................................................................................................... 68 
Figure 3.4 .................................................................................................................................... 75 
Figure 3.5 .................................................................................................................................... 78 
Figure 3.6 .................................................................................................................................... 82 
Figure 3.7 .................................................................................................................................... 83 
Figure 3.8 .................................................................................................................................... 85 
Figure 4.1 .................................................................................................................................... 96 
Figure 4.2 .................................................................................................................................. 109 
Figure 4.3 .................................................................................................................................. 109 
Figure 4.4 .................................................................................................................................. 114 
Figure 4.5 .................................................................................................................................. 119 
Figure 4.6 .................................................................................................................................. 121 
Figure 4.7 .................................................................................................................................. 122 
Figure 4.8 .................................................................................................................................. 124 
Figure 4.9 .................................................................................................................................. 125 
Figure 4.10 ................................................................................................................................ 133 
Figure 5.1 .................................................................................................................................. 143 
Figure 5.2 .................................................................................................................................. 153 
Figure 5.3 .................................................................................................................................. 157 
Figure 5.4 .................................................................................................................................. 159 
Figure 5.5 .................................................................................................................................. 160 
Figure 5.6 .................................................................................................................................. 167 
Figure 5.7 .................................................................................................................................. 169 
xiv 
 
Figure 6.1 .................................................................................................................................. 181 
Figure 6.2 .................................................................................................................................. 182 
Figure 6.3 .................................................................................................................................. 183 
Figure 6.4 .................................................................................................................................. 184 
Figure 6.5 .................................................................................................................................. 191 
Figure 8.1 .................................................................................................................................. 200 
Figure A1 .................................................................................................................................. 227 
Figure A2 .................................................................................................................................. 228 
Figure A3 .................................................................................................................................. 229 
Figure A4 .................................................................................................................................. 235 
Figure A5 .................................................................................................................................. 236 
Figure A6 .................................................................................................................................. 237 
  
1 
 
Chapter 1 Introduction 
 
1.1 MRI & Functional MRI 
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology, 
biomedical research, and clinic diagnostics to visualize internal structures of the body in detail 
[1]. MRI is a noninvasive technique which uses magnetic field and electro-magnetic waves as 
probe to detect tissues and organs inside the body. It makes use of the property of nuclear 
magnetic resonance (NMR) of atoms for imaging [2] [3]. Body tissue contains lots of water, and 
hence protons, which can get aligned with a larger magnetic field. When people lie inside a MRI 
scanner, large static magnetic field (produced by a superconducting magnet) makes protons 
aligned with the direction of the field. A gradient magnetic field (produced by gradient magnet 
coil) is often added to select the proper layer or location of the body that is to be imaged. Then a 
transient radio frequency current pulse (produced by radio frequency coil) is transmitted to the 
body, with the frequency corresponds to the static magnetic field strength of the layer selected, 
such that a resonance of precession results. After the electromagnetic wave is turned off, the 
precession of protons relaxes and bulk magnetization becomes re-aligned to the static magnetic 
field. During this course, a radio frequency electromagnetic wave is generated from the imaged 
layer and received by coils for imaging. By using different gradient magnetic field design, it can 
be made magnetizations at different spatial locations precess in different patterns, which enables 
different k-space encoding of spatial information [4]. Also in this way, 2D images or 3D 
volumes can be obtained in any arbitrary orientation. Using inverse Fourier transformation, k-
space information is transformed into image domain, recovering the spatial information of 
scanned area.  
2 
 
Protons in different tissues return to their equilibrium state at different relaxation rates. 
Different tissue has different proton density, T1 and T2 relaxation times (for T1 and T2 
relaxation mechanism, please see [3]), which can be utilized to construct images of different 
contrast. Images of different contrast can reflect different properties of scanned area, and thus 
have different applications, such as those of functional MRI and diffusion tensor MRI. 
Hitherto, MRI is the imaging technique known that can provide the most amount of imaging 
modalities and best image quality: good contrast between different tissues and high resolution. 
Thus, it has broad prevalence in brain imaging, muscles, heart, and cancer imaging, over other 
medical imaging techniques like X-rays and computed tomography (CT) [5] [6]. A schematic of 
MRI scanner is illustrated in Fig.1.1. 
 
Figure 1.1 Schematic of a MRI scanner 
 
Functional magnetic resonance imaging (fMRI) is now a primary tool to study the 
organization of a working brain, and relevant clinical applications are growing exponentially [7] 
[8] [9] [10]. Since the early 1990s, fMRI has become to dominate brain mapping research 
because this non-invasive technique does not require people to undergo shots, surgery, or to 
Superconducting 
magnet 
Scanner 
Patient Patient table 
Radio frequency 
coil 
Gradient coil 
3 
 
ingest substances, or be exposed to radiation. So it is relatively ecologically safe. FMRI 
technique measures the blood oxygenation level dependent signal (BOLD) in the brain, based on 
which the neuronal activity in the brain can be inferred [11]. There is an intrinsic physiological 
agent that signifies blood susceptibility: deoxyhemoglobin (dHb). Deoxyhemoglobin is 
paramagnetic and thus changes the susceptibility of blood. As local blood becomes more 
deoxygenated, the MR (magnetic resonance) signal drops. The brain does not store glucose 
which is the primary source of its energy. When neurons go active, getting them back to their 
original (polarized) state requires actively pumping ions back and forth across the neuronal cell 
membranes. The energy for these motor pumps is produced from glucose. More blood flows in 
to transport more glucose, also bringing in more oxygen in the form of oxygenated hemoglobin 
molecules in red blood cells. This is from both a higher rate of blood flow and an expansion of 
blood vessels. The blood-flow change is localized to within 2 or 3 mm of where the neural 
activity is. Usually the oxygen brought in is more than the oxygen consumed for burning glucose, 
and this causes a net decrease in dHb in that brain area's blood vessels [12] [9]. In a word, 
neuronal activity and cerebral blood flow are coupled in such a way that when neuron fires, the 
demand of energy and thus metabolism rate around the firing place increase, leading to the 
increase of regional blood flow and decrease of capillary and venous dHb concentrations. As a 
consequence, an increase in magnetic spin-spin relaxation times T2* and T2 occurs, resulting in 
an increase of intensity in T2*- and T2-weighted MR images [3]. Such a complicated relationship 
between neuronal activity and BOLD signal reflects as the hemodynamic response (HDR). The 
HDR normally starts about 1 to 2 seconds after the triggering of neuronal activity, and then rises 
up to a peak at about 5 seconds thereafter. Then, it falls till below the baseline, forming a small 
4 
 
?undershoot?, and finally goes back to the baseline. If the neuron keeps firing, the peak would 
spread to a flat plateau [9] [10].  
Functional MRI takes snapshots of brain consecutively in time in order to track functionality 
of the brain (Fig.1.2). Therefore, the temporal resolution is of great importance. Nowadays, the 
temporal resolution can reach to as small as 200ms, but the BOLD signal has intrinsic limitation 
of temporal resolution, which prevents the temporal resolution from further increasing. This 
blockage can be overcome by deconvolution technique [13]. 
Although functional MRI has relatively poor temporal resolution compared with underlying 
neuronal signals, it does have a relatively high spatial resolution when compared with other 
imaging techniques. The spatial resolution of fMRI is measured by size of voxels, which is 
determined by scanning parameters like slice thickness and in-plane matrix resolution. Normally, 
the spatially resolution ranges from 1mm to 5mm. A full brain scan uses larger voxels, while a 
region of interest (ROI) study within the brain typically uses smaller voxels. To offset the 
shortage of temporal resolution and draw on its strength of spatial resolution, fMRI can be and 
has been combined with other modalities of brain physiology imaging such as electroencephalo-
graph (EEG) and magnetoencephalogram (MEG) [10]. Meanwhile new techniques which 
improve both spatial and temporal resolutions are being researched [14]. 
For every time of repetition (TR), a 3D volume image is generated by the scanner. All 3D 
images generated during the scan can be put together to form a 4D volume image. Since fMRI is 
designed to track the change of brain BOLD signal and one volume should be imaged timely fast, 
the signal-to-noise ratio (SNR) cannot be very high and corruption from noise is not negligible. 
The statistical post-processing is often employed to suppress noise and extract the underlying 
true signal or true activation. A statistical activation means the signal in one region passes the 
5 
 
statistical hypothetical testing and the null assumption is rejected. The activation map can be 
displayed graphically by color-coding the strength of activation. Currently the activation map 
can be localized to within millimeter scope. 
Pertaining to clinic applications, physicians use fMRI to assess brain healthy condition, provide 
reference for surgery or invasive treatment, and get insights into how a normal, diseased or 
injured brain is functioning. A mapping of brain regions to real world functionalities such as 
speaking, walking, and smelling offers valuable information for diagnostics. Clinicians also use 
fMRI to inspect the anatomy of the brain and detect tumors, stroke, lesion, or atrophy [15].  
An example of fMRI volume image acquired at one TR is illustrated in Fig.1.2. 
6 
 
 
Figure 1.2 An example of functional MRI volume image acquired at one TR. This functional 
volume of EPI (echo-planar imaging) images acquired at one TR is comprised of 14 axial slices 
of a resting human brain. All axial slices are sequentially shown with each slice?s z coordinate 
(slice number) shown at top left corner. (A: anterior, P: posterior, L: left, R: right) 
 
1.2 FMRI Data Preprocessing 
Raw fMRI data cannot be directly used for brain functionality analysis, since there exist noise, 
head motion, field non-uniformity, acquisition asynchrony and so on [10]. Normally, a standard 
preprocessing pipeline of raw fMRI data includes slice timing correction, realignment, reslice, 
coregistration/normalization, temporal filtering, white matter and cerebrospinal fluid (CSF) 
z=14 z=13 z=12 z=11 
z=9 z=10 z=8 z=7 
z=0 z=1 z=2 
z=6 z=5 z=4 z=3 
7 
 
signal removal, and spatial smoothing. Some preprocessing pipelines may include grand mean 
normalization. 
1.2.1 Slice Timing Correction 
Slice timing correction is to align each slice in temporal domain. Since the slices at different z 
positions have staggered acquisition time, the data on one slice will represent a point in time as 
far removed as 1/2 the TR from an adjacent slice (in the case of an interleaved sequence). Slice 
timing correction performs interpolation such that all slices appear to be acquired at the same 
instant. This is accomplished by a simple shift of the phase of the sines that make up the signal. 
The shifted signal is typically resampled using sinc-interpolation. 
1.2.2 Realignment & Reslice 
While slice timing performs alignment of images in the temporal domain, realignment does it 
in the spatial domain. Due to head motion during the scanning which is inevitable, and even 
physiological noise such as breathing and heartbeat, the images acquired at different time 
instants cannot be perfectly matched. Thus a spatial realignment of all images is needed. The 
motion effect can be accounted for by rigid body translations in 3 directions and rotations in 3 
directions. A reference image (normally the first image or the mean image) is set as to calculate 
the rigid body transformation parameters between the reference image and the image to be 
realigned. Then the rigid body transformation is imposed on each image so that all images are 
aligned to each other. The 6 parameters (3 translations and 3 rotations) are calculated under least 
square sense.  
After realignment, the function ?reslice? performs resampling a series of registered images 
such that they are on the same volume of slices and match each other voxel-by-voxel. During 
this procedure, interpolation is effected for which there are many algorithms including nearest 
8 
 
neighbor method, trilinear and spline methods. Normally the B-spline method is preferred over 
others. 
1.2.3 Coregistration & Normalization 
Coregistration and normalization [16] serve to jiggle about one or a bunch of images to best 
match the reference image, which we call it the template. Spatial coregistration or normalization 
is necessary because we need to accumulate fMRI data of different sessions and different 
subjects for statistical analysis, in order to boost statistical power. However, different subjects 
have different head shapes and sizes, even the same subject, when in different sessions, may 
have slight difference in head profile. Therefore, to perform group-level analyses, we need to 
normalize all fMRI images to a standard template. Coregistration and normalization differ in the 
transformation algorithm, with the former using affine transformation to register images, and the 
latter using non-linear transformation for registration. The criteria for both transformations is to 
optimize some cost function, which can be the mutual information,  entropy correlation 
coefficient, or sum of squared difference plus membrane energy of the deformation field. For 
humans, several extant standard template atlases such as MNI (Montreal Neurological Institute) 
template [17] are available for this registration. 
1.2.4 Temporal Filtering 
Temporal filtering is intended since there are unwanted noise and artifacts mingled with the 
signal of usefulness. These noise and artifacts come from thermal noise, physiological noise 
from heartbeat and breathing, and magnetic field shifting, etc. One common characteristic among 
them is normally their power is limited within a certain frequency band. Thus, if we use 
lowpass/highpass/bandpass filters to remove their power from corresponding frequency band, we 
make the signal purged. 
9 
 
1.2.5 White Matter and Cerebrospinal Fluid Signal Removal 
Sometimes the gray matter signal is the only signal of interest, so we hope to remove, or 
regress out the white matter and CSF signal from original signal. Normally this is done by using 
white matter mask and CSF mask to extract only the white matter portion and CSF portion of the 
brain, taking the mean signal within the mask, and regressing out this signal from time series of 
all voxels. 
1.2.6 Spatial Smoothing 
Spatial smoothing, also called spatial filtering, is the idea of averaging the intensities of nearby 
voxels to produce a smooth spatial map of intensity across the image. This operation aims to 
suppress spatial noise, facilitating statistical inference afterwards. The averaging is often done by 
convolution with a smoothing kernel, usually a Gaussian kernel. If the true spatial extent of 
activation matches the width of the kernel used, this process improves the signal-to-noise ratio 
since signal power adds in in-phase manner while noise cancels out. It also makes the noise for 
each voxel more approximately follow the Gaussian distribution. This is intended since the 
statistical analysis thereafter is normally based on the assumption that noise follows Gaussian 
distribution, both temporally and spatially. 
Grand mean normalization is also recruited in preprocessing by a lot of studies. It is in nature 
the normalization of mean intensity of each fMRI image volume acquired at each TR, i.e., to 
make the mean intensity of each fMRI image volume equal to each other. This is intended to 
eliminate the disruptive effect caused by grand mean signal intensity bias of each fMRI image 
volume. This step often goes before spatial normalization step. 
There are also some other preprocessing issues that need to be taken account of, though not 
often encountered, such as distortion corrections for field nonuniformities. For this issue, one 
10 
 
method is to use shimming coils and another one is to recreate a field map of the main field by 
acquiring two images with differing echo times. If the field were uniform, the differences 
between the two images also would be uniform. Bias field can be estimated using some 
mathematical model of the noise from distortion and used for correction. 
1.3 Organization of This Dissertation 
This first chapter gives introduction of relevant background knowledge, briefly expounding 
MRI, fMRI and its preprocessing procedures. Other chapters are organized as follows. The 
second and third chapters deal with univariate analysis of fMRI data with two projects. Chapter 2 
investigates the olfactory system in canines using fMRI, and compares activation maps between 
low and high concentration of odorant stimuli, as well as between lightly sedated and fully 
conscious dogs. Chapter 3 is about the fMRI investigation of zinc nanoparticles? enhancement 
effect on canines? olfactory perception, and comparisons are made with pure odorant, as well as 
gold nanoparticles + odorant as controls. Similar to Chapter 2, another comparison is made on 
activation maps between lightly sedated and fully conscious dogs. Chapter 4, 5 and 6 
demonstrate (dynamic) multivariate analysis of fMRI data. In Chapter 4, we use the multivariate 
metric: dynamic functional connectivity, to cluster brain network states, and correlate this metric 
and its static counterpart with behavioral measures. In Chapter 5, another two multivariate 
metrics: static and dynamic effective connectivity are researched. With dynamic effective 
connectivity and the similar clustering strategy as in Chapter 4, human resting state fMRI data is 
explored to find brain effective connectivity network patterns. Also, the relationship from these 
patterns to real world functionalities is inspected. In Chapter 6, the dynamics of connectivities 
are compared with static connectivities in terms of performance on discriminating patients with 
mental disorders from healthy controls, with an application to classify between post-traumatic 
11 
 
stress disorder (PTSD) patients and healthy controls. The classification is realized via support 
vector machine. In the end, the entire dissertation is concluded with Chapter 7. The information 
on published and submitted papers is in Chapter 8. 
  
12 
 
Chapter 2 Univariate Analysis:  
Functional MRI of the Olfactory System in Conscious Dogs 
 
Univariate analysis technique has been introduced into fMRI processing for a long time. Its 
realization in fMRI processing is based on the assumption that, each voxel is independent of 
other voxels. We process the time series for a given voxel only using its own information, and 
assume information from other voxels has no contribution to the time series of the voxel being 
investigated. The variable of interest is calculated usually by mass univariate general linear 
regression model. A comprehensive elaboration on univariate analysis can be found in Ref. [18] 
and its characterization in fMRI can be found in Ref. [19]. The work in this chapter is based on 
this assumption and our main contribution is that we constructed a novel dog fMRI olfactory 
system, used it to acquire dog fMRI data and analyzed the data of anesthetized and conscious 
dogs to investigate their olfactory system at the cognitive level. 
2.1 Introduction 
The properties of the dog?s olfactory system result from physical and biochemical events that 
occur at the olfactory epithelium of its nasal cavity where olfactory receptor neurons interact 
with odorants. Based on previous reports involving in vitro studies and in vivo studies in canines 
and other species (mainly humans), we can construct the following hypothesis about the cerebral 
architecture of the canine olfactory system. Olfaction begins with sniffing, which transports 
odorant molecules into the nose and delivers them to the mucus layer covering the olfactory 
epithelium [20]. The binding of the odorant by a receptor protein initiates an intracellular 
cascade of signal transduction events, including the G-protein-dependent production of second 
messenger molecules, leading to opening of ion channels and passing of ion currents. This 
13 
 
process triggers an action potential in the axon of the olfactory receptor neuron that projects 
directly to the olfactory bulb (OB) [20] [21]. The OB generally functions as a filter and has three 
non-exclusive functions: discriminating among odors, enhancing sensitivity of odor detection 
and filtering out background odors to enhance the transmission of selected odors. OB neurons 
then transmit signals to pyramidal neurons in the olfactory cortex that is composed of the 
anterior olfactory cortex, piriform cortex, periamygdaloid cortex and entorhinal cortex. The 
anterior olfactory cortex detects and stores correlations between olfactory features, creating 
representations (gestalts) for particular odorants and odorant mixtures, as shown by Haberly in 
humans [22]. Piriform cortex carries out functions that detects and learns correlations between 
olfactory gestalts formed in anterior olfactory cortex and a large repertoire of behavioral, 
cognitive and contextual information to which it has access through reciprocal connections with 
frontal, entorhinal, and periamygdaloid areas [22]. The periamygdaloid area participates in 
emotional processing of olfactory stimuli and facilitates memory encoding, as shown by Zald et 
al with human PET (positron emission tomography) data [23], and entorhinal cortex functions as 
a hub for memory network and navigation [22]. The pathway then projects to the hippocampal 
formation and thalamus, which relays information to neocortical areas such as the medial and 
orbitofrontal cortex where the olfactory signal is interpreted [24] (see Fig.2.1 for schematic). The 
medial and orbital parts of the frontal cortex are known to be involved in cognitive integration of 
all sensory stimuli in relation to prior experiences, as shown using functional neuroimaging in 
humans [25]. The hippocampal formation is involved in recognition memory of odors [22]. The 
thalamus? involvement in olfaction as a relaying hub is still under debate, however its 
involvement in odor thresholding has been acknowledged, at least in humans [26]. Also, 
previous studies have shown that dogs possess much more olfactory receptors per square 
14 
 
centimeter of the olfactory epithelium as compared to humans [27]. This clearly demonstrates the 
dogs? advantage over humans in sensory transduction at the cellular level. However, how this 
advantage is carried forward higher into the odorant detection chain remains unexplored. 
While much is known about the canine olfactory system at the in vitro cellular level [28] [29] 
[30] [31] [32] [33] and behavioral level [34] [35], little work has been done at the cognitive level, 
which is an important and largely unexplored link in the series of events leading to odor 
detection. It is critical to bridge the gap between cellular findings and systemic behavioral 
observations by investigating the sense of smell at the cognitive level. For example, an increase 
in the concentration of odorant will induce a change in response at the cellular level according to 
Weber?s law [36]. How this change in response translates to a change in odorant detection in 
vivo, however, is unknown, and could potentially be explored by using fMRI, which allows 
noninvasive mapping of brain function without the administration of an exogenous contrast agent 
[37] [7]. 
In this study, we characterized the cognitive response in dogs? brain to odorants of different 
concentrations using dogs that were fully conscious, and compared the response to that of lightly 
sedated dogs. Awake animal fMRI studies are methodologically challenging but more valuable 
because the data reflect the brain activity under more ecologically valid conditions. Anesthesia 
affects the neural activity as well as the regulation of cerebral circulation significantly [38] [39]. 
Only a small amount of animal fMRI studies have been published under awake conditions due to 
the difficulty of restricting motion effect [38] [39] [40]. Here, awake dog imaging was made 
possible by using an optical head motion tracking system [41] for retrospectively correcting for 
artifacts created by head motion. FMRI provides for the apparatus to investigate the dog 
olfactory system in vivo and noninvasively, and has been used to study the neural basis of 
15 
 
olfaction in humans [42] [43], monkeys [44] and rodents [45]. But, to our knowledge, there has 
been no investigation of the olfactory system in dogs (either awake or sedated) using fMRI or 
any other imaging modality. Dog imaging techniques developed in this study measure activity in 
the olfaction-related brain areas and quantify concomitant changes with different odorant 
concentrations. We believe that the techniques we report here will serve as a seminal 
noninvasive method for the exploration of the dog?s olfactory system at the cognitive level.  
The broader impacts of this endeavor are multifold. Currently, we depend upon the olfactory 
abilities of dogs for what are considered highly specialized and critical tasks such as detecting 
explosive devices, hazardous chemicals, and illicit substances. The societal importance of such 
tasks has increased efforts to enhance the technological sophistication by which canine olfaction 
is employed. To support such enhancement, greater emphasis has been placed on understanding 
fundamental olfactory function and capacities. Non-invasive imaging techniques such as fMRI, 
coupled with animal psychophysics based techniques, hold significant promise for advancing the 
understanding of fundamental olfactory function and associated cognitive processing of odor 
sensory information. A mechanistic understanding of canine odorant detection is not only 
important from a basic science perspective but also to understand how canine detection 
capabilities change with different odorants and operating environments. Federal agencies in 
United States (Federal Aviation Administration, Department of Homeland Security and 
Department of Defense) have invested millions of dollars to support research into basic science 
of canine odor detection and training because of the increase in terrorism threats, domestic and 
foreign narcotics trafficking.  
16 
 
 
Figure 2.1 A schematic of the olfactory pathway in canines. Arrows indicate the olfactory 
signal flow. Anterior olfactory cortex, piriform cortex, periamygdaloid cortex, and entorhinal 
cortex are contained in a green box and the green arrows extending from this green box indicate 
the olfactory signal from them go to frontal cortex and thalamus. The gray arrow from entorhinal 
cortex to hippocampal formation indicates the olfactory signal to hippocampus comes only from 
the entorhinal cortex. For functions of each site, please refer to [20] [21] [22] [23] [25] [26]. 
 
2.2 Material and Methods 
Ethics Statement: Approval was obtained from the Auburn University Institutional Animal 
Care and Use Committee for performing this study. 
2.2.1 Overview of the Dog FMRI Olfactory Imaging System 
The components of the dog fMRI olfactory imaging system are shown in Fig.2.2. First, the 
dogs were trained to insert and keep their heads as still as possible inside the human knee coil 
when being scanned (Fig.2.2 (A)). This was achieved by positive reinforcement training 
techniques using a target stick and bridging stimulus (i.e., clicker) for head placement maintained 
by delivery of edible treats for emission of desired responses. Second, a custom-built odor 
applicator was used for controlled delivery of odorant stimulus (Fig.2.2 (B)). Third, the scanner 
17 
 
system consisted of a 3T Siemens Verio scanner and a human knee coil which perfectly fit into 
the role of a dog head coil. Fourth, an optical head motion tracking system was employed for 
tracking dog head motion during fMRI (Fig.2.2 (B), (C)), and consisted of an infrared (IR) 
camera, an IR illuminator, a video monitor, and a data recording palmtop. A schematic of the 
interlinking and triggering among them is shown in Fig.2.3. Finally, post-processing of 
functional data was performed with SPM8 (statistical parametric mapping) [46]. 
 
Figure 2.2 Components of the dog fMRI olfactory imaging system. (A) dog training to insert 
and keep their heads as still as possible inside the human knee coil using positive reinforcement 
learning (a black dog can be seen inside the coil); (B) components of imaging system outside the 
MRI room showing odorant applicator, air tank, motion parameter recording palmtop, video 
monitor, laptop with VT-8 software (see Section 2.2.3), and the entrance port to the MRI room; 
(C) components of imaging system inside the MRI room, showing human knee coil, infrared 
camera and infrared radiator. 
18 
 
 
 
Figure 2.3 The interlinked trigger system. Arrows denote the triggering direction. A laptop 
with VT-8 software [47] provided the interface to trigger the odorant applicator. The VT-8 
software is a platform that can be used to design and display sequence of odorant flow and 
clearance, and provides communication and control to odorant applicator to generate the 
expected experimental sequence. Once the odorant applicator started to give odorant stimulus, it 
sent a signal to the trigger synchronizer, which then triggered the scanner and sent a signal to the 
manual trigger. The manual trigger, as the name suggests, was manually set for switching 
between two states. One was waiting for signals from trigger synchronizer, and the other was 
waiting for signal from a hand-pressed button. In our experiment, the first state was used for data 
collection and the second was used only for testing. Upon receiving the signal, it triggered the 
infrared radiation transmitter to give off infrared rays, and the infrared camera to start recording 
infrared reflections from the dog?s head, and the motion parameter recording palmtop to start 
calculating displacement parameters. When the camera was triggered, it sent the signal to the 
monitor for display.   
 
2.2.2 Dog Training and Preparation 
We recruited six Labrador Retriever dogs (five males) from the Auburn University Canine 
Detection Research Institute with ages in the range of 12 to 60 months. For anesthetized imaging, 
dogs were sedated with intramuscularly administered xylazine (2.2 mg/kg) and lightly 
anesthetized with ketamine HCl (11mg/kg). For awake imaging, the dogs were trained to move 
19 
 
to the correct position within the scanner, insert their heads within a human knee coil, and remain 
still for the required duration of imaging using positive reinforcement behavior shaping 
procedures. 
All training used positive reinforcement to obtain the desired performance by the dogs.  Prior 
to training for fMRI scanning, the dogs were trained to follow, touch, and remain touching the 
end of a ?target-stick? (3/8 inch diameter, 36 inch long, wooden dowel with red tape as target on 
one end) with their nose using small bits of commercial dog food treats as rewards to shape and 
maintain this response. Concomitantly, a tin clicker was established as a conditioned reinforcer 
by pairing the click with the delivery of food treats for correctly touching and holding their nose 
to a touch-stick. Such a conditioned reinforcer is also known as a ?bridge? because it provides an 
immediate signal to the animal that the desired response has been emitted and bridges the gap in 
time until a food treat can be delivered. This sort of target-stick and bridging signal training is a 
common practice in pet animal as well as professional husbandry with animals in zoos to train 
them to present themselves for medical monitoring and treatment, conduct 
educational/entertainment animal shows, and to generally reduce the dangers associated with 
managing animals. The use of the clicker allows more precise delivery of a rewarding stimulus to 
shape (i.e., build, develop) a desired response. Establishing the target-stick repertoire to a 
proficiency level adequate for moving onto training for fMRI took from 30 minutes to an hour 
for each dog.   
The first round of training for awake, unrestrained fMRI of the dogs took place outside of the 
actual scanning using a fixture to replicate the human knee coil (i.e., 2.5 gal plastic bucket with 
the bottom cut out) affixed to one end of a table that approximated the height and width of the 
MRI table. The dogs were prompted to jump up on the table or, if unable to easily jump on the 
20 
 
table, place their front paws upon the edge of the table so they could be easily lifted upon the 
table by one person. The previously established clicker and target-stick repertoire was used to 
train the dog to place its head within the simulated MRI coil and position its nose within the 
olfactory stimulus delivery mask, which was affixed inside the simulated human knee coil. The 
dogs were trained to hold their heads relatively motionless within the simulated coil by clicking 
the clicker only when their head was in the correct position and held still. The amount of time 
that a dog had to hold its head still in the correct position to receive the click followed by a food 
treat was gradually increased. Meanwhile, throughout this process, a recording of the sound from 
the operation of the MRI was played through a portable stereo, the volume of which was 
gradually increased until similar in intensity to that of being in the actual scanning.  The final 
training performance was the dog holding its head relatively motionless in the correct position 
while the MRI sounds were played at approximately the same intensity as that of being in the 
actual MRI for 5 minutes and repeating this performance several times across the course of an 
hour-long training session. This training phase took, on average, about 20, 1-hour training 
sessions across a 4-week period for each dog. 
The second round of training was performed inside the real scanner with the human knee coil 
and with running of the functional and structural sequences. The dogs were acclimated and 
transitioned to performing the head positioning response in the actual MRI scanner in one, 
approximately hour-long session each. The dog trainer always accompanied and monitored it 
(see Fig.2.2 (A)) in the scanning room.  The dog was prompted onto the MRI table, into the MRI 
core, to place its head within the human knee coil, and position its nose in the olfactory stimulus 
delivery mask. Starting with a relatively short duration of holding its head in position and 
relatively motionless with the fMRI intermittently operating, the time requirement for receiving a 
21 
 
click followed by a food treat was variably and rapidly increased until the dog reliably executed 
the performance for one fMRI sequence to be used in the experiment.  The click was presented at 
the end of the sequence followed by delivery of the food treat from the hand of the trainer to the 
dog. A recent paper demonstrated a similar training approach for imaging the reward system in 
awake dogs [48]. However, even with training, some head movement was inevitable (e.g. 
respiratory repositioning). Therefore, we used a single camera optical head motion tracker to 
monitor the motion of the dog?s head and retrospectively correct for motion effect. 
2.2.3 Olfactory Stimulus Device 
Odorant delivery 
The accurate delivery of odor stimulus is very important in olfactory physiological 
experiments. When used with fMRI, demanding additional constraints are placed on 
olfactometers [49] [50] [51] [52]. The most obvious one is the absence of any magnetized 
material in the MRI room. Other features of the instrument include computer control and odorant 
presentation of accurate and reproducible duration of a preselected sequence with no additional 
stimulation (e.g., tactile, auditory) [49] [53]. 
We built a custom device for the precise computer-controlled delivery of pre-determined 
quantities of odorants over a precise time interval (Fig.2.4). The device provided for the flow of 
air under pressure through a series of filters, valves, and manifolds to sweep the headspace over 
containers into a mask, for the precise quantitative delivery of odorants to the nasal cavity of 
dogs. A vacuum suction then cleared the odorant after a precise amount of time. In this manner, 
the device controlled the precise extent and time of exposure of substances to olfactory tissue. 
The moisture content of the air was controlled to a constant humidity using a drierite type air 
filter. The drierite type air filter is a purifier that is specially designed for gas chromatography 
22 
 
and other applications requiring pure and dry gas. It dries, purifies, and filters gases used for 
chromatography and spectrometry. 
During the fMRI experiment, the air tank, odorant applicator, and computer were positioned 
outside the MRI room in the close proximity from the utility entrance port into the MRI room. 
Six 6-mm plastic tubes were passing through the entrance port for connection with the animal 
mask. Each tube, channel, and bottle was used only for the particular odorant sample to avoid 
cross contamination. Valve 2 and pressure regulator (PR) (see Fig.2.4) were purged and cleaned 
after each experimental session. All materials and components used in this device were 
chemically stable and are not odoriferous.  
As illustrated in Fig.2.4, the computer (PC) used VT-8 software [47] to send a signal to the 
VT-8 Warner Valve Timer (indicated as ?Timer? in Fig.2.4) that in turn communicated with the 
VC-8 Warner Valve Controller (Controller) to open one of six Oxygen Clean 2-way normally 
closed electronic valves (EV1) installed in the 6-port Oxygen Clean Manifold (Clippard 
Instrument Laboratory, Manifold 1). When EV1 was open, the corresponding LED (light 
emitting diode) control light was on, and air entered from the Air Tank into the Miniature 
Clippard Air Flow Control Valve (Valve 1). Then through the W.A. Hammond Drierite 
Laboratory Gas Drying Unit (Filter1) the air went to the open EV1, the first Clippard 
Unidirectional Valve (VU1), the head space of 100mL bottle, and then the second Clippard 
Unidirectional Valve (VU2). After that, it followed through the corresponding normally open 
channel of the Clippard Manifold 2 and via the second Miniature Clippard Air Flow Control 
Valve (Valve 2) to the Clippard Pressure Regulator (PR), with air pressure measured by DT-
8890CEM Ruby-electronics Digital Differential Air Vapor Pressure Meter Gauge Manometer 
23 
 
(Manometer). Finally, the air with odorant exited the odor applicator and entered the SurgiVet 
Pet Oxygen Mask (Mask) [54] via the 6-mm tubing. 
At the end of activation time (10 s) the Controller closed EV1 in the Manifold 1 and 
simultaneously opened the Oxygen Clean 2-way normally closed electronic valve (EV2) and the 
vacuum pump (AM6BS Metropolitan Vacuum) (VP) in the applicator exhaust path. The air with 
odorant was cleared from Mask, Valve 2, open channel of Manifold 2, EV2, and W.A. 
Hammond Carbon Filter (Filter 2). After the clearance of odorant (10 s) the EV2 and the vacuum 
pump were shut off and the system rested 20 s before a new activation began. The full cycle of 
the odor applicator, therefore, was typically composed of 10 s of odor application and 30 s of no 
odor. The no odor time was composed of 10 s clearance of odorant and 20 s rest time.  
The pressure pulses were measured by Manometer and sent to computer (PC). The odor 
applicator was synchronized with MRI by the Timer signal sent to MRI computer. A cooling fan 
(CF) helped to maintain the temperature of odorants and device components. We used a known 
odorant mixture of ethyl butyrate, eugenol, and (+) and (?) carvone in water at concentrations of 
0.016mM (low concentration) and 0.16mM (high concentration) each [55]. 
24 
 
 
Figure 2.4 Diagrammatic representation of the olfactory stimulation device. The device 
consists of inflow & clearance air paths and an electronic control system. The inflow air/odorant 
path consists of a tank, flow control Valve 1, dry-rite type air Filter 1, Manifold 1 (6 isolated 
channels with electronically controlled valves), an electronic valve (EV1), 6 unidirectional 
pressure controlled valves (VU1, VU2), 6 odor bottles, Manifold 2 (6 flow-through isolated 
channels), flow control Valve 2, pressure regulated valve (PR), and electronic Manometer. The 
clearance path includes vacuum pump (VP), charcoal Filter 2, and electronic valve (EV2). The 
electronic control system consists of a 6-channel valve Timer, 6-channel valve Controller; 
Power-supply (feeds the VP, the visual LED control pane, and the cooling fan (CF)). Power for 
the Timer and Controller comes from the personal computer (PC). The protocols of timing and 
sequencing are stored and directed by the PC connected to the Timer. The Timer is synchronized 
with MRI. The experimental air pressure directed to the Mask are measured by the electronic 
Manometer and recorded by PC. 
 
Plastic caps were modified for air-tight connection with the bottles containing odor solutions. 
The removable platform for bottles containing odorants, LED assembly and various clamps for 
positioning the parts were custom built. The odor applicator was controlled by the Warner VT-8 
software [47] and was programmed to generate the experimental sequence of odorant flow and 
clearance (Fig.2.5). Since the odorant airstream was unwarmed and introduced at room humidity, 
excessive flow rate was not desirable. Also, animals subjected to continuous un-humidified flows 
could have nasal drying and discomfort. High air flow can present air flow turbulence, impacting 
rise times [56]. Because the mask had two valves that supported unrestricted exhaling and 
25 
 
inhaling, the incoming air flow was limited to 1 l/min based on American Animal Hospital 
Association (AAHA) guidelines [56].  
Mask 
A SurgiVet Pet Oxygen Mask [54] was used in our experiments. This mask is made of 
polycarbonate and has two valves that aid unrestricted exhaling and inhaling, and a port to which 
the tube for odorant delivery and evacuation was attached. The mask was mounted on the frame 
of the knee coil such that when the dog placed its nose in the mask, its head was correctly 
positioned within the coil for imaging (Fig.2.6). 
 
Figure 2.5 Odorant applicator sequences controlled by VT-8 Warner Timer software and 
fMRI experimental block design. For the first sequence, green arrows indicate the onset time of 
the odorant stimulus and red arrows indicate when the stimulation ends. For the second one, 
green arrows indicate the onset of clearance of odorant, and red arrows indicate when it ends. 
The third sequence shows the fMRI block design in this work, matching the first sequence. ?0? 
and ?1? denote the odor ?on? and ?off? conditions. 
 
26 
 
 
Figure 2.6 A black dog positioned with muzzle in mask for odorant delivery. The dot 
reflector is mounted to dog?s head for motion tracking, the knee coil encompasses the dog?s head 
and the mask is mounted on the front frame of the knee coil. 
 
2.2.4 Optical Head Motion Tracking 
Head movement is a critical issue for all modalities of brain imaging, especially for fMRI. 
Excessive movement results in image ghosting and blurring. Because head movement is a 
significant obstacle in imaging studies of conscious animals, and some cognitive processes such 
as olfaction are impossible to comprehensively study in anesthetized animals [38] [39] [40], we 
have adopted an approach involving both dog training and optical head motion tracking. Even 
the best trained dogs will inevitably make slight, sometimes jerky, head movement. In the 
present case, the dogs would sometimes pant, which is a physiologically mediated response that 
is difficult to reliably control through positive reinforcement procedures. Such motions are 
difficult to remove using post-hoc image transformations. Therefore, the ability to compensate or 
reduce motion artifacts is one of the most challenging difficulties while acquiring MR images 
from a conscious animal. To solve this problem, two approaches have been tried in the past. First, 
the head of the animal can be immobilized [57] using external constraints. But this method 
makes the animal uncomfortable and hence the data collected is not fully ecologically valid; 
27 
 
furthermore, such restraint is aversive and considered to be a higher level of invasiveness from 
an animal welfare point of view. The second approach is to independently record motion 
parameters during the scan, and then retrospectively use it to correct for motion or as a regressor 
of no interest in the activation analysis. This method is more ecologically valid, so in our 
experimental setting, we utilized an optical head motion tracking system [41] [58] based on a 
single camera to monitor and record motion parameters. However, originally this system was not 
specially designed for dog imaging, and thus can be adopted for general use.  The advantages of 
single camera system over multi-camera systems are as follows [41]. First, the former does not 
need calibration of the angle and settings between the cameras, which must be routinely and 
repeatedly established in the daily function of the MRI facility. Second, the former avoids the 
technical difficulty of mounting multi-camera systems in-bore. Third, many MRI bores limit the 
field of view of cameras and this narrow aperture hinders the placement and efficacy of the 
second camera.  
The single camera optical head motion tracking system was an MRRA Inc. model HT-1000 
comprised of an IR (infrared) illuminator, an optical IR camera with a built-in DSP (digital 
signal processing) processor, a dot reflector, a video monitor and a palmtop computer. The IR 
illuminator provided an IR source that was reflected by the dot reflector mounted on the dog?s 
head; the IR camera picked up the reflected IR light from the dot reflector and aided in 
calculating the change in dot position. Specifically, the image taken by the IR camera was 
binarized so that the round dot reflector was clearly separated from the background. The 
binarized image, the x, and y displacement of the centroid of the dot reflector as well as its area 
calculated by the DSP processor in the IR camera were digitally transmitted to the video monitor 
and palmtop computer. The sampling rate was 1 kHz. By doing so, we obtained the time series of 
28 
 
the x, y coordinates and the area in units of millimeter and mm2, respectively. Then, these time 
series were downsampled to fMRI temporal resolution of TR = 1s, and the relative displacements 
of x(t), y(t) with respect to x(0), y(0), which were the x, y coordinates corresponding to the first 
fMRI volume, were obtained and used as a regressor of no interest (Qi(t) as in Eqn.2.3 of 
?General Linear Modeling and Statistical Testing? section which is explained later) in the 
activation analysis, after correcting for motion using image transformation based realignment. 
The dot reflector was a one-inch diameter disk of engineering grade-10 retro-reflective tape (3M 
Corp.) attached by adhesive to the forehead of the dog. The video monitor allows the operator to 
check for proper image framing.  
It is noteworthy that the system described above was only capable of 2-dimensional tracking, 
i.e. x and y directions, anterior-posterior direction missing. However, with a properly designed 
3D target [41] and scanner interface, prospective online motion correction could potentially be 
performed with animals which cannot be trained to minimize head movement.  
2.2.5 Stimulation Paradigm 
Each run consisted of 5 blocks of odor stimulation of 10s duration, with a fixed resting (no 
odor) interval of 30s between the end of one block and the start of the next, as illustrated in the 
fMRI block design sequence in Fig.2.5. The order of low and high concentration runs were 
randomized for both awake and anesthetized dogs. The no-odor interval was thrice the duration 
of the odor stimulation interval in order to prevent the adaptation of the dog?s olfactory system to 
the odorant. Previously it was shown that repetitive brief odorant pulses (?10 s) can evoke 
activity in the rat olfactory bulb measurable through fMRI [59]. The choice of 10 s for odor 
stimulation and 30 s for baseline was motivated by previous studies showing that such a 
paradigm is effective for eliciting measurable neural response and at the same time, prevent 
29 
 
habituation [60] [61]. In an fMRI analysis of the rat olfactory bulb, odorant stimulation for 4.8 
minutes failed to show a reduction in activation [62]. Within a much longer stimulation (27.6 
min) the activation declined, displaying habituation. Extra- and intracellular recordings of the 
main olfactory bulb of the rat support these results, showing just a small reduction in activation 
when a long stimulus of 50 s was given [63].   
2.2.6 Data Acquisition 
T2*-weighted functional images were acquired using a single-shot gradient-recalled echo-
planar imaging (EPI) [64] sequence for blood oxygenation level dependent (BOLD) contrast on a 
Siemens 3 Tesla Verio scanner. Two hundred temporal volume repetitions of 14 axial slices with 
3 mm thickness were acquired using the following parameters: repetition time (TR)=1000 ms, 
echo time (TE)=29 ms, field of view (FOV)=192 ?192 mm2, flip angle (FA)=90 degree, in-plane 
resolution 3?3 mm, in-plane matrix 64?64, and whole brain coverage. A total of 34 low and 34 
high concentration runs were obtained from anesthetized dogs whereas a total of 32 low and 32 
high concentration runs were obtained from awake dogs. However, 4 runs of low and 4 runs of 
high concentration obtained from awake dogs were excluded due to excessive motion. The 
exclusion criterion was: >10 mm displacement between two consecutive acquisition time points 
in x, y or z direction. Also, in the z direction, if there was 10mm total displacement between any 
two acquisition time points in one run, it meant that the dog?s nose was not fully inserted in the 
mask at some time. This would have jeopardized the odorant effect at that time point. Therefore, 
any runs with > 10mm total displacement between any two acquisition time points in the z 
direction were also discarded. Anatomical images were acquired using magnetization-prepared 
rapid gradient echo (MPRAGE) [65] sequence for overlay and localization, with parameters as: 
30 
 
TR=1550 ms, TE=2.64 ms, voxel size: 0.792?0.792?1mm3, FA=9?, and in-plane matrix 
192?192, FOV=152?152 mm2, number of slices: 104.  
2.2.7 Image Processing 
Image processing was performed using SPM8 [46] and consisted of slice timing correction, 
realignment to the first functional image, spatial normalization to a template, spatial smoothing, 
and general linear modeling (GLM) analysis. For spatial normalization, we adopted a customized 
strategy to deal with dog data as described below. For spatial smoothing, a Gaussian smoothing 
kernel with full width half maximum (FWHM) of 4 ? 4 ? 4 mm3 was employed. Considering 
that the dog?s brain is smaller than that of humans, the FWHM employed by us was smaller than 
a FWHM of 8 ? 8 ? 8 mm3 usually employed with human data. 
Spatial Normalization 
Spatial normalization [16] is necessary because dogs have different head shapes and sizes. 
Therefore, to perform group-level analyses, we need to normalize them to a standard template. 
For human as well as monkey and rodent imaging, a standard template is available (for example, 
the MNI template for humans and MNI monkey atlas) [66]. Unlike human anatomical templates 
such as MNI which are derived using data from hundreds of subjects, the existing dog 
anatomical templates are derived from less than 10 dogs and hence do not capture the entire 
spectrum of head size variability [67]. Therefore, we adopted a more principled two-step 
approach. First, since for the normalization step to produce a good estimate of the spatial 
transformation, the modality of images should be similar, it was inappropriate to directly 
normalize all functional images of different dogs to one anatomical template. As a substitute, we 
chose a good quality anatomical image from the pool of anatomical images, obtained from an 
anesthetized dog, as the template. This choice was motivated by the fact that movement is 
31 
 
negligible when dogs were anesthetized, and hence the quality of anatomical images obtained 
were superior. Then we chose one functional image from the same session as that of the 
anatomical template, and normalized it to the chosen template. Since both images were obtained 
from the same anesthetized dog in the same session, the normalization was relatively accurate 
and reliable. In the subsequent step, we used this transformed functional image as a template to 
normalize functional images obtained from other sessions (involving both anesthetized and 
conscious dogs). Since the images involved in this step were of the same modality, the 
normalization was relatively accurate. Note that by ?session?, we mean the period during which 
we performed a number of runs for one dog. For example, in a session for one dog, we 
performed 1 structural run, 2 low concentration runs, 2 high concentration runs, and 2 resting 
state runs. So, one session included one subject with several consecutive runs in one day. The 
schematic of the proposed approach is shown in Fig.2.7 and each step of the proposed 
normalization procedure was realized in SPM with the following parameters: 1. Template 
smoothing: 8 mm FWHM for step-1 and 4 mm FWHM for step-2. Since the structural image had 
higher resolution than the functional, we could afford to use higher smoothing in step-1 
compared to step-2. 2. Source image smoothing: 4mm FWHM for both steps. 3. Interpolation: 4th 
B spline. 4. Voxel sizes: [2 2 2] mm. 
32 
 
 
Figure 2.7 Flow chart of proposed spatial normalization procedure. A good quality 
anatomical image of an anesthetized dog was chosen as the template from Session 4 (4, being 
just an example). Then one functional image from the same session (Session 4) was chosen and 
normalized to the template. Subsequently, this transformed functional image was used as a 
template to normalize other functional images of other sessions. (*Anes: Anesthetized) 
 
2.2.8 General Linear Modeling and Statistical Testing 
Modeling the contrast of low/high odor concentration vs. rest condition 
The pre-processed data was fed into a GLM for regression analysis and statistical testing of 
the effects of interest. The general linear equation can be briefly formulated as below.  
1 1 2 2                   1 ...j j j N j N jY X X X j M? ? ? ?? ? ? ? ? ?                     (2.1)  
Where Yj is the response variable (fMRI time series at each voxel), j=1? M indexes the 
observation; each Xjk is an explanatory variable, k=1? N, ?k, k=1? N are parameters to be 
regressed, under least square sense. In practice, the independent identically distributed (i.i.d.) 
33 
 
normal distribution assumption for the error term is violated, but as long as we gather sufficient 
amount of data, the deviation from this assumption is deemed trivial. In our case, as indicated by 
the third sequence in Fig.2.5, a block design for task conditions was employed, so a boxcar 
function corresponding to each of the two conditions (odor ON condition and odor OFF 
condition) was generated such that  
1,   () 0,   odor onbt odor off?? ??                                                              (2.2) 
The boxcar function was then convolved with a standard hemodynamic response function 
(HRF) hrf(t) used in SPM so as to obtain a vectorial explanatory variable X1(t)= )()( thrftb ? . 
This HRF was not measured directly from dogs, but in order to model the variability of HRF in 
experimental data, we included time derivatives and dispersion derivatives of the HRF as 
regressors X2(t) and X3(t) in the GLM. Also, in order to regress out motion effects, the 6 rigid 
body transformation motion parameters Pi(t), i=1,?,6 resulting from realignment, and camera 
tracking parameters Qi(t), i=1, 2 corresponding to head motion captured by the camera in x and y 
directions, were also added in the GLM as regressors. The resulting GLM equation is as follows. 
62
1 1 2 2 3 3 11( ) ( ) ( ) ( ) ( ) ( ) ( )i i i iiiY t X t X t X t P t Q t t? ? ? ? ? ???? ? ? ? ? ???
                    (2.3) 
Where ?, ?, ?, s are the coefficients and Y(t) is the observed fMRI signal at the given voxel. We 
tested for the statistical significance of ?1, which represents the main contrast of odor versus rest, 
using a t-test and obtained corresponding activation maps.  
Modeling the parametric modulation of the BOLD signal by low and high odor concentrations  
We will use ?parametric modulation? for short when referring to ?parametric modulation of 
the BOLD signal by odor concentration? in the following sections. To test the effect of 
concentration modulation, parametric modulators were included in the GLM based on the 
34 
 
following considerations. As is well known, the intensity of odor perception I, as a function of 
odorant concentration C, can be described by the Weber-Fechner law [36]:  
lnI a C b? ? ?                                                            (2.4) 
Where I is the perceived psychological intensity, a is the Weber-Fechner coefficient, and b is a 
constant. The experimental values of a and b measured for many odorants are approximately 
equal to 1.3 and 0.5, respectively. Thus, the change in perception due to a 10-fold increase in 
odorant concentration is equal to 1.3?ln(10) ? 3 [31]. In vitro data recently reported by our group 
showed elegant agreement with this, i.e., a 10-fold increase in odorant concentration resulted in 
approximately 3-fold increase of the electro-olfactogram (EOG) signal [33], under the 
assumption that amplitudes of EOG signals elicited by various odorants in vitro correlate with 
perception of odor intensity. If we assume the fMRI signal has the same correlation with 
perception of odor intensity, a parametric modulation of the fMRI signal with a ratio of 1:3 for 
increasing the odorant concentration by 10 times is suggested. Therefore, we concatenated one 
run of low concentration and one run of high concentration from the same session to form one 
observed variable. We constructed a parametric modulator M with a value of 1 for representing 
low concentration, and 3 for representing high concentration, and then included it into the GLM. 
So Eq.2.3 changes to Eq.2.5 as below. 
               312
1 2 3 3() ()( ) ( ). . .() ()( ) ( )low m o d m o d m o dhighYt XtX t X tM M MYt XtX t X t? ? ??? ??? ? ? ?? ? ? ? ? ??? ??? ? ? ?? ? ? ? ????  
62
11
( ) ( ) ( )( ) ( ) ( )l o w l o w l o w
i m o d i m o dh i g h h i g h h i g hii
P t Q t tP t Q t t??? ?
??
? ? ? ? ? ?? ? ?? ? ? ? ? ?
? ? ? ? ? ???
                            (2.5) 
Here, .? means array multiplication, and subscripts ?low? and ?high? indicate corresponding 
regressors in Eq.2.5 obtained from low or high concentration runs, with corresponding 
coefficients named ?1mod, ?2mod, ?3mod, ?imod, i=1:6, and ?imod, i=1:2. 
35 
 
After solving Eq.2.5 with regression coefficients as unknowns, a t-test was conducted for the 
significance of the parametric modulator ?1mod. The numerical value of ?1mod represents the effect 
of the concentration modulation, meaning that the brain area with significant nonzero ?1mod 
showed three times the response for high concentration as opposed to low concentration.  
Correction for multiple comparisons  
To account for the false positive activations, we used a multiple comparison correction 
procedure called AlphaSim algorithm [68] [69] [70]. AlphaSim provides a means of estimating 
the overall significance level (the probability of a false detection) for an entire 3D functional 
image. This is accomplished by Monte Carlo simulation of the process of image generation, 
spatial correlation of voxels, voxel intensity thresholding, masking, and cluster identification. 
Based on the combination of individual voxel probability thresholding and minimum cluster size 
thresholding, the probability of a false positive detection per image is determined from the 
frequency count of cluster sizes.  The underlying principle is that true regions of activation will 
tend to occur over contiguous voxels, whereas noise has much less of a tendency to form clusters 
of activated voxels. Therefore, the presence of clustering can be used as one criterion to 
distinguish between signal and noise. We used the dog brain mask created by ourselves as the 
image within which the activation was of interest to us and fed it into this algorithm. And we set 
the number of iterations to be 1000, the individual voxel probability threshold as p=0.05, and 
consequently the minimum cluster size threshold was calculated to be equal to 15 voxels, 
corresponding to false positive detection probability = 0.05 for the entire image. 
2.3 Results 
2.3.1 Spatial Normalization 
36 
 
Figure 2.8 shows one representative set of images before and after the spatial normalization 
using the procedure described in Figure 2.7. It can be seen that the functional image (Fig.2.8 (B)) 
is normalized well to its own anatomical (Fig.2.8 (A)). The mismatch between functional images 
from different dogs is conspicuous before normalization (Fig.2.8 (B) and (C)). After the second 
normalization step, they look similar (Fig.2.8 (B) and (D)).  
 
Figure 2.8 Normalization of functional images to anatomical template. The image (A) is the 
chosen anatomical template, its functional counterpart acquired in the same session is normalized 
to this template, which is shown in (B). The image (C) is a functional image of another dog. 
After normalization to the functional image (B), it becomes the image (D). (A: Anterior, P: 
posterior, S: superior, I: inferior, L: left, R: right) 
 
37 
 
2.3.2 Low and High Odor Concentration in Anesthetized and Conscious Dogs 
The statistical activation maps shown in Figs.2.9, 2.10, and 2.11 were obtained using a t-
contrast, cluster size threshold of 15 voxels calculated from AlphaSim algorithm applied to 
account for multiple comparisons, and individual voxel probability threshold p=0.05 (the t 
threshold corresponding to this p value is 1.645). It is noteworthy that humans normally lie in the 
scanner facing up (i.e. head first-supine), but in our scenario, dogs were in ?head first-prone? 
position in the scanner. Therefore, there is a difference in orientations between Fig.2.8, 2.9, 2.10, 
2.11 and 2.14 in this paper and the routinely reported human images. The names of activated 
areas were identified by Professor Edward Morrison and Vitaly Vodyanoy who have vast 
experience with dog neuroanatomy and olfactory physiology. They based their conclusions on 
visual comparison of activation images with published dog brain atlases [71]. Figure 2.9 shows 
activation maps obtained from anesthetized dogs for low odor concentration (Fig.2.9 (A)), and 
for high odor concentration (Fig.2.9 (B)). Corresponding cluster-level activation statistics are 
summarized in Table 2.1 and Table 2.2. Figure 2.10 illustrates the activation maps for low 
(Fig.2.10 (A)) and high odor concentration (Fig.2.10 (B)) in conscious dogs. Tables 2.3 and 2.4 
show corresponding cluster-level activation statistics for conscious dogs. For both awake and 
anesthetized dogs, we observed expected strong activation in the olfactory bulb and bilateral 
piriform lobes, including anterior olfactory cortex, piriform cortex, periamygdala, and entorhinal 
cortex for both low and high odor concentration. The ventro-posterior location of the activation 
in the olfactory bulb is in agreement with previous studies in rats [72]. Visual comparison of the 
maps obtained from low odor vs. rest and high odor vs. rest contrasts reveals that the spatial 
extent and intensity of activations are larger for high odor concentration as compared to low 
concentration in both anesthetized (see Tables 2.1 and 2.2) and awake dogs (see Tables 2.3 and 
38 
 
2.4). A visual comparison of activation maps of anesthetized and conscious dogs shows dramatic 
differences in the spatial localization of activation. Activations in cognition-related areas such as 
medial, superior and orbital frontal cortices, and cerebellum are mainly found in conscious dogs.  
 
 
39 
 
 
 
Figure 2.9 Group activation maps for anesthetized dogs. (Overall FDR=0.05, cluster 
threshold =15 voxels using AlphaSim, t-contrast) Three orthogonal views are shown above and 
key sagittal slices are shown below for each subfigure. Hot colormap is used for activation 
intensity, and important areas are indicated by arrows with labels. Subfigure (A) corresponds to 
low concentration odorant (0.016mM), subfigure (B) corresponds to high concentration odorant 
(0.16mM). (A: Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) The image order in 
sagittal slices is from left to right hemisphere, with coordinate labels shown atop. 
 
40 
 
 
 
41 
 
 
 
Figure 2.10 Group activation maps for awake dogs. (Overall FDR=0.05, cluster threshold =15 
voxels using AlphaSim, t-contrast) Three orthogonal views are shown above and key sagittal 
slices are shown below for each subfigure. Hot colormap is used for activation intensity, and 
important areas are indicated by arrows with labels. Subfigure (A) corresponds to low 
concentration odorant (0.016mM), subfigure (B) corresponds to high concentration odorant 
(0.16mM). The activation in olfactory bulb for low concentration is not visible in this view; 
please refer to Table 2.3 for activation statistics with regard to this region. (A: Anterior, P: 
posterior, S: superior, I: inferior, L: left, R: right) The image order in sagittal slices is from left to 
right hemisphere, with coordinate labels shown atop. 
 
Table 2.1 Cluster-level statistics of activations for anesthetized dogs, low concentration of 
odorant.* 
Number of activated clusters: 4, total number of activated voxels: 365 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 olfactory bulb 105 3.53 
#2 left anterior olfactory cortex, left 146 3.05 
42 
 
piriform cortex, left 
periamygdaloid  cortex, left 
entorhinal cortex 
#3 thalamus, hypothalamus 89 2.95 
#4 
right anterior olfactory cortex, 
right piriform cortex, right 
periamygdaloid  cortex 
25 2.64 
*: ROIs shown in bold face were commonly activated for low and high (Table.2.2) odor 
concentration, as well as parametric modulation by odor concentration (Table.2.5) 
 
Table 2.2 Cluster-level statistics of activations for anesthetized dogs, high concentration of 
odorant. * 
Number of activated clusters: 5, total number of activated voxels: 424 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 
left anterior olfactory cortex, left 
piriform cortex, left 
periamygdaloid  cortex, left 
entorhinal cortex,  left frontal 
cortex 
159 5.16 
#2 
right anterior olfactory cortex, 
right piriform cortex, right 
periamygdaloid  cortex, right 
entorhinal cortex 
97 4.16 
#3 olfactory bulb 113 4.00 
#4 left piriform cortex 24 2.75 
#5 mid-cingulate 31 2.43 
*: ROIs shown in bold face were commonly activated for low (Table.2.1) and high odor 
concentration, as well as parametric modulation by odor concentration (Table.2.5) 
 
Table 2.3 Cluster-level statistics of activations for awake dogs, low concentration of odorant. * 
Number of activated clusters: 3, total number of activated voxels: 379 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 
right superior frontal, right mid-
frontal, right orbito-frontal cortex, 
right piriform cortex, right 
periamygdaloid  cortex, right 
entorhinal cortex 
124 4.15 
#2 occipital cortex, cerebellum 172 3.75 
#3 
Olfactory bulb, left mid-frontal, 
left and central orbito-frontal 
cortex, left piriform cortex, left 
periamygdaloid  cortex, left 
entorhinal cortex 
83 3.35 
43 
 
*: ROIs shown in bold face were commonly activated for low and high (Table.2.4) odor 
concentration, as well as parametric modulation by odor concentration (Table.2.6) 
 
Table 2.4 Cluster-level statistics of activations for awake dogs, high concentration of odorant. * 
Number of activated clusters: 7, total number of activated voxels: 759 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 
bilateral anterior olfactory cortex, 
bilateral piriform cortex, bilateral 
periamygdaloid cortex, bilateral 
entorhinal cortex,  medial and 
lateral olfactory stria, olfactory 
tubercle, left and right prefrontal, 
mid-frontal cortex 
430 5.15 
#2 right cerebellum 57 3.88 
#3 cerebellum 185 3.64 
#4 olfactory bulb 18 2.90 
#5 left mid-frontal cortex 19 2.84 
#6 left orbito-frontal cortex 27 2.81 
#7 thalamus 23 2.58 
*: ROIs shown in bold face were commonly activated for low (Table.2.3) and high odor 
concentration, as well as parametric modulation by odor concentration (Table.2.6) 
 
2.3.3 Parametric Modulation of BOLD Signal by Odor Concentration 
The differential response to odor concentration in terms of intensity can be quantified by using 
parametric modulators in GLM analysis as discussed before. The activated regions shown in 
Fig.2.11 corresponding to anesthetized (Fig.2.11 (A)) and conscious dogs (Fig.2.11 (B)), 
respectively, have higher amplitude of activation in response to high as compared to low odorant 
concentration. Cluster-level activation statistics for parametric modulation are summarized for 
anesthetized and awake dogs in Tables 2.5 and 2.6, respectively. For anesthetized dogs, the 
regions showing parametric modulation are in the olfactory bulb, olfactory tubercle, piriform 
lobes, and part of brain stem, while those regions for conscious dogs are mainly in the olfactory 
bulb and cerebellum (see Tables 2.5 and 2.6).  
While Fig.2.11 shows the spatial localization of regions parametrically modulated by odor 
concentration, Figs 2.12 and 2.13 show their temporal profile. Figure 2.12 gives a comparison of 
44 
 
the fitted time series for low and high concentration in anesthetized dogs. The fitted time series 
were derived from the GLM and were mean time series for region of interests (ROIs) within 
anatomical areas which were activated by both low and high concentrations, as well as the 
parametric modulator. These anatomical areas were the olfactory bulb, left and right piriform 
lobes for anesthetized dogs. In each of the anatomical areas, the ROI was determined by a 2 mm 
radius sphere centered at the location of highest activation of parametric modulation. Fig.2.13 
gives a comparison of the fitted time series for low and high concentrations in conscious dogs. 
The anatomical areas were the olfactory bulb and cerebellum. These fitted time series 
demonstrate higher activation intensity for high, as compared to low, odor concentration, 
suggesting the modulation of response by odor intensity in these ROIs. It is noteworthy that the 
fitted time series for awake dogs in ROIs approximately follow the 1:3 ratio in accordance with 
Weber?s law [36] whereas in anesthetized dogs, it is approximately 1:2. 
 
45 
 
 
 
 
Figure 2.11 Group activation maps for parametric modulation in anesthetized dogs (A) and 
awake dogs (B). (Overall FDR=0.05, cluster threshold =15 voxels using AlphaSim, t-contrast). 
Three orthogonal views are shown above and key sagittal slices are shown below for each 
subfigure. Hot colormap is used for activation intensity, and important areas are indicated by 
arrows with labels. (A: Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) The image 
order in sagittal slices is from left to right hemisphere, with coordinate labels shown atop. 
 
Table 2.5 Cluster-level statistics of activations for parametric modulation of anesthetized dogs.* 
Number of activated clusters: 8, total number of activated voxels: 345 
46 
 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 olfactory bulb 42 5.49 
#2 medial and lateral olfactory stria, olfactory tubercle, 112 3.77 
#3 right superior frontal cortex 35 3.49 
#4 
right anterior olfactory cortex, 
right piriform cortex, right 
periamygdaloid  cortex, right 
entorhinal cortex 
61 3.36 
#5 brain stem 15 3.36 
#6 
left anterior olfactory cortex, 
left piriform cortex, left 
periamygdaloid  cortex, left 
entorhinal cortex 
26 3.26 
#7 mid-occipital cortex 18 2.80 
#8 left cerebellum 36 2.55 
*: ROIs shown in bold face were commonly activated for low (Table.2.1) and high (Table.2.2) 
odor concentration, as well as parametric modulation by odor concentration. 
 
Table 2.6 Cluster-level statistics of activations for parametric modulation of awake dogs.* 
Number of activated clusters: 2, total number of activated voxels: 52 
Cluster Anatomical areas included Number of activated voxels Peak T value 
#1 olfactory bulb 24 4.53 
#2 right occipital cortex, cerebellum 28 3.51 
*: ROIs shown in bold face were commonly activated for low (Table.2.3) and high (Table.2.4) 
odor concentration, as well as parametric modulation by odor concentration. 
 
47 
 
 
Figure 2.12 Comparisons of fitted time series obtained from the GLM for ROIs in 
anesthetized dogs. The ROIs are in brain regions that were activated by low and high odor 
concentration, as well as parametric modulation by odor intensity in anesthetized dogs. These 
regions are olfactory bulb and bilateral piriform lobes, which are shown in bold face in Tables 
2.1, 2.2, and 2.5. In each of these regions, the ROI was determined by a sphere which centers at 
the peak activation of parametric modulation and has a radius of 2mm. Fitted time series for low 
concentration are shown in blue, and high concentration in red.  
 
48 
 
 
Figure 2.13 Comparisons of fitted time series obtained from the GLM for ROIs in awake 
dogs. The ROIs are in brain regions that were activated by low and high odor concentration, as 
well as parametric modulation by odor intensity in awake dogs. These regions are olfactory bulb 
and cerebellum, which are shown in bold face in Tables 2.3, 2.4, and 2.6. In each of these 
regions, the ROI was determined by a sphere which centers at the peak activation of parametric 
modulation and has a radius of 2mm. Fitted time series for low concentration are shown in blue, 
and high concentration in red. 
 
2.3.4 Effect of Motion 
Figure 2.14 shows a comparison of the activation maps obtained with only realignment 
parameters obtained from rigid body transformations performed in SPM used as regressors in the 
GLM versus using both camera motion tracking and SPM realignment parameters as regressors 
in the GLM. It can be seen that, many activated areas can be identified using either methods, but 
there are non-trivial differences. We can see apparent additional activation in olfaction-related 
areas such as the orbitofrontal cortex and right piriform lobe when using motion parameters 
obtained from the camera as regressors in the GLM. This shows that jerky movements cannot be 
solely accounted for by SPM realignment and hence optical head motion tracking is valuable for 
imaging awake dogs.  
49 
 
Each subfigure in Figure 2.15 shows 6 realignment parameters obtained by using SPM for 
anesthetized or awake dogs. The realignment was referenced to the first functional image for 
each run, so all curves have zero values at the first time point, the basis point. Figures 2.15 (A) 
and (B) show mean and standard deviation time series of affine parameters for anesthetized dogs, 
respectively, while (E) and (F) show mean and standard deviation time series for awake dogs, 
respectively. (C) and (D) show affine parameters for the worst and best performing dogs, 
respectively, under anesthesia. Likewise, (G) and (H) show affine parameters for the worst and 
best performing awake dogs, respectively. Note that the worst performing awake dog was not 
included in the analysis. As expected, the motion for anesthetized dogs is significantly smaller, 
i.e. much smaller than the size of a single voxel, than that for awake dogs. Also, for awake dogs, 
we can observe jerky movements in Fig.2.15. It is difficult to correct for such jerky movements 
using the realignment procedures based on rigid body transformations. Therefore, it is advisable 
to use optical head motion tracking to account for these jerky movements.  
Additionally, we examined the proportion of variance in the signal explained by motion for 
the low/high concentration vs. rest condition contrast in awake dogs. For the proportion of signal 
variance explained by motion parameters in Eqn.2.3, we found the mean power (variance) of 
?1Q1(t) to be 1.58 (since the fMRI signal does not have specific units, no units can be assigned to 
the power as well) and that of ?2Q2(t) to be 1.25.  The powers of ?iXi(t), i=1:3 were 9.9, 4.6, and 
2.6. Similarly, the powers of ?iPi(t), i=1 to 6, were 0.43, 0.35, 0.21, 0.18, 0.20, 0.31, wherein the 
first three values corresponded to x, y, z translations and last three corresponded to 3 rotations. 
So, the proportion of variance in the signal explained by camera motion parameters was 
(1.58+1.25)/(9.9+4.6+2.6+1.58+1.25+0.43+0.35+0.21+0.18+0.2+0.31)=0.131, i.e. 13%, and the 
proportion of variance explained by SPM realignment parameters  was  
50 
 
(0.43+0.35+0.21+0.18+0.2+0.31)/(9.9+4.6+2.6+1.58+1.25+0.43+0.35+0.21+0.18+0.2+0.31)=0.
078, i.e. about 8%. Both were not very large. Hence this verified that retrospective motion 
correction sufficed. 
 
Figure 2.14 Comparison of activation maps with and without camera motion tracking 
parameters as regressors. (Overall FDR=0.05, cluster threshold =15 voxels using AlphaSim, t-
contrast) The activtion maps were for low concentration (0.016mM) in awake dogs. The 
activation map obtained with only SPM realignment parameters as regressors is shown in cool 
colormap. The activation map with camera motion tracking parameters and SPM realignment 
parameters as regressors is shown in hot colormap. The common areas are overlaid such that 
they appear as purple. We found 3 clusters, 379 voxels in cool-colored map (same as in Table 
2.3); 3 clusters, 396 voxels in hot-colorred map, and 3 clusters, 340 voxels in the common area. 
(A: Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) 
 
51 
 
 
 
 
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52 
 
 
Figure 2.15 Affine parameters relative to the first functional image volume calculated by 
SPM realignment procedure. (A) mean time series of 6 affine parameters for anesthetized dogs; 
(B) standard deviation time series of 6 affine parameters for anesthetized dogs; (C) The time 
series of 6 affine parameters for the worst performing dog run at anesthetized state; (D) The time 
series of 6 affine parameters for the best performing dog run at anesthetized state; (E) mean time 
series of 6 affine parameters for awake dogs; (F) standard deviation time series of 6 affine 
parameters for awake dogs; (G) The time series of 6 affine parameters for the worst performing 
dog run at awake state (not included in the analysis); (H) The time series of 6 affine parameters 
for the best performing dog run at awake state. 
 
2.4 Discussion 
Canine detection is one of the most efficient and effective tools used by law enforcement 
agencies to locate and identify a wide range of explosives and illicit substances. Despite the 
legendary accomplishment of the canine detector, a full understanding of its olfactory system is 
lacking. This study is the first to our knowledge to explore the canine olfactory system at in vivo 
cognitive level using fMRI. Previous studies explored the canine olfactory system either at in 
vitro cellular level, at the behavior level, or at the anatomical level. For example, at the cellular 
level, distribution of putative neurotransmitter amino acids in the dog olfactory bulb [28], anisole 
binding protein in dog olfactory epithelium [29] and changes of dog olfactory system with age 
[30] have been studied. Electrophysiological responses from the olfactory epithelium to odorant 
mixtures have been investigated to characterize the relationship between odorant stimulation and 
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53 
 
olfactory response at the cellular level [31] [32] [33]. Psychophysical studies regarding the dog's 
olfactory sensitivity [73] [74] and discrimination [75] [76], as well as behavioral assessments of 
trained detector dog performance characteristics have been performed [34] [35]. However, the 
neural substrates connecting the cellular level findings with behavior have been rarely explored. 
From our understanding of other sensory systems, the cognitive link is critical. For example, in 
the visual system, neurons in the primary visual cortex contain a faithful representation of the 
visual field [77]. However, the behavior of the organism is driven by different aspects in the 
visual field which are filtered through attention and higher level cognitive integration [78]. It is 
this contextual ?understanding? of the visual field which drives behavior, rather than the entire 
visual field. By analogy, the olfactory map in the olfactory bulb is projected onto neocortical 
areas where an ?understanding? of what the olfactory cue means to the organism at that moment 
is constructed, which drives behavior. Therefore, it is not possible to map cellular recordings in 
the olfactory bulb directly onto behavior unless a cognitive-level understanding is obtained. 
This study is the first attempt to propose a framework to bridge this gap by performing 
noninvasive functional imaging of conscious and anesthetized dogs. We found activations in the 
olfactory bulb, anterior olfactory cortex, piriform cortex, periamygdala and entorhinal cortex for 
both awake and anesthetized dogs, and they were modulated by odor concentrations. The 
cerebellum and cognition-related areas such as superior, medial, and orbital parts of the frontal 
cortex were activated mainly in the awake dogs. However, only the activations in the cerebellum 
and olfactory bulb were parametrically modulated by odor concentration in awake dogs. These 
activations are consistent with known anatomical projections from the olfactory cortex [79] [80] 
[81]. It is noteworthy that mainly unilateral activations in low concentration condition in awake 
dogs became bilateral in the high concentration condition, in agreement with previous reports of 
54 
 
such findings in human data [81]. Other structures, such as the hippocampus, which have 
structural connectivity with the olfactory cortex, did not have enough activated voxels to pass the 
cluster size threshold imposed by us for correcting for multiple comparisons. In addition, 
activation of higher order structures in conscious dogs is consistent with the role of homologous 
structures in other species (such as humans) as reported previously. For example, it has been 
shown in humans that the medial and orbital parts of the frontal cortex are involved in cognitive 
integration of all sensory stimuli in relation to prior experiences [25] and the cerebellum is 
implicated in sniffing and odorant threshold detection [82]. This shows that the olfactory 
stimulus is not being processed in higher cognitive structures in anesthetized dogs to the extent 
that it is in conscious dogs, thus justifying the need for awake dog imaging.  
Our interpretation regarding the parametric modulation of the BOLD signal in 1:3 ratio for a 
ratio of 1:10 for odor concentration is based on the assumption that the scaling of EOG signal by 
odorant concentration can be extrapolated to the BOLD signal. Admittedly, the latter is not 
solely and linearly coupled with neural electrical activity. Rather, the latter is linked to neural 
activity through the convolution with HRF, or more accurately, the Volterra kernel of HRF [83]. 
Therefore, it is remarkable that we indeed used the same scaling with BOLD as with EOG to 
identify olfactory related areas which are parametrically modulated. However, there is need for 
cautious interpretation of these results till they can be replicated by other studies. 
The utility of a practical method for assessing the cognitive processing of olfactory 
information in awake dogs is significant. Clinically, degradation of the sense of smell is a 
sentinel condition, particularly for neurodegenerative diseases such as Alzheimer?s. The dog is 
recommended as a particularly good model of human age-related neurological disease as its 
brain shows neuro-pathologies and its behavior displays attendant cognitive deficits that are 
55 
 
similar to that of humans [84]. Understanding normal cognitive processing of olfactory 
information may allow for identification of abnormalities of such processing well before it 
manifests in detectable alteration in sensory capabilities. Furthermore, the method may allow for 
elucidation of mechanisms underlying such olfactory degeneration that inform the etiology of 
such diseases. 
The method described may allow for important enhancements in the use of dogs for detection 
of hazardous substances. The trained detector dog is widely regarded as the most versatile and 
capable tool for the detection of hazardous materials such as explosive devices [85]. However, 
there are many unresolved issues regarding how best to select, train, and employ dogs for such 
tasks [85]. The method described may allow for identification of olfactory processing 
characteristics of individual dogs indicative of exhibiting superlative performance in performing 
detection tasks. Thus, it may provide a means to select breeding stock for more efficient and 
effective production of working dogs. Description of the perceptual odor space (i.e., the physical 
dimensions responsible for the degree of similarity/difference of the perceptual experience of 
different odorants) through behavioral psychophysical methods has proven difficult and 
amenable to only relatively simple variation between individual chemical compounds [86]. 
Description of the perceptual space of olfaction relative to typical substances that are the targets 
of detector dogs, which are often composed of complex mixtures of chemical compounds, could 
significantly enhance detector dog technology.  Detector dog technology could be greatly 
enhanced by the ability to examine the variation in cognitive processing of odorants that vary 
across different chemical dimensions, such as odorants to which a dog has been trained to detect 
vs. neutral odorants, through fMRI imaging of awake dogs. A cognitive processing model of the 
perceptual odor space could provide insights in explaining and ameliorating the occurrence of 
56 
 
false alerts to particular non-target materials and misses of target materials within particular odor 
contexts. Phenomena such as the masking or overshadowing of target odors by other odors as 
well as the enhancement or disturbance of olfactory capability by the presence of particular 
substances could be examined using the awake fMRI imaging. Additionally, the ability to map 
cognitive olfactory processing could prove to be a valuable tool in characterizing the mechanism 
underlying the learning of odor discriminations.  It is noteworthy that all of the dogs used in the 
current study had previous explosive odor detection training and their experience ranged from a 
few months of detector dog work in research projects to operational employment as a working 
detector dog. However, the odor detection experience of the dogs was not guided by any 
experimental design implications, rather, they were chosen because of their availability and 
because they are representative of the size and general disposition of dogs that are used as 
working detector dogs; hence allowing us to demonstrate the feasibility of this technique for 
future studies of such dogs. For the current study, none of the dogs had previous experience in 
detecting the specific odorants used in this study. We purposefully used odorant mixture with 
which the dogs had no learning history in order to not confound brain activity related to olfactory 
perception or the effects of previous learning history on perceptual processing of the odor 
stimulus. At the same time, the odorant mixture we have used is related to explosives and is 
recognized by dogs [87]. We intend to examine brain activity related to ?learned? odors in future 
work by controlling the amount of exposure and training with specific odors, but in this first 
experiment, our intention was to confine our investigation to odors with which the dogs had no 
prior experience.   
Apart from specific implications for the use of canine capabilities for detecting hazardous 
substances, our results also have implications for the advancement of dog non-invasive cognition 
57 
 
and neurophysiology research in general. Previously researchers have made the case that 
physiological measures of canine cognition are required to complement behavioral studies, and 
have used non-invasive electroencephalography (EEG) to measure neural responses to auditory 
stimulus discrimination [88] and visual stimuli (specifically dog and human faces) [89, 90]. This 
work follows in their footsteps by incorporating fMRI as a non-invasive measure of brain 
function. Given the complementary strengths of EEG and fMRI, our work is likely to advance 
the cause of exploring the functions of deeper brain structures in canines. Further, the 
conclusions of this study have general implications for olfactory and sensory research in other 
animals. 
In addition to the scientific contributions and implications discussed above, this work is likely 
to advance technical knowledge in the field of olfactory fMRI. First, head movement is a critical 
issue for fMRI. Excessive movement will corrupt the data and has been one of the barriers for 
imaging awake animals, though it is very well accepted that some cognitive processes are very 
difficult to study in anesthetized animals [38] [39] [40]. Specifically in the case of olfaction in 
dogs, we have demonstrated that different brain regions are recruited in awake and anesthetized 
dogs. In addition to passively studying cognition, even simple sensory acquisition may involve 
an active process which cannot be executed during anesthesia. For example, awake dogs can 
sniff but anesthetized dogs cannot, and hence jeopardizing the sensory acquisition process [91].  
Though the case for awake animal imaging is strong, the technical challenges for achieving it 
are enormous. Some approaches used by previous researchers include the use of external 
constraints to limit motion [57] and head motion tracking using dual optical cameras in-bore [92] 
or external to the scanner [93]. Our proposed approach comprised of a combination of training 
and optical head motion tracking during awake dog imaging. The training part was employed to 
58 
 
restrict large-scale movements which cannot be compensated retrospectively, while the optical 
head motion tracking part can account for jerky movements. In addition, our optical head 
tracking system was detached from the scanner, thus not suffering the problems caused by 
mount-in-bore camera systems. The results with integration of optical head tracking parameters 
showed the same basic activation pattern obtained by using only SPM realignment parameters, 
but also additional areas of activation in the orbitofrontal cortex and piriform lobe. This verifies 
the efficacy of the optical head tracking system. It is to be noted though, that constructing an 
appropriate target for the dog as done for humans before [41], could potentially allow the optical 
head motion system to track head movements in all six degrees of freedom thereby not requiring 
SPM realignment altogether. We will concentrate our future endeavors in this direction. 
Next, the functional and anatomical data obtained from all dogs must be spatially normalized 
into one space for cross-subject comparison and group-level inference. We have proposed a 
strategy wherein we first chose one anatomical image with good image quality as a template, 
chose one functional image from the same session to normalize to the chosen anatomical, and the 
resulting functional image was then used as a template to normalize other functional images. 
This strategy was superior to directly normalizing all functional images to one anatomical 
template because, unlike human anatomical templates such as MNI which are derived using data 
from hundreds of subjects, the existing dog anatomical templates are derived from less than 10 
dogs and hence do not capture the entire spectrum of head size variability [67]. 
Finally, the simultaneous delivery of odorants such that it is synchronized with fMRI data 
acquisition requires additional features in olfactometers. The most obvious one is that the 
components of the olfactometer which will be within the scanner?s magnetic field be free of any 
metallic components. The desirable features of the device include computer control and odorant 
59 
 
delivery of precise and reproducible duration at selected times, without any added stimulation (e. 
g., tactile, auditory) [49]. Our custom built device met all these specifications. Additionally, 
since it is portable, it can be used for both electrophysiological and fMRI studies. 
  
60 
 
Chapter 3  Univariate Analysis: 
 Enhancement of Odor-induced Activity in the Canine Brain by Zinc Nanoparticles: A 
Functional MRI Study in Conscious Dogs 
 
  The work in this chapter is a continuation of the work in Chapter 2. In Chapter 2, we construct 
the dog fMRI olfactory system and use it to acquire dog fMRI data and compare the effect of low 
concentration of odorant with that of high concentration of odorant. In this chapter, we continue 
to use this system (including fMRI scanning, dog training, odorant stimulus and optical motion 
tracking subsystems) to further investigate dog olfactory processing at the cognitive level. Our 
main contribution is that we conducted experiments with zinc nanoparticles added to the odorant 
and compared their enhancement effect on olfactory perception of dogs at the cognitive level, 
with pure odorant and odorant + gold nanoparticles as control conditions. 
3.1 Introduction 
It is well known that dogs possess extraordinary olfactory senses compared to humans. The 
human society relies heavily on the superior olfactory capabilities of dogs for detecting threats 
such as explosives arising from terrorism, narcotics trafficking, hazardous chemicals and other 
illicit substances. In many operating environments (e.g. airports, warzones, border crossings), the 
concentration of such odorants can be extremely low. Specifically, detecting explosives buried in 
soil or otherwise camouflaged is extremely difficult. Physical and chemical explosive detection 
methods work relatively well in the laboratory but serious challenges exist for detection in the 
field [76]. Sniffer dogs have been the most effective explosive detectors [85], but even trained 
dogs are limited because most plastic explosive materials have very low vapor pressures and 
their detection is therefore difficult. Therefore techniques which are capable of enhancing 
61 
 
detector dogs? olfactory capabilities have received attention in the past decade. In this vein, 
previous studies [33] [94] have demonstrated that a dose-dependent addition of zinc metal 
nanoparticles to odorants can strongly increase the in vitro responses of olfactory sensory 
neurons as measured by electro-olfactogram (EOG). Through intracellular or extracellular 
perfusion, zinc nanoparticles will approximately locate at the interface between the guanine 
nucleotide-binding protein and the receptor proteins, and are engaged in triggering signals at the 
start of olfactory cascade. Further, it was demonstrated that zinc nanoparticles alone without 
odorants, or Zn2+ ions with or without odorants cannot produce such enhancement effects. Also, 
it was shown that gold, silver, and copper nanoparticles produced mildly stronger response than 
pure odorants which faded away rapidly and did not produce as much an increase in response as 
compared to zinc nanoparticles. Importantly, zinc nanoparticles are nontoxic to the dogs for the 
concentrations used [95] and it does not significantly alter the operating environment. Therefore, 
introduction of zinc nanoparticles into the operating environment could lead to a potential 
approach for the enhancement of canine olfactory detection capabilities. 
Most of the previous investigations of the canine olfactory system, regarding the effect of zinc 
nanoparticles have been carried out at the cellular level [33] [94] [96]. This, however, presents 
challenges for translating these findings on in vitro olfactory enhancement effects into a method 
deployable in the field. Specifically, the in vivo cognitive mechanisms underlying olfactory 
enhancement by zinc nanoparticles in canines and corresponding behavioral modifications [75]  
need to be investigated. The former part is the subject of our investigation in this work. 
Specifically, we employed fMRI to investigate the in vivo effect of zinc nanoparticles on 
olfaction-related brain regions in awake dogs. 
62 
 
Since its advent, fMRI has become a very powerful tool to non-invasively investigate the 
cognitive and neuroscientific mechanisms of brain functions [37] [7]. Specifically with respect to 
olfaction, Savic et al and Zald et al investigated the cognitive basis of olfaction in humans [42] 
[43], while Boyett-Anderson et al. and Mori et al have reported similar work in monkeys [44] 
and rodents [45], respectively. Chapter 2 demonstrates the use of fMRI for investigating the 
cognitive basis of odor processing in fully conscious and unrestrained dogs. Specifically, we 
built a computer-controlled odorant applicator capable of delivering specified amount of odors at 
specified intervals of time to the dog inside the scanner, enabling a block design fMRI paradigm. 
In order to address motion-related issues in awake dogs, optical motion tracking of the dog?s 
head was employed using external cameras. Further, the camera and odor applicator were 
synchronized with acquisition of fMRI data. In this work, we demonstrate the utility of this 
experimental framework for non-invasively investigating the in vivo effect of zinc nanoparticles 
on olfaction in the dog brain. We test the hypothesis that enhancement of cellular response in 
olfactory receptor neurons by zinc nanoparticles will lead to corresponding increase in activity in 
olfaction-related and higher order brain areas of the canine brain. We will employ odorant 
without zinc nanoparticles and with gold nanoparticles as control conditions to test the above 
hypothesis.  
A brief overview of the olfactory cascade in the dog brain would facilitate the elucidation of 
our hypothesis. Please refer to the introduction section in Chapter 2 for details about olfactory 
processing chain inside the dog brain. To facilitate, a graphic illustration of the olfactory 
pathway rendered on dog brain surface is in Fig 3.1. We hypothesize that all regions inside the 
brain displayed in Fig.3.1 will show up-regulated activity in the presence of zinc nanoparticles 
mixed with odorant. 
63 
 
 
Figure 3.1 Olfactory pathway in canines rendered on inflated canine brain surface. Arrows 
indicate the olfactory signal flow. (A: anterior, P: posterior, L: left, R: right, S: superior, I: 
inferior)  
 
A 
R L 
P 
S 
I 
Mucus 
Olfactory cortex 
Olfactory receptor neurons 
Olfactory 
bulb 
 Anterior 
olfactory nucleus 
 
Anterior 
olfactory nucleus 
 
Piriform cortex 
 
Piriform cortex 
 
Periamygdala 
 
Periamygdala 
 
Entorhinal 
cortex 
 
Entorhinal 
cortex 
 
Frontal cortex 
 
Hippocampus Hippocampus 
Thalamus 
 
Odorant molecules 
Olfactory tubercle 
64 
 
This study consists of three aspects. First, we compared the effect of zinc nanoparticles in the 
up-regulation of activity in olfaction-related brain areas with pure odorant, i.e., no metal 
nanoparticles added, and gold nanoparticles + odorant as control conditions. The second aspect 
of this study was to compare olfactory responses for dogs in lightly anesthetized state with that in 
fully conscious state. As illustrated in Chapter 2, sedated dogs cannot sniff and remain 
unconscious, thus the activation pattern in the brain for anesthetized dogs can be quite different 
from awake dogs. We explored this aspect again here in the context of zinc nanoparticles. Third, 
the validity of optical motion tracking system [41] for imaging awake dogs had been verified in 
Chapter 2, therefore we continued to use this system to retrospectively correct for head motion 
for awake dogs. This method proved to be ecologically valid and imposed nearly no restrictions 
on the dog being scanned.  
3.2 Material and Methods 
3.2.1 Dog Preparation 
The same six Labrador Retriever dogs as in Chapter 2 raised in the Auburn University Canine 
Detection Research Institute, with ages between 12 to 60 months, were recruited. Ethical 
approval for the study was obtained from the Auburn University Institutional Animal Care and 
Use Committee. Institutional and national guidelines for the care and use of laboratory animals 
were followed. It is noteworthy that, zinc nanoparticles were nontoxic to the dogs for the 
concentrations used [95] and hence their use was not unethical in this study. For anesthetized dog 
imaging, subjects were sedated with intramuscularly administered xylazine (2.2 mg/kg) and 
lightly anesthetized with administered ketamine HCl (11mg/kg,). For imaging of conscious dogs, 
a first set of experiments were conducted wherein they were trained to lie prone on the scanner 
bed, insert their heads into a human knee coil which elegantly acted as a dog head coil, and 
65 
 
remain still during a specified length of scanning period. Positive reinforcement behavior 
shaping procedures was used to keep them as still as possible and desensitize them to loud 
scanner noise. The second round of experiments was conducted for data acquisition with both 
structural and functional sequences.  
3.2.2 Odorant 
The odorant was the mixture of ethyl butyrate, eugenol, and (+) and (?) carvone in water at a 
concentration of 0.016mM. This odorant mixture and the training procedure were the same as in 
Chapter 2. It is noteworthy that the odorant concentration (0.016mM) used was the low 
concentration in Chapter 2, for which the activation of olfaction related areas in the dog?s brain 
can be detected. However, we were able to detect increased activation when a higher 
concentration (0.16 mM) was used in this previous study. This indicates that by using a low 
concentration of 0.016 mM in the current study, there is sufficient latitude for zinc nanoparticles 
to take effect to enhance olfaction related activation in the brain without saturating the brain 
responses. 
The metal nanoparticles (zinc and gold) were prepared in the following way and then mixed 
with odorant. We used colloidal zinc and gold suspensions from Purest Colloids, Inc., and 
Indigenous Products as sources of zinc and gold nanoparticles. The suspensions were processed 
by filtering through 0.22-micrometer Fisherbrand Syringe Filters and centrifuged at 40,000 ? g 
for 90 min at 18oC. The metal concentration in the suspension was surveyed by atomic 
absorption spectra (GTW Analytical Services). Then, aliquots of the suspension were dried onto 
coated grids, and the particles were counted in dark field transmission electron microscope 
images [97] [33]. Finally, the suspensions of nanoparticles were mixed with odorant solutions at 
a particle concentration of 5 nM. 
66 
 
3.2.3 Dog FMRI Olfactory Imaging System 
The dog fMRI olfactory imaging system was the same as in Chapter 2. Here we put this 
system and data processing pipeline together to show a complete picture of the project process in 
Fig.3.2. Please refer to Chapter 2 for details about optical motion tracking system and odorant 
stimulus devices. 
 
Figure 3.2 Schematic of dog fMRI olfactory imaging system and post processing 
procedures. The dashed arrows indicate triggering directions, and the solid arrows indicate flow 
of procedures. 
Laptop with 
VT-8 software 
Odorant 
applicator 
Slice 
timing 
Realignment Spatial 
normalization 
Spatial 
smoothing 
GLM 
(group level) 
Motion parameter 
recording palmtop 
Trigger 
synchronizer 
Manual 
trigger 
Dog and Trainer 
Mask Infrared 
camera 
Monitor 
Dog inside the scanner Infrared radiation 
transmitter 
67 
 
 
3.2.4 Data Acquisition  
Functional data were acquired using T2*-weighted single-shot gradient-recalled echo-planar 
imaging (EPI) [64] on a Siemens 3 Tesla Verio scanner. Imaging parameters were set as: 200 
volumes, 14 axial slices with 3 mm thickness and 0.75 mm gap, repetition time (TR)/ echo time 
(TE) =1000/29 ms, field of view (FOV)=192?192 mm, flip angle (FA)=90?,  in-plane resolution 
of 3?3 mm, and in-plane matrix of 64?64. Dogs were scanned once per week, but data were 
gathered only every other week, alternating with mock scanning (used for the purpose of 
training). For each dog, one scanning session generally included 1 run of structural scan, 2 runs 
of functional scans involving odor stimulation without metal nanoparticles, 2 runs of functional 
scans involving odor stimulation with zinc nanoparticles, 2 runs of functional scans involving 
odor stimulation with gold nanoparticles. The order of the functional scans was randomized. The 
final dataset used for post-processing included 22 anesthetized dog sessions consisting of 110 
runs including 34 runs for pure odorant, 38 runs for zinc nanoparticles, and 38 runs for gold 
nanoparticles; and 25 awake dog sessions consisting of 122 runs including 42 runs for pure 
odorant, 40 runs for zinc nanoparticles, and 40 runs for gold nanoparticles. 2 runs with zinc 
nanoparticles and 2 runs with gold nanoparticles were excluded from post processing because of 
excessive motion which could not be corrected even from motion parameters obtained from the 
camera. The exclusion criterion was: >10 mm displacement between any two consecutive 
acquisition time points in x, y or z direction (x: left ? right; y: up ? down; z: front ? back). 
Also, in the z direction, if there was 10mm total displacement between any two acquisitions in 
one run (not necessarily consecutive), it meant that the dog?s nose was not fully inserted in the 
mask at some time. This would have jeopardized the odorant effect at that time point. Therefore, 
any runs with > 10mm total displacement between any two acquisition time points in the z 
68 
 
direction were also discarded. Structural images were acquired with magnetization-prepared 
rapid gradient echo (MPRAGE) sequence [65] to provide a template for spatial normalization, 
localization, and overlay. The imaging parameters for MPRAGE were set as follows: 
TR/TE=1550/2.64ms, voxel size of 0.792?0.792?1mm3, FA=9?, in-plane matrix 192?192, 
FOV=152?152 mm2, and 104 axial slices of 1mm thickness. 
3.2.5 Experimental Paradigm 
The experimental paradigm was the same as that in Chapter 2. So we brief it as follows for 
convenience. For details, please refer to Chapter 2. Each functional run with odorant stimulus 
had 5 blocks with each block consisting of 10s of odorant stimulation and 30s of rest. The 
paradigm started with a 10s resting condition in order to allow the scanner to enter steady state 
and for dogs to adjust themselves to the context. The odorant stimulation paradigm and the fMRI 
block design sequence are illustrated in Fig. 3.3. 
 
Figure 3.3 Odorant applicator sequences controlled by VT-8 Warner Valve Timer and the 
corresponding fMRI experimental block design. Top: odorant stimulus sequence, wherein 
0 
0 
0 
Odorant stimulus sequence  
Odorant clearance sequence 
fMRI block design sequence 
VT-8 Valve Timer 
30 20 60 70 100 110 140 150 180 190 
10 20 50 60 90 100 130
0 
140
0 
170
0 
180
0 
200
0 
200
0 
Time in s 
10 20 50 60 90 100 130
0 
140
0 
170
0 
180
0 
200
0 
Time in s 
Time in s 
          
0 0 0 0 0 0 1 1 1 1 1 
69 
 
green arrows indicate the onset time of the odorant stimulus in the three conditions (pure odorant, 
odorant + zinc nanoparticles, and odorant + gold nanoparticles) and red arrows indicate the time 
when the stimulation ends. Middle: odorant clearance sequence, with green arrows indicating the 
onset of clearance of odorant, and red arrows indicating when it ends. Bottom: fMRI block 
design sequence used in this work, which matches with the odorant stimulus sequence on the top 
row. ?0? denotes the odor ?on? condition and ?1? denotes the odor ?off? condition. 
 
3.2.6 Post Processing 
The post-processing of fMRI data was performed using SPM8 toolbox [46] including slice 
timing correction, realignment to the first functional image, spatial normalization to one 
structural template of good quality with 2?2?2 mm resampling and 4th order B-spline 
interpolation, spatial smoothing with full width half max (FWHM) =4 ? 4 ? 4 mm3 Gaussian 
kernel, general linear modeling (GLM) and statistical testing. A schematic illustrating this is 
shown at the bottom of Fig.3.2. 
It is noteworthy that for spatial normalization [16], as aforementioned in Chapter 2, currently 
there is no standard and comprehensive brain atlas for dogs. Existing dog brain atlases cannot 
cover the full spectrum of all dog brain shapes and sizes across different canine breeds [67]. On 
the other hand, data from different human brains can be spatially normalized into existing 
templates such as MNI [66] which are derived from a large number of subjects so as to capture 
the full spectrum of head size and shape variability. Since such a template is currently not 
available for canines, we adopted the normalization strategy as demonstrated in Chapter 2 to 
spatially normalize all functional runs to a chosen structural image acquired by us. For details 
and graphic illustration of this procedure, please see Section 2.2.7 in Chapter 2.  
Then, the processed fMRI data were input to a GLM for obtaining voxels in the canine brain 
which were activated by each of the three odor conditions (pure odorant, odorant + zinc 
nanoparticles, and odorant + gold nanoparticles) as compared to no odor. In order to account for 
the variability of the hemodynamic response, time and dispersion derivatives were used in the 
70 
 
design matrix. In addition, similar to our previous study in Chapter 2, motion parameters (3 
translations in x, y, and z directions and 3 rotations about x, y, and z axes) obtained from rigid 
body registration in SPM as well as x and y motion parameters calculated from optical head 
motion tracking camera device were used as nuisance regressors in the design matrix of the 
GLM. The results from GLM were passed through statistical F test to find activation maps. 
Correction for multiple comparisons  
The multiple comparison correction step is the same as in Chapter 2. We applied the 
parameters obtained via AlphaSim algorithm to both the study in Chapter 2 and the study in this 
chapter. We had: individual voxel probability threshold was p=0.05, minimum cluster size 
threshold was equal to 15 voxels, and false positive detection probability of the entire image was 
0.05. 
3.3 Results 
The group level statistical activations for anesthetized dogs are shown in Fig.3.4. The 
functional activations are overlaid on the structural template which was used to spatially 
normalize other functional images. Fig.3.4 (A) corresponds to the activation map with pure 
odorant stimulus. Fig.3.4 (B) corresponds to the activation map obtained from odorant stimulus 
with zinc nanoparticles added, and Fig.3.4 (C) corresponds to the activation map obtained from 
odorant stimulus with gold nanoparticles added. Cluster level statistics of the activations and 
corresponding anatomical areas are summarized in Tables 3.1-3.3. The anatomical labels of 
activated areas were identified based on visual comparison of activation images with published 
dog brain atlases [71]. We can observe that for anesthetized dogs, with no nanoparticles added to 
the odorant, all activations have low intensity, and the activated areas mainly include olfactory 
bulb, periamygdala, entorhinal cortex and anterior cingulate cortex. The anterior cingulate has 
71 
 
been proved to be connecting to prefrontal area activated during odor-processing [98]. It also has 
been shown to be activated for pleasant and unpleasant odors [99].  By contrast, very strong 
activation (both in terms of intensity and spatial extent) is observed for odorant with zinc 
nanoparticles. Clearly, the activation pattern in the axial view in Fig.3.4 (B) has a shape similar 
to the profile of olfactory processing pathway shown in Fig.3.1. Other clusters of activations can 
be found in orbitofrontal cortex, superior frontal cortex, visual cortex, mid cingulate and 
cerebellum. The regions activated by the odorant stimulus with gold nanoparticles are the 
olfactory bulb, orbitofrontal cortex, bilateral piriform cortices, periamygdala, entorhinal cortices, 
and parietal cortex (Fig.3.4 (C)). Compared with the result obtained from zinc nanoparticles, the 
activations for the gold nanoparticle are weaker both in terms of intensity and spatial extent. 
Overall, the results indicate that the activations for odorant with gold nanoparticles are generally 
greater than that for odorant with no nanoparticles and less than that for odorant with zinc 
nanoparticles. This is in agreement with results obtained from in vitro cellular EOG data [33] 
[94]. 
Activation maps for awake dogs are shown in Fig.3.5 and corresponding cluster level statistics 
are summarized in Tables 3.4, 3.5, and 3.6. Fig.3.5 (A) corresponds to the activation map with 
pure odorant stimulus. Fig.3.5 (B) corresponds to the activation map obtained from odorant 
stimulus with zinc nanoparticles added, and Fig.3.5 (C) corresponds to the activation map 
obtained from odorant stimulus with gold nanoparticles added. All these activation maps are 
overlaid on the same structural image as used for anesthetized dogs in Fig.3.4. The activation 
map in Fig.3.5 (A) includes areas of olfactory bulb, superior frontal cortex, and mid cingulate. 
The cingulate cortex receives inputs from the thalamus and the frontal cortex, and projects to 
the entorhinal cortex via the cingulum [100]. It acts as a bridge for communications between 
72 
 
entorhinal cortex on the one hand and thalamus and frontal cortex on the other. As shown by 
Savic et al [101], the cingulate cortex is engaged in odor processing in humans. In contrast, the 
activations in Fig.3.5 (B) involve areas of olfactory bulb, bilateral periamygdala and entorhinal 
cortices, hippocampus, medial and posterior frontal cortex, superior frontal cortex, cerebellum, 
visual cortex, posterior cingulate cortex, as well as thalamus. Many more olfaction related areas 
are activated in the presence of zinc nanoparticles than without, especially in the piriform lobes 
and hippocampus. Also, higher order cortical areas such as medial frontal cortex, which are 
involved in cognition, are strongly activated in terms of both intensity and spatial extent, as 
compared to Fig.3.5 (A). This suggests that enhanced olfactory response at olfactory receptor 
neurons is transmitted into this higher order cognitive area. During odorant stimulation with gold 
nanoparticles, the activations in olfactory bulb and piriform lobes are much less than that for zinc 
nanoparticles as evident from Fig.3.5 (C). While we expected the olfactory bulb to be activated 
by odorant with gold nanoparticles, such activation did not survive corrections for multiple 
comparisons. The activated areas include superior frontal cortex, anterior cingulate cortex, 
cerebellum, visual cortex, posterior cingulate cortex, thalamus, right periamygdala and right 
entorhinal cortex. Generally, the piriform lobes, and hippocampus have stronger activations in 
Fig.3.5 (B) than Figs.3.5 (A) and (C). Also, the cerebellum, posterior cingulate cortex, visual 
cortex, mid frontal cortex and thalamus, are activated more in terms of both intensity and spatial 
extent for odorant with zinc and gold nanoparticles than with no nanoparticles.  
73 
 
 
 
 
(A) Group activation for anesthetized dogs for pure odorants 
Olfactory bulb 
Periamydala, 
entorhinal 
cortex 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Brainstem 
Anterior 
cingulate 
-13 -9 -5 -2 0 3 10 
74 
 
 
 
(B) Group activation for anesthetized dogs for odorants + zinc nanoparticles 
Visual cortex 
Entorhinal 
cortex 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Olfactory stria, 
olfactory tubercle 
Piriform cortex, 
periamygdala 
Hippocampus 
Olfactory bulb 
Orbitofrontal cortex Superior frontal cortex 
-16 -12 -9 -6 -3 0 3 5 10 
75 
 
 
 
Figure 3.4 Group activation maps for anesthetized dogs (F test, p-value threshold (FDR 
corrected) =0.05, cluster threshold =15 voxels using AlphaSim). Subfigure (A) corresponds to 
odorants with no nanoparticles added; subfigure (B) corresponds to odorant with zinc 
nanoparticles added; and subfigure (C) corresponds to odorant with gold nanoparticles added. 
Three orthogonal views are shown above and key sagittal slices are shown below for each 
subfigure. The image order in sagittal slices is from left to right hemisphere, with coordinate 
labels shown atop. Hot color map is used for activation intensity, and important areas are 
indicated by arrows with labels. (A: Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) 
 
(C) Group activation for anesthetized dogs for odorants + gold nanoparticles 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Piriform cortex, 
periamygdala, 
entorhinal cortex 
 
Olfactory bulb 
Orbitofrontal cortex 
-17 -13 -8 -4 0 3 7 10 14 
76 
 
 
 
(A) Group activation for awake dogs for pure odorants 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Mid cingulate 
cortex 
Olfactory bulb 
-8 -4 0 3 
77 
 
 
 
(B) Group activation for awake dogs for odorants + zinc nanoparticles 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Thalamus 
Hippocampus 
Visual cortex 
Cerebellum 
Olfactory bulb 
Medial and posterior frontal cortex 
-18 -10 -5 -2 0 3 6 14 18 
78 
 
 
 
Figure 3.5 Group activation maps for awake dogs (F test, p-value threshold (FDR corrected) 
=0.05, cluster threshold =15 voxels using AlphaSim). Subfigure (A) corresponds to odorants 
with no nanoparticles added; subfigure (B) corresponds to odorant with zinc nanoparticles added; 
and subfigure (C) corresponds to odorant with gold nanoparticles added. Three orthogonal views 
are shown above and key sagittal slices are shown below for each subfigure. The image order in 
sagittal slices is from left to right hemisphere, with coordinate labels shown atop. Hot color map 
is used for activation intensity, and important areas are indicated by arrows with labels. (A: 
Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) 
 
Table 3.1 Cluster-level statistics of activations for anesthetized dogs for odorant with no 
nanoparticles 
Number of activated clusters: 6, total number of activated voxels: 171 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 olfactory bulb 34 6.19 
#2 anterior cingulate cortex 25 5.85 
#3 left piriform cortex, left 42 5.68 
(C) Group activation for awake dogs for odorants + gold nanoparticles 
L R 
I 
S 
A 
L R 
P 
I S 
P 
A 
Thalamus 
Cerebellum Posterior cingulate 
Entorhinal cortex Anterior cingulate 
-14 -11 -8 -4 0 3 6 9 15 
79 
 
periamygdaloid cortex 
#4 brainstem 16 4.73 
#5 left periamygdaloid cortex, left entorhinal cortex 35 4.70 
#6 right periamygdaloid cortex, right entorhinal cortex 19 4.44 
 
Table 3.2 Cluster-level statistics of activations for anesthetized dogs for odorant with zinc 
nanoparticles. 
Number of activated clusters: 12, total number of activated voxels: 1033 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 medial and right superior frontal cortex, mid cingulate 233 19.42 
#2 
olfactory bulb, left and right 
anterior olfactory cortex, left 
piriform cortex, left 
periamygdaloid  cortex, right 
piriform cortex, right 
periamygdaloid cortex, medial 
and lateral olfactory stria, 
olfactory tubercle, left entorhinal 
cortex, orbitofrontal cortex 
410 18.31 
#3 left hippocampus 46 13.85 
#4 right superolateral frontal cortex 51 12.52 
#5 right entorhinal cortex 49 12.13 
#6 left hippocampus 42 11.24 
#7 right hippocampus 30 10.91 
#8 left cerebellum, brainstem 48 10.89 
#9 left caudate tail 21 10.62 
#10 left cerebellum 20 9.19 
#11 right caudate tail 15 8.92 
#12 right cerebellum, right and mid occipital cortex 68 8.58 
 
Table 3.3 Cluster-level statistics of activations for anesthetized dogs for odorant with gold 
nanoparticles. 
Number of activated clusters: 4, total number of activated voxels: 317 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 olfactory bulb, orbitofrontal cortex 60 15.44 
#2 
left anterior olfactory cortex, left 
piriform cortex, left 
periamygdaloid  cortex, left 
lateral olfactory stria, left 
127 15.28 
80 
 
entorhinal cortex 
#3 
right piriform cortex, right 
periamygdaloid  cortex, right 
entorhinal cortex 
94 14.71 
#4 parietal cortex 36 11.26 
 
Table 3.4 Cluster-level statistics of activations for awake dogs for odorant with no nanoparticles. 
Number of activated clusters: 2, total number of activated voxels: 205 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 mid cingulate cortex, superior frontal cortex, left caudate 171 14.84 
#2 olfactory bulb 34 8.42 
 
Table 3.5 Cluster-level statistics of activations for awake dogs for odorant with zinc 
nanoparticles. 
Number of activated clusters: 12, total number of activated voxels: 433 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 left entorhinal cortex 20 14.88 
#2 right entorhinal cortex, right hippocampus 64 14.03 
#3 left occipital cortex, cerebellum, posterior cingulate 132 12.78 
#4 mid occipital cortex 24 12.44 
#5 olfactory bulb, orbitofrontal cortex 36 12.39 
#6 right entorhinal cortex 31 12.38 
#7 right periamygdaloid cortex 16 11.93 
#8 medial and posterior frontal cortex 37 10.72 
#9 cerebellum 22 10.66 
#10 left periamygdaloid cortex 21 8.96 
#11 left superior frontal cortex 15 8.67 
#12 thalamus 15 6.43 
 
Table 3.6 Cluster-level statistics of activations for awake dogs for odorant with gold 
nanoparticles.  
Number of activated clusters: 11, total number of activated voxels: 331 
Cluster Anatomical areas included Number of activated voxels Peak F value 
#1 posterior cingulate, mid occipital cortex, cerebellum 154 13.57 
#2 anterior cingulate cortex 38 12.90 
#3 right superior frontal cortex 18 10.99 
81 
 
#4 left cerebellum 26 9.33 
#5 left caudate 19 8.52 
#6 left superior frontal cortex 29 7.91 
#7 right entorhinal cortex, right periamygdaloid cortex 31 7.50 
#8 thalamus 16 7.15 
 
While Fig.3.4 and Fig.3.5 show the spatial localization of areas activated, Figs.3.6 and 3.7 
show the temporal profile of activation in selected ROIs for anesthetized and awake dogs, 
respectively. The fitted time series, representing temporal profiles of activations [43], were 
obtained from the GLM for selected ROIs that of most interest in our study: olfactory bulb and 
medial frontal cortex. Olfactory bulb, as is well known, is a very major and crucial part in 
olfactory perception, and it is activated for most of our scenarios. On the other hand, medial 
frontal cortex participates in the cognition of olfaction, and is hypothesized to be activated to a 
different extent in conscious and anesthetized states. The medial frontal cortex is selected 
because it has strong activations by zinc nanoparticles for conscious dogs, while the superior 
frontal cortex has activations in all experimental conditions for conscious dogs and these 
activations are not at the same spot. In each ROI, a sphere of 2 mm radius was defined with the 
strongest activated voxel as the center. Then the average fitted time series from this sphere was 
extracted and plotted. Fig.3.6 gives a comparison of the fitted time series obtained in response to 
odorant stimulation with no/zinc/gold nanoparticles in anesthetized dogs. Likewise, Fig.3.7 gives 
a comparison of the fitted time series obtained in response to odorant stimulation with 
no/zinc/gold nanoparticles in conscious dogs.  
82 
 
 
 (A) Olfactory bulb                                (B) Medial frontal cortex 
Figure 3.6 Comparisons of fitted time series obtained from the GLM for ROIs in 
anesthetized dogs. The fitted time series were obtained for two selected ROIs that are closely 
related with olfaction and of most interest to our study: olfactory bulb and medial frontal cortex. 
The average fitted time series are shown for olfactory bulb (A) and medial frontal cortex (B). 
Fitted time series for odorant stimulus without nanoparticles are shown in blue, for odorant 
stimulus with zinc nanoparticles in red and for odorant stimulus with gold nanoparticles in green. 
There is no unit for fitted time series and the experimental block design is shown below for each 
subfigure as a reference.  
 
 
(A) Olfactory bulb                               (B) Medial frontal cortex 
83 
 
Figure 3.7 Comparisons of fitted time series obtained from the GLM for ROIs in awake 
dogs. The fitted time series were obtained for two selected ROIs that are closely related with 
olfaction and of most interest to our study: olfactory bulb and medial frontal cortex. The average 
fitted time series are shown for olfactory bulb (A) and medial frontal cortex (B). Fitted time 
series for odorant stimulus without nanoparticles are shown in blue, for odorant stimulus with 
zinc nanoparticles in red and for odorant stimulus with gold nanoparticles in green. There is no 
unit for fitted time series and the experimental block design is shown below for each subfigure as 
a reference.  
 
Based on the activation maps resulted, two hypotheses can be tested as follows. First, 
according to many authors, specifically [102] [103], it is specified that in humans, the intensity 
of odor is presented by piriform cortex, amygdala complex (including periamygaloid cortex), 
entorhinal cortex, and inferior frontal gyrus, while the valence of odor is shown in the 
orbitofrontal cortex. Zinc nanoparticles enhance odor intensity without change of odor valence, 
according to previous works [33] [94]. Therefore, it is desirable to test this hypothesis in this 
work on dogs. Table 3.7 shows statistics including number of activated voxels and mean F 
values for bilateral piriform lobes and orbitofrontal cortex for each condition (pure odor/zinc 
nanoparticles/gold nanoparticles) in conscious dogs, separately. To more in depth examine this 
hypothesis, both statistics with and without multiple comparison correction are given in Table 
3.7. It can be seen that activation increases in the piriform lobes when odorant is mixed with 
metal nanoparticles (more so for zinc than gold) while no such effect is apparent in the 
orbitofrontal cortex. So, these results support the hypothesis that zinc nanoparticles enhance odor 
intensity without change of odor valence. Given that anesthetized dogs cannot infer the valence 
of odorant, this analysis was carried out only in awake dogs. 
The second hypothesis is pertaining to sniffing. It has been shown that in humans, whether 
odorant is present or absent, sniffing induces activation primarily in the piriform cortex of the 
temporal lobe and in the medial and posterior orbitofrontal gyri of the frontal lobe. In contrast, a 
smell, regardless of sniffing, induces activation mainly in the lateral and anterior orbitofrontal 
84 
 
gyri of the frontal lobe [104] [82]. Since only awake dogs can sniff, sniff-related regions should 
be exclusively activated in them. To test this hypothesis in canines, we calculated the mean 
activation map of 3 conditions for anesthetized dogs and that for awake dogs, and put them into 
manually created mask including bilateral piriform lobes and ventral frontal cortex (including 
anterior olfactory cortex, olfactory stria and tubercle), and medial and posterior frontal cortex 
mask to only preserve activations within the masks. The masks were created with reference to 
existing dog atlas [71]. The result is shown in Fig.3.8. Mean activations for awake dogs are 
rendered using cool colormap, while those for anesthetized dogs are rendered using hot colormap 
(the overlapped area is purple, if any). It is quite clear that the medial and posterior frontal area, 
together with piriform in right temporal lobe are only activated for awake dogs, while anterior 
part of piriform lobes and ventral frontal area are only activated for anesthetized dogs. Thus, our 
results support this hypothesis about sniffing. 
Table 3.7 Comparison of spatial extent and strength of activations in bilateral piriform lobes and 
orbitofrontal cortex for awake dogs.  
Condition 
Awake, bilateral piriform lobes (no multiple comparison 
correction) 
Pure odorant Odorant + zinc Odorant + gold 
Number of activated voxels 28 118 76 
Mean F value 5.08 6.31 5.47 
 
Condition Awake, bilateral piriform lobes (multiple comparison corrected) Pure odorant Odorant + zinc Odorant + gold 
Number of activated voxels 0 103 26 
Mean F value 0 6.41 5.26 
 
Condition Awake, orbito-frontal cortex (no multiple comparison correction) Pure odorant Odorant + zinc Odorant + gold 
Number of activated voxels 4 2 5 
Mean F value 4.92 4.65 5.55 
 
Condition Awake, orbito-frontal cortex (multiple comparison corrected) 
85 
 
Pure odorant Odorant + zinc Odorant + gold 
Number of activated voxels 4 2 0 
Mean F value 4.92 4.65 0 
 
 
 
Figure 3.8 Mean activation maps for anesthetized and awake dogs within piriform lobes, 
ventral frontal cortex, medial and posterior frontal cortex (F test, p-value threshold (FDR 
corrected) =0.05, cluster threshold =15 voxels using AlphaSim). Two mean activation maps are 
calculated by averaging activation maps (Fig.3.4 and 3.5) of 3 conditions for anesthetized (hot 
colormap for activation intensity) and awake dogs (cool colormap for activation intensity), 
respectively. The green outline defines the medial and posterior frontal cortex, the pink outline 
defines ventral frontal cortex, and the yellow outline defines piriform lobes (including piriform 
cortex, periamygdaloid cortex, entorhinal cortex). Three orthogonal views are shown above and 
key sagittal slices are shown below. The image order in sagittal slices is from left to right 
hemisphere, with coordinate labels shown atop. Important areas are indicated by arrows with 
labels. (A: Anterior, P: posterior, S: superior, I: inferior, L: left, R: right) 
 
Ventral frontal 
cortex 
Medial and 
posterior frontal 
cortex 
Piriform lobe 
A 
S I 
R 
A 
L 
L 
P 
R 
P 
I 
S 
-17 -13 -6 -2 0 3 15 18 20 
86 
 
3.4 Discussion 
Canines have much more olfactory sensitivity than many other animals, including humans. 
This makes them a powerful tool in odor detection, which has been utilized by humans for a 
wide range of tasks including locating and identifying explosives and other illicit substances. 
Consequently, investigations leading to a mechanistic understanding of the canine olfactory 
system and enhancement of its olfactory capabilities are required. Such efforts have mostly 
concentrated on either in vitro cellular approaches or behavioral approaches. For example, at the 
cellular level, distribution of putative neurotransmitter amino acids in the dog olfactory bulb [28] 
and anisole binding protein in dog olfactory epithelium [29] have been studied. 
Electrophysiological responses from the olfactory epithelium to odorant mixtures have been 
investigated to characterize the relationship between odorant stimulation and olfactory response 
[31] [32] [33]. At the behavioral level, psychophysical studies regarding the dog's olfactory 
sensitivity [73] [74], discrimination [75] [76], as well as behavioral assessments of trained 
detector dog performance characteristics have been explored [34] [35]. However, in vivo 
exploration of the cognitive basis of canine olfaction which links cellular level findings with 
behavior has been largely missing. In order to address this gap, our previous work in Chapter 2 
described, for the first time, a framework to investigate the cognitive basis of canine olfaction 
using non-invasive imaging techniques such as fMRI. This study is a continuation of the work in 
Chapter 2 with the same canine olfactory fMRI system, but for investigating previously reported 
in vitro cellular results regarding the enhancement of the canine olfactory response by zinc 
nanoparticles.  
Specifically, we test the hypothesis that enhancement of cellular response in olfactory receptor 
neurons by zinc nanoparticles will lead to corresponding increase in activity in olfaction-related 
87 
 
and higher order brain areas of the canine brain. This hypothesis is motivated by previous works 
which have shown in vitro enhancement of olfactory response in olfactory sensory neurons (as 
measured by EOG) in the presence of zinc nanoparticles [33] [94]. Additionally, it was reported 
that zinc nanoparticles alone without odorants, or Zn2+ ions did not produce any enhancement of 
the cellular response. Gold, silver, and copper nanoparticles produced mildly stronger response 
than pure odorants which faded away rapidly. Our hypothesis is that similar in vivo effects can 
be observed in higher order brain regions by non-invasive imaging using fMRI. The results 
presented in the previous section clearly provide support for this hypothesis, both in terms of 
higher activation intensity and larger spatial extent of activation for odorant stimulation in the 
presence of zinc nanoparticles as compared to odorant stimulation in the presence of gold/no 
nanoparticles. 
An additional factor which we investigate is the dependence of the results on the state of 
consciousness of the dog, i.e. whether the dog is anesthetized or is fully conscious. As indicated 
in Chapter 2, anesthetized dogs cannot sniff but conscious dog can, and activities in higher 
cognitive areas such as the frontal cortex would be greatly influenced by anesthesia. Therefore, 
we hypothesize that brain regions recruited in response to olfactory stimulation will be different 
between anesthetized and awake dogs. Accordingly, our results show that for anesthetized dogs, 
most olfaction related regions including olfactory bulb, anterior olfactory cortex, piriform cortex, 
periamygdala, entorhinal cortex, hippocampus, superior frontal cortex (we predict activations in 
these regions as shown in Fig.3.1), are activated strongly (both intensity and spatial extent) for 
odorant stimulation with zinc nanoparticles as compared to activation from odorants with no 
nanoparticles. The brain regions with the enhanced activations for zinc nanoparticles? 
experiments are consistent with known anatomical projections from the olfactory cortex [79] 
88 
 
[80]. Activations obtained from odorants with gold nanoparticles show enhancement of 
activations in olfactory bulb and olfactory cortex as compared to no nanoparticles situation, but 
the enhancement is not as strong as that obtained by odorant with zinc nanoparticles, which is in 
agreement with in vitro cellular results [33] [94]. It is noteworthy that odorant with zinc 
nanoparticles induces enhanced response in the hippocampus while that is not the case for 
odorant stimulation with gold nanoparticles.  
Some activations in anesthetized dogs are found outside of the conventional olfactory pathway 
laid out in Fig.3.1. Below, we discuss the implications of such findings. First, mid cingulate 
cortex is activated by odorant stimulation with zinc nanoparticles. The role of cingulate cortex in 
odorant perception has been shown in some human studies [101]. However, the activation in this 
area is very small and it is also activated in awake dogs, pure odorant. So we cannot conclude the 
enhancement effect of zinc nanoparticles exists in this area. Second, we observe activations in 
caudate and brainstem due to odorant stimulation in the presence of zinc nanoparticle. Previous 
human studies have shown that during discrimination of odor quality, activations can be found in 
caudate and brainstem [101], whereas discrimination of odor intensity mainly recruits core 
olfactory regions. Besides, anatomical evidence shows that the neurons in olfactory cortex and 
amygdala reach targets including brainstem and caudate [101]. Third, the anterior cingulate 
which is a posterior part of medial frontal cortex is activated for pure odorant (also in awake 
dogs, gold nanoparticles). Previous works have shown its link to odor perception [98] [99] [105]. 
A direct anterior cingulate pathway to the primate primary olfactory cortex is also found in 
shaping olfaction [106]. 
For conscious dogs, we observe activations in the olfactory bulb and superior frontal cortex 
with pure odorant. Other activated areas include caudate and mid cingulate. Zinc nanoparticles 
89 
 
enhance the activations in many regions of the olfactory pathway listed in Fig.3.1 such as 
piriform cortex, periamygdalda, entorhinal cortex, hippocampus, thalamus and medial frontal 
cortex. Also, regions outside the traditional olfactory pathway such as the posterior cingulate, 
visual cortex, and cerebellum are also activated by odorant with zinc nanoparticles. Though 
activation in the olfactory bulb does not survive multiple comparisons correction for odorant 
stimulation with gold nanoparticles, activations in the thalamus, anterior cingulate cortex, 
posterior cingulate, visual cortex, and cerebellum are observed.  
The modulatory effect of metal nanoparticles (zinc & gold>none) is observed by visual 
comparison over thalamus, visual cortex, cerebellum, and posterior cingulate. Also, through 
visual inspection, for olfactory cortex, medial frontal cortex and hippocampus, zinc nanoparticles 
enhancement effect is quite conspicuous, larger than gold nanoparticles. Visual comparison of 
activation maps (and accompanying statistics in the Tables) obtained by odorant with zinc 
nanoparticles with those obtained by pure odorant and odorant with gold nanoparticles reveals 
that enhancement of activation, both in terms of intensity and spatial extent, in the latter case is 
evident in olfactory bulb, medial frontal cortex, hippocampus, thalamus, visual cortex, 
cerebellum, and posterior cingulate. Figs.3.6 and 3.7 illustrate the fitted response for two chosen 
ROIs: the olfactory bulb and the medial frontal cortex, in anesthetized and awake dogs, 
respectively. The following inferences can be drawn about the enhancement effect of zinc 
nanoparticles from these results. First, the fitted time series demonstrate higher amplitude of the 
BOLD response for odorant stimulation with zinc nanoparticles, as compared to odorant 
stimulation with gold nanoparticles and odorant with no nanoparticles. This demonstrates the 
enhancement of odor-induced activity by zinc nanoparticles in these ROIs. Second, the 
90 
 
amplitude of the fitted time series for odorant with gold nanoparticles is comparable with no 
nanoparticles in both anesthetized and conscious dogs for selected ROIs.  
Next, we discuss the comparison of activation maps obtained from anesthetized dogs and 
conscious dogs. For both anesthetized and conscious dogs, visual inspection reveals that there 
exists bilateral asymmetry of activations appearing in olfactory cortex for gold nanoparticles, and 
this becomes more symmetric for zinc nanoparticles. This phenomenon is in agreement with 
previous reports of bilateral symmetry of activation in the olfactory cortex in human data [81]. 
Second, in general, we find that the medial frontal cortex, visual cortex, cerebellum, thalamus 
and posterior cingulate are much more activated for conscious dogs than anesthetized dogs, 
while olfactory bulb and olfactory cortex are less activated for conscious dogs than anesthetized 
dogs. This can be explained as follows. Medial frontal cortex, visual cortex, cerebellum, 
thalamus and posterior cingulate [107] are involved in higher order cognitive processing of 
olfaction. The visual cortex is reported to have an influence on high-level olfactory perception 
for humans [108]. Also, it has been shown in humans that the medial part of the frontal cortex is 
involved in cognitive integration of all sensory stimuli in relation to prior experiences [25] and 
the cerebellum is implicated in sniffing and odorant threshold detection [82]. This indicates that 
the olfactory stimulus is not being processed in higher cognitive structures in anesthetized dogs 
to the extent that it is in conscious dogs.  
In addition, two hypotheses which have been proven validate on human olfactory perception 
are tested on canines in this work and justified. First, the zinc nanoparticles dramatically enhance 
the response in piriform cortex, periamygaloid cortex, and entorhinal cortex which is associated 
with intensity of odor, and gold nanoparticles have a moderate enhancement in these areas. And 
we find zinc and gold nanoparticles have no apparent enhancement effect in orbitofrontal cortex 
91 
 
as compared to pure odorant for awake dogs. Previous works have shown the valence of odor is 
presented in the orbitofrontal cortex for humans and zinc nanoparticles do not enhance the 
perception of odor valence. Therefore, our results generally support the hypothesis that the above 
conclusion on humans can be transplanted to canines. Noteworthy, for anesthetized dogs, the 
ratio of number of activated voxels between zinc + odorant and pure odorant is roughly 2-3.5, 
and the ratio between zinc + odorant and gold + odorant is roughly 1.5. After examining Table 
2.1 and Table 2.2 in Chapter 2, we find the number of activated voxels related to odor intensity 
for high concentration is 280, and that for low concentration is 84, the ratio is 280/84 ?3.3. This 
ratio is approximate to the first ratio above mentioned, which solidifies the conclusion about zinc 
nanoparticles? enhancement effect on odor intensity perception. 
Second, we have shown that the sniffing related areas, including medial and posterior frontal 
area, as well as piriform cortex in close approximation to temporal lobe are only activated for 
awake dogs, while anterior part of piriform lobes and ventral frontal area are only activated for 
anesthetized dogs. Although the sniffing related areas are derived from studies on humans, the 
activation patterns in perfect agreement with the fact that dogs can sniff only in conscious state 
inform us that the sniffing related areas for canines are the same as for humans.  
The results described in this work imply that if the odorant is mixed with zinc nanoparticles, it 
will enhance the neural response to olfaction in the dog brain?s olfactory and higher order 
cognitive areas, possibly leading to better olfactory sensitivity and better detection of target 
substances. Future behavioral studies must perform verification of enhanced olfactory sensitivity 
of canines in the presence of zinc nanoparticles. Further, the conclusions of this study may be 
applicable to other animals and further research is needed in the future to test this. Also in this 
work, we used a standard odorant mixture at a concentration of 0.016mM and zinc/gold 
92 
 
nanoparticles at concentrations of 5nM. Future studies must explore the enhancement effect 
induced by combinations of odorant and zinc/gold nanoparticles at different concentrations and 
with different combinatorial ratios, and find the optimal one which can maximally enhance the 
olfactory sensitivity of canines. 
  
93 
 
Chapter 4  Dynamic Multivariate Analysis: 
 Behavioral Relevance of the Dynamics of Functional Brain Connectome 
 
In fMRI the concept of multivariate analysis is based on the assumption that the information in 
each voxel/region is not independent of other voxels/regions. The time series for each 
voxel/region affects and is affected by time series from other voxels/regions. There exists 
information exchange between them. A prevailing concept, called connectivity, is to describe 
this interaction. Generally, there are two kinds of connectivities. One is instantaneous correlation 
between two voxels/regions, which we call functional connectivity (FC) which is usually 
calculated via correlation technique. The other one is the causal influence between two 
voxels/regions, called effective connectivity (EC). It is usually mathematically formulated via 
multivariate general linear regression model, such as Granger causality. Also, connectivities can 
be classified through another categorization: static connectivity and dynamic connectivity. The 
static one is measured over the entire time series from two voxels/regions, while the dynamic one 
is calculated in a time-varying way, implying the correlation/causality between two 
voxels/regions is dynamically changing over time. A comprehensive elaboration on multivariate 
analysis can be found in Ref. [18] and its application in fMRI can be found in Ref. [19]. Our 
main contribution for the work in this chapter is that we proposed an adaptive windowing 
strategy for calculating dynamic FC, applied adaptive evolutionary clustering algorithm for 
clustering brain FC network states, and showed FC dynamics had better predictive capability of 
behaviors than FC statics. 
4.1 Introduction 
94 
 
The view that human brain works as a structurally connected and functionally integrated entity 
has been widely appreciated for more than a decade [109] [110] [111] [112] [113] [114] [115] 
[116] [117] [118] [119] [120]. With the advent of fMRI, different methods for characterizing 
brain connectivity and integration from a functional view point has received a lot of attention 
[113] [114] [115] [116] [117]. FC measures the instantaneous (zero-lag) temporal correlation of 
fMRI signals obtained from different brain regions. FC in different brain networks have been 
characterized both during resting state and task performance [114] [121]. The resting state 
studies assume importance given the sensitivity of resting state networks to brain pathology [122] 
[123] [124] and the ease of performing resting state studies in patient populations.  
Previous resting state FC studies suffered from a few limitations. First, previous studies 
mainly investigated FC by obtaining one connectivity value for the entire duration of the 
experiment based on the assumption that connectivity did not change significantly over time 
[125] [126]. Given that the brain is a dynamic and adaptive system whose state is likely to 
change over time, the stationarity assumption has been relaxed by some recent works which 
explored the dynamics of connectivity in time and frequency domains [127, 128, 129, 130, 131, 
132, 133, 134, 135, 136] [137, 138, 139, 140, 141, 142, 143, 144, 145]. For a comprehensive 
review, please see Hutchison?s work [135]. Further, recent works have also reported diagnostic 
implications of dynamic connectivity for mental disorders such as PTSD (post-traumatic stress 
disorder) [146], and schizophrenia [144]. As pointed out in Hutchison?s work [147], resting-state 
FC can exhibit non-stationary and spontaneous relationships which can be smeared when using 
single, averaged connectivity for the entire length of the experiment. For exploring dynamics of 
FC, previous studies have used sliding windows of fixed length [130] [131]. However, it cannot 
be assumed that non-stationary dynamics implies fixed stationary windows. In order to address 
95 
 
this issue, we propose an approach capable of capturing temporal variations in FC by employing 
dynamic windows of changing length such that FC dynamics is statistically guaranteed to be 
stationary within a given window. In order to demonstrate the feasibility of this approach, we 
performed simulations followed by application to human resting state fMRI data obtained from 
the Human Connectome Project (HCP) (Q3 release, 40 subjects; (http://humanconnectome.org).  
The amount of information obtained from the assessment of dynamic FC can be quite large. 
Hence, it has been often difficult to interpret the underlying neuroscientific meaning [127]. Some 
previous studies showed snapshots of FC at various points during the experiment obtained by 
using different window lengths [131, 132] or template pattern matching [134]. Some other 
studies, such as a study by Kiviniemi et al. [148], did not use any criterion for the determination 
of sliding window length and the window length was assumed to be constant over time. Though 
these are very good exploratory technique, the results and interpretation from such approaches 
can become subjective, depending on the window length and frames chosen. One principled 
approach adopted by some recent reports is to find connectivity configurations which are quasi-
stable for a certain period of time [146]. This follows from similar quasi-stable scalp voltage 
configurations, called microstates, obtained from agglomerative clustering of 
electroencephalographic (EEG) data [138] [149]. Such approaches assume that a single 
functional configuration exists across the whole brain at any given time instant. Additionally, 
they also assume that the dynamics of connectivity is essentially due to the brain changing from 
one across-the-brain connectivity configuration to another. The assumptions behind 
agglomerative clustering and PCA [130] to some extent lose generality. For example, each of the 
two networks shown in Fig.4.1 (A) does not change over time (having same nodes), but the 
connections change with time. Though previous studies have attempted to capture this type of 
96 
 
dynamics, the example showed in Fig.4.1 (B), wherein both connections between nodes and the 
networks themselves change with time (having different nodes at different time instants), 
represents a more general scenario of dynamic changes in FC. In order to capture the latter type 
of dynamics without losing generality, we propose an approach based on adaptive evolutionary 
clustering (AEC) [150] for finding brain network FC configurations at each time instant. The 
network configurations at different time instants differ in terms of connectivity strength between 
regions/nodes, as well as the nodal configuration itself. Then, by performing second-level 
clustering over these time-varying configurations, we found several patterns (2nd level clusters) 
which could represent different brain states alternating over time. 
 
 
 
 
 
 
 
 
 
 
 
       
 
 
 
 
 
 
 
A 
C B 
D E 
F 
A 
C B 
D E 
F 
A 
C B 
D E 
F 
A 
C B 
D E 
F 
Time 
(A) 
(B) 
97 
 
Figure 4.1 Schematic of two types of temporally dynamic FC network configurations. (A) 
The first type illustrating a dynamic network configuration wherein all nodes are part of the same 
FC network, only the connections between them change with time. (B) The second type 
illustrating a dynamic FC network configuration wherein both connections between nodes and 
the networks themselves are changing with time. 
 
Second, there is an abundance of resting state connectivity studies examining specific 
networks, usually involving less than ten anatomically identified regions, rather than the entire 
brain. These studies are motivated by specific hypotheses regarding the functionality of specific 
networks. The methods used for this purpose include seed-based correlation [151] [152] [115], as 
well as PCA (principle component analysis) and ICA (independent component analysis) based 
multivariate analysis [153] [154] [155]. For example, Greicius et al. specially investigated the 
default mode network (DMN) [118] [151], Deshpande et al. investigated the connectivity within 
DMN, hippocampal cortical memory network (HCMN), dorsal attention network (DAN) and 
fronto-parietal control network (FPCN) [114], and Roy et al. considered amygdala-based 
network to analyze adolescent anxiety disorder [156]. Even though convenient for testing 
targeted hypotheses, the effect of other regions in the brain cannot be ignored and it is difficult to 
obtain the complete picture when investigating brain networks consisting of a few regions in 
isolation. Accordingly, many studies have explored whole-brain static FC [157] [158]. Even a 
few recent studies employed a method based on principal component analysis for investigating 
whole-brain dynamic FC patterns [130] [159]. However, they suffered from the following 
limitations. First, some works, such as Leonardi et al. [130], employed a partitioning of the 
whole brain according to AAL (automated anatomical labeling) atlas whose segmentation is 
solely based on anatomy, thus making the ROIs functionally heterogeneous. Second, some other 
works, like Allen et al. [159], employed ICA based functional definition of ROI such that 
anatomically distant regions were combined into a single ROI which is really not an appropriate 
98 
 
parcellation scheme. We recognize that some sort of dimensionality reduction is essential given 
that dynamic evaluation of connectivity from all voxels in the brain can be quite expensive in 
terms of time and computational resources. Therefore, unlike previous studies, we have adopted 
a dimensionality reduction strategy which parcellated voxel time series into 190 functionally 
homogeneous gray matter regions using spectral clustering [160]. This 190-region atlas was 
derived using a large resting state dataset [160]. We extracted mean time series from each of the 
190 regions and fed it into the dynamic FC model.  
One of the imports of conducting connectivity analysis lies in its diagnostic implications as 
well as its link to human behavior. Previous works have shown that FCs between brain regions is 
more informative in predicting behavior than activity of functional regions in isolation. For 
example, Cole et al. found global connectivity of prefrontal cortex predicted control and 
intelligence [161] and He et al. investigated the influence of FC on episodic memory for old 
people [162]. Further, aberrant behavior in subjects with mental and neurological disorders has 
been linked to alterations in FC of specific brain networks [163] [164]. Notably, recent works 
have linked both inter-individual and intra-individual variability in FC to corresponding 
variability in behavior [165] [166]. Given these reports, we hypothesize that the variance of the 
dynamics of the whole brain resting state functional connectome will predict human behavior in 
various domains such as alertness, cognition, emotion and personality traits.  Further, we surmise 
that greater temporal variability of FC increases the adaptability and efficiency of brain networks. 
Accordingly, we hypothesize that variance of FC dynamics will be a better predictor of human 
behavior than conventional static measures of FC obtained from the entire length of the time 
series. In order to test these hypotheses, we obtained whole brain FC dynamics using the 
proposed model involving adaptive windowing and evolutionary clustering and then correlated 
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its temporal variance with behavioral data from the HCP database (for details, please go to 
http://humanconnectome.org/documentation/Q3 /Q3_Release_Reference_Manual.pdf). For 
comparison, a similar analysis was carried out using conventional static FC measures.  
4.2 Materials and Methods 
4.2.1 Data Acquisition and Pre-processing 
All HCP subjects were scanned on a customized Siemens 3T ?Connectome Skyra? housed at 
Washington University in St. Louis. The resting-state fMRI (rfMRI) session1 minimally 
preprocessed data were downloaded and used in this work. This data set included 40 unrelated 
subjects (age range: 22~35 years, 21 females), each having 2 runs. During the scan, subjects 
were instructed to lie at rest with eyes open and fixated on bright cross-hair on a dark 
background. For each subject, oblique axial acquisitions alternated between phase encoding in a 
right-to-left direction in one run and phase encoding in a left-to-right direction in the other run. 
The rfMRI raw images were collected with a multiplexed gradient echo planar imaging sequence 
and the following parameters: 1200 volumes, field of view (FOV) =208? 180 mm2; flip angle 
(FA) =52?; TR (repetition time)/TE (echo time) =720ms/33.1ms, in-plane matrix: 104? 90; 72 
slices per volume with slice thickness =2mm; multiband factor=8; echo spacing=0.58 ms. For 
details about scanner hardware, data acquisition and preprocessing, please see HCP Q3 release 
manual (http://humanconnectome.org/documentation/Q3/Q3_Release_Reference_Manual.pdf).  
The HCP?s minimal preprocessing of rfMRI images involved a functional pipeline named 
fMRIVolume. It removed spatial distortions (gradient distortion correction, field map based 
correction), realigned volumes to compensate for subject motion, registered the fMRI data to the 
structural image, nonlinear registration from structural to MNI, reduced the bias field, 
normalized the 4D image to a global mean, and masked the data with the final brain mask based 
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on FreeSurfer [167] segmentation. For details regarding HCP minimal preprocessing, please 
refer to HCP Q3 release reference manual. We performed additional preprocessing using Data 
Processing Assistant for Resting-State fMRI software (DPARSF) [168] including mean and 
linear trend removal for each voxel time series, temporal filtering with passing band: 0.01~0.1Hz, 
and regressing out the white matter and CSF signals. Subsequently, the 190-region version of the 
CC200 brain atlas [160], which contains a parcellation of all gray matter voxels in the brain to 
190 homogeneous functional regions based on spectral clustering, was employed for ROI 
definition. We extracted the mean time series from all 190 regions for subsequent use. Please 
refer to Appendix A, Table A1 for anatomical labels and MNI coordinates of the 190 regions.  
4.2.2 Behavioural and Individual Difference Measures 
Apart from rfMRI data, we also used HCP?s behavioral data from the same subjects to 
investigate the relevance of the dynamics of FC to human behavior as compared to conventional 
static FC. The HCP collected behavioral measures developed for the NIH (National Institutes of 
Health) Toolbox Assessment of Neurological and Behavioral function 
(http://www.nihtoolbox.org) and several additional measures to assess domains not covered by 
the NIH Toolbox. The behavioral measures were categorized into several domains and the 
domains that were employed in this work were: alertness, cognition, personality, and emotion. 
We did not incorporate categories of motor and sensory functions into our analysis since they 
were relatively less relevant to resting state data. Details about all behavioral measures can be 
found at http://humanconnectome.org/documentation/Q3/Q3_Release_Reference_Manual.pdf. 
For detailed description about behavioral measures employed in this work, please refer to 
Appendix A, Table A2. 
4.2.3 Dynamic Functional Connectivity Model 
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Functional connectivity is a measure of instantaneous (zero-lag) temporal association between 
time series from different brain regions. Pearson?s correlation, by measuring the normalized 
statistical covariance between time series, is a widely employed direct measure of FC in the brain. 
Pearson?s correlation calculated over entire time series reflects the average FC over the entire 
length of the experiment, or in other words, static FC. For capturing the dynamic variations in 
FC, we used sliding windowed Pearson?s correlation along the time axis. Previous reports used 
fixed window length with rectangular [127] [130], or Hamming windows [131]. But there was no 
evidence supporting the superiority of any given window shape over others. Therefore, we have 
employed a rectangular window shape for simplicity. However, for fixed window length, the 
length adopted mattered very much and different lengths produced different results [130] [127] 
(for an overview, please see Hutchison?s work [135]). This is because previous studies made 
arbitrary choices for the length of the fixed window. On the contrary, we employed an approach 
wherein the stationarity of the time series under consideration dictated the length of the window. 
To guarantee that the time series within the length of the window was locally stationary, we 
employed the Dickey-Fuller test (DF test) [169] to determine the window length. The DF test is a 
hypothesis test for the existence of unit root in a given time series with zero mean. A given time 
series y(t) can be modeled as. 
       ( ) ( 1) ( )y t y t t??? ? ?                                            (4.1) 
Where t is the time index,   is a coefficient, and      is the error term. A unit root is present 
when    , in which case, the mean and variance of      are a function of time t, implying that 
     is non-stationary. The DF test has a null hypothesis that a unit root exists and the time series 
is non-stationary. The test procedure in our work was as follows. At a given time point t1, we 
chose the initial window length to be m- (m-=14 TRs in this work. The deduction of this initial 
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window length is described in Appendix A, Section A.1), and did the DF test on time series 
within [t1-m-+1, t1] from all 190 regions. If no unit root existed for all 190 time series, we 
assumed they were consistently stationary and used these windowed time series to calculate 
Pearson?s correlation for time point t1. Otherwise, the window length was increased by 1 time 
point (or 1 TR) such that the windowed time series started from t1-m- to t1, and then we redid the 
DF test. We iterated this procedure until consistent stationarity was achieved or the maximum 
window length was reached. The maximum window length m+ was chosen as 140 TRs. (see 
Appendix A, Section A.1 for mathematical deduction). The windowed Pearson?s correlation 
calculated was the ?valid? section of it, i.e. only those parts that were calculated without the 
zero-padded edges. The sliding window was moved forward one TR each time, i.e. from t1 to 
t1+1, and we repeated the above procedure to calculate the window length at that time point. The 
first 140 data points of the time series were utilized for the DF test of the first sliding window. 
Thus, t1 started from 141st time point and dynamic FC had a length of 1060 time points (1200 is 
the total number of time points for human resting state data).  
4.2.4 Clustering 
The output from the dynamic connectivity model was a matrix of size A?A?B?C where A 
=190, the number of brain regions covering all gray matter, B=1060, the number of time points 
of dynamic FC and C=80, the number of runs over all subjects. Note that at each time point of 
each run, A?A represented a functional connectivity matrix of all possible paths between the 190 
regions. Then, we employed adaptive evolutionary clustering method [150] to adaptively cluster 
all regions according to their FC matrix at each time point such that the smoothness of the 
transition of the whole brain clustering from one time point to the next is controlled by a 
forgetting factor. This first-level clustering allowed us to capture dynamic FC network 
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configurations wherein both connections between regions and the networks themselves were 
changing with time (Fig.4.1 (B)). In second-level clustering, we investigated which of the first-
level clustering configurations consistently occurred over time, i.e. it was a clustering of the first-
level results over time. This informed us of brain network configurations which were similar to 
each other at different time instants, thus shaped into a pattern for a given subject. Then the 
second-level brain network patterns which occurred consistently across runs and subjects were 
identified using a third-level clustering across runs and subjects. A schematic illustrating all three 
levels of clustering is illustrated in Fig.4.2. Below, we elaborate on each of these clustering 
approaches. 
First level clustering 
The input to the first-level clustering algorithm was a distance matrix constructed from the 
dynamic FC matrix. We assumed that higher the absolute value of FC, the closer the two regions 
were in feature space. Note that we did not differentiate between ?correlated? and ?anti-
correlated? interregional relationships in this work, whereas we plan to add this additional layer 
of complexity in future work. However, we cannot directly use interregional FC as the ?distance 
measure? for the following reasons. First, the closer the two regions in feature space, the smaller 
their distance should be, but their connectivity?s absolute value was bigger. This implies a 
monotonically decreasing transformation be required to convert FC to distance measure. Second, 
distances should be nonnegative, with the value being zero if and only if the distance is between 
one region to itself. But the FCs have negative values and the FC from one region to itself is one. 
In order to meet these requirements, we used a distance measure D, defined by D=1-|P|, where 
Pearson?s correlation P ranges between -1 and 1. This transform is monotonically decreasing, the 
result is nonnegative, and the distance from one region to itself is zero. Other requirements of 
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distance measures including reciprocity (the distance from one region to another should be same 
as the other way around) and triangular inequality are also met by D.  
After the distance matrix D was obtained for each time instant, it was fed to the adaptive 
evolutionary clustering algorithm [150]. This clustering was based on the distances between 
regions at each time point and the smoothness of the transition of the whole brain clustering of 
FC patterns from one time point to the next was controlled by a forgetting factor. The forgetting 
factor was actually a weighting of previous clustering results on the calculation of clustering at 
current time instant, which was determined by Bayesian information criterion (BIC) [170]. The 
hierarchical method [171]was chosen as the clustering method.  
The choice of the number of clusters in any clustering algorithm can be based on mathematical 
criteria such as the silhouette index [172] or based on heuristics and prior information regarding 
the underlying variables. The latter case is preferable when information is available to make that 
decision, otherwise mathematical criteria are preferred. Specifically with respect to the number 
of FC networks in the brain, many previous works used methods including fuzzy clustering [173], 
ICA based methods, especially PICA (probabilistic ICA) [174] and tensor PICA [175], graph 
theory-based network analysis [176], and fully exploratory network ICA (FENICA) [177] [178] 
[179] to find the number of consistent resting state networks (RSNs). The current understanding 
of human resting state networks comprises a set of 10 confirmed networks that are specialized in 
functionality: visual network, working memory network, executive network, dorsal attention 
network, ventral attention network, auditory network, sensorimotor network, basal ganglia 
network, language network, as well as the well-known default mode network. Further, the RSNs 
are hierarchically organized [179] [173]. This implies that when the number of networks 
(clusters) increase, some networks will split into sub-networks, usually into left and right lateral 
105 
 
parts or peripheral and foveal parts, rather than reshape into a new network which seemingly has 
no relation with the previous ones. Previous studies have demonstrated that if the number of 
networks is 2, the brain can be functionally divided into task-positive and task-negative networks 
[173]. However, if the number of clusters/networks increases to a number between 5 and10, 
aforementioned 10 networks emerge gradually one by one [175] [173]. Specifically, Damoiseaux 
et al. [175] used tensor PICA in which a three-dimensional tensor represented spatial, temporal 
and subject-specific loadings to find group representatives of these 10 networks. Futher, Kalcher 
et al. [179] regressed a linear relationship between scan time and number of networks. According 
to this work, it can be inferred that when scan time reduce to smaller than 100s, the number of 
networks that can be consistently found across groups was approximately 10. The first level 
clustering was conducted at each time instant, which can be seen as having a very short scan time. 
In this regard, 10 was an appropriate choice for the number of clusters at the first level. Also, 
when the number of networks is specified to be more than 10, these RSNs will split into its 
subparts, but it is noteworthy that structured artifacts (such as head motion and field 
inhomogeneity) may also appear as individual networks [179]. Given these factors, we specified 
10 as the number of clusters during first-level clustering.   
Second level clustering 
We investigated which of the first-level clustering configurations consistently occurred over 
time using second level clustering. Technically speaking, second-level clustering was the 
clustering of first-level results over time. Unlike first-level clustering which was dynamic in 
nature, i.e. clustering configurations at each time instant impacted those at later time instants, 
second level clustering was static in nature. Hierarchical approach to clustering was employed 
and the number of clusters was determined by silhouette index (with a search range between 2 
106 
 
and 20) given that a priori heuristics for determining the number of clusters in this situation are 
yet to be established. The search range was determined according to current understanding of the 
number of quasi-stable FC configurations which recur over time during the course of an 
experiment.  The number of temporal FC patterns found by previous works is normally less than 
20. For example, Li et al. [146] found 16 reproducible temporal FC patterns across healthy 
people via effective dictionary learning and sparse coding algorithms. Zhang et al. [180] found 
12 representative functional states using a dynamic Bayesian variable partition model. Besides, 
the number of temporally quasi-stable patterns of EEG topography, called microstates, found by 
previous literatures is also generally less than 20. Britz et al. [138] found the optimal number to 
be 4, Musso et al. [149] found 10 recurrent microstates. Thus, we set the search range to be 2-20 
to accommodate all possibilities. 
The distance measure between two first level clustering configurations was calculated using a 
procedure illustrated in Fig.A5 of Appendix A, Section A.7. Suppose at time point tm, the first 
level clustering result is called M and at a different time point tn, the first level clustering result is 
called N. M has 10 clusters represented by mi, i=1, 2? 10, and N has 10 clusters represented by 
nj, j=1, 2? 10. Firstly, we compare the number of common regions (common members) between 
each possible pair mi, nj, and then among them we select the pair mi*, nj* that has the maximal 
number of common regions, and we assign the same label to all regions in mi* and all regions in 
nj*. Then we remove this pair and find the next pair which has the maximal number of common 
regions in remaining possible pairs, and assign regions belonging to this pair the same label (this 
label is different from previous label). Then we remove this pair and continue this procedure for 
remaining clusters. If the maximal number of common regions becomes zero for remaining 
possible pairs, then we assign all regions in all remaining clusters in M some label (different 
107 
 
from all previous labels) and all regions in all remaining clusters in N a different label (different 
from all previous labels). Consequently, no pairs are left in M and N and all regions are labeled 
in both M and N. Finally, the distance measure is devised to be the number of regions having 
different labels in M and N. It is evident that this distance measure meets requirements of 
reciprocity, non-negativeness, triangular inequality, and self-distance being zero.  
The outcome of second-level clustering was a number of clusters with first level 
configurations as their members. Theoretically, each second-level cluster centroid was a 
weighted sum of first level configurations such that each region in theoretical centroid had fuzzy 
belongingness to each first level cluster. This was awkward to maneuver, display, and used for 
next level clustering. So, for each second level cluster, we calculated the mean matrix  ? from 
first level distance matrices Di of all its members, wherein i indexes all members in the given 
second level cluster. The member whose distance matrix was closest to  ? in the Euclidean sense 
was chosen to represent the theoretical centroid of the second level cluster. The Euclidean 
distance E between  ? and Di was calculated using Eq.4.2 below.  
            22
11 ( ( , ) ( , ) )
rr
inmE m n m n?????? DD
                                            (4.2) 
Where r represents the number of columns (and rows), which is equal to the number of regions, 
in the corresponding matrix.  
Third level clustering 
Each second level cluster represented a brain network pattern in one run. Not all second-level 
patterns were of interest to us, only those patterns with a lot of members (first level 
configurations) were dominating and important patterns. The dominating second-level patterns 
which occurred consistently across runs/subjects were identified using the third-level clustering 
across all runs. For the third-level clustering, the centroids representing dominating second-level 
108 
 
patterns as mentioned above were used as members for clustering. Dominating second-level 
patterns were predicated based on the histogram of second level clusters? occurrence times (the 
number of first level members included in one second level cluster, one member took up 1 TR) 
obtained from all runs/subjects (Fig.4.3). It is evident that the majority of second-level clusters 
had occurrence times less than 100 TRs. Therefore, we used occurrence times of 100 as the 
threshold to determine dominating second level clusters, which were then input to third level 
clustering. Transient second level patterns with occurrence times less than 100 were inconsistent 
and hence were not input to third level clustering since the objective of performing third level 
clustering was to find dominant and consistent brain network patterns across subjects/runs.  
To calculate the distance measure between dominating second level centroids, the strategy 
adopted in second level clustering was not feasible since each centroid had a weight, i.e. the 
occurrence times of the second level cluster it represented. Therefore, we performed weighted 
clustering at the third level. For any dominating second level centroid i, we had its FC distance 
matrix Di. We picked out all the lower (or upper) triangular elements of Di and vectorized it to 
represent its corresponding point in feature space. The diagonal elements were all zeros and 
hence not considered. Then weighted K-means algorithm was employed to cluster these points in 
feature space. The number of clusters was determined by silhouette criterion and each cluster?s 
centroid was calculated by weighted mean. Similar to the second level clustering, each region in 
theoretical third level centroid had fuzzy memberships to each second level cluster centroid, 
hindering display and subsequent analysis. So, the member whose distance matrix was nearest to 
the theoretical third level centroid was selected as third level centroid agent. The procedure for 
all three levels of clustering is schematically illustrated in Fig.4.2. 
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Figure 4.2 Schematic of the procedure for all three levels of clustering. The top left part 
illustrates the transformation of dynamic FC to a distance measure; top right part is the first level 
clustering; below is the second level clustering and at the bottom is the third level clustering.  
 
 
Figure 4.3 Histogram of occurrence times (in TRs) of second level clusters from all runs 
 
4.2.5 Behavioral Relevance of Dynamic FC 
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We defined three metrics to represent dynamic FC based on the first level clustering result. 
The first was the mean time that two regions were in connected (or disconnected) state before 
transitioning into a disconnected (or connected) state, called mean time before state transition 
(MTST). The second was standard deviation of the time before state transition (SDTST). The 
third was called CFP (clustering frequency percentage), which measured the percentage of total 
time that two regions were clustered relative to total scanning time. In addition, the conventional 
static FC (SFC) obtained from the entire time series was adopted as the fourth metric. An 
illustrative example demonstrating state transitions and the procedure to calculate MTST, 
SDTST and CFP is shown in Fig.A6 in Appendix A, Section A.8. 
The behavioral scores obtained from a variety of behavioral tests capturing alertness, 
cognition, emotion, and personality were input into a GLM as the dependent variables with 
dynamic and static FC metrics as explanatory variables as given below: 
       , , , , , , , , , ,M T S T S D T S T C F P S F Ci j i j i j i j i j i j i j i j i j i jB ? ? ? ? ?? ? ? ? ? ? ? ? ?               (4.3) 
Where i indexes different behavioral tests, j indexes the FCs between different pairs of regions, 
     is a vector of behavioral scores for all subjects, MTSTi,j, SDTSTi,j, CFPi,j and SFCi,j are 
vectors of corresponding metrics for all subjects. ?i,j, ?i,j, ?i,j, and ?i,j are their coefficients, 
respectively, and ?i,j is residual. It should be noted that we had the 4 metrics from 80 runs (2 runs 
for each of the 40 subjects), but behavioral scores only from 40 subjects. So each subject?s 
behavioral score was used twice corresponding to its two runs. The coefficients from this GLM 
were estimated using a standard least squares procedure and were tested for statistical 
significance using a z test. A Bonferroni corrected p-value threshold of p=0.05/75=0.00067 (75 
is the number of behavioral tests) was used to infer significant relationships between dynamic 
and static FC metrics and behavior. Then, the variance explained in this GLM model by each 
111 
 
metric was calculated. For example, ? ?2
,,?MTSTi j i j?
 is the variance explained by MTST. The 
overline denotes mean operation over all is and js. And ? ? ? ?22
, , , ,?M TS T M TS Ti j i j i j i j??? ???
+
? ?2,,?SDTSTi j i j? +? ?2,,?CFPi j i j? +? ?2,,?SFCi j i j? ??? represents the relative percentage of variance explained 
by MTST.  
4.3 Results 
4.3.1 Simulations 
To validate our proposed method for dynamic FC calculation and clustering, simulations were 
performed on artificial data. We simulated time series from 12 regions, each with 1000 time 
points, using a multivariate vector autoregressive model (MVAR) given as: 
         
1( ) ( )
p
iit A t i?? ? ? ??VV ?
                                                     (4.4) 
Where V(t) denotes the vector of signals from 12 regions, Ai is the regression coefficient matrix, 
and ? represents noise vector with covariance matrix C, which has autocorrelation coefficients 
normalized to 1. To exclusively test time-varying FC, 3 scenarios were used:  
(i) Ais were all zero matrices (thus time-lagged connectivity was excluded, and there was no 
need to specify p), C was constant over time, 12 regions? time series were divided into 4 
clusters each having 3 members connected to each other (regions 1, 2, 3 were in one cluster, 
regions 4, 5, 6 were in one cluster, regions 7, 8, 9 were in one cluster, and regions 10, 11, 12 
were in one cluster). In this case, C was a blocked symmetric positive definite matrix with 
3?3 blocks on the diagonal.  
112 
 
(ii) Same as first scenario except that every non-zero element in C was slowly varying over time 
in a sinusoidal manner with period equal to 200? and randomized phases. The belongingness 
of each region to each cluster was not changed as compared to scenario (i).  
(iii) Same as first scenario except after every 200 time points, C was circularly shifted by one 
column and one row such that the membership of each time series changed with respect to 
its cluster.  
It should be noted that the lower and upper limits of sliding window length for DF test were 
set to 10 and 100 time points as derived in Appendix A, Section A.1. And the windowed 
Pearson?s correlation calculated was the ?valid? section of it, i.e. only those parts that were 
calculated without the zero-padded edges. The sliding window moved forward one time point 
each time, and the [1, 100] section of simulated time series were preserved for DF test of the first 
sliding window. Thus the resultant time series of dynamic FC had 900 time points, 
corresponding to [100, 1000] section of simulated MVAR time series. Above rule was applied to 
experimental fMRI data analysis also. 
The simulation was conducted 100 times for each scenario and the results are shown in Figure 
4.4. The mean and standard deviation (over all 100 iterations) of the resulting time-varying FC 
time series from several representative regions are illustrated. In Fig.4.4, subfigure (A) 
corresponds to scenario (i) specifically showing the connections from region 1. As shown on the 
left, the ground truth FCs between regions are constant and the auto-correlation is one. The 
estimated time-varying FCs (right) approach the ground truth very well and the auto-correlation 
is constantly one. Subfigures (B) and (C) show the results corresponding to scenarios (ii) and (iii) 
wherein the estimated time-varying FCs track the ground truth sufficiently well, and the regions 
belonging to different clusters (regions 4 & 11 in Fig.4.4 (B) and regions 1 & 8 in Fig.4.4 (C)) 
113 
 
have nearly zero correlation, indicating no false positives. In particular, when the simulated 
cluster belongingness changes in Fig.4.4 (C), the estimated time-varying FCs respond to it 
swiftly and converge quickly. Subfigure (D) demonstrates one representative realization of AEC 
algorithm over time (first level clustering) for simulated time-varying FCs of scenario (iii). 
Along the time axis, regions rendered the same color belong to the same cluster. After 200 time 
points, the cluster belongingness (and hence the nodal configuration for the networks) is 
simulated to be circularly shifted once. For example, from time points 1 to 200, regions 1, 2, 3 
are clustered together, region 4, 5, 6 are clustered together, and so on. Then from time points 201 
to 400, regions 2, 3, 4 belong to the same network, regions 5, 6, 7 belong to the same 
network, ? , regions 11, 12, 1 belong to the same network. This switching pattern is tracked 
correctly using estimated dynamic FCs, with only short transitional time. (Fig.4.4 (D), right). 
Note that since the time-varying FC time series corresponds to [100, 1000] section of MVAR 
time series, the cluster belongingness switches occur at time point 100, 300, 500, and 700. In 
summary, the simulations demonstrate the feasibility of the proposed approach for tracking 
dynamic FC and ascertaining the clustering of regions based on dynamic FC over time through 
the AEC algorithm.  
   
(A)                                                       
114 
 
   
 (B) 
    
(C) 
  (D) 
 
Figure 4.4 Simulation results for time-varying FC and first level clustering. The simulated 
MVAR processes consisted of 12 regional time series, each with 1000 time points. (A) left: 
example showing simulated ground truth for time-varying FCs of scenario (i); right: estimated 
mean and standard deviation (std) of simulated time-varying FCs. Color bands span [mean-std, 
mean+std] with mean in the middle. (B) left: example showing simulated ground truth for time-
varying FCs of scenario (ii); right: estimated mean and standard deviation of simulated time-
T i m e
R
e
g
io
n
 l
a
b
e
l
100 200 300 400 500 600 700 800 900
1
2
3
4
5
6
7
8
9
10
11
12
T i m e
R
e
g
io
n
 l
a
b
e
l
100 200 300 400 500 600 700 800 900
1
2
3
4
5
6
7
8
9
10
11
12
115 
 
varying FCs. (C) left: example showing simulated ground truth for time-varying FCs of scenario 
(iii); right: estimated mean and standard deviation of simulated time-varying FCs. (D) left: 
ground truth clustering pattern for one representative example of simulated time-varying FCs 
corresponding to scenario (iii); right: corresponding estimated clustering pattern calculated using 
AEC algorithm. Regions rendered with the same color are connected to each other and hence 
belong to the same cluster.   
 
4.3.2 Application to Experimental Resting State FMRI Data from HCP 
Resting state fMRI data obtained from HCP were minimally preprocessed and underwent 
additional pre-processing by us as elaborated in Material and Methods section. We applied our 
framework for calculating dynamic FC and three levels of clustering to this fully pre-processed 
dataset. Figure 4.5 shows the centroids obtained from third level clustering, which represent 
whole brain connectivity patterns which appear consistently across time and subjects. In this 
figure, brain regions with the same color are functionally connected to each other and the 
strength of those connections are stronger than those between them and brain regions with a 
different color. Note that clustering is a vector quantization scheme which assigns each region in 
the brain to a cluster such that the distance between the given region and other regions inside the 
cluster is minimized and the distance between the given region and other regions outside the 
cluster is maximized. A statistical summary is listed in Table 4.1, which presents each third level 
cluster?s statistics including number of members (dominating second level centroids), and the 
sum of occurrence times of members in TRs. Together, these two metrics determine the relative 
dominance of each third level cluster. We obtained 8 third level clusters according to the 
silhouette criterion [172]. It is clear that cluster #1, 2, 6 and 7 are more dominant than others, and 
cluster #8 is the least dominant. Note that the numbers assigned to clusters are incidental and 
carry no particular meaning. Also, the cluster centroids in Fig.4.5 are in the same order as in 
Table 4.1. The DMN can be observed in the centroids of cluster #3, #4, #6 and #8. These four 
clusters account for approximately 32% of the total occurrence times of dominating second level 
116 
 
clusters (OTDSLC). Also, it is to be noted that the regions of the DMN are connected to regions 
outside the DMN in addition to being connected to each other in clusters #2, #5, and #7. Taken 
together, this implies that the regions of the DMN are connected to each other and appear as part 
of the same cluster for approximately 78% of OTDSLC. The visual network, comprising of 
regions in the primary and secondary visual cortices, appears in centroids #1, #3, #4, #5 and #6, 
with #6 having only occipital area, #3 having occipital-parietal-frontal interaction (merged with 
dorsal attention network) and others having frontal-occipital interaction. They account for 57% 
of OTDSLC. The language network, comprising of Broca?s and Wernicke?s areas, appears in 
centroid #6 and clusters with cerebellar regions. This network accounts for 15% of OTDSLC. 
The sensorimotor network appears in centroid #1 and splits into bilateral parts in centroid #4, 
accounting for 33% of OTDSLC. The dorsal attention network merges with the visual network in 
centroid #3 and appears as an individual network in centroid #6. So, in total it accounts for 19% 
of OTDSLC. The executive network can be seen only in centroid #4 which accounts for 11% of 
OTDSLC. The ventral attention network appears as a clear network (dark red) only in centroid 
#8 which accounts for 11% of OTDSLC. The limbic network can be seen in its entirety in 
centroid #1 which accounts for 22% of OTDSLC, and splits into several parts (thalamus, caudate, 
basal ganglia, etc.) with each part having connections with cortical regions in centroids #3, #5, 
and #7. Brainstem appears as an individual cluster in centroid #2, and in centroid #2 we can 
observe that the ventral frontal areas also shapes into individual clusters, such as rectus, 
indicating that they have weak FC with other areas. It should be noted that since many networks 
co-occur in certain centroids, percentages of the total occurrence times of dominating second 
level clusters for all RSNs do not sum to 100%. 
117 
 
 (A) Third level clustering centroid #1 
 (B) Third level clustering centroid #2 
 (C) Third level clustering centroid #3 
-64                         -54                         -44                          -34                         -24 
-14                         -4                           6                             16                           26 
36                           46                            56                           66 
-64                         -54                         -44                          -34                         -24 
-14                         -4                           6                             16                           26 
36                           46                            56                           66 
-64                         -54                         -44                          -34                         -24 
-14                         -4                           6                             16                           26 
36                           46                            56                           66 
118 
 
 (D) Third level clustering centroid #4 
 (E) Third level clustering centroid #5 
 (F) Third level clustering centroid #6 
-64                         -54                         -44                          -34                         -24 
-14                         -4                           6                             16                           26 
36                           46                           56                            66 
-64                         -54                         -44                          -34                         -24 
-14                         -4                            6                            16                           26 
36                           46                            56                            66 
-64                         -54                         -44                          -34                         -24 
-14                         -4                            6                            16                           26 
36                           46                            56                            66 
119 
 
 (G) Third level clustering centroid #7 
 (H) Third level clustering centroid #8 
Figure 4.5 Third level clustering centroids. Each subfigure shows one third level centroid. The 
order of third level centroids is the same as in Table 4.1. There are a total of 8 clusters with each 
centroid chosen as the cluster member (which is one of second level dominating centroids) that is 
nearest to the theoretically calculated centroid. Each color in each subfigure represents regions 
connected to each other. The number shown at the top left of each sagittal slice is the x 
coordinate (left to right), in mm. 
 
Table 4.1 Statistical summary of third level clustering 
Third level 
cluster 
Cluster 
#1 
Cluster 
#2 
Cluster 
#3 
Cluster 
#4 
Cluster 
#5 
Cluster 
#6 
Cluster 
#7 
Cluster 
#8 Sum 
No. of 
cluster 
members 
33 19 7 19 4 15 15 1 113 
Sum of all 
members? 
occurrence 
times (TR) 
13776 14702 2787 6838 2744 9140 11209 813 62009 
 
Characterization and quantification of dynamic and static FC 
-64                         -54                         -44                         -34                          -24 
-14                         -4                           6                             16                           26 
36                           46                            56                           66 
-64                         -54                         -44                          -34                         -24 
-14                         -4                            6                            16                           26 
36                           46                            56                            66 
120 
 
We used three metrics: MTST, SDTST, and CFP to characterize dynamic FC based on the 
first level clustering result. In addition, the SFC obtained from the entire time series was adopted 
as the fourth metric.  
Fig.4.6 shows interregional MTST, SDTST, CFP and SFC matrices averaged over all runs. 
Generally a higher value of MTST indicates lesser dynamic variations of FC between regions. 
We can observe that several regions have much less dynamics of FC in relation to other regions, 
such as regions 35, 36 and region 168, corresponding to brainstem and right rectus gyrus (for 
corresponding AAL anatomical area of each region, please see Appendix A, Section A.2). Also 
noteworthy is that many regions having higher MTSTs generally have lower CFPs and SFCs. 
This indicates that regions such as brainstem and rectus gyrus with high MTSTs are barely 
connected with other regions during the course of the experiment.  
   (A)                                                             (B) 
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  (C)                                                             (D) 
Figure 4.6 Interregional MTST, SDTST, CFP, SFC matrices averaged over all runs. 
Numbers along horizontal and vertical axis are region labels. For the AAL nomenclature 
corresponding to these numeric labels, please see Appendix A, Section A.2. (A) MTST; (B) 
SDTST; (C) CFP; (D) SFC. (Note: for each matrix, diagonal elements represent the dynamic or 
static FC metric between a given region and itself. Therefore, the colors of diagonal elements 
have no meaning and not comparable to off-diagonal elements) 
 
Fig.4.7 shows the paths (connections between regions) with MTSTs within the top and bottom 
0.1% of MTSTs of all paths. The MTSTs here are averaged over all runs. The red paths represent 
interregional MTSTs whose values are among the top 0.1% of all MTSTs, and blue paths 
represent interregional MTSTs whose values are among the bottom 0.1% of all MTSTs. We 
choose top and bottom 0.1% here in order to improve visualization such that paths with most 
significance could be emphasized.  Figures showing top and bottom 0.5% and 1% MTSTs are in 
Appendix A, Section A.4 (Fig.A1 and A2, respectively). If the threshold is set beyond 1%, the 
number of paths is too big such that it prevents any meaningful visualization. These results 
reinforce the point we made about large MTSTs for the rectal gyrus, that it is seldom clustered 
with other regions and for most of the time it appears as a sole cluster at the first level, implying 
that it has very weak dynamic FC with other regions. On the other hand, right superior occipital 
cortex and left cuneus had a large MTST due to the fact that they are always connected, 
indicating a very strong FC in between. This can be verified by inspecting interregional CFP 
122 
 
matrix (Fig.4.6 (C)). The blue paths with low MTSTs represent connections with highly dynamic 
FC. One network involving the mid-frontal cortex, anterior and mid cingulate, insula and 
supplemental motor area, as well as another intra-cerebellar network stands out. 
 
Figure 4.7 Paths with most and least interregional MTSTs. The red paths represent 
interregional MTSTs whose values are among the top 0.1% of all MTSTs, and blue paths 
represent interregional MTSTs whose values are among the bottom 0.1% of all MTSTs. All 
MTSTs have been averaged over all runs. 
 
Each brain region has 189 paths associated with it and hence the same number of MTSTs. We 
define a metric, regional MTST (rMTST), by finding the mean MTST of all paths associated 
with a given region. Brain regions with rMTST in the top 30% and bottom 30% are shown in 
Fig.4.8 (A) and (B), respectively. Similarly, regional CFP (rCFP) is defined as the mean CFP of 
all paths associated with a given region and regions with rCFP in the top 30% and bottom 30% 
are shown in Fig.4.8 (C) and (D), respectively. We choose top and bottom 30%, because at this 
proportion, known RSNs are revealed. For comparison, a figure showing regions with top and 
123 
 
bottom 20% rMTST and rCFP is shown in Appendix A, Section A.5 (Fig.A3). It is noted that 
fewer number of regions, which do not constitute known RSNs are revealed in this figure. It can 
be seen from Fig.4.8 that the brainstem and rectus have highest rMTST and lowest rCFP, which 
is in agreement with the results presented above, i.e. low dynamics and unconnected to other 
regions for a major portion of the experiment. Superior occipital cortex has high rMTST as well 
as high rCFP for the reason that it is frequently connected with nearby occipital regions. Besides, 
DMN, DAN, and FPCN have low rMTST, indicating high dynamics of FC. Especially 
noteworthy is DMN, which has the lowest rMTST, i.e. highest dynamics of FC. Most occipital, 
temporal, superior frontal and parietal areas have high CFP, indicating they generally have 
strong FC to other regions. 
   (A)                                                                (B) 
 
124 
 
  
(C)                                                              (D) 
Figure 4.8 Regions with top and bottom 30% rMTST and rCFP. Each brain region has 189 
paths associated with it and hence the same number of MTSTs. We define a metric, regional 
MTST (rMTST) and regional CFP (rCFP), by finding the mean MTST/CFP of all paths 
associated with a given region. Regions with top 30% of all rMTST are shown in (A) and with 
bottom 30% of all rMTST are shown in (B).Corresponding maps for top and bottom 30% rCFP 
are shown in (C) rand (D), respectively. Hot colormap is used to represent the numeric value of 
corresponding metric for each region shown. (A: anterior, P: posterior, S: superior, I: inferior, L: 
left, R: right) 
 
Behavioral relevance of dynamic and static FC 
Dynamic and static FC metrics were together input into a general linear model with HCP 
behavioral measures as dependent variables for investigating their behavioral relevance. Fig.4.9 
presents the relative percentage of variance explained by each metric for 75 behavioral scores 
pertaining to alertness, cognition, emotion, and personality, obtained using a general linear 
model with each behavioral score as the dependent variable and dynamic and static FC metrics 
as independent variables. Each relative percentage of variance explained is shown as an error bar 
with mean and standard deviation derived across all paths between 190 regions in the brain. It is 
remarkable that the variances explained by dynamic FC metrics MTST and SDTST are clearly 
higher than those by CFP and SFC for every behavioral measure. MTST in particular, has much 
more power in explaining behavioral variability than the other three. This is significant because 
125 
 
it implies the dynamics of FC can be a better predictor of human behavior than conventional 
static FC.  
 
Figure 4.9 Percentage of variances in behavioral measures explained by dynamic and static 
FC metrics. Percentages of variances are shown as error bars with mean and standard deviation 
derived across all paths between the 190 regions in the brain. Three metrics were derived from 
dynamic FC: MTST (mean time before state transition), SDTST (standard deviation of the time 
before state transition) and CFP (clustering frequency percentage. SFC (static FC) is the 
conventional Pearson?s correlation between time series. Along the horizontal axis are labels for 
various behavioral tests (a total of 75 tests, for details of each test, please refer to Appendix A, 
Section A.3). The broad behavioral domains of groups of behavioral tests are indicated above 
and below the figure.  
 
Fig.4.10 shows the paths whose MTSTs significantly predicted several selected behavioral 
measures (for some other selected behavioral measures, please see Appendix A, Section A.6; for 
details of behavioral measures, please go to 
http://humanconnectome.org/documentation/Q3/Q3_Release_ Reference_Manual.pdf.), wherein 
the predictive ability was quantified by regression coefficient ? for each MTST in the GLM 
MTST 
SDTST 
CFP 
SFC 
126 
 
shown in Eq.4.3 of the Materials and Methods section. The coefficient ? was passed through a z-
test and Bonferroni corrected for multiple comparisons (corrected p=0.05/75=0.00067, where 
0.05 is uncorrected p value, and 75 is number of behavioral tests). In each subfigure, cobalt blue 
paths have negative ? values, and red paths have positive ? values. Note that subfigure (C) and 
(F) underwent further processing. Since there were a lot of paths whose MTSTs significantly 
correlated with true positives and false negatives of SCPT (Short Penn Continuous Performance 
Test) task, we obtained a distribution of the number of paths emanating from each region and 
found that only 10% of regions had more than 4 paths emanating from them. Based on this, we 
retained only those paths which connected at least one of the regions with a nodal degree of 5 or 
more. In this way, we were able to identify only the prominent hubs for proper visualization. 
However, the original figures without any processing are shown in Appendix A, Section A.6 and 
all of our conclusions would still be valid with the original result. In Fig.4.10 (A), all paths are 
cobalt blue, implying that higher the episodic memory score, lower the MTST and greater the 
dynamics of FC (please refer to Appendix A, Section A.3 for description of the picture sequence 
memory task corresponding to episodic memory). Many of these paths involve the cerebellum 
which makes sense given previous reports of its role in episodic memory retrieval [181] [182]. 
Other important areas include frontal cortex, occipital cortex, temporal cortex, parahippocampal 
area, precentral and parietal areas. Previous works have shown that these areas are activated in 
an episodic memory retrieval task [182] [183]. As stated by Miyashita [184], the temporal cortex 
is involved in memory encoding and retrieval, and acts as the integrator of memory and 
perception of objects. In Fig.4.10 (B), all paths? MTSTs are significantly negatively correlated 
with self-regulation and impulsivity (please refer to Appendix A, Section A.3 for description of 
the delay discounting task corresponding to self-regulation). The regions seen in this figure, i.e. 
127 
 
prefrontal cortex [185], interior parietal cortex [186], thalamus and caudate [187] [188], have 
been previously implicated in self-regulation. Fig.4.10 (C), (D), (E), and (F) belong to the 
behavior test of the same category: sustained attention, also termed vigilance (please refer to 
Appendix A, Section A.3 for description of the behavioral tests and associated scores 
corresponding to sustained attention). It is conspicuous that Fig.4.10 (C) and (F) are exactly the 
same except for the color (cobalt blue and red); and so are Fig.4.10 (D) and (E). This is due to 
the fact that (C) corresponds to true positives of SCPT as behavioral scores in the GLM and (F) 
corresponds to false negatives of SCPT. Similarly, (D) corresponds to true negative and (E) 
corresponds to false positives of SCPT. Also noteworthy is that paths in (C) and (D) are almost 
all cobalt blue and in (E) and (F) are almost all red. Taken together, these imply that lower 
MTST and hence greater dynamics of FC are associated with better performance on SCPT (i.e. 
true positives and true negatives in Fig.4.10 (C) and (D)). On the other hand, higher MTST and 
hence lower dynamics of FC are associated with poorer performance on SCPT (i.e. false 
positives and false negatives in Fig.4.10 (E) and (F)). The specific paths whose MTSTs predict 
behavioral variability involve brain regions including frontal cortex, precentral cortex, insula, 
occipital cortex, temporal cortex, inferior parietal cortex, and cingulate gyrus, which have been 
previously implicated in sustained attention and vigilance [189] [190] [191]. 
128 
 
 
(A) Episodic memory (picture sequence adjusted) 
129 
 
 
(B) Self-regulation/impulsivity (AUC_40k) 
130 
 
 (C) Sustained attention (SCPT_TP)* 
131 
 
 
(D) Sustained attention (SCPT_TN) 
132 
 
 
(E) Sustained attention (SCPT_FP) 
133 
 
 (F) Sustained attention (SCPT_FN)* 
Figure 4.10 Paths whose MTSTs significantly predict variability in selected behavioral 
measures. The predictive ability is quantified by regression coefficient ? for each MTST in the 
GLM shown in Eq.4.3 of the Materials and Methods section. The coefficient ? is passed through 
a z-test and Bonferroni corrected for multiple comparisons (corrected p=0.05/75=0.00067, where 
0.05 is uncorrected p value, and 75 is number of behavioral tests). In each subfigure, cobalt blue 
paths have negative ? values, and red paths have positive ? values. The behavior tests for 
subfigure are: (A) episodic memory (picture sequence test, adjusted). (B) Self-
regulation/impulsivity (AUC_40k). (C) Sustained attention (SCPT_TP) processed.  (D) 
Sustained attention (SCPT_TN). (E) Sustained attention (SCPT_FP). (F) Sustained attention 
(SCPT_FN) processed. Please refer to Appendix A, Section A.3 for description of behavioral 
tests and corresponding scores (*: subfigure (C) and (F) have been further processed. Original 
subfigures have too many paths that hamper visualization. Therefore, we only show paths that 
connect to nodes with 5 or more paths in subfigure (C) and (F). Please see Appendix A, Section 
A.6 for original subfigures.)  
 
4.4 Discussion 
134 
 
In this work, we have proposed a framework for estimating dynamic FC between functionally 
homogeneous regions across the entire brain using adaptive windowing based on time series 
stationarity. This framework was first validated using simulations and subsequently applied to 
resting state fMRI data obtained from healthy individuals recruited through the HCP. The multi-
dimensional connectivity pattern obtained from each subject was subjected to three levels of 
clustering across space, time and subjects in order to find brain FC network patterns and derive 
metrics for capturing connectivity dynamics. Both dynamic and conventional static FC metrics 
were correlated with behavioral variables in order to test the hypothesis that information derived 
from dynamic variations in FC better predicts behavior as compared to conventional static 
measures and that greater dynamic variability supports superior behavioral performance in 
healthy individuals. This section is organized as follows. We first discuss the third-level 
clustering results which show the most consistent whole-brain connectivity patterns across time 
and subjects. Second, we discuss the implications of paths as well as regions which exhibit 
highest and lowest dynamics. Third, we discuss the behavioral relevance of the dynamics of FC 
and support for the above stated hypothesis based on our results. Finally, we list certain future 
directions that may be worth pursuing. 
First, among the RSNs revealed by third-level clustering results shown in Fig.4.5, DMN and 
visual network occupy more than 50% of the total occurrence times of dominating second level 
clusters, apparently higher than other RSNs. This is easy to apprehend since DMN has been 
shown to be a commonly observed network in the resting human brain by many previous reports 
[118] [151] and visual information processing is expected to be an ongoing phenomenon during 
resting with eyes open.  
135 
 
Second, results shown in Fig.4.6, 4.7, and 4.8 consistently indicate that gyrus rectus has very 
weak static FC and low dynamics of FC with other regions reflected as high MTST, low CFP, 
and low SFC. This indicates that it seldom clusters with other regions, i.e. appears as an 
individual cluster. The function of gyrus rectus is currently yet unclear, but anterior parts of the 
orbito-frontal cortex in general have been implicated in the processing of motivational 
information [192, 193]. Given that there is little motivational information to process during a 
resting state scan inside a scanner with eyes open and fixed on a target, it is understandable that 
there is very little static connectivity as well as its dynamics associated with paths between this 
region and other parts of the brain. The brainstem also has low FC and high MTST with other 
regions. Brainstem does not show up in Fig.4.7 which only displays top and bottom 0.1% of 
MTSTs. But in Fig.A1 and A2 (shown in Appendix A, Section A.4) showing top and bottom 0.5% 
and 1%, respectively, of MTSTs it does appear as the second hub with a lot of red paths 
associated with high MTSTs. The brainstem plays an important role in regulating cardiac, 
respiratory function, maintaining consciousness and regulating sleep. Brain stem?s resting state 
connectivity with the neocortex is tightly coupled with corresponding variations in physiological 
fluctuations [140]. Therefore, removal of physiological fluctuations during pre-processing might 
have decreased the variance of the brain stem?s signal to an extent that it appears disconnected 
with large parts of the brain for most of the time. 
On the other hand, a network consisting of the mid frontal cortex, anterior and mid cingulate, 
insula, supplemental motor area, as well as an intra-cerebellum network stand out as having 
highly dynamic FC (Fig.4.7). Results with a higher threshold of 0.5% indicate that these two 
networks are connected by paths converging to the parietal cortex (Fig. A1 in Appendix A, 
Section A.4). In other words, the fontal-parietal-cerebellar circuit displays high FC dynamics. 
136 
 
When the threshold is further heightened to 1% (Fig. A2 in Appendix A, Section A.4), direct 
fronto-cerebellar paths emerge. These regions are involved in a range of functions which are too 
exhaustive to be listed here. Briefly, the mid frontal cortex is implicated in planning complicated 
cognitive processes [194], while the anterior cingulate plays a role in many cognitive functions 
such as initiation, motivation, and goal-directed behaviors [195]. Insula plays a role in various 
functions including perception, motor control, self-awareness, cognitive functioning, and 
interpersonal experience [196]. Stoodley et al. [197] suggested that different regions of the 
cerebellum containing sensorimotor, cognitive and limbic representations interacted with the 
parietal cortex. Taken together, fronto-parietal, intra-cerebellar and cortico-cerebellar networks 
which support a large range of brain functions appear to display highest dynamics of FC. 
A closer look at regions having high dynamics of FC to all other brain regions in Fig.4.8 (B) 
reveals that nodes of common RSNs such as DMN, DAN and FPCN have similar dynamics. As 
pointed out by Vincent et al. [198], DAN and DMN are two opposing brain networks that are 
implicated in attention to the external world versus internally directed mentation, and the fronto-
parietal control network (which includes regions implicated in cognitive control and are 
structurally located in between DMN and DAN regions) controls the switching between DAN 
and DMN. This controlling mechanism and the competing roles of DAN and DMN may underlie 
their high dynamics of FC. The PCC (posterior cingulate cortex) and precuneus have high 
dynamic FC and high CFP, probably as a result of strong FC paths with high dynamics linking it 
to frontal and cerebellar regions as discussed above.  
Third, emerging evidence suggests that important individual differences can be associated 
with patterns of resting state brain connectivity, and the variability of static FC patterns across 
individuals can be reflected in corresponding variability of important cognitive and behavioral 
137 
 
variables that affect real world function [163] [165] [166] [161] [162]. Recent reports indicate 
that dynamic FC is also predictive of behavioral performance in healthy individuals [165] [166].  
However, it is yet unclear whether dynamic FC can provide additional predictive value over and 
above that provided by static FC. In order to answer this question, we obtained the predictive 
power of both dynamic and static FC on behavioral performance using a single general linear 
model. Our results clearly demonstrate that dynamic FC metrics, especially MTST, have much 
more power in explaining variance in behavioral performance tasks than static FC metric for 
each of the 75 behavioral tests considered, which include tests of alertness, cognition, emotion 
and personality. Further, results from Fig.4.10 demonstrate that higher dynamics of FC is 
predictive of superior behavioral performance. For example, higher episodic memory score, 
better sustained attention, higher self-regulation and lower impulsivity are all predicted by lower 
MTST and hence greater dynamics of FC.  This supports our hypothesis that information derived 
from dynamic variations in FC better predicts behavior as compared to conventional static 
measures and that greater dynamic variability supports superior behavioral performance in 
healthy individuals.  
The results presented here have profound implications for our understanding of what 
constitutes a healthy and desirable brain. Conventional wisdom dictates that deviations of static 
FC from what one would typically observe in a matched control population represent altered 
neural circuitry underlying various disorders. For example, hyper-connectivity has been observed 
in psychiatric disorders such as psychosis [199], schizophrenia [200] and post-traumatic stress 
disorder [201] [202] and hypo-connectivity has been observed in disorders such as autism [203]. 
In addition to the static FC value, the amount of variability of FC values over time may provide 
additional dimensions on which brain alterations may be assessed. For example, the inability to 
138 
 
disengage from a state of altered connectivity may explain why one observes altered static 
connectivity in the first place. The fact that higher dynamics predicts better behavioral 
performance in healthy individuals indicates that the ease with which brain regions engage or 
disengage with other regions may be potential biomarkers for disorders involving altered neural 
circuitry. 
We suggest that future work should be oriented in three directions. First, for dynamic FC 
calculation, we did not differentiate between ?correlated? and ?anti-correlated? interregional 
relationships in this work, and we plan to add this additional layer of complexity in future study. 
This is important because in addition to characterizing functional associations between regions, 
the nature of such associations can be characterized by including the sign. Second, fluctuations 
of brain states represented by RSNs measured by fMRI should coordinate with EEG microstates 
[204]. Thus, it is necessary to conduct a similar analysis using simultaneously acquired EEG data. 
Third, FC does not provide information on the directionality of connections. Previous reports 
have shown that directional connections provide a complimentary mode of communication 
between brain regions in resting state and that regions which seem to be dissociated at zero-lag 
might as well have time-lagged relationships [114]. Therefore, a similar analysis must be carried 
out using EC. Further, the predictive ability of dynamic EC on human behavior must be deduced 
and compared with that of dynamic FC and static EC.   
  
139 
 
 
Chapter 5  Dynamic Multivariate Analysis: 
 Finite Number of Directional Brain Network Configurations Revealed from Time-Varying 
Connectivity Assessment of Resting State FMRI 
 
The work in this chapter is a continuation of that in Chapter 4. Chapter 4 deals with FC statics 
and dynamics with clustering strategy and correlation with behavioral measures, while in this 
chapter, we investigate the EC dynamics of the issue with similar clustering strategy, and we 
survey its relationship to cognitive behaviors in a somewhat different way. Our main 
contribution is that we proposed a dynamic EC model, applied AEC algorithm for dynamic EC 
pattern clustering, showed dynamics of EC network pattern had fractal-like quasi-stable 
character, and related them to real world functionalities. 
5.1 Introduction 
Previous Chapter 4 focuses on the exploration of functional connectivity (FC) and its 
correlates with behavioral measures. In this chapter, we focus on the study of effective 
connectivity (EC) and its relationship with real world functionalities. EC is a term used to 
describe measures of directional relationships between brain activity in different brain regions 
[110] [111] [114] [116]. Not only did most previous studies investigating FC assume the 
connectivity is stationary in time, but also most studies on EC assumed so. These static studies 
on connectivities have been linked to behavior and brain disorders for FC [125] [126] and EC 
[205] [206]. Further, some studies have reported that static EC relationships at rest represent a 
mode of communication between brain regions whose activities are not synchronized [114], and 
hence, both FC and EC taken together, provide complementary characterizations of brain 
connectivity at rest. As discussed in Chapter 4, evidences have pointed out that resting state FC 
140 
 
is not stationary in time and an array of methods have been proposed to capture dynamic 
variations in FC. This raises the possibility that dynamic alterations in resting state EC cannot be 
ignored and needs to be investigated. This raises the possibility that dynamic alterations in 
resting state EC cannot be ignored and needs to be investigated. However, to the best of our 
knowledge, there has been no literature on dynamic EC of resting state fMRI, and most focus is 
drawn on task-based fMRI dynamic EC [207] [129]. 
As discussed in Chapter 4, to characterize the whole picture of resting state brain networks, it 
is necessary to employ the whole brain regions to conduct connectivity analysis. In this regard, 
FC runs ahead of EC. There exists a bulk of works exploring whole-brain static FC [157] [158], 
and several others exploring whole-brain dynamic FC [130] [159] using PCA or ICA based 
method. However, literatures on whole-brain EC are far less. This may due to the reason that the 
computational complexity is prohibitively high and very time-consuming if whole-brain regions 
are employed. And methods such as dynamic causal modeling [208] and structural equation 
modeling [209] impose restrictions on the number of regions that can be included in the model. 
In addition, it becomes difficult to formulate a priori hypotheses regarding connections between 
all brain regions which are required by these methods. Therefore, data driven approaches have 
become more popular while investigating EC between large numbers of brain regions. One such 
model is the multivariate autoregressive (MVAR) model which is used to capture time-lagged 
Granger causal influences between brain regions [210, 211] [114]. It has been previously 
demonstrated that the precision of the MVAR model increases when more variables containing 
information regarding the underlying system are included in the model [212]. Yet, to estimate the 
parameters of an MVAR model fit using all voxel time series in the brain would have a very high 
time cost which makes it practically impossible. Besides, an MVAR model with too many voxel 
141 
 
time series as regressors is ill-conditioned and highly sensitive to noise. To address this issue, 
dimensionality reduction strategy is devised and an exemplary work employing whole-brain 
regions/voxels for static EC can be found in [213]. But, to the best of our knowledge, no work 
has been done on whole-brain dynamic EC analysis. In this work, we adopted dynamic Granger 
causality to represent dynamic EC, and the same dimensionality reduction strategy as in Chapter 
4 which spectrally clusters voxel time series into functionally homogeneous brain regions. The 
CC200 atlas was designed for this purpose, partitioning the whole brain (gray matter) into 
functionally homogeneous regions [160]. The 190-region version within CC200 atlas was 
adopted in this work and this version took into account the balance between functional 
homogeneity and anatomic homology using a large resting state dataset [160]. But, our data did 
not have coverage of the cerebellum, thus we considered the leftover 164 cerebral regions from 
the 190-region version of CC200 atlas and fed mean time series from these regions into the 
dynamic MVAR model. This can be thought of as a pilot study to employ all cerebrum brain 
regions to assess dynamic EC. 
As suggested in Chapter 4, evidences from dynamic FC analysis with fMRI and EEG data 
show the synchronized BOLD signal fluctuations over the brain organize into a finite number of 
ordered and patterned configurations alternating with each other in time [127] [146] [138] [149]. 
In this work, we hypothesized that dynamics of EC can also organize into a finite number of 
ordered and patterned configurations alternating with each other in time. To examine this 
hypothesis, we employed a similar clustering strategy to that in Chapter 4. Specifically, we 
performed simulations in order to demonstrate the efficacy of the dynamic EC model and then 
applied it to resting state fMRI data, and the resulting dynamic EC metric was transformed to 
distance measure for clustering. The adaptive evolutionary clustering (AEC) algorithm was 
142 
 
adopted at this stage to find time-varying configurations of EC networks, a second level and a 
third level clustering were conducted to find dominant patterns across all runs and subjects. As 
shown in the case of static connectivity [114], absence of significant zero-lag connectivity does 
not imply the absence of brain connectivity. Rather, such regions could be connected via time-
lagged relationships. This work is supposed to complement our FC work as introduced in 
Chapter 4, since both synchronization and causality are established mechanisms of brain 
connectivity and one needs to assess both measures in order to gain a complete understanding 
[110]. 
As discussed in Chapter 4, the amount of information obtained from assessment of dynamic 
connectivities over the whole brain is enormous, hindering the interpretation of underlying 
neuroscientific meaning [127]. To evade this issue, a lot of works such as those based on 
agglomerative clustering [138] [149] and principal component analysis [130] assume that the 
connectivity networks may have different weights in spatial or temporal domain, but the 
connectivity networks themselves do not change. This assumption suffers from loss of generality. 
The AEC approach proposed in Chapter 4 can evade the drawbacks brought by this assumption 
and we will continue to base our analysis on this approach for dynamic EC. A schematic 
illustrating both directional connections between nodes and the networks themselves change with 
time is in Fig.5.1.  
143 
 
 
Figure 5.1 Schematic of two types of dynamic EC network configurations. (A) Schematic 
illustrating network configuration over time wherein all nodes are part of the same network, only 
the directional connections between them change with time. (B) Schematic illustrating network 
configuration over time wherein both directional connections between nodes and the networks 
themselves are changing with time. 
 
5.2 Material and Methods 
5.2.1 Data Acquisition and Pre-processing 
Resting state fMRI data were acquired from a 3T Siemens Verio scanner in Auburn University 
MRI Research Centre from 21 healthy adults (aged 29.68? 11.06 years, 6 females). Informed 
consent was obtained from all subjects after explaining and reviewing detailed written 
information about the study protocol, which was approved by the IRB of Auburn University. In 
 
 
 
 
 
 
 
 
 
 
       
 
 
 
 
 
 
 
Time 
(A) 
(B) 
A 
B C 
D E 
F 
A 
B C 
D E 
F 
A 
B C 
D E 
F 
A 
B C 
D E 
F 
144 
 
all experiments, subjects were lying at rest during the scan with eyes open, and they were 
instructed to relax without falling asleep or thinking about anything in particular. After the scan, 
all subjects confirmed adherence to these guidelines. T2*-weighted echo planar imaging with the 
following parameters were used for fMRI data acquisition: 1000 volumes (TRs (repetition time)) 
per run, in-plane matrix of 64? 64, 16 axial slices covering the entire cerebral cortex, field of 
view (FOV) =225? 225 mm2, flip angle (FA) =90?, TR/TE (echo time) =1000ms/29ms, in plane 
voxel size =3.5156? 3.5156 mm2, slice thickness 5mm with 1.25 mm gap. Preprocessing was 
performed using Data Processing Assistant for Resting-State fMRI software (DPARSF) [168] 
and included slice timing, rigid body registration to first functional image, normalization to MNI 
template with resampling to 2? 2? 2 mm3 resolution, spatial smoothing with 4? 4? 4 mm3 
FWHM (full width at half magnitude) Gaussian kernel, 0.01~0.1 Hz band pass filtering, 
detrending of mean and linear trend, and regressing out of white matter (WM) and cerebrospinal 
fluid (CSF) signals as well as six motion parameters. Then, the 190-region version of the CC200 
brain atlas [160] was used as the reference brain segmentation template. We extracted the mean 
time series from 164 cerebral regions for subsequent use (26 regions of the CC200 template 
belonging to the cerebellum were not considered because our field of view covered only the 
cerebrum; this was done in order to reduce the TR which would be beneficial for EC analysis). 
5.2.2 Dynamic Effective Connectivity Model 
  Various techniques have been invented for eliciting static measure of effective connectivity, 
prevailing among which are dynamic causal modeling (DCM) [208], structural equation 
modeling (SEM) [214] and Granger causality [215, 216]. But, when it changes to dynamic 
situation, many methods fail to adapt themselves for dynamic version such as DCM and SEM. 
First this is because of the high computational demanding [217], and secondly, methods like 
145 
 
DCM and SEM are model based methods which require much a priori information, but this high 
volume of a priori information is impracticable to be estimated in a time-varying manner timely. 
By contrast, Granger causality is totally data driven, and does not impose such high 
computational complexity as for DCM and SEM, therefore it can be dynamically computed. On 
the other hand, we have segmentations of 164 regions over the whole brain, and it is 
impracticable to make a priori assumptions about underlying causal connections once for all 
regions. Thus, we adopted dynamic version of Granger causality to calculate whole brain EC 
dynamics. 
  To facilitate the derivation of formulae for dynamic Granger causality, we first illustrate the 
traditional static formulation of Granger causality. The Granger causality can be modeled on 
multivariate vector autoregressive (MVAR) process as shown below. 
          
1( ) ( ) ( ) ( )
p
nt n t n t?? ? ? ? ??X V A X ?
                                        (5.1) 
Where X(t) =[x1(t) x2(t) ? xk(t)], a vector autoregressive process including k individual 
univariate processes (in our scenario, k is 164), V is the intercept vector representing nonzero 
mean component, n denotes time lag and A(n) is corresponding model coefficient matrix, p is 
regressive order, and E(t) is the vector noise process. During preprocessing, the data was 
detrended such that V vanished. Then, the Granger causality (static version) representing direct 
causal influences from region i to region j is formulated as below. 
         2
1 [ ( )]
p
ij ijnD a n???
                                                     (5.2) 
Where each aij, i, j=1: k, is one entry of matrix A which is determined in the least square sense. 
The order p of this MVAR model is determined by Bayesian Information Criterion (BIC) [170]. 
For estimation of EC in a time-varying manner, we adopted dynamic Granger causality (DGC). 
146 
 
In this, the coefficient matrix A is allowed to vary over time. Such a temporally adaptive MVAR 
model with X(t) as input time series is shown below.  
   
1( ) ( ) ( , ) ( ) ( )
p
nt t n t t n t?? ? ? ? ??X V A X ?
                                 (5.3) 
It is noteworthy that coefficient matrix A(n,t) is now a function of both lag n and time t, and can 
be updated with  Kalman filter [218]. The DGC metric is then given by 
                                            2
1( ) [ ( , ) ]
p
ij ijnD G C t a n t?? ?
                                               (5.4) 
The model order is determined by BIC. A forgetting factor (FF) is introduced in order to take 
recent past Kalman filter estimate into account of current estimation to enhance stability. The 
determination of forgetting factor is accomplished by minimizing the variance of estimated error 
energy [207] [219]. 
             2?a r g { m in ( v a r ( ( ) ) }F F t?  E                                       (5.5) 
Where ?()tE  is the estimate of E(t) and ?var? is the variance operation over time. 
In order to estimate a reasonable initial condition for the Kalman filter we used the following 
procedure. The Kalman filter coefficients were randomly initialized and updated coefficients 
were obtained from the first run of the first subject which were in turn used as initial conditions 
for the following run/subject. Using this procedure iteratively, Kalman coefficients which were 
updated using the entire subject group were obtained. This represented Kalman coefficients of 
the entire group as a whole. This group value was used as the initial condition for all 
runs/subjects and DGC values were re-estimated at the individual subject level. This procedure 
ensured that for each subject, the Kalman filter coefficients were initialized to the same value 
which was representative of the group average, to help achieving a quick convergence. However, 
the DGCs obtained from the first 50 time points were discarded before being input into the 
147 
 
clustering algorithm for the following reasons. First, initial time points in fMRI time series are 
routinely discarded to allow the MR signal to achieve T1 equilibration. Second, even with group-
averaged Kalman coefficients as the starting condition, the Kalman filter needed time to 
converge to ground truth connectivity. 
5.2.3 Clustering 
  The DGC matrix calculated via above procedures was of size A?A?B?C where A=164, 
counting of cerebral regions, B=950, the number of TRs in dynamic Granger causality 
calculation (each run had a total of 1000 TRs, first 50 TRs discarded), and C=21, the number of 
runs over all subjects. So, for each run, at each time instant, the EC between all pairs of regions 
had a dimension of A?A. This DGC matrix was then fed into AEC algorithm [150]. This 
algorithm dynamically adaptively clustered all 164 regions according to their distances (the 
distances were transformed from the EC metric, see next section: First level clustering) at every 
time instant. Likewise, a forgetting factor was introduced to control the impact of recent past of 
clustering result on current calculation, with the purpose of enhancing stability of clustering 
operation. This clustering is termed first level clustering in the following. The first level 
clustering result was time-varying brain network configurations which were then fed to second 
level clustering as members. Through second level clustering, similar configurations at the first 
level were clustered forming a ?pattern?. So through second level clustering, several patterns 
were resulted reflecting the distribution and consistency of the integrity of first level 
configurations for a given run. Last but not the least, the dominating second level patterns from 
all runs were identified and used as members for the third level clustering. Resultantly, by the 
third level clustering the dominant and consistent brain EC network patterns across all runs and 
subjects were identified.  
148 
 
First level clustering 
  The first level clustering was implemented using the AEC algorithm employing a distance 
measure computed from the DGC matrix. A reasonable assumption is that the higher the absolute 
value of DGC, the closer the two regions are in feature space. Note that we did not differentiate 
between positive and negative DGC influences since the neuronal underpinnings of their sign are 
yet unclear. Also noteworthy is that the DGC values between regions cannot be utilized directly 
as distances between regions for clustering. We know that the distance is inversely proportional 
to the closeness between regions, but the DGC metric (magnitude) is proportional to the 
closeness. Next, distance measure is greater or equal to zero, being zero only when it is measured 
from one region to itself. However, DGC metrics have both positive and negative values, and the 
diagonal entries of DGC matrix measuring auto-DGC are not zeros. Moreover, DGC matrices 
are not symmetric, i.e. the distance from one region to another is not equal to the other way 
around, violating the condition of reciprocity required of any distance measure. 
  In order to convert DGC values into distance measure, we devised a transformation algorithm 
as described below. We represent the DGC from region i to region j by DGCij, and the other way 
around is DGCji. DGC is transformed as shown below to meet the nonnegative and reciprocity 
requirements.  
C= (|DGCij |m+| DGCji |m)1/n                                                    (5.6) 
Where m and n determine the characteristics of this transformation. According to Eq.5.6, C will 
increase along with the increase of either DGCij or DGCji. We chose m=2 and n=1 in this work, 
as such is usually employed for second order matrix norm. If n is relatively big compared to m, 
then C would not be sensitive to the change of DGC, thus cannot distinguish significant 
connectivity from trivial one. If m is relatively big compared to n, the result will be sensitive to 
149 
 
noise. Next, we used a reversed ?S? shaped function applied to C to meet the requirement of a 
monotonically decreasing transformation: 
              1
CD a b f? ??
                                                               (5.7) 
Where a, b, f are control parameters determining the behavior of this function. After this 
transformation, the significant connectivity between two regions is highlighted while non-
significant ones are not. In order to find the boundary between significant and insignificant 
connectivities, we employed the method of surrogate data [210] [220]. Specifically, we 
transformed the time series to their frequency domain representation, randomized the phase of 
time series from all 164 regions in the frequency domain with magnitude unchanged, reconverted 
the phase-randomized data into time domain signals, and then the DGC was recalculated. Since 
the temporal structure of time series relative to each other was destructed, the DGCs obtained 
belonged to a null distribution of no influence between regions. After this procedure was 
repeated in a Monte Carlo manner (1000 times) a statistical null distribution of insignificant 
DGCs was obtained. Then we applied Eq.5.6 to get the null distribution of C and found the 
threshold at 95th percentile, denoted by th0. It is obvious that parameter a just controls the scaling 
of D, thus is trivial, and hence we set it to 1 for normalization. In this way, D can attain its 
maximum at 1/(1+b) and minimum at around 0. Assume b is sufficiently small such that the 
maximal value that D can reach is nearly 1. Then it is reasonable to let D be 0.5 when C is equal 
to th0, and when C approaches 0, D is approximate 1 adequately with low steepness. With 
surrogate data, we found th0 to be equal to 0.01. To find b, we restricted D to be no less than 0.8 
and steepness to be less than 0.02 when C is 0. So, when D=0.8, steepness is 0.02 when C is 0, 
we calculated b to be 0.2, and f as 5100 which were used subsequently. Above sigmoid curve 
design aims to balance the separation of null and significant connectivities, and sensitivity to 
150 
 
noise. The sigmoid curve design and parameters determination have been widely applied in 
many fields [221] [222]. After the transformation of Eq.5.7, we let the Ds which were from one 
region to itself be zero, resulting in the final distance measure Dfinal. Then matrix Dfinal at each 
time point was fed into the AEC algorithm [150]. In AEC, the clustering method was chosen to 
be hierarchical [171].  
The number of clusters can be chosen either based on prior information about the 
neurophysiological system being investigated (which is preferable when that information is 
available) or based on mathematical criteria such as the silhouette index [172] (which is 
preferable when no a priori heuristics are available). Many previous studies have reported on the 
appropriate number of clusters, or in other words, the number of resting state networks (RSNs). 
To derive an eloquent result, various methods have been tried. The most representative ones are 
ICA based methods. In particular, PICA (probabilistic ICA) [174] and tensor PICA [175] are 
variants of ICA which attract a lot of attention recently. Operating at a grand scale, fully 
exploratory network ICA (FENICA) [177] [178] [179] [223] is best to find consistent networks 
among a group which may include thousands of subjects. Besides, fuzzy clustering [173] and 
graph theory [176] are also two prevailing methods to find the number of RSNs with their own 
merits. Except a few studies which employ task-related data [223], most studies focus on resting 
state fMRI data. However, these findings are in terms of FC, and corresponding EC results are 
very sparse. A data-driven pilot study conducted by Wu et al [213], reported 6 communities from 
resting state EC networks. Therefore, we used 6 as the number of clusters at first level clustering. 
Also, we assume that EC networks are hierarchically organized, similar to FC networks [179] 
[173]. Accordingly, if the specified number of networks or clusters increases, some networks 
will split into sub-networks, such as into left and right lateral parts, rather than reshape into a 
151 
 
new set of networks which has no relation with the previous one. Based on this assumption, if 
the number of networks/clusters is heuristically specified to be 6, it will not lead to loss of 
generality. 
Second level clustering 
We performed second level clustering for characterizing the consistently recurring first-level 
configurations over time. This aided us to answer the question about whether there exists finite 
number of directional brain network patterns which consistently recur in time at an individual 
subject level. The difference from first level clustering is that this is a static clustering along the 
time axis. Hierarchical method was employed as the clustering method, and the number of 
clusters was determined by silhouette criterion in the absence of prior heuristics.  
The calculation for the distance measure, between first level clustering configurations at two 
different time instants is the same as in Chapter 4. Please refer to Section 4.2.4 in Chapter 4 for 
details.  
The result from second level clustering is a number of clusters with first level clustering 
configurations as their members. Each second level cluster can be represented by its centroid but 
the theoretical centroid would be a weighted sum of first level clustering configurations such that 
each region in this sum has fuzzy belongingness to each first level cluster. To address this issue, 
Chapter 4 uses second level centroid agent to represent the theoretical centroid (Eq.4.2 in 
Chapter 4). In this work, the same strategy was adopted.  
Third level clustering 
  The second level clustering gave clustered patterns over time for each run. The dominating 
second level patterns/clusters were predicated based on the histogram of second level clusters? 
occurrence times. Here the occurrence times is formulated as follows. For each run, each second 
152 
 
level cluster covered a number of first level clustering configurations, the number of which was 
the times this second level cluster ?occurred?, so was defined as occurrence times for this second 
level cluster. The histogram mentioned above was calculated over second level clusters from all 
runs. The threshold separating dominating and non-dominating clusters was determined as 
follows. The point where the histogram value first hit zero and the first order derivative was also 
zero was set as the threshold. Then this threshold was found to be at 95 (occurrence times). 
There was clearly a gap encompassing 95, and the majority of second level clusters had 
occurrence times less than 95, while beyond 95, second level clusters were relatively scarce and 
mainly distributed over the range: 100-200, 270-360, and 450-850, clearly indicating they were 
dominant clusters. In order to assess the consistency of these dominating patterns across subjects, 
we performed the third level clustering.  
The strategy used to calculate the distance measure between dominating second level centroid 
agents was the same as for FC in Chapter 4. Also, the weighted K-means was employed for 
clustering at the third level. Same as second level, the number of clusters were optimized using 
silhouette criterion, and each third level cluster theoretical centroid was represented by its agent 
since the regions in theoretical centroid had fuzzy memberships to dominating second level 
clusters. The agent had smallest Euclidean distance to the theoretical centroid in terms of 
distance matrix. Above three-level clustering procedure for dynamic EC is illustrated in Fig.5.2. 
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Figure 5.2 Schematic of the three-level clustering procedure for EC. The top left part shows 
the transformation of dynamic EC measure (DGC) to a distance measure. The top right part 
shows first level clustering, below which, second and third level clustering are illustrated. 
 
5.2.4 Potential Correlates with Real World Functionalities 
  Through the third level clustering, the brain EC network patterns which were dominant and 
consistent across all subjects were obtained. To interpret the connotation of these patterns, we 
related them to real world cognitive functionalities using Brainmap Sleuth search engine [224]. 
Specifically, for a given third level centroid agent, the 164 regions inside the cerebrum were 
divided into 6 clusters as mentioned before. It should be noted that one of the 6 clusters 
(networks) was trivial because it included all other brain regions which were not present in the 5 
other clusters. This is because clustering algorithm partitions all members exhaustively. If the 5 
networks are definitive networks, the 6th one will include every other member not inside the 5 
154 
 
networks. The trivial cluster can be separated from 5 other networks by visual inspection since it 
embodies the most regions. As such, for each of the 5 definitive networks, we used the set of 
regions it included as input to Brainmap Sleuth search engine to find literatures that found 
involvement of these regions in certain kinds of cognitive functionalities. In this way, the 
correlates between these networks and real world cognitive functionalities were established.  
5.2.5 Simulation Setup 
Simulations were performed in order to validate the proposed method for calculating DGC and 
the efficacy of subsequent clustering using the AEC algorithm. We simulated time series with a 
total length of 1000 time points from 12 regions using an autoregressive model as given below: 
             
1( ) ( )
p
iit A t i?? ? ? ??VV ?
                                                  (5.8) 
Where V(t) denotes the vector of signals from multiple regions, Ai is the regression coefficient 
matrix, and ? represents noise term with covariance matrix C, which has autocorrelation 
coefficients set to 1 for normalization. The order p was chosen to be 1. Three scenarios were 
used:  
(i) C was identity matrix and did not change over time so as to remove the effect of 
instantaneous correlation, i.e. FC part. 12 time series were divided into 4 clusters each 
having 3 members (region1, 2, 3 were in one cluster, region4, 5, 6 were in one cluster, 
region 7, 8, 9 were in one cluster, and region 10, 11, 12 were in one cluster).  Thus, A1 had 
block structure with 3?3 blocks on the diagonal, but constant over time. Each non-zero 
element in A1 was selected such that A1 had all eigenvalues within unit circle and all 
diagonal terms being negative, so that the simulated time series were stable and power 
spectral energy was concentrated in the low frequency band, in accordance with the fact that 
the signal of interest in fMRI lies in the low frequency band.  
155 
 
(ii) Same as first scenario, but each non-zero element in A1 was slowly varying over time 
sinusoidally with period equal to 200? and randomized phases. The scope of this variation 
was limited to guarantee the stability of each time series. The belongingness of each region 
was the same as (i).  
(iii) Same as first scenario but after every 200 time points, A1 was circularly shifted by one 
column and one row to change the cluster belongingness of each region. Specifically, from 
time point 1 to 200, regions 1, 2, 3 belonged to the same cluster (i.e. they were connected to 
each other), regions 4, 5, 6 belonged to the same cluster, and so on. Then from time point 
201 to 400, regions 2, 3, 4 belonged to the same cluster, regions 5, 6, 7 belonged to the same 
cluster?  and regions 11, 12, 1 belonged to the same cluster. Then from time point 401-600, 
region 3, 4, 5 belonged to the same cluster, and so on.  
It should be noted that in the simulation, the DGCs calculated for all time points were used in 
AEC algorithm, as illustrated in Fig.5.3. However for real fMRI data, initial 50 time points were 
discarded for calculation of DGCs and the Kalman filter initial condition was calculated by 
running over all runs, rather than released condition as in the simulation. Both of these concerns 
were for a better tracking performance of DGC. 
For each scenario listed above, the simulation was conducted 1000 times to get a group of 
simulated MVAR processes, and then the statistics of the DGCs were obtained. 
5.3 Results 
5.3.1 Simulation Result 
The simulation results are shown in Fig.5.3. In each subfigure of Fig.5.3, the simulated ground 
truth of DGCs are shown on the left and the estimated DGCs using the dynamic MVAR model 
employed in this work are shown on the right. The estimated DGCs converge to the ground truth 
156 
 
quickly, and suitably respond to dynamic variations in ground truth DGC as shown in subfigure 
(B) and (C). Also, the regions belonging to different clusters have nearly zero causality, such as 
region1?region12 in subfigure (A) and region4?region8 in subfigure (B), indicating no false 
positives. The standard deviations of estimated DGCs over all instantiations of the MVAR 
process are modest, indicating good fidelity. Subfigure (D) presents a representative realization 
of first level clustering using AEC algorithm for simulated DGCs in scenario (iii). Along the 
time axis, regions rendered the same color belong to the same cluster. It can be seen that in 
subfigure (D), the AEC first level clustering clearly separates the 12 regions into clusters with 
correct memberships in a time-varying manner (maybe with very short transitions). In summary, 
the simulations demonstrate that the proposed DGC model qualifies for tracking true dynamic 
ECs, and the true time-varying clustering patterns can be reliably reproduced by the AEC 
algorithm. 
 
(A)                                                       
0 200 400 600 800 1000
- 0 .5
- 0 .4
- 0 .3
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- 0 .1
0
0 .1
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GC
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T im e
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GC
157 
 
 
 (B) 
  
(C) 
      (D) 
Figure 5.3 Exemplary simulation result for dynamic Granger causality and first level AEC 
clustering. MVAR processes of 12 regions were simulated, with a length of 1000 time points. 
Three scenarios were used to corroborate the validity of formulated DGC. Exemplary ground 
truth causality of scenario (i) is shown in subfigure (A) left, and corresponding mean ? standard 
deviation (std) of calculated DGCs is shown at right. Color bands extend from mean-std to 
mean+std with mean values at the center. Below is same. Exemplary ground truth causality of 
scenario (ii) is shown in subfigure (B) left, and corresponding mean ? standard deviation (std) of 
0 200 400 600 800 1000
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- 0 .4
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T i m e
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calculated DGCs is shown at right. Exemplary ground truth causality of scenario (iii) is shown in 
subfigure (C) left, and corresponding mean ? standard deviation (std) of calculated DGCs is 
shown at right.  Exemplary ground truth clustering pattern corresponding to scenario (iii) is 
shown in subfigure (D) left and corresponding clustering result estimated using AEC algorithm 
is shown at right. Regions rendered the same color belong to the same cluster. 
 
5.3.2 Experimental Data Result 
We estimated the DGC metric for each run of pre-processed resting state fMRI data and fed it 
into the three-level clustering algorithm. The results are shown in Figs.5.4, 5.5, 5.6 and relevant 
statistics are summarized in Tables 5.1 and 5.2. Fig.5.4 presents exemplary second level 
clustering patterns along the time axis. Different colors represent different clusters. The numbers 
of second level clusters from the top bar to the bottom bar in Fig.5.4 are 10, 6, 6, 10, 11 and 11. 
These numbers are representative numbers of second level clusters, as reflected in Table 5.1. 
Please note the same colors in different runs do not mean they are of the same pattern. Table 5.1 
presents corresponding second level clustering statistics for all fMRI runs. By visual inspection, 
it is clear that there exist 1-3 dominant clusters at the second level. Critically, we can observe 
features similar to quasi-stability in Fig.5.4, i.e. each dominant pattern lasts for a period of time, 
during which it may swiftly switch to a few non-dominant patterns and switch back, and then 
switches to another dominant pattern. Certainly, dominant patterns last longer than non-dominant 
patterns, as expected.  
Table 1 also conveys information about the number of second level clusters for each subject 
and the time spent before state (pattern) transition. Normally, the larger the number of clusters, 
the smaller the mean time (and its standard deviation) spent before a state transition. Their 
relationship is illustrated in Fig.5.5 using linear regression. The regression of mean time spent 
before state transition with respect to number of clusters is shown in Fig.5.5 (A), and 
159 
 
corresponding results for standard deviation of time spent before state transition is shown in 
Fig.5.5 (B).  
 
Figure 5.4 Exemplary second level clustering patterns over time axis from six runs. Along 
each bar, each color represents one second level cluster and the time instants it occupies indicate 
the first-level configurations at these time instants belong to it. Different colors represent 
different second-level clusters. The number of second level clusters for each bar is 10, 6, 6, 10, 
11 and 11 (from top to bottom). Please note the same colors in different runs do not mean they 
are of the same pattern.  
 
Table 5.1 Summary of statistical characteristics of second level clusters 
Subject No. of clusters 
Time spent (s) 
before any state 
transition 
(mean?standard 
deviation) 
Time spent (s) in each cluster 
(descending) 
#1 11 9.79?18.65 350, 329, 116, 33, 31, 28, 22, 17, 13, 10, 1 
#2 7 35.19?67.08 777, 69, 60, 26, 13, 4, 1 
#3 16 16.18?21.62 456, 172, 79, 69, 62, 27, 22, 19, 11, 10,  6, 4, 4, 3, 3, 3 
#4 4 30.65?105.84 732, 179, 24, 15 
#5 12 11.59?18.61 348, 307, 112, 70, 68, 16, 8, 8, 5, 4, 2, 2 
#6 7 15.57?36.98 775, 135, 24, 9, 3, 2, 2 
#7 6 13.97?34.38 636, 143, 105, 57, 5, 4 
 
160 
 
#8 15 13.19?30.04 662, 78, 59, 56, 23, 19, 18, 11, 9, 7, 4, 1, 1, 1, 1 
#9 14 10.92?14.45 294, 149, 132, 85, 81, 65, 53, 49, 14, 12, 9, 5, 1, 1 
#10 10 12.18?20.94 369, 226, 220, 68, 26, 25, 8, 6, 1, 1 
#11 7 24.36?43.06 591, 196, 112, 26, 20, 4, 1 
#12 6 13.57?24.68 506, 277, 77, 51, 38, 1 
#13 15 7.98?11.36 574, 147, 47, 39, 36, 34, 15, 15, 15, 12, 5, 5, 3, 2, 1 
#14 11 12.18?48.36 534, 140, 123, 53, 38, 36, 12, 7, 4, 2, 1 
#15 16 10.78?19.03 346, 296, 147, 65, 42, 11, 11, 5, 5, 5, 4, 3, 3, 3, 2, 2 
#16 10 13.19?25.68 839, 29, 23, 21, 16, 9, 8, 3, 1, 1 
#17 5 45.24?101.86 851, 74, 15, 9, 1 
#18 14 10.88?12.97 476, 116, 108, 96, 52, 34, 26, 11, 7, 6, 5, 5, 4, 4 
#19 12 11.88?22.20 659, 169, 25, 22, 15, 13, 13, 12, 8, 7, 6, 1 
#20 9 27.14?70.18 813, 84, 20, 17, 7, 4, 2, 2, 1 
#21 10 25.00?44.62 582, 326, 13, 11, 6, 4, 3, 2, 2, 1 
Summary 
(Mean?standard 
deviation) 
10.52?4.05 13.47?35.95 90.27?177.96 
 
 
(A)                                                  (B) 
Figure 5.5 Illustration of regression of mean/std of time spent before state transition with 
regard to number of second level clusters. (A) is for mean time spent before state transition 
P=1.80?10-3 P=3.70?10-4 
161 
 
and (B) is for standard deviation of time spent before state transition. Regression line is shown in 
red, and scattered dots represent data points from 21 resting state runs. 
 
The result for third level clustering is illustrated in Fig.5.6 and Table 5.2, and potential neural 
correlates of those connectivity patterns to real world functionalities is depicted in Fig.5.7. At the 
third level, 7 clusters were found from all dominating second level clusters obtained from all 
subjects, but only the 4th cluster was dominant and consistent across all subjects (see Table 5.2). 
Fig.5.6 visualizes the 5 first level clusters which make up the centroid of the 4th third level 
cluster. It is noted that at the first level, the number of clusters was set to 6, and one of those 
clusters (networks) was trivial because it included all other brain regions which were not present 
in the 5 other clusters. This happened because clustering partitioned the input space, and if there 
were 5 definitive clusters, the 6th cluster would include everything that was excluded from the 5 
clusters. In Fig.5.6, green dots represent the centers of the functionally homogeneous CC200 
regions under consideration, and arrowed paths represent directional connectivities between 
regions with thickness and color indicating the absolute connectivity value. Network #1 in 
Fig.5.6 (A) illustrates directional causal influences among right mid temporal area, left calcarine, 
left postcentral and left inferior temporal area, as well as pons and left superior orbital frontal 
area. According to activation likelihood estimation (ALE) based meta-analyses using the 
BrainMap database these regions are co-activated by emotional stimuli [225], language 
processing [226], working memory [227], spatial information processing [228]. Network #2 in 
Fig.5.6 (B) involves supplementary motor area (SMA), postcentral area, supramarginal area, mid 
temporal area, and thalamus in the right hemisphere, and insula, mid and inferior temporal area, 
precentral area in the left hemisphere. These regions are mostly distributed in parietal lobe, 
temporal lobe, as well as limbic lobe. According to ALE based meta-analyses using BrainMap, 
the co-activation of most of these regions is due to interoception [229] [196], working memory 
162 
 
[230], language [231], observation [229], execution [231], as well as emotion regulation [232] 
[233]. Besides the functionalities for areas above mentioned in network #1, the supplementary 
motor area and precentral area involve in movement control and execution [234]; insula involves 
in emotion, perception, motor control, self-awareness and interoception; postcentral area 
involves in tactile sense. Network #3 shown in Fig.5.6 (C) involves frontal middle area, inferior 
and mid temporal in the right hemisphere, and mid temporal area, caudate, inferior orbital frontal 
area in the left hemisphere. We can clearly see the temporal to caudate causal pass way and 
frontal to caudate causal pass way. Caudate nucleus has been demonstrated to highly involve in 
learning and memory [235], particularly regarding feedback processing (rewarding and 
motivation) [187], as well as emotion [236] [237]. Together with temporal area and frontal area, 
these two pass ways indicate several functionalities using Brainmap Sleuth: memory [238]; 
execution, emotion [239]; social cognition [240]. Network #4 as in subfigure (D) includes 
inferior parietal area, caudate, rectus, superior frontal area in the right hemisphere, as well as left 
inferior temporal area.  Rectal gyrus has been linked to attention and memory processing [241]. 
Inferior parietal lobule involves in interpretation of sensory input and perception of emotions. By 
using Brainmap Sleuth, the co-activation of most these areas involves in functionalities of 
execution [242], memory [243], visual and somesthesis perception [244] and language 
processing [226] [245]. Lastly, Network #5 in subfigure (E) involves left SMA, left postcentral 
area, left supramarginal area, bilateral lingual gyrus, bilateral cuneus, superior bilateral occipital 
area, right fusiform, right inferior orbital & opercular frontal area, left parahippocampus gyrus, 
part of vermis and left thalamus. Using Brainmap Sleuth, most of these areas are co-activated by 
emotion & social cognition [240], interoception & observation [229]. Fusiform, superior 
occipital area, cuneus relate to visual perception and processing, lingual gyrus participates in 
163 
 
visual processing and visual memory encoding, supramaginal relates to language processing, and 
postcentral area and parahippocampal gyrus relate to memory encoding and retrieval. 
 
(A) 
164 
 
  (B) 
165 
 
 (C) 
166 
 
 
 (D) 
167 
 
  
(E)                                                          
Figure 5.6 Five directional connectivity networks of the most reproducible third level 
clustering centroid. In each subfigure, green dots represent the centers of corresponding 
functionally homogeneous CC200 regions and arrowed paths represent directional connectivity 
between regions with thickness and color representing the absolute connectivity value. Autumn 
colormap is used with red indicating small value and yellow indicating big value.  
 
168 
 
 (A) 
 
(B) 
 (C) 
 (D) 
169 
 
 
 (E) 
Figure 5.7 Functional relevance of the five networks obtained from the most consistent 
third level clustering centroid. The digits in pink balls mark the corresponding directional 
networks in Fig.5.6. The head nodes of networks indicate the functionality that co-activates the 
regions of corresponding networks as ascertained through activation likelihood estimation (ALE) 
based meta-analyses using the BrainMap database.(A) is for functionality of action; (B) is for 
perception; (C) is for interoception; (D) is for emotion; (E) is for cognition. 
 
Table 5.2 Summary of number of members and total occurrence times for third level clusters 
Cluster 
Number of members 
(dominant 2nd level clustering 
patterns)  
Total 
occurrence 
times (TRs) 
#1 3 789 
#2 3 899 
#3 2 910 
#4 31 11850 
#5 4 796 
#6 2 783 
#7 2 721 
Sum 47 16748 
 
5.4 Discussion 
We devised a method of three levels of clustering based on dynamic EC measure calculated 
through dynamic Granger causality as to find time-varying EC configurations, dominating and 
consistent EC patterns across all subjects, and the relation to real word functionalities. The major 
contributions of this work can be concluded into three aspects as below. First,  to the best of our 
knowledge, this is the first time the dynamics,  EC measure, clustering, and whole brain gray 
170 
 
matter regions are put together to analyze human brain EC networks. We believe that the work 
reported here will serve as a seminal exploration of whole brain EC dynamics.  
Second, the second level results showing the alternating brain EC network patterns feature one 
to three dominating patterns, and assume quasi-stable fractal-like property. This phenomenon 
means the second level clustering result over time has a hierarchical organization. A dominating 
pattern will dominate for a period of time and during this period, no other dominating patterns 
exist. After this period, another dominating pattern takes over. Within the period it dominates, 
there may appear several sub-patterns, and each sub-pattern will appear and alternate with the 
dominating one for only an episode of time, and after this time episode, another sub-pattern takes 
over. Then, under the sub-patterns, there may appear even smaller sub-patterns which behave 
similarly to the former sub-patterns, but at a finer scale. Previous reports have found this fractal-
like quasi-stable phenomenon on EEG/fMRI analysis [138] [149] [204]. Both functional 
connectivity networks and the topography of the spontaneous EEG show stable global brain 
states remaining quasi-stationary for a period of time, called microstates. But to our knowledge, 
no such work has been reported on EC networks. This is the first time the EC microstates are 
found. It suggests that not only the simultaneous correlation over distant brain regions can 
assume quasi-stable microstates, but the time lagged causal influence between distant brain 
regions also can. Further study is necessary to inspect this phenomenon and verify this 
conclusion, which is one of our future research directions. 
Third, at the third level, we obtained 7 clusters and among them, we found one dominating 
and consistent EC network pattern across all subjects. Detailed analysis of all networks in this 
pattern demonstrates that there are 5 EC networks in this pattern, and these networks centralize 
on nodes of several regions: mid and inferior temporal cortex, frontal cortex, supplementary 
171 
 
motor area, pre and postcentral area, parietal cortex and occipital cortex. These areas are 
frequently recruited when the brain is engaged in visual and motor processing, memory retrieval, 
and emotion regulation. These cognitive functions are most frequently encountered for resting 
state human brain when lying in scanner. Other regions like caudate, hippocampus, fusiform, 
lingual cortex are also implicated in above functions [246] [247] [248]. The language and 
execution functions each involve 3 networks which is less than that of memory and emotion. 
This may be due to the reason that language and execution processes are not as frequently 
recruited as memory and emotion. Functionalities such as observation, interoception, space 
cognition, and social cognition involve even less networks maybe due to the reason these 
functions are less frequently employed when lying rest during fMRI scan. 
Admittedly, this work suffers from several drawbacks. First, the data did not cover cerebellum 
such that this part was not considered into analysis. For future work, using resting state data 
covering the whole brain for analysis of this kind is necessitated. It is expected that whether the 
cerebellum will appear as an individual network or cluster with other brain areas. On the other 
hand, the switching pattern of brain network configurations in this work is similar to that of EEG 
microstates which have been shown to have fractal property [204]. In the future, it is advised to 
conduct a simultaneous EEG-fMRI study, and compare the patterns obtained from EEG and 
fMRI. A cross validation from both EEG and fMRI sides will further deepen and fortify our 
knowledge about connectivity dynamics, and thus its clinical indications. 
  
172 
 
Chapter 6 Dynamic Multivariate Analysis: 
 Dynamic Brain Connectivity Is a Better Predictor of PTSD than Static Connectivity 
 
The work in this chapter continues the works in Chapter 4 and 5. Chapter 4 deals with FC 
statics and dynamics and Chapter 5 deals with EC dynamics, while this chapter frames together 
all of above plus EC statics and systematically compares their efficacies in clinical diagnostics. 
Our main contribution is that we compared EC and FC statics and dynamics in terms of their 
capabilities of discriminating patients with mental disorders and healthy individuals using 
support vector machine classification, and concluded that the dynamics of connectivities was 
more sensitive to the changes brought by mental disorders.  
6.1 Introduction 
Previous Chapter 4 and 5 demonstrate the significance and use of dynamics of FC and EC in 
neuro-scientific research, by exploring dynamic brain network patterns and relation to various 
behavioral measures and cognitive functions. In this chapter, both FC and EC metrics, and both 
static and dynamic measures are framed together in an effort to systematically compare their 
values in diagnostic implications. As mentioned in Chapter 4 and 5, dynamics of connectivity 
received a lot of attention in recent years and many works have explored them using resting state 
fMRI. The studies investigating dynamic FC used the strategy of sliding windows to account for 
the dynamics [128] [130] [134] [140] [141] [143]. In particular, Handwerker et al. conducted a 
sliding window analysis on dynamic FC mainly in frequency domain [131], Lee et al. explored 
sliding windowed dynamic FC at different frequency bands using high sampling rate achieved 
through MR-encephalography [132], and Chang & Glover explored dynamic FC by using 
wavelet based time-frequency analysis [127]. In addition, observations from electrophysiological 
173 
 
studies using EEG [137] and simultaneous EEG/fMRI [133] [145] [138] have demonstrated the 
existence of temporal variations in FC derived from resting state fMRI and their 
electrophysiological correlates. On the other hand, there have been few studies exploring 
dynamic EC brain networks. For example, Havlicek et al. proposed an approach to estimate 
dynamic Granger causality in in the frequency domain [207], while Sato et al. [129], Lacey et al. 
[249], and Kapogiannis et al [250] used wavelet extension of Granger causality to investigate 
dynamic EC in the time domain. These studies were illustrated with applications to task-based 
fMRI.  
While there is evidence to believe that non-stationary dynamics exists in brain networks 
obtained from resting state fMRI, it is yet unclear whether such dynamics provide any additional 
sensitivity to underlying neuronal processes, especially in clinical diagnostic applications. A 
recent report showed that dynamic FC is related to real-world cognitive behaviors [166]. Further, 
recent works have shown that dynamic connectivity signatures in healthy subjects are different 
from that in subjects diagnosed with mental diseases such as PTSD (post-traumatic stress 
disorder) [146] and schizophrenia [144]. However, the above studies do not answer the key 
question of whether dynamic connectivity provides any additional sensitivity to underlying 
neuronal processes than what is provided by conventional static connectivity. 
In this study, we propose that the ability of brain regions to engage and disengage from other 
brain regions provides a characterization which is fundamentally different from that obtained 
from conventional static connectivity. Consequently, we hypothesize that the healthy brain is 
characterized by greater temporal variability of corresponding brain connections as compared to 
unhealthy brains in general. We specifically test this hypothesis in case of PTSD, wherein we 
postulate that brains with PTSD symptoms can be characterized by elevated static connectivities 
174 
 
(as shown by previous reports [251] [201]), coupled with decreased temporal variability of those 
connections, leading to a situation wherein hyper-connected brain regions do not disengage 
frequently enough. Further, we hypothesize that dynamic FC and EC will provide additional 
sensitivity to the discrimination of PTSD from healthy controls than that provided by static 
counterparts. 
In this work, we tested the above hypotheses by estimating both dynamic FC (DFC) and 
dynamic EC (DEC) in addition to conventional static measures, static FC (SFC) and static EC 
(SEC) from resting state fMRI data. For obtaining DFC, we adopted the same strategy as in 
Chapter 4, i.e., employing moving windowed Pearson?s correlation with window length being 
determined by Dickey-fuller unit root test (DF test). SFC was estimated using Pearson?s 
correlation between the entire time series. For obtaining DEC, we employed dynamic Granger 
causality (DGC) while correlation-purged Granger causality (CPGC) [211] was used as the SEC 
measure. Similar to Chapter 4 and 5, these measures were estimated from mean resting state time 
series extracted from 190 functionally homogeneous regions from CC200 atlas [160]. In order to 
test whether dynamic connectivity measures provide additional sensitivity to underlying neuronal 
processes which are altered in PTSD, we used each of the measures: SFC, SEC, variance of DFC 
and variance of DEC, as features for four separate recursive cluster elimination support vector 
machine (RCE-SVM) classifiers in order to estimate the accuracy with which they were able to 
predict the diagnosis of a novel subject.  
6.2 Material and Methods 
6.2.1 Data Acquisition and Preprocessing 
PTSD patients and healthy controls (all right handed) were recruited after the 2008 Wenchuan 
earthquake, Sichuan, China. Data analysed in this work came from 99 runs from 76 trauma-
175 
 
exposed healthy subjects and 146 runs from 73 PTSD patients. Informed consent was obtained 
from all subjects after they understood detailed information about the study protocol, which was 
approved by the IRB of the Second Xiangya Hospital and the Central South University, 
Changsha, China. Controls were matched in terms of gender and age (within 2 years), as well as 
education (within 5 years).  
 
T2*-weighted echo planar functional images were acquired from participants. The acquisition 
parameters were: 200 volumes per scan, In-plane matrix of 64? 64 (voxels), 30 axial slices, field 
of view (FOV) =220? 220 mm2, flip angle (FA) =90?, TR (repetition time)/TE (echo time) 
=2000ms/30ms, slice thickness 4mm with 1 mm gap. Preprocessing of data was accomplished 
using Data Processing Assistant for Resting-State fMRI software (DPARSF) [168] and included 
slice timing correction, rigid body registration, normalization to MNI template with 2? 2? 2 
mm3 resolution, spatial smoothing with 4? 4? 4 mm3 Gaussian kernel, 0.01~0.1 Hz band pass 
filtering, detrending, and regressing out of white matter (WM) and cerebrospinal fluid (CSF) 
signals as well as 6 motion parameters. 190 functionally homogeneous brain regions derived 
from spectral clustering of resting state fMRI data were identified from the CC200 brain atlas 
[160]. Finally, mean time series from each of the 190 regions was extracted from each subject for 
subsequent use.  
6.2.2 Static and Dynamic Effective Connectivity 
As discussed in Chapter 5, we used 190 regions covering the entire brain, no assumptions 
could be made about the underlying connectional architecture, thus the totally data driven 
measure, Granger causality was recruited for representing EC. Further, model-based methods 
become computationally intractable when the number of ROIs becomes very large [217].  
176 
 
The Granger causality is based on the principle that if the past of one time series helps predict 
the present and future of another time series, then there must be a causal influence from the 
former time series to the latter. We used CPGC to represent SEC and DGC to represent DEC. To 
elicit the concept of CPGC, we restate the multivariate vector autoregressive (MVAR) model 
below. Given k time series X(t) =[x1(t) x2(t) ? xk(t)], with k being 190 in this study, the MVAR 
model with parameters A(n) of order p is given by: 
             
1( ) ( ) ( ) ( )
p
nt n t n t?? ? ? ? ??X V A X ?
                                      (6.1) 
Where V is the intercept vector representing nonzero mean component, n is the time lag, and E(t) 
is the vector corresponding to the residuals. In our scenario, time series were detrended so that 
V=0. Direct causal influences among k time series can be inferred from the MVAR coefficients 
as follows. 
  2
1 [ ( )]
p
ij ijnD a n???
                                                       (6.2) 
Where each aij, i, j=1:k, is one element of matrix A. The effects of instantaneous correlation is 
modeled as the zero-lag terms and introduced into the modified MVAR model as below [211]. 
       
0( ) ( ) ( ) ( )
p
nt n t n t? ??? ? ? ? ??X V A X ?
                                   (6.3) 
Where the diagonal elements of A'(0) are zeros such that only instantaneous cross-correlation, 
rather than zero-lag auto-correlation, are modeled. Accordingly, correlation-purged Granger 
causality (CPGC) [211] is defined as:  
      2
1 [ ( )]
p
ij ijnC P G C a n? ?? ?
                                                  (6.4) 
Where each a'ij is one element of the matrix A'. Note that A'(1) ? A' (p) ? A(1) ? A(p) and the 
A'(1) ? A' (p) represent the causal influence which is purged of zero-lag correlation ?leakage? 
177 
 
effects as shown before [211]. The order p of this modified MVAR is determined by Bayesian 
Information Criterion (BIC) [252]. For methodological details and applications of Granger 
causality based SEC to task-based and resting state fMRI data, please refer to the following 
previous publications [253, 254, 255, 256, 257, 258, 259, 260] [261, 262, 170, 263, 264] [114] 
[210]. 
For formulation of DGC, please refer to Section 5.2.2 in Chapter 5. Note that it was 
empirically observed that the Kalman filter estimated needed 10-15 time points to converge. 
Also considering the fact that initial time points in fMRI time series are routinely discarded to 
allow the MR signal to achieve equilibration, the DGC values obtained from the first 20 time 
points were discarded in this work.  
6.2.3 Static and Dynamic Functional Connectivity 
In this work, we used Pearson correlation between entire time series from different ROIs as 
SFC measure, and sliding windowed Pearson correlation as DFC measure. Both were the same 
as those in Chapter 4. The sliding window length was determined by DF test. For details 
regarding this, please see Section 4.2.3 in Chapter 4.  
Being worthy of mentioning, previous studies have used fixed sliding windows of lengths 
varying from 15 to 120 TRs and similar step size [130] [265] [131] [127] [147]. The data used in 
this work had a relatively longer TR of 2 seconds, and hence we set the minimum window length 
to be 10 TRs (20 seconds) and maximum window length to be 40 TRs (80 seconds). The choice 
of minimum window length was motivated by the consideration that it must have sufficient 
sampling points to capture temporal dynamics of FC. Two factors influenced the choice of 
maximum window length. First, it had to be long enough to capture the slowest variations, but 
short enough so that it does not encompass a large portion of the relatively short time series of 
178 
 
200 TRs we had at our disposal. In order to balance these requirements, a maximum window 
length of 40 TRs was chosen. We empirically observed that in a vast majority of cases, the 
window lengths calculated by the DF test were between 10 and 40 TRs. However, it is 
noteworthy that if the time series were longer, it is possible to choose a bigger maximum 
window length while performing the DF test. The first 40 data points of time series were 
preserved for performing the DF test of the first sliding window and the sliding window moved 
forward by one TR each time. Thus, the dynamic FC had a length of 160 time points (200 is the 
total number of time points).  
6.2.4 RCE-SVM Classification 
Here we describe the method used to classify PTSD subjects and healthy controls data using 
dynamic and static connectivity metrics. Four separate classifiers were employed, with each one 
receiving one of the following metrics as features from all subjects as inputs: CPGC for SEC, 
Pearson?s correlation for SFC, variance of DGC for variance of DEC and variance of windowed 
Pearson?s correlation for variance of DFC. The variances of dynamic connectivity metrics were 
employed in order to capture information regarding the temporal variability of brain 
connectivities. For each of the four classes of features (SEC, SFC, DEC, DFC), there were 190 
(number of regions) ? 190 (number of regions) =36,100 features for every subject. To 
effectively reduce the number of features, we conducted a two sample t-test in order to determine 
those features which were significantly (p<0.05) different between the two groups (PTSD and 
healthy controls). After this t-test filtering, the number of features dramatically reduced to 
around 2000 (the precise number of features which were significantly different between the 
groups were different for different metrics). In order to make the classifier performances 
179 
 
comparable, we selected the top 1000 features with the lowest p-values and input those into the 
RCE-SVM [266] [267] classifier.  
The statistical separation of features obtained from a t-test does not guarantee the predictive 
power or generalizability of those features for inferring the diagnostic label of a novel subject, 
which can be provided by classifiers. Wide applicability of support vector machine (SVM) as a 
machine learning approach [268] with successful applications in many different fields [269] 
motivated our choice of SVM for classification. More so, SVM has been the most popular 
classifier in neuroimaging applications [270]. The recursive cluster elimination (RCE) algorithm 
is a ?wrapper? method for feature selection within SVM wherein uninformative feature clusters 
are eliminated based on their contribution to classification accuracy, and is considered to be 
more powerful than ?filtering? methods such as t-test which pick the discriminative features a 
priori based on statistical separation [271] [272]. However, we used t-test ?filtering? to reduce 
the number of input features and then used the RCE ?wrapper? approach on the remaining 
significant features in an effort to utilize the merits of both ?filtering? and ?wrapper? approaches. 
A schematic illustrating the roles of t-test and RCE algorithm within the overall analysis pipeline 
is shown in Fig.6.1. The classification accuracy was obtained at each iteration. Also, the 
contribution of each feature towards obtaining highest classification accuracy was estimated and 
an SVM ?score? was assigned to each feature. As shown in previous works, the RCE-SVM 
algorithm maintained full separation of training and testing data [273] and hence avoided any 
bias in classification.  
Specifically in this work, the 1000 significant features for all 146 PTSD and 99 healthy 
subjects were evenly partitioned into 10 subsets in terms of subjects, i.e., the first subset had all 
1000 significant features for 15 PTSD subjects and 10 healthy subjects, ?, the 10 th subset had 
180 
 
all 1000 significant features for last 11PTSD subjects and 9 healthy subjects. We did this because 
with less number of subjects, the classification result was relatively reliable and converged 
quickly. Then for each subset, the following procedure of RCE-SVM was realized. At the start, 
all input features were allocated into two parts, each containing half of PTSD subjects and half of 
healthy controls. The first part was aimed for training and the second part for testing. Next was 
the clustering step. Input features were clustered into n clusters using clustering method (k-
means was used and n=40 for our scenario). Then SVM scoring step followed. The SVM score 
of one cluster was a measure of its ability to correctly classify the two groups of subjects, as 
reflected in the hit rate of classification. Linear SVM scheme was employed because of its 
computational efficiency and sufficient quality [274]. Specifically, to calculate the score of each 
cluster, the training features were first randomly divided into 6 subsets of equal size (6 folds) 
without overlap. Then 5 subsets were trained using linear SVM and the last one was used to test 
classification performance. After that, the training features were randomly re-divided into 6 
subsets, and the SVM training and cross-validation were conducted again. This procedure 
repeated 100 times in order to account for all possible groupings of features. The score for one 
cluster was determined as its average accuracy of SVM over all folds and repetitions. Next 
followed the cluster elimination step, in which 50% of the clusters with lowest scores were 
eliminated. The surviving features were merged and re-clustered using k-means, with n being 
halved. Then the above three steps were iterated until there was only one cluster left. For each 
iteration, the testing data was used to evaluate the performance of the classifier with half number 
of features in previous iteration. Nevertheless, the useful information for subsequent analysis was 
only the classifier performance and feature scores when maximum accuracy was reached. The 
features corresponding to that iteration were tabulated and rank ordered based on their scores, 
181 
 
and then summed over all 10 subsets, resulting in their global performance index. A flowchart of 
RCE-SVM algorithm is shown in Fig. 6.2. Please refer to previous publications for more details 
about the RCE-SVM algorithm [267, 266, 264]. 
 
Figure 6.1 Schematic illustrating the roles of t-test and RCE-SVM algorithm within the 
overall analysis pipeline  
 
182 
 
 
Figure 6.2 Flowchart of RCE-SVM algorithm for scenario in this work 
 
6.3 Results 
Fig.6.3 shows the mean classification accuracies obtained by SFC and DFC while Fig.6.4 
shows the mean classification accuracies obtained by SEC and DEC. It can be seen that with 
each RCE step, uninformative features are eliminated and the remaining features are re-classified 
until we are left with only two feature clusters. The classification accuracy tends to increase with 
the removal of redundant features at each RCE step. However, there exists a point of inflection 
183 
 
for variance of DFC and DEC, which is at the fourth RCE step with only 5 feature-clusters 
remaining, at which the accuracy peaks at 94.5% and 91.3% for variance of DFC and DEC, 
respectively.  
 
Figure 6.3 Mean classification accuracy obtained from SFC and variance of DFC. X-axis 
represents recursive cluster elimination steps in RCE-SVM algorithm. Green line: mean 
classification accuracy obtained using variance of DFC. Blue line: mean classification accuracy 
obtained using SFC. The number pairs above each knot denote the number of feature-clusters 
remaining (first number) and the number of features remaining (second number) at every cluster 
elimination step. Numbers in circles represent the p-value obtained by doing a one-sided t-test 
comparing classification accuracy obtained by SFC with variance of DFC (alternative hypothesis: 
accuracy using variance of DFC > accuracy using SFC) at every cluster elimination step.   
 
Removal of any more DFC and DEC features resulted in decreased accuracy indicating that 
those features were essential for peak accuracy. This was not the case for SFC and SEC, wherein 
the accuracy kept increasing until the final RCE step with peak accuracies of 86.8% and 88% for 
SFC and SEC, respectively.  
 
184 
 
 
Figure 6.4 Mean classification accuracy obtained from SEC and variance of DEC. X-axis 
represents recursive cluster elimination steps in RCE-SVM algorithm. Green line: mean 
classification accuracy obtained using variance of DEC. Blue line: mean classification accuracy 
obtained using SEC. The number pairs above each knot denote the number of feature-clusters 
remaining (first number) and the number of features remaining (second number) at every cluster 
elimination step. Numbers in circles represent the p-value obtained by doing a one-sided t-test 
comparing classification accuracy obtained by SEC with variance of DEC (alternative hypothesis: 
accuracy using variance of DEC > accuracy using SEC) at every cluster elimination step.   
 
It is noteworthy here that for both functional and effective connectivity measures, the 
variances of their dynamics have higher discriminatory power between the groups as compared 
to their conventional static counterparts. Digits in circles at every feature-cluster elimination step 
represent the p-value obtained by performing a one-sided t-test comparing classification 
accuracy of DFC to SFC, and DEC to SEC. The alternative hypothesis for this t-test is that the 
accuracy by the variance of DFC/DEC is greater than that obtained by SFC/SEC. Fig.6.3 and 6.4 
demonstrate that at each RCE step, the accuracies obtained by dynamic connectivity metrics are 
significantly greater than that obtained by static connectivity metrics.   
185 
 
The features responsible for obtaining maximum accuracy were ascertained and displayed as a 
network of interconnected nodes using BrainNet Viewer visualization toolbox [275] as shown in 
Fig.6.5. The nodes represent centroids of brain regions, and each path represents each individual 
feature. The labels for the nodes in Fig.6.5 correspond to the names of corresponding ROIs 
derived from the AAL atlas (please refer to Table A1 in Appendix A, Section A.2 for MNI co-
ordinates and AAL labels of all regions in the CC200 atlas). Paths with arrows denote EC, while 
paths without arrows denote FC. Further, the width and color of the paths correspond to their 
weights, which are calculated based on their SVM scores. Specifically, the SVM scores denote 
the importance of the corresponding feature for classification between the two groups [270].  
From Fig.6.5, a pattern emerges wherein PTSD subjects have stronger overall connectivity, 
but reduced temporal variability as compared to healthy controls. Specifically, we observe 
substantially less number of DEC and DFC paths whose variances are larger in PTSD subjects as 
compared to healthy controls than the other way around (Fig.6.5 (A), (B) and (E)). Conversely, 
we observe substantially more number of SEC and SFC paths whose connectivity strength are 
larger in PTSD subjects as compared to healthy controls than the other way around (Fig.6.5 (C), 
(D) and (F)). Note that no significant DFC paths are observed whose variances are larger in 
PTSD subjects as compared to healthy controls and at the same time have the discriminatory 
power to classify subjects with highest accuracy. Also, no significant SFC paths are observed 
whose connectivities are stronger in healthy controls as compared to PTSD and simultaneously 
have the discriminatory power to classify subjects with highest accuracy.  
Apart from the general pattern mentioned above, there are specific patterns in each subfigure 
of Fig.6.5 which are noteworthy. First, it can be seen that both static and dynamic connectivity in 
cortico-cerebellar pathways are implicated in almost all subfigures of Fig.6.5 with predominantly 
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increased static connectivity and decreased temporal variability in PTSD. Mid prefrontal cortex, 
pre- and post-central cortices, caudate and insula also show increased static connectivity with 
decreased variability in PTSD. Inferior and medial temporal lobes emerge as important hubs with 
highly ranked paths associated in Fig.6.5 (B), (C) and (D), indicating their important roles in 
altered causal brain networks underlying PTSD. On the other hand, the brainstem has 
predominantly stronger SFC in the PTSD. The numbers of incoming and outgoing paths for each 
region in each subfigure of Fig.6.5 (or just the number of paths associated with a given region for 
FC measures) along with their summed connectivity weight are shown in Tables B1 and Table 
B2 in Appendix B.  
 
(A) Variance of DEC: PTSD>Control 
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 (B) Variance of DEC: Control> PTSD 
188 
 
 (C) SEC: PTSD>Control 
189 
 
 
 
(D) SEC: Control> PTSD 
190 
 
 (E) Variance of DFC: Control>PTSD 
191 
 
 
(F) SFC: PTSD>Control 
Figure 6.5 Static and Dynamic connectivity features responsible for providing maximum 
classification accuracy between PTSD and healthy control groups. (A) Top ranked paths 
whose variances of DEC over time for PTSD subjects are significantly greater than those for 
healthy controls (p<0.05). (B) Top ranked paths whose variances of DEC over time for healthy 
controls are significantly greater than those for PTSD subjects (p<0.05). (C) Top ranked SEC 
paths which are significantly (p<0.05) stronger in PTSD subjects as compared to healthy controls. 
(D) Top ranked SEC paths which are significantly (p<0.05) stronger in healthy controls as 
compared to PTSD subjects. (E) Top ranked paths whose variances of DFC over time for healthy 
controls are significantly greater than those for PTSD subjects (p<0.05). (F) Top ranked SFC 
paths which are significantly (p<0.05) stronger in PTSD subjects as compared to healthy controls. 
DFC and SFC Paths have no arrows since correlation has no directionality. Note that no 
significant DFC paths are observed whose variances are larger in PTSD subjects as compared to 
healthy controls and at the same time have the discriminatory power to classify subjects with 
highest accuracy. Also, no significant SFC paths are observed whose connectivities are stronger 
in healthy controls as compared to PTSD and at the same time have the discriminatory power to 
classify subjects with highest accuracy. Therefore no subfigures are displayed for them. In all 
sub-figures, blue nodes represent centroids of functionally homogeneous CC200 brain regions, 
and paths with arrows connecting nodes represent EC metrics, whereas those without arrows 
represent FC metrics. The thickness and color of paths correspond to their weights (SVM scores) 
192 
 
calculated from RCE-SVM. Autumn color map is used with red representing low SVM score and 
yellow representing high SVM score.  
 
6.4 Discussion 
In this work, we tested the hypothesis that brains with mental disorders are characterized by 
reduced temporal variability of their brain connections compared to healthy brains, as inferred 
through resting state fMRI. The motivation for this general hypothesis stems from evidence in 
biological systems pointing to dynamic adaptability of function as a hallmark of health [276]. 
We specifically tested this hypothesis in subjects diagnosed with PTSD, and predicted that their 
brains will be characterized by elevated static connectivity (as shown in previous reports [251] 
[201]), coupled with decreased temporal variability of those connections. Further, we 
investigated whether temporal variability of brain connectivity will provide additional sensitivity 
for predicting the diagnostic label of a novel subject, over and above the discriminatory power 
provided by conventional static connectivity. 
The results presented in this paper support the hypotheses stated above. Specifically, large 
number of DEC and DFC paths have variances which are significantly larger in healthy controls 
as compare to PTSD. In comparison, substantially less number of DEC paths, and no DFC paths, 
whose variances are larger in PTSD subjects as compared to healthy controls are observed. On 
the other hand, large number of SEC and SFC paths whose connectivity strengths are higher in 
PTSD subjects as compared to healthy controls are observed. In comparison, substantially less 
number of SEC paths, and no SFC paths, whose connectivities are significantly stronger in 
healthy controls as compared to PTSD are observed. Taken together, these results support the 
notion that PTSD subjects have stronger overall connectivity, but reduced temporal variability as 
compared to healthy controls. Consequently, they serve as an example for our general hypothesis 
that unhealthy brains are characterized by reduced temporal variability of their brain connections 
193 
 
compared to healthy brains. Future studies must examine whether this hypothesis holds true for 
other mental disorders. 
Even though previous studies have demonstrated that dynamic connectivity signatures in 
healthy subjects are different from that in subjects diagnosed with mental diseases such as PTSD 
[146] and schizophrenia [144], a key question has remained unanswered: whether dynamics of 
connectivity inferred from resting state fMRI provides additional sensitivity to underlying causes 
of pathology or is it just a detailed characterization of conventional static connectivity with no 
additional predictive value. Our results support the hypotheses that dynamic connectivity indeed 
provides novel information as compared to static connectivity which has additional predictive 
value in clinical diagnosis. The classification results demonstrate that, at every iteration 
including the one providing maximum accuracy, variance of DFC and DEC provide significantly 
higher classification accuracy than that provided by SFC and SEC. The fact that the maximum 
accuracies provided by variances of DFC and DEC exceed 90% shows that it holds promise as a 
potential neuroimaging biomarker of PTSD. 
PTSD is a psychiatric disorder which is associated with exposure to traumatic events that have 
a profound impact such that three symptom clusters ensue: re-experiencing of the event and 
flashback, avoidance/numbing/depression, hyper-arousal, along with a high rate of dissociative 
symptoms [277] [278]. The pathogenesis of PTSD is not yet clear. FMRI studies have provided 
invaluable information about PTSD, although many of them are task-related and hence difficult 
for subjects to perform with same accuracy as healthy controls [279] [280]. Recent studies have 
increasingly explored the use of resting state data [281] [201] [202] given the ease of acquiring 
such data from patient populations and lack of requirements such as matching task performance 
with a control group. Below we discuss some specific dynamic and static connectivity patterns 
194 
 
(as in Fig.6.5) that emerge from a statistical comparison between the groups in the context of the 
three symptom clusters mentioned above. Note that these paths as shown in Fig.6.5 are 
significantly different between the groups, as well as possess the most predictive power (as 
ascertained through SVM score) for determining the diagnostic label of a novel subject. First, 
both dynamic and static EC/FC paths associated with cerebellum emerge as having significant 
differences between the two groups in Fig.6.5. As pointed out by Schmahmann et al. [282], the 
cerebellum is engaged in the experience and regulation of emotions, especially fear perception, 
anxiety, anticipation, and recollection, and has afferent and efferent connections to the limbic 
system and brainstem [283]. Thus, cerebellar function is known to be associated with PTSD 
symptom clusters [284] [285]. In addition, paths associated with the vermis region of the 
cerebellum are mainly implicated in FC differences between the groups. This region is believed 
to be functionally implicated with bodily posture and locomotion [286], and has been shown to 
be associated with early traumatic life experiences [284]. Many EC paths associated with inferior 
and medial temporal lobes are significantly different between the two groups. Previous studies 
have shown that inferior and medial temporal lobes are crucial in relaying information among 
frontal lobe, limbic areas, cerebellum, and visual cortex. For example, as discussed by Miyashita 
[184], the inferior temporal cortex is referred to as the link from visual cortices to limbic system 
and frontal lobe, acting to bind object perception with memory [287]. Medial temporal lobe is 
known to be involved in memory encoding and retrieval [288]. Since PTSD symptoms such as 
flashback and event re-experiencing are associated with memory systems, connectivity 
alterations in these regions are in line with previous research implicating them in PTSD [202]. 
The precentral and postcentral cortices, which contain the primary motor cortex and primary 
somatosensory cortex, respectively, have many associated EC and FC (both static and dynamic) 
195 
 
paths which are different between PTSD and controls. In association with mid and inferior 
temporal cortices (these regions are connected to postcentral gyrus in Fig.6.5 (B) and (C)), 
postcentral gyrus has been previously implicated in emotion recognition, especially in social 
anxiety disorder [289] [290], which relates to PTSD symptoms of numbing and depression. The 
precentral gyrus has been shown to be activated with the contrast of flashbacks versus ordinary 
episodic trauma memories in PTSD, as shown by Whalley et al [279]. Additional activated areas 
for this contrast are sensory and motor areas including the insula, supplementary motor area 
(SMA), and mid-occipital cortex, as well as decreased activation in the midbrain, 
parahippocampal gyrus, and precuneus/posterior cingulate cortex. These regions are indeed 
involved in the significant differentiation between the two groups as in Fig.6.5: mid brain in 
Fig.6.5 (F); mid-occipital cortex reflected in FC subfigures; precuneus in Fig.6.5 (B), (C) and (F); 
parahippocampal gyrus in Fig.6.5 (B), (C), (D) and (F); SMA in Fig.6.5 (A) and (C); insula in 
Fig.6.5 (B), (C), (E) and (F). The brain stem has many SFC connections to occipital and 
precuneus regions, as well as a path to the mid frontal cortex and a path to inferior temporal 
cortex, which are stronger in PTSD as compared to controls. The brain stem has been previously 
implicated in various PTSD symptom clusters [291] [292]. However, this feature is not as 
discriminative as DFC differences between the groups. Other regions with multiple paths 
showing group differences, and which have been previously shown to be important regions 
underlying the pathophysiology of PTSD, are the caudate and insula [293], parietal and occipital 
cortex [279], fusiform [294] and thalamus [201]. Among them, the insular cortex deserves to be 
highlighted since it is closely associated with pain and emotion, and an increasing number of 
neuroimaging studies show that both physical pain and depression involve the insular cortex 
[295] [296] [297]. The activation of fusiform has been shown by Shaw et al. [294] to be linked to 
196 
 
hyper-arousal and abnormal reactivity in PTSD. Besides, the parietal cortex is involved in the 
dorsal visual stream which appears to be altered in PTSD as compared to healthy controls [279].  
This paper presents some methodological advances which are noteworthy. First, few studies in 
the past have simultaneously examined both SFC and SEC from resting state fMRI [114]. None 
has done so using both DFC and DEC in addition to conventional static metrics. Second, most 
previous studies limit the number of ROIs either because they are using a seed-based approach 
[201] or because including more ROIs in EC models make them computationally intractable 
[217]. Exceptions to this include whole brain FC studies employing PCA [298], ICA [125] and 
graph-theoretic approaches [299] [300] and a limited number of whole brain EC studies 
employing conditional Granger causality [213]. None so far has simultaneously examined both 
FC and EC at the whole brain level and our approach demonstrates a framework for doing so. 
Third, since truly multivariate EC models (which do not make sparcity assumptions) cannot be 
estimated in a voxel-wise fashion across the whole brain for typical lengths of time series 
obtained in fMRI studies, prior studies have used anatomically defined ROIs (for example, from 
the AAL atlas [130], which makes ROIs functionally heterogeneous) or have considered ROIs 
from pre-defined networks such as the default mode network [202]. Contrary to previous 
approaches, we have used functionally homogeneous ROIs obtained from spectral clustering of 
resting state fMRI data [160]. This allowed us to perform whole brain analysis without adopting 
a voxel-wise approach (and hence avoiding computational intractability issues), and at the same 
time respect functional boundaries in the brain in ROI definition. Fourth, previous dynamic FC 
studies have used fixed-length sliding windows of arbitrary length. However, different window 
lengths would produce different smoothing effects [130] [127] and there is no data to suggest 
that the minimum length of the window within which resting state fMRI data is stationary, is 
197 
 
constant over time. Therefore, we relaxed the restriction of fixed window length and used time-
varying window lengths instead. The principle we adopted is that the window length used must 
be the minimum length at which the time series becomes stationary, so that FC can be calculated 
over a period when the signals are stationary. The minimum window length condition allows us 
to capture maximum available dynamics. Similarly for dynamic EC calculation, adapting the 
Kalman filter based approach [301] and calculating the forgetting factor (which controls the 
smoothness) from the data make parameter choices objective and hence the results reproducible. 
These proposed windowing strategies provide a principled approach for controlling the 
smoothness of estimated dynamic connectivity while respecting non-stationarity in the data. 
Finally, we propose a framework using machine learning based approach called RCE-SVM to 
determine the predictive values of connectivity metrics for diagnosis.  
  
198 
 
Chapter 7 Conclusion 
 
In this dissertation, five projects are put forward with analysis on functional MRI data. 
Basically, the five projects can be divided into two categories. One is treating fMRI data in view 
of univariate process, in which time series from each voxel is assumed to be independent from 
others. We investigated the olfactory system in canines using fMRI from this view point. The 
other one is treating fMRI data as an integrated entity of dynamic multivariate processes, in 
which the signal from each voxel/region is interacting with others. With this view point, we 
investigated resting state human fMRI data to find its connectivity metrics, correlated them to 
behavior and real world functionalities, and compared the capabilities of connectivity metrics to 
predict the diagnostic label of a patient with mental disorders or a healthy control.  
Through univariate analysis, we located the olfaction related canine brain areas, examined 
how their activations were modulated with the change of odorant concentration and dog?s 
consciousness state: lightly anesthetized or fully conscious. We also inspected zinc nanoparticles? 
enhancement effect on canines? olfactory processing occurring in the anesthetized and conscious 
brain, compared to pure odorant and gold nanoparticles + odorant as controls. In addition, we 
framed the canine fMRI olfactory system and utilized the single camera optical motion tracking 
system to minimize motion effect. The result shows that olfactory bulb and piriform lobes were 
commonly activated in both awake and anesthetized dogs, while the frontal cortex and 
cerebellum were activated mainly in conscious dogs. Responses to high odorant concentration 
showed enhancement in either the intensity or spatial extent of activation in the olfactory bulb, 
piriform lobes, cerebellum, and frontal cortex as compared to low odorant concentration. Zinc 
nanoparticles immensely enhanced activations of olfactory bulb, olfactory cortex, and olfactory 
199 
 
related sub-cortical areas for anesthetized dogs and apparent enhancement for conscious dogs in 
areas of olfactory bulb, olfactory cortex, medial and posterior frontal areas, compared to pure 
odorant condition. Gold nanoparticles showed moderate enhancement for activations in olfaction 
related areas as compared to pure odorant condition. The optical motion tracking system was 
proven effective in eliminating jerky movements.   
Through multivariate analysis, human resting state fMRI data were studied and four 
connectivity metrics: static FC, dynamic FC, static EC, and dynamic EC were thoroughly 
researched and compared. With dynamic FC and EC, we conducted a three-leveled clustering 
over time, space, and subjects to find the major brain network patterns. We correlated dynamic 
FC metrics with behavioral measures and compared dynamic FC?s ability to predict behavior 
with static FC. We also linked dynamic EC patterns to real world functionalities. The major 
findings are briefed as follows. First, we observed several major patterns of brains states 
alternating with each other in a quasi-stable way, featuring default mode network (DMN) in FC 
patterns and temporal-parietal-frontal interactions in EC patterns. Second, the dynamics of FC 
had much more power in explaining and predicting a wide variety of behaviors than its static 
counterpart. Third, the major dynamic EC patterns mainly engaged in the functionalities of 
execution, emotion, and memory, in agreement with our knowledge. The last project was in an 
effort to use fMRI technique to find its diagnostic value. It compared above four connectivity 
metrics with regard to their ability to distinguish between patients with mental disorders and 
healthy controls. We used support vector machine technique as a classifier to classify PTSD 
patients and healthy controls. Our result favorably indicates that the temporal variability of 
connectivities had more sensitivity in predicting the diagnostic label of a novel subject than static 
connectivities, based on their classification performances. 
200 
 
Chapter 8 Information on Published and Submitted Papers 
 
The work described in Chapter 2 (see Chapter2) has been published in PLoS One and a 
snapshot of relevant information is shown in Fig.8.1. Author contributions: conceived and 
designed experiments: PW, CW, JB, EM, NS, TD, VV, GD. Performed experiments: HJ, OP, 
PW, RB, JS. Analyzed data: HJ. Contributed reagents/materials/analysis tools: HJ, OP, PW, CW, 
VV, GD. Wrote the paper: HJ, PW, VV, GD.   
 
Figure 8.1 A snapshot of the publication information of the work in Chapter 2. 
 
The paper for the work in Chapter 3 (see Chapter3) is currently under review, with title 
?Enhancement of Odor-induced Activity in the Canine Brain by Zinc Nanoparticles: A 
Functional MRI Study in Conscious Dogs? and authors: Hao Jia, Oleg M Pustovyy, Paul 
Waggoner, Ronald J Beyers, John Schumacher, Chester Wildey, Jay Barrett, Edward Morrison, 
Nouha Salibi, Thomas S Denney, Vitaly J Vodyanoy, and Gopikrishna Deshpande. Author 
contributions: conceived and designed experiments: PW, CW, JB, EM, NS, TD, VV, GD. 
Performed experiments: HJ, OP, PW, RB, JS. Analyzed data: HJ. Contributed 
reagents/materials/analysis tools: HJ, OP, PW, CW, VV, GD. Wrote the paper: HJ, PW, VV, GD. 
201 
 
The paper for the work in Chapter 4 (see Chapter4) is currently under review, with title 
?Behavioral Relevance of the Dynamics of Functional Brain Connectome? and authors: Hao Jia, 
Xiaoping Hu, and Gopikrishna Deshpande. Author contributions: conceived the idea: XH, GD. 
Performed simulations and analyzed data: HJ. Contributed reagents/materials/analysis tools: HJ, 
GD. Wrote the paper: HJ, XH, GD. 
The paper for the work in Chapter 5 (see Chapter5) is currently under review, with title ?Finite 
Number of Directional Brain Network Configurations Revealed from Time-Varying 
Connectivity Assessment of Resting State fMRI? and authors: Hao Jia, Xiaoping Hu and 
Gopikrishna Deshpande. Author contributions: conceived and designed experiments: GD. 
Performed experiments: HJ, GD. Performed simulations and analyzed data: HJ. Contributed 
reagents/materials/analysis tools: HJ, GD. Wrote the paper: HJ, XH, GD. 
The paper for the work in Chapter 6 (see Chapter6) is currently under review, with title 
?Dynamic Brain Connectivity Is a Better Predictor of PTSD than Static Connectivity? and 
authors: Hao Jia, Changfeng Jin, Lingjiang Li, Tianming Liu, Xiaoping Hu and Gopikrishna 
Deshpande. Author contributions: conceived and designed experiments: CJ, LL, TL, GD (only 
conceived and designed the analysis part presented in Chapter 6). Performed experiments: CJ. 
Analyzed data: HJ. Contributed reagents/materials/analysis tools: HJ, GD. Wrote the paper: HJ, 
XH, GD.  
  
202 
 
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217 
 
Appendix A 
 
A.1 Selection of Sliding Window Length Range 
In this work, we use sliding windows to calculate dynamic FC at each time instant. The 
window length is determined by Dickey-Fuller (DF) test. However, this hypothesis test is just for 
testing stationarity for a given time series, i.e. to test the existence of unit root. It does not 
provide the window length that is most appropriate for correlation calculation. Consequently, 
there remain two issues to solve. First, at a given time point, for all window lengths that can 
successfully reject the null hypothesis (i.e. those window lengths within which the time series are 
stationary), which one should be chosen for appropriate calculation of dynamic FC? Second, 
within what range of window lengths should the DF test be conducted? 
We adopt the following strategy in order to answer the first question. At a given time point, 
we start performing the DF test from the specified minimum window length and increase the 
window length by one time point (or one TR) if it could not reject the null hypothesis. Once 
stationarity is established at some window length for all 190 regions, we stop performing the test 
and use these windowed time series to calculate FC. In other words, the minimum length of the 
window which is stationary for all 190 regions is used. This strategy ensures that maximum 
available dynamics in FC is captured.  
The second question pertains to the specification of the range of window length [m-, m+] 
within which the DF test should be conducted. The factors guiding the choice of the window 
length are elaborated below. Time series      can be modeled as an AR (1) process shown by the 
equation below 
 ( ) ( 1) ( )y t y t t??? ? ?                                 (A1) 
218 
 
Where t is the time index,   is a coefficient, and      is the error term. A unit root is present 
when    , in which case, the mean and variance of      are a function of time (t). This implies 
that      is non-stationary.  
                 ( ) ( 1) ( )y t y t t??? ? ? ?                        (A2) 
The DF test informs whether the process y(t) is stationary or not within a given window. Given 
that our time series are restricted to the frequency band [0.01, 0.1] Hz, we provide a frequency 
domain explanation for the choice of minimum and maximum window lengths considered in this 
work. For a signal with highest and lowest frequencies of 0.1 Hz and 0.01 Hz, period T ranges 
from 10s to 100s. If we chose the maximum window length to be 100s, we can make sure that 
the window covers at least one period of the slowest varying signal component. Similarly, if we 
chose a minimum window length of 10s, we can guarantee that the window covers at least one 
period of the fastest varying signal component. It is imperative that the window encompasses at 
least one period of signal variation to capture all its dynamics. The above strategy ensures that 
the minimum window length can capture maximum available dynamics. Since fMRI data used in 
this work had a TR=0.72s, the minimum window length should be at least 10/0.72=14 (TRs), and 
maximum length should be 100/0.72=140 (TRs). This range was employed in this work. 
As for simulations, we assumed the sampling rate was 1 sample/s (TR=1s), so to be consistent, 
the minimum window length should be 10/1=10 (TRs), and maximum length should be 
100/1=100 (TRs), as stated in the main text. 
A.2 190 ROI Version of CC200 Atlas: Anatomical Labels and MNI Co-ordinates 
Table A1. MNI co-ordinates of the centroids of 190 regions of CC200 atlas with corresponding 
AAL anatomical labels 
Region No. AAL label of region centroid Coordinate x (mm) Coordinate y (mm) Coordinate z (mm) 
1 Pons -3 -25 -38 
2 Frontal_Sup_Orb_R 12 59 -22 
219 
 
3 Frontal_Inf_Tri_R 49 35 14 
4 Lingual_R 22 -58 0 
5 Insula_R 38 -6 9 
6 Putamen_L -25 -5 -8 
7 Cerebelum_6_L -29 -38 -35 
8 Temporal_Mid_R 71 -30 -2 
9 Precuneus_R 18 -65 25 
10 Frontal_Sup_Medial_L -1 25 41 
11 ParahippocampaGyrus -21 -26 -14 
12 Temporal_Pole_Mid_L -31 19 -40 
13 Frontal_Sup_L -13 46 42 
14 Frontal_Inf_Orb_L -20 9 -25 
15 Temporal_Inf_R 63 -28 -26 
16 Cerebelum_Crus1_L -48 -67 -32 
17 Postcentral_R 15 -43 75 
18 Precuneus_L -13 -64 64 
19 Temporal_Mid_R 63 -7 -18 
20 Frontal_Mid_R 35 14 57 
21 Paracentral_Lobule_R 15 -35 48 
22 Fusiform_L -23 3 -47 
23 Frontal_Inf_Tri_L -45 37 11 
24 Cuneus_L -9 -90 33 
25 Lingual_R 19 -99 -10 
26 Cerebelum_Crus1_R 50 -68 -34 
27 Caudate_R 15 14 2 
28 Temporal_Sup_L -62 -26 13 
29 Caudate_L -14 -8 19 
30 Supp_Motor_Area_R 15 8 67 
31 Temporal_Mid_L -58 -5 -20 
32 Calcarine_R 3 -80 7 
33 Frontal_Mid_Orb_L -31 57 -13 
34 Frontal_Inf_Orb_R 50 36 -12 
35 Brainstem 2 -43 -61 
36 Rectus_R 12 37 -29 
37 SupraMarginal_R 63 -45 33 
38 Precuneus_L -10 -78 50 
39 Precentral_R 38 -18 66 
40 Pallidum_R 24 -7 -5 
41 Thalamus_R 20 -31 9 
42 Postcentral_R 35 -45 67 
43 Frontal_Inf_Orb_L -46 37 -13 
44 Temporal_Pole_Mid_R 34 20 -42 
45 Cerebelum_8_R 39 -65 -56 
46 SupraMarginal_L -59 -29 39 
47 Cingulum_Ant_L -10 45 10 
220 
 
48 Parietal_Inf_R 34 -51 42 
49 Caudate_Head_L -11 12 4 
50 Lingual_L -19 -76 -9 
51 Supp_Motor_Area_L -12 -10 73 
52 Cerebelum_Crus2_L -34 -78 -44 
53 Precentral_R 24 -4 50 
54 Insula_R 36 20 1 
55 Postcentral_R 40 -22 43 
56 Cerebelum_8_L -31 -63 -59 
57 Temporal_Inf_R 63 -47 -18 
58 Cuneus_L -13 -69 25 
59 Occipital_Mid_R 39 -82 30 
60 Temporal_Inf_L -55 -15 -37 
61 Insula_L -35 -7 11 
62 Thalamus_R 3 -14 7 
63 Cerebelum_6_R 27 -62 -31 
64 Temporal_Mid_R 51 -32 -3 
65 Cingulum_Mid_L -12 -37 50 
66 Temporal_Inf_R 56 -13 -38 
67 Frontal_Mid_L -45 23 36 
68 Frontal_Mid_R 47 27 37 
69 Frontal_Mid_L -28 21 48 
70 Cuneus_R 16 -100 12 
71 Temporal_Inf_L -39 -23 -27 
72 Frontal_Sup_R 15 47 43 
73 Cerebelum_Crus2_L -13 -80 -49 
74 Cingulum_Post_L 0 -43 27 
75 Fusiform_L -34 -11 -43 
76 Postcentral_L -38 -24 42 
77 Occipital_Mid_R 35 -89 8 
78 Frontal_Sup_Orb_L -8 40 -29 
79 Frontal_Mid_L -31 39 28 
80 Precentral_L -47 0 49 
81 Fusiform_R 24 3 -47 
82 Cingulum_Mid_R 2 6 35 
83 Frontal_Sup_Medial_R 10 60 25 
84 Temporal_Inf_R 42 -3 -47 
85 Lingual_L -16 -59 1 
86 Occipital_Mid_L -28 -96 -2 
87 Precentral_R 50 0 50 
88 Calcarine_L -8 -99 -11 
89 Frontal_Mid_L -26 -3 54 
90 Frontal_Mid_Orb_R 33 57 -14 
91 Frontal_Sup_L -16 58 26 
92 Angular_R 55 -66 32 
221 
 
93 Precentral_R 16 -17 73 
94 Cerebelum_Crus2_L -46 -51 -47 
95 Parietal_Sup_L -32 -50 65 
96 Cerebelum_Crus2_R 33 -84 -37 
97 Cerebelum_8_R 17 -76 -52 
98 Temporal_Mid_R 65 -53 7 
99 Cingulum_Mid_L 0 -18 33 
100 Cerebelum_8_L -21 -44 -52 
101 Temporal_Mid_L -61 -55 10 
102 Temporal_Pole_Mid_R 51 11 -32 
103 Temporal_Inf_L -46 5 -39 
104 Frontal_Sup_R 14 30 57 
105 Thalamus_L -16 -31 9 
106 Postcentral_L -57 -7 28 
107 Frontal_Mid_R 42 50 4 
108 Frontal_Mid_L -33 54 7 
109 Temporal_Sup_R 63 -8 6 
110 ParaHippocampal_R 19 -12 -26 
111 Lingual_R 21 -74 -11 
112 Cingulum_Ant_R 2 27 21 
113 Vermis_9 1 -55 -41 
114 Temporal_Mid_L -64 -24 -16 
115 Postcentral_R 58 -25 49 
116 Insula_L -33 20 2 
117 Caudate_R 16 -7 20 
118 Angular_L -48 -74 29 
119 Frontal_Mid_Orb_L -25 34 -17 
120 Postcentral_R 60 -2 29 
121 Olfactory 0 0 -13 
122 Occipital_Mid_L -30 -87 23 
123 Fusiform_R 37 -18 -33 
124 Frontal_Sup_Medial_L -11 66 5 
125 Temporal_Mid_R 50 -75 8 
126 Vermis_4_5 2 -49 6 
127 SupraMarginal_R 65 -25 25 
128 Precentral_L -29 -25 67 
129 Insula_R 42 -7 -14 
130 Frontal_Sup_Medial_L -10 31 56 
131 Parietal_Sup_R 18 -63 65 
132 Temporal_Inf_L -53 -61 -11 
133 Occipital_Inf_R 41 -86 -14 
134 Frontal_Sup_Medial_R 10 67 -1 
135 Temporal_Sup_L -42 -17 -7 
136 Vermis_6 0 -64 -20 
137 Occipital_Sup_R 15 -89 33 
222 
 
138 Frontal_Med_Orb_R 0 35 -10 
139 Supp_Motor_Area_L -11 11 65 
140 Parietal_Inf_R 53 -47 54 
141 Frontal_Mid_R 33 47 26 
142 Cerebelum_8_R 32 -41 -46 
143 Fusiform_L -28 -44 -12 
144 Cerebelum_9_L -7 -61 -57 
145 Precuneus_L 0 -57 45 
146 Temporal_Pole_Sup_R 55 11 -6 
147 SupraMarginal_L -58 -50 32 
148 Rolandic_Oper_L -56 1 2 
149 Cerebelum_Crus2_L -14 -87 -30 
150 Vermis_1_2 -2 -43 -23 
151 Supp_Motor_Area_L -2 -11 54 
152 Angular_R 40 -69 51 
153 Temporal_Mid_R 46 -53 17 
154 Fusiform_R 44 -43 -24 
155 Cerebelum_8_R 19 -55 -58 
156 Precuneus_L -12 -46 73 
157 Parietal_Inf_L -49 -54 51 
158 ParaHippocampal_L -18 -14 -28 
159 Temporal_Pole_Sup_L -42 13 -20 
160 Cerebelum_3_R 15 -32 -39 
161 Frontal_Mid_R 25 28 38 
162 Occipital_Mid_L -46 -80 4 
163 Postcentral_L -48 -26 58 
164 Frontal_Inf_Oper_R 40 9 29 
165 Midbrain 0 -24 -12 
166 Precentral_L -37 6 29 
167 Rolandic_Oper_L -40 -33 17 
168 RectalGyrus    3 19 -26 
169 Parietal_Inf_L -32 -51 41 
170 Frontal_Inf_Oper_L -52 18 13 
171 Occipital_Sup_L -10 -101 12 
172 Frontal_Inf_Orb_R 28 34 -17 
173 Frontal_Sup_R 27 62 9 
174 Cerebelum_6_L -26 -62 -30 
175 Fusiform_R 26 -38 -13 
176 Rolandic_Oper_R 43 -27 17 
177 Paracentral_Lobule_L -4 -29 72 
178 Temporal_Inf_R 51 -64 -11 
179 Temporal_Mid_L -42 -58 15 
180 Temporal_Inf_L -52 -42 -26 
181 Fusiform_L -38 -83 -18 
182 Cerebelum_Crus2_R 51 -50 -44 
223 
 
183 Parietal_Inf_L -33 -75 48 
184 Parietal_Sup_R 16 -76 52 
185 Temporal_Pole_Sup_R 28 10 -25 
186 Cerebelum_Crus2_R 11 -86 -31 
187 Temporal_Mid_L -58 -39 -5 
188 Rectus_L -9 60 -17 
189 Cingulum_Ant_R 13 44 6 
190 Frontal_Inf_Oper_R 57 16 16 
 
A.3 Description of Behavioral Measures Employed in This Work 
Table A2. Description of categorized behavioral measures employed in this work 
(For more details, please refer to HCP Q3 release manual 
(http://humanconnectome.org/documentation/Q3/Q3_Release_Reference_Manual.pdf).) 
Category: Alertness 
Variable Name Description Values 
Instrument: Cognitive Status (Mini Mental Status Exam/MMSE)  
 
1. MMSE Score       Mini Mental Status Exam Total Score  
 
  Instrument: Sleep (Pittsburgh Sleep Questionnaire/PSQI) 
2. PSQI Score  Sleep (Pittsburgh Sleep Questionnaire) Total Score  
 
Category: Cognition 
Variable Name Description Values 
  Instrument: Episodic Memory (Picture Sequence Memory) 
3. Picture Sequence 
Unadjusted  
NIH Toolbox Picture Sequence Memory 
Test Unadjusted Scale Score  
 
4. Picture Sequence 
Adjusted  
NIH Toolbox Picture Sequence Memory 
Test Age-Adjusted Scale Score  
 
  Instrument: Executive Function/Cognitive Flexibility (Dimensional Change Card Sort) 
5. Card Sort 
Unadjusted  
NIH Toolbox Dimensional Change Card  
Sort Test Unadjusted Scale Score  
 
6. Card Sort 
Adjusted  
NIH Toolbox Dimensional Change Card  
Sort Test Age-Adjusted Scale Score  
 
  Instrument: Executive Function/Inhibition (Flanker Task) 
7. Flanker Task 
Unadjusted  
NIH Toolbox Flanker Inhibitory Control 
and Attention Test Unadjusted Scale Score  
 
8. Flanker Task 
Adjusted  
NIH Toolbox Flanker Inhibitory Control 
and Attention Test Adjusted Scale Score  
 
  Instrument: Fluid Intelligence (Penn Progressive Matrices) 
9. PMAT24_A_CR  Penn Matrix Test: Number of Correct 
Responses  
0-24 
 
10. PMAT24_A_SI  Penn Matrix Test: Total Skipped Items 
(items not presented because maximum 
errors allowed reached)  
0-19 
 
11. PMAT24_A_RTCR  Penn Matrix Test: Median Reaction Time 
for Correct Responses  
Typical range: 
2730?51730  
 
224 
 
  Instrument: Language/Reading Decoding (Oral Reading Recognition) 
12. Reading Test 
Unadjusted  
NIH Toolbox Oral Reading Recognition  
Test Unadjusted Scale Score  
 
13. Reading Test 
Adjusted  
NIH Toolbox Oral Reading Recognition  
Test Adjusted Scale Score  
 
  Instrument: Language/Receptive vocabulary 
14. Picture Vocabulary 
Test Unadjusted  
NIH Toolbox Picture Vocabulary  
Test Unadjusted Scale Score  
 
15. Picture Vocabulary 
Test Adjusted  
NIH Toolbox Picture Vocabulary  
Test Adjusted Scale Score 
 
  Instrument: Processing Speed (Pattern Completion Processing Speed) 
16. Processing Speed 
Unadjusted  
NIH Toolbox Pattern Comparison Processing Speed  
Test Unadjusted Scale Score  
 
17. Processing Speed 
Adjusted  
NIH Toolbox Pattern Comparison Processing Speed  
Test Adjusted Scale Score  
 
  Instrument: Self-regulation/Impulsivity (Delay Discounting) 
18. SV_1mo_200  Subjective Value for $200 at 1 month  0-200  
 
19. SV_6mo_200  Subjective Value for $200 at 6 months  0-200  
 
20. SV_3yr_200  Subjective Value for $200 at 3 years  0-200  
 
21. SV_1yr_200  Subjective Value for $200 at 1 year  0-200  
 
22. SV_5yr_200  Subjective Value for $200 at 5 years  0-200  
 
23. SV_10yr_200  Subjective Value for $200 at 10 years  0-200  
 
24. SV_1mo_40K  Subjective Value for $40,000 at 1 month  0-40000  
 
25. SV_6mo_40K  Subjective Value for $40,000 at 6 months  0-40000  
 
26. SV_1yr_40K  Subjective Value for $40,000 at 1 year  0-40000  
 
27. SV_3yr_40K  Subjective Value for $40,000 at 3 years  0-40000  
 
28. SV_5yr_40K  Subjective Value for $40,000 at 5 years  0-40000  
 
29. SV_10yr_40K  Subjective Value for $40,000 at 10 years  0-40000  
 
30. AUC_200  Area Under the Curve for Discounting of $200  0.0-1.0  
 
31. AUC_40K  Area Under the Curve for Discounting of 
$40,000  
0.0-1.0  
 
  Instrument: Spatial Orientation (Variable Short Penn Line Orientation Test) 
32. VSPLOT_TC  Penn Line Orientation: Total Number Correct  0-24  
 
33. VSPLOT_CRTE  Penn Line Orientation: Median Reaction 
Time Divided by Expected Number of Clicks 
for Correct Trials  
Typical range: 
640?2800  
 
34. VSPLOT_OFF  Penn Line Orientation: Total Positions Off for All 
Trials  
0-165  
 
  Instrument: Sustained Attention (Short Penn Continuous Performance Test) 
35. SCPT_TP  Short Penn CPT True Positives = Sum of 
CPN_TP and CPL_TP  
0-60  
 
36. SCPT_TN  Short Penn CPT True Negatives = Sum of 
CPN_TN and CPL_TPN  
0-120  
 
37. SCPT_FP  Short Penn CPT False Positives = Sum of 
CPN_FP and CPL_FP  
0-120  
 
225 
 
38. SCPT_FN  Short Penn CPT False Negatives = Sum of 
CPN_FN and CPL_FN  
0-60  
 
39. SCPT_TPRT  Short Penn CPT Median Response Time for 
True Positive Responses  
0-1000 ms  
 
40. SCPT_SEN  Short Penn CPT Sensitivity = 
SCPT_TP/(SCPT_TP + SCPT_FN)  
Typical range: 0.8-
1.0  
 
41. SCPT_SPEC  Short Penn CPT Specificity = 
SCPT_TN/(SCPT_TN + SCPT_FP)  
Typical range: 0.8-
1.0  
 
42. CPT_LRNR  Short Penn CPT Longest Run of Non-
Responses)  
5-16  
 
  Instrument: Verbal Episodic Memory (Penn Word Memory Test) 
43. IWRD_TOT  Penn Word Memory: Total Number of Correct 
Responses  
0-40  
 
44. IWRD_RTC  Penn Word Memory: Median 
Reaction Time for Correct 
Responses  
Typical range: 1100-
3200  
 
  Instrument: Working Memory (List Sorting) 
45. List Sorting 
Unadjusted  
NIH Toolbox List Sorting Working Memory  
Test Unadjusted Scale Score  
 
46. List Sorting 
Adjusted  
NIH Toolbox List Sorting Working Memory  
Test Adjusted Scale Score  
 
Category: Emotion 
Variable Name Description Values 
  Instrument: Emotion Recognition (Penn Emotion Recognition Test) 
47. ER40_CR  Penn Emotion Recognition: Number of Correct 
Responses  
0-40  
 
48. ER40_CRT  Penn Emotion Recognition: Correct 
Responses Median Response Time (ms)  
Typical range: 
1435-2746  
 
49. ER40ANG  Penn Emotion Recognition: Correct Anger 
Identifications  
0-8  
 
50. ER40FEAR  Penn Emotion Recognition: Correct Fear 
Identifications  
0-8  
 
51. ER40HAP  Penn Emotion Recognition: Correct Happy 
Identifications  
0-8  
 
52. ER40NOE  Penn Emotion Recognition: Correct Neutral 
Identifications  
0-8  
 
53. ER40SAD  Penn Emotion Recognition: Correct Sad 
Identifications  
0-8  
 
  Instrument: Negative Affect 
54. Anger-Affect  NIH Toolbox Anger-Affect Survey  
 
55. Anger-Hostility  NIH Toolbox Anger-Hostility Survey  
 
56. Anger-Aggression  NIH Toolbox Anger-Physical Aggression Survey  
 
57. Fear-Affect  NIH Toolbox Fear-Affect Survey  
 
58. Fear-Somatic  NIH Toolbox Fear-Somatic Arousal Survey  
 
59. Sadness  NIH Toolbox Sadness Survey  
 
226 
 
  Instrument: Psychological Well-being 
60. Life Satisfaction  NIH Toolbox General Life Satisfaction Survey  
 
61. Meaning and Purpose  NIH Toolbox Meaning and Purpose Survey  
 
62. Positive Affect  NIH Toolbox Positive Affect Survey  
 
  Instrument: Social Relationships 
63. Friendship  NIH Toolbox Friendship Survey  
 
64. Loneliness  NIH Toolbox Loneliness Survey  
 
65. Perceived Hostility  NIH Toolbox Perceived Hostility Survey  
 
66. Perceived Rejection  NIH Toolbox Perceived Rejection Survey  
 
67. Emotional Support  NIH Toolbox Emotional Support Survey  
 
68. Instrumental Support  NIH Toolbox Instrumental Support Survey  
 
  Instrument: Stress and Self Efficacy 
69. Perceived Stress  NIH Toolbox Perceived Stress Survey  
 
70. Self-Efficacy  NIH Toolbox Self-Efficacy Survey  
 
Category: Personality 
Variable Name Description Values 
  Instrument: Five-Factor Model (NEO-FFI) 
71. NEOFAC_A  NEO-FFI Agreeableness  Typical range: 19-44  
 
72. NEOFAC_O  NEO-FFI Openness  14-42  
 
73. NEOFAC_C  NEO-FFI Conscientiousness  23-46  
 
74. NEOFAC_N  NEO-FFI Neuroticism  4-36  
 
75. NEOFAC_E  NEO-FFI Extroversion  11-45  
 
 
A.4 Paths with Most and Least MTSTs 
227 
 
 
Figure A1 Paths with top and bottom 0.5% MTSTs. The red paths represent interregional 
MTSTs whose values are among the top 0.5% of all MTSTs, and blue paths represent 
interregional MTSTs whose values are among the bottom 0.5% of all MTSTs. The MTSTs 
mentioned here have been averaged over all runs. 
 
228 
 
 
Figure A2 Paths with top and bottom 1% MTSTs. The red paths represent interregional 
MTSTs whose values are among the top 1% of all MTSTs, and blue paths represent interregional 
MTSTs whose values are among the bottom 1% of all MTSTs. The MTSTs mentioned here have 
been averaged over all runs. 
 
A.5 Regions with Top and Bottom 20% rMTST and rCFP 
Rectus.R 
229 
 
   
(A)                                                         (B) 
   
(C)                                                      (D) 
Figure A3 Regions with top and bottom 20% rMTST and rCFP. Each brain region has 189 
paths associated with it and hence the same number of MTSTs and CFPs. We define metrics, 
regional MTST (rMTST) and regional CFP (rCFP), by finding the mean MTST/CFP of all paths 
associated with a given region. Regions within top 20% of all rMTSTs are shown in (A) and 
within bottom 20% of all rMTSTs are shown in (B).Corresponding maps for top and bottom 20% 
rCFPs are shown in (C) and (D), respectively. Hot colormap is used to represent the numeric 
value of corresponding metric for each region shown. (A: anterior, P: posterior, S: superior, I: 
inferior, L: left, R: right) 
 
Compared with Fig.4.8 in main text, there are fewer regions highlighted in Fig.A3. It is 
noteworthy that some important resting state networks are even missing, like visual network in 
Fig.4.8 (A) in main text and so do some important regions like anterior cingulate cortex (ACC) 
  
 
S S 
L P R A 
A 
L R 
P 
I I 
  
 
S S 
L P R A 
A 
L R 
P 
I I 
  
 
S S 
L P R A 
A 
L R 
P 
I I 
  
 
S S 
L P R A 
A 
L R 
P 
I I 
230 
 
in Fig.4.8 (A) and posterior cingulate cortex (PCC) in (C) in main text. This implies that with 
proportions of only top and bottom 20%, Fig.A3 is not as informative as Fig.4.8, missing some 
important regional information. On the other hand, if more than 30% of rMTSTs and rCFPs are 
shown, the amount of regions will be too numerous for any meaningful visualization. Thus we 
choose to illustrate top and bottom 30% of rMTSTs and rCFPs in Fig.4.8 of the main text. 
A.6 Paths with MTSTs Significantly Correlating with Selected Behavioral Measures 
 (A) Episodic memory (picture sequence unadjusted) 
231 
 
 
(B) Fluid intelligence (PMAT24_A_CR) 
 
(C) Fluid intelligence (PMAT24_A_SI) 
232 
 
 
(D) Self-regulation/impulsivity (AUC_200) 
 
233 
 
(E) Sustained attention (SCPT_TP) 
 (F) Sustained attention (SCPT_FN) 
234 
 
  
(G) Sustained attention (SCPT_SEN)  
 
235 
 
(H) Sustained attention (SCPT_SPEC) 
 
(I) Sustained attention (CPT_LRNR) 
Figure A4 Paths with MTSTs significantly predicting variability in selected behavioral 
measures. The predictive ability is quantified by regression coefficient ? for each MTST in the 
GLM shown in Eq.4.3 of the Methods section in the main text. The coefficient ? is passed 
through a z-test and Bonferroni corrected for multiple comparisons (corrected 
p=0.05/75=0.00067, where 0.05 is uncorrected p value, and 75 is number of behavioral tests). In 
each subfigure, cobalt blue paths have negative ? values, and red paths have positive ? values. 
The behavior tests for subfigures are: (A) episodic memory (picture sequence test, unadjusted). 
(B) Fluid intelligence (PMAT24_A_CR). (C) Fluid intelligence (PMAT24_A_SI). (D) Self-
regulation/impulsivity (AUC_200). (E) Sustained attention (SCPT_TP). (F) Sustained attention 
(SCPT_FN). (G) Sustained attention (SCPT_SEN). (H) Sustained attention (SCPT_SPEC). (I) 
Sustained attention (CPT_LRNR). 
 
A.7 Schematic of Distance Measure Calculation in Second Level Clustering   
236 
 
 
Figure A5 A schematic of distance measure calculation in second level clustering. The 
schematic starts with any two first level clustering configurations at different time points as 
shown on the upper left corner. Red arrows indicate the direction of the procedure. (R1,?, R8 
denote  region#1 to region#8, and C1, C2, C3 denote cluster#1, cluster#2, and cluster#3) 
 
A.8 An Illustrative Example of the Calculation of Metrics: MTST, SDTST, CFP. 
237 
 
 
Figure A6 An illustrative example of the calculation of three metrics: MTST, SDTST, CFP. 
The first level clustering result leads to a series of state transitions for every pair of regions 
between clustered and unclustered states. Specifically, two regions either belong to the same 
cluster (connected, clustered state) or different clusters (disconnected, un-clustered state), and 
switch between these two states, as reflected in the black-and-white bar with ?Yes? and ?No? 
indicating whether they are clustered or not. Then the three metrics: MTST, SDTST, CFP are 
calculated as in corresponding boxes. Note the fourth metric: SFC is widely known and thus not 
illustrated here. 
  
238 
 
Appendix B 
 
Table B1. AAL labels, MNI co-ordinates, and statistical summary of DEC and SEC paths 
associated of the CC200 regions having at least one path connected  
Variance of DEC, healthy controls<PTSD 
AAL name of region 
centroids 
MNI coordinates of 
centroid  
x     y     z 
Inflow 
degree 
Outflow 
degree 
Sum of 
connecting paths? 
weights 
Cerebelum_8_R 18.95  -55.38  -57.68 3 1 4.090 
Pons -2.59  -25.20  -37.88 2 0 2.327 
Precentral_L -46.96  0.03  48.80 0 1 1.323 
Supp_Motor_Area_L -1.54  -10.90  53.54 0 1 1.055 
Cinglulum_Post_L 0.40  -42.74  7.41 0 1 1.024 
Precentral_R 37.56  -18.39  65.54 0 1 1.007 
Variance of DEC, healthy controls>PTSD 
Cerebelum_Crus2_R 51.31  -50.19  -44.12 10 0 11.524 
Temporal_Mid_R* 
70.74  -30.26  -1.79 
65.09  -53.34  7.39 
50.35  -74.53  7.56 
0 4 5.999 
Postcentral_R 14.95  -43.44  74.55 34.70  -44.88  66.60 3 1 4.850 
Precentral_R 37.56  -18.39  65.54 16.09  -17.07  72.69 3 0 4.712 
Frontal_Mid_R 
34.76  14.33  56.50 
47.11  26.56  37.07 
42.05  50  3.54 
1 3 4.504 
Lingual_L -16.00  -59.48  0.57 2 2 4.402 
Cerebelum_Crus2_L -34.43  -78.48  -44.10 -45.96  -51.08  -46.94 1 2 3.844 
Fusiform_R 43.93  -42.84  -24.22 3 0 3.664 
Temporal_Inf_L -52.45  -42.24  -26.11 0 2 3.233 
Postcentral_L -47.64  -26.20  58.17 2 0 2.753 
Cingulum_Mid_L -11.88  -37.10  50.28 0 2 2.750 
Parietal_Inf_R 52.80  -47.15  54.41 0 2 2.639 
Cerebelum_6_R 27.25  -61.78  -30.95 0 2 2.450 
Parietal_Inf_L -49.33 -54.47 51.09 2 0 2.377 
Frontal_Sup_L -12.54  45.79  42.41 -15.71  58.38  25.89 0 2 2.282 
Fusiform_L -28.28  -43.98  -12.04 0 2 2.037 
Precuneus_L -10.08  -77.95  50.04 -11.90  -46.47  73.35 1 1 1.970 
Precuneus_R 17.96  -65.15  24.97 1 1 1.965 
Brainstem 1.60  -42.77  -60.82 0 1 1.556 
239 
 
Temporal_Mid_L -41.72  -58.20  15.26 0 1 1.431 
ParaHippocampal_L -18.26  -13.95  -28.16 0 1 1.355 
Cerebelum_8_R 32.05  -40.52  -45.65 1 0 1.353 
Insula_R 38.0   -5.77  9.15 0 1 1.349 
Temporal_Inf_R 63.34  -47.21  -17.55 0 1 1.334 
Paracentral_Lobule_L -3.72  -29.33  71.68 1 0 1.312 
Angular_L -47.75  -73.73  28.59 0 1 1.023 
Temporal_Sup_L -42.28  -17.34  -6.55 0 1 1.021 
Calcarine_R 1.01  -79.9  5.81 1 0 0.997 
Precentral_L -46.96  0.03  48.80 1 0 0.995 
Rolandic_Oper_L -55.53  0.62  1.72 0 1 0.994 
SEC, healthy controls<PTSD 
Caudate_R 14.71  13.69  1.91 15.97  -6.95  19.68 0 10 14.536 
Frontal_Mid_R 42.05   50   3.54 25.30  28.13  38.15 10 0 12.111 
Temporal_Inf_R 62.82  -27.60  -26.10 63.34  -47.21  -17.55 0 7 10.799 
Thalamus_R 19.64  -30.83  8.98 2.58  -14.49  6.76 0 6 9.019 
Postcentral_R 34.70  -44.88  66.60 39.87  -22.35  43.17 5 0 8.003 
Temporal_Inf_L 
-39.13  -22.77  -27.44 
-52.85 -60.85 -11.17 
-52.45 -42.24 -26.11 
1 5 7.938 
Insula_R 38.08  -5.77  9.15 3 0 4.548 
Frontal_Inf_Oper_R 56.83  16.15  15.70 1 2 4.346 
Rolandic_Oper_R 42.75  -26.59  17.49 3 0 4.257 
SupraMarginal_R 64.52  -25.08  24.80 3 0 3.969 
Thalamus_L -16.41  -30.63  8.50 0 3 3.875 
Temporal_Mid_R 46.27  -53.41  16.87 2 0 3.521 
Parietal_Inf_L -49.33  -54.47  51.09 -33.183  -74.54  48.03 2 0 3.482 
Cingulum_Ant_R 2.14  26.57  21.06 0 2 2.943 
Postcentral_L -37.63  -24.31  42.38 2 0 2.877 
Frontal_Inf_Orb_L -46.14  36.88  -12.56 0 2 2.730 
Fusiform_R 26.47  -37.83  -13.28 0 2 2.520 
Insula_L -35.12  -7.20  11.28 2 0 2.437 
Cerebelum_6_L -29.18  -38.20  -34.81 -25.93  -61.76  -30.25 1 1 2.411 
Temporal_Mid_L -57.99  -39.32  -5.05 1 0 1.738 
Cerebelum_Crus1_L -47.83  -66.58  -32.01 1 0 1.719 
Precentral_L -28.74  -24.84  67.26 1 0 1.438 
Cerebelum_Crus2_R 10.93  -86.19  -31.32 1 0 1.346 
Supp_Motor_Area_R 14.86  7.67  67.07 1 0 1.292 
240 
 
Temporal_Sup_L -61.82  -25.83  12.92 1 0 1.283 
Frontal_Inf_Tri_R 49.15  35.12  14.47 1 0 1.260 
Frontal_Inf_Tri_L -44.94  37.29  10.94 1 0 1.253 
Occipital_Sup_R 15.33  -88.55  33.41 1 0 1.230 
Temporal_Pole_Sup_L -42.34  12.70  -19.94 0 1 1.210 
ParaHippocampal_R 19.36  -12.39  -25.52 0 1 1.206 
Cerebelum_8_L -31.00  -62.73  -58.85 0 1 1.197 
Precuneus_L -12.80  -64.47  64.14 0 1 1.193 
Lingual_R 21.29  -74.31  -11.23 1 0 1.186 
Cerebelum_6_R 27.25  -61.78  -30.95 0 1 1.185 
SEC, healthy controls>PTSD 
Temporal_Inf_L -52.45  -42.24  -26.11 2 0 2.677 
ParahippocampaGyrus -20.96  -26.24  -14.20 2 0 2.543 
Frontal_Mid_R 32.92  47.43  25.66 0 2 2.536 
Cerebelum_6_R 27.25  -61.78  -30.95 0 1 1.352 
Cerebelum_6_L -25.93  -61.76  -30.25 0 1 1.325 
Paracentral_Lobule_R 14.90  -35.03  48.29 0 1 1.245 
Fusiform_L -28.28  -43.98  -12.04 1 0 1.239 
 
Table B2. AAL labels, MNI co-ordinates, and statistical summary of DFC and SFC paths 
associated of the CC200 regions having at least one path connected 
Variance of DFC, healthy controls<PTSD 
AAL name of region 
centroids 
MNI coordinates of 
centroid  
x     y     z 
connectivity 
degree 
Sum of connecting 
paths? weights 
None 
Variance of DFC, healthy controls>PTSD 
Postcentral_L 
-37.63  -24.31  42.38 
-57.19  -7.03  27.78 
-47.64  -26.20  58.17 
7 18.733 
Caudate_R 15.97  -6.95  19.68 7 17.619 
Frontal_Mid_L 
-45.47  22.97  35.66 
-31.43  39.14  28.32 
-26.41  -3.30  54.27 
-32.82  53.61  6.90 
6 15.912 
Precentral_L -46.96  0.03  48.80 -28.74  -24.84  67.26 6 14.701 
Vermis_1.2 -1.59  -42.74  -22.95 4 10.470 
Occipital_Mid_R 34.59  -89.14  8.39 4 10.391 
Temporal_Inf_R 63.34  -47.21  -17.55 55.82  -12.56  -37.76 4 9.321 
Putamen_L -24.75  -4.85  -7.63 3 8.699 
Frontal_Sup_R 14.36  29.64  56.74 27.43  61.62  8.53 3 7.716 
Cerebelum_Crus2_L -34.43  -78.48  -44.10 3 7.213 
241 
 
Rectus_L -8.66  60.41  -17.42 2 6.238 
SupraMarginal_L -59.12  -28.81  38.92 2 6.013 
Cerebelum_Crus2_R 10.93  -86.19  -31.32 2 5.879 
Occipital_Mid_L -28.43  -96.04  -2.15 -45.62  -80.15  4.03 2 5.843 
Cerebelum_6_L -25.93  -61.76  -30.25 2 5.724 
Parietal_Inf_R 34.32  -50.54  42.06 2 5.417 
Cerebelum_8_L -21.37  -43.64  -52.50 2 5.289 
Fusiform_L -34.50  -10.84  -43.47 2 5.118 
Parietal_Inf_L -49.33  -54.47  51.09 2 5.022 
Fusiform_R 26.47  -37.83  -13.28 2 4.729 
SupraMarginal_R 64.52  -25.08  24.80 2 4.718 
Caudate_L -14.24  -7.50  18.68 2 4.525 
Temporal_Sup_L -61.82  -25.83  12.92 1 3.287 
Paracentral_Lobule_L -3.72  -29.33  71.68 1 3.008 
Temporal_Pole_Sup_R 28.48  9.58  -25.46 1 2.808 
Insula_R 42.49  -6.88  -13.98 1 2.803 
Pallidum_R 23.97  -7.16  -5.32 1 2.718 
Frontal_Mid_R 47.11  26.56  37.07 1 2.710 
Frontal_Mid_Orb_R 33.15  56.72  -14.39 1 2.702 
Cerebelum_8_R 32.05  -40.52  -45.65 1 2.636 
Insula_L -35.12  -7.20  11.28 1 2.479 
Occipital_Inf_R 41.00  -85.82  -14.07 1 2.473 
Temporal_Pole_Sup_L -42.34  12.70  -19.94 1 2.445 
Vermis_6 0.42  -63.99  -19.92 1 2.430 
Cerebelum_Crus1_L -47.83  -66.58  -32.01 1 2.347 
Precentral_R 49.75  -0.38  49.78 1 2.329 
Postcentral_R 39.87  -22.35  43.17 1 2.304 
Frontal_Sup_Medial_R 10.33  60.23  24.68 1 2.244 
Calcarine_L -8.37  -99.02  -11.19 1 2.217 
SFC, healthy controls<PTSD 
Vermis_1.2 -1.59  -42.74  -22.95 9 18.765 
Brainstem 1.60  -42.77  -60.82 10 17.705 
Lingual_L -18.66  -75.95  -8.83 -16.00  -59.48  0.57 7 12.652 
Lingual_R 
21.80  -58.16  0.46 
19.34  -98.75  -9.67 
21.29  -74.31  -11.23 
6 12.160 
Midbrain 0.05  -23.79  -11.82 5 10.420 
Vermis_9 1.42  -54.85  -40.97 5 9.719 
Parietal_Inf_L -49.33  -54.47  51.09 -31.61  -51.45  41.04 4 8.182 
SupraMarginal_R 62.81  -45.26  33.38 4 7.266 
Vermis_6 0.42  -63.99  -19.92 4 6.919 
SupraMarginal_L -58.22  -50.21  31.77 4 6.906 
242 
 
Postcentral_L -37.63  -24.31  42.38 -47.64  -26.20  58.17 4 6.825 
Calcarine_R 3.01  -79.95  6.81 4 6.762 
Fusiform_R 26.47  -37.83  -13.28 3 6.202 
Occipital_Mid_L -28.43  -96.04  -2.15 -30.29  -87.38  23.13 3 6.023 
Fusiform_L -28.28  -43.98  -12.04 2 4.428 
Temporal_Mid_R 50.35  -74.53  7.56 2 4.338 
Temporal_Pole_Sup_L -42.34  12.70  -19.94 2 4.104 
Temporal_Inf_R 55.82  -12.56  -37.76 42.46  -2.63  -47.00 2 3.828 
Cerebelum_6_R 27.25  -61.78  -30.95 2 3.738 
Precuneus_R 17.96  -65.15  24.97 2 3.621 
Precentral_R 37.56  -18.39  65.54 49.75  -0.38  49.78 2 3.604 
Precentral_L -28.74  -24.84  67.26 2 3.203 
Temporal_Pole_Sup_R 28.48  9.58  -25.46 1 2.853 
Cerebelum_9_L -7.22  -60.78  -57.42 1 2.390 
Cuneus_R 16.20  -99.93  12.08 1 2.026 
ParahippocampaGyrus -20.96  -26.24  -14.20 1 2.013 
Frontal_Mid_L -32.82  53.61  6.90 1 2.011 
Occipital_Sup_R 15.33  -88.55  33.41 1 1.991 
Angular_R 39.76  -69.40  51.04 1 1.965 
Cingulum_Mid_L 0.35  -18.33  32.96 1 1.806 
Insula_R 42.49  -6.88  -13.98 1 1.657 
Cuneus_L -13.14  -68.67  24.72 1 1.654 
Cerebelum_6_L -25.93  -61.76  -30.25 1 1.637 
Occipital_Mid_R 38.64  -82.44  29.50 1 1.572 
SFC, healthy controls>PTSD 
None 
 
*: When more than one centroid is indicated for a given AAL regions, it means that multiple 
CC200 regions are associated with the same AAL label. Since CC200 regions are functionally 
homogeneous and AAL labels can span a large anatomical region, it is to be expected that 
multiple CC200 regions would be associated with a single AAL label.