Development of Test Protocols for Analysis of Low Back Exertions in Standing
Position
by
Varun Vinod Soman
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
Requirements for the Degree of
Master of Science
Auburn, Alabama
August 4, 2012
Keywords: Stability, Variability, Range of Motion, Approximate Entropy, Correlation
Dimension
Copyright 2012 by Varun Soman
Approved by
P. K. Raju, Thomas Walter Distinguished Professor of Mechanical Engineering
M. Ram Gudavalli, Associate Professor, Palmer College of Chiropractic, IA
Jeffrey Suhling, Quina Distinguished Professor of Mechanical Engineering
Dan Marghitu, Professor of Mechanical Engineering
i
ABSTRACT
More than 80 percent of people suffer from low back pain at some point in their
lifetime costing losses of up to $9 billion because of treatment and loss of work hours in
the US alone. Kinematics and kinetics of body movements can be affected by low back
pain and may result in spinal instability.
The aim of this study was to develop testing procedure to quantify stability of the
spine during low back motion using both traditional and non-linear methods in standing
position. The objective was to quantify movements that are performed repetitively in
flexion - extension (FE), lateral bending (LB), and rotation (ROT) of the trunk using
traditional and non-linear methods. The study was approved by Institutional Review
Boards (IRB) of Auburn University, AL as well as Palmer College of Chiropractic, IA.
Nine healthy test subjects were recruited for the study using word of mouth and screened
for eligibility by licensed clinicians. Participants were asked to perform 10 cycles of
flexion - extension, lateral bending and rotation motion against no resistance, 5 lb, 10 lb
and 15 lb resistance. Motion data was recorded at a frequency of 120 Hz for each
exertion and for each resistance. Range of Motion (ROM) and non-linear techniques
(Correlation Dimension (CoD), Approximate Entropy (ApEn)) were employed to analyze
the motion data. EMG data was recorded at a frequency of 1200 Hz from six muscle
groups: Erector Spinae, Multifidus, Latissimus Dorsi, Internal Obliques, External
ii
Obliques and Rectus Abdominis. Mean and median frequency of the recorded signals
were analyzed to see the effect of increasing load on muscle fatigue.
The ROM values varied from 7.5 ? 40.2 Deg. For FE, 9.06 ? 44.6 Deg. for LB
and 6.68 ? 21.3 Deg. for ROT, the ApEn values ranged from 0.133 ? 0.40 while the CoD
values ranged from 1.79 ? 2.47. The overall results indicated that variability did not
change significantly with increasing loads. The EMG results indicated that fatigue was
not induced in participant?s muscles which might have helped them provide required
neuromuscular response to increasing loads. However it is important to keep in mind that
the main objective of the thesis was development of test protocol for analysis of low back
motion. The test protocol developed herein needs to be further fine tuned before it can be
applied for larger studies. Testing method for data recording during rotations needs
improvement as there might be inaccuracy involved due to skin motion altering the
position of sensors. Also, once the protocol is perfected, further testing needs to be
carried out on a larger sample size so that the results can be generalized. Future studies
need to consider the following recommendations for obtaining more meaningful data
based on healthy subjects. 1) Increase the resistance to motion so that higher fatigue is
induced in the participant. 2) Ask the participant to perform the exertions at two different
fixed speeds. 3) To minimize the effect of skin stretching during rotation, a plastic plate
can be attached to the skin before motion sensors are attached. Once the data base on
healthy subjects is obtained, studies on low back pain subjects can be undertaken.
iii
ACKNOWLEDGEMENT
I would like to express my deep gratitude to my academic advisor, Dr. P. K. Raju,
for providing me with the opportunity to work under him on this project. I would also
like to thank Dr. M. Ram Gudavalli for being a co-advisor and great mentor and guide
during my work at Palmer Center for Chiropractic Research, IA. Also, a special thank
you to Dr. Jeffrey Suhling and Dr. Dan Marghitu for all the help they have provided to
me during my study period at Auburn University. I would also like to specially mention
Dr. Xia Ting who provided valuable technical help during my work at Palmer Center for
Chiropractic Research, IA. I also appreciate the help provided by Ms. Kristen Billy in
editing the draft of the thesis.
I would like to thank my parents, Mr. Vinod P. Soman and Mrs. Vrunda V.
Soman, as well as my younger brother Vikram Soman, for having faith in me and
providing endearing love, encouragement and moral support. I would also like to thank
all my friends and colleagues for their priceless friendship and support.
Special thanks to Auburn University, National Institutes of Health (NIH) (Grant
numbers - 1U19AT004137-01) and National Center for Research Resources (Grant
Number - C06 RR15433-01) for providing financial support for the study.
iv
Table of Contents
Abstract ........................................................................................................................... i
Acknowledgement ......................................................................................................... iii
List of Tables................................................................................................................ vii
List of Figures ............................................................................................................. viii
List of Abbreviations ..................................................................................................... xi
1 Introduction ..................................................................................................................1
1.1 Low Back Pain (LBP) ? ........................................................................................1
1.2 Stability of Spine ....................................................................................................3
1.3 Variability...............................................................................................................4
1.4 Quantification of Variability ...................................................................................4
1.5 Nonlinear Methods to Quantify Variability .............................................................7
1.6 Objectives of the Study ....................................................................................... 10
2 Anatomy of Human Spine........................................................................................... 14
2.1 The Vertebral Column .......................................................................................... 14
2.1.1 Thoracic Vertebrae ...................................................................................... 16
2.1.2 Lumbar Vertebrae ....................................................................................... 17
2.2 Low Back Musculature ......................................................................................... 18
v
2.2.1 Erector Spinae ............................................................................................. 19
2.2.2 Multifidus ................................................................................................... 19
2.2.3 Latissimus Dorsi ......................................................................................... 19
2.2.4 Internal Obliques ......................................................................................... 20
2.2.5 External Obliques ........................................................................................ 21
2.2.6 Rectus Abdominis ....................................................................................... 21
3 Methods and Techniues Used ..................................................................................... 23
3.1 Experimental Protocol........................................................................................... 23
3.2 Sample Size .......................................................................................................... 25
3.3 Data Acquisition ................................................................................................... 26
3.4 Motion Data Analysis ........................................................................................... 29
3.4.1 Time series ................................................................................................... 29
3.4.2 Range of Motion (ROM) .............................................................................. 30
3.4.3 Classification of time series as periodic or chaotic ........................................ 32
3.4.4 Approximate Entropy (ApEn) ...................................................................... 33
3.4.5 Calculation of ApEn ..................................................................................... 35
3.4.6 Correlation Dimension (CoD) ...................................................................... 36
3.4.7 Phase Plane Plots ......................................................................................... 37
3.4.8 Standard Phase Space ................................................................................... 38
3.4.9 Pseudo Phase Space ..................................................................................... 39
vi
3.4.10 Time Lag .................................................................................................... 40
3.4.11 Embedding Dimension ............................................................................... 41
3.4.12 Measuring Correlation Dimension .............................................................. 42
3.5 EMG Data Analysis .............................................................................................. 50
3.5.1 Identifying muscle activation........................................................................ 50
3.5.2 Mean and Median Frequency of SEMG signals ............................................ 51
4 Results ........................................................................................................................ 52
4.1 ROM Results ........................................................................................................ 52
4.2 Phase Plane Plots .................................................................................................. 54
4.3 Fast Fourier Transformation (FFT)........................................................................ 56
4.4 Approximate Entropy (ApEn) Results ................................................................... 58
4.5 Correlation Dimension (CoD) Results ................................................................... 60
4.6 EMG Frequency Analysis Results ......................................................................... 63
4.6.1 Mean and Median Frequency during Flexion ? Extension motion ................ 64
4.6.2 Mean and Median Frequency during Lateral Bending motion ...................... 68
4.6.3 Mean and Median Frequency during Rotation motion ................................. 70
5 Discussion .................................................................................................................. 73
6 Conclusion.................................................................................................................. 80
References ..................................................................................................................... 81
Appendix ....................................................................................................................... 87
vii
List of Tables
Table 1 Demographics ............................................................................................ 25
Table 2 EMG sensor placement .............................................................................. 28
Table 3 One factor ANOVA test on ApEn results for FE ........................................ 54
Table 4 p-values for ROM results ........................................................................... 54
Table 5 One factor ANOVA test on ApEn results for FE ........................................ 60
Table 6 p-values for ApEn results ........................................................................... 60
Table 7 One factor ANOVA test on CoD results for FE .......................................... 62
Table 8 p-values for CoD results............................................................................. 62
Table 9 Muscle recruitment during FE, LB and ROT by number of participants. .... 63
Table 10 Mean values of Mean Frequencies with increasing loads during FE ......... 67
Table 11 Mean values of Median Frequencies with increasing loads during FE ...... 67
Table 12 Mean values for Mean Frequencies with increasing loads during LB........ 69
Table 13 Mean values for Median Frequencies with increasing loads during LB ..... 69
Table 14 Mean values of Mean Frequencies with increasing loads during ROT ...... 72
Table 15 Mean values of Median Frequencies with increasing loads during ROT ... 72
viii
List of Figures
Figure 1 The Human Spine (Uwe Gille, Wikipedia.com) ........................................................... 15
Figure 2 Thoracic Vertebra (Anatomist90, Wikipedia.com) ....................................................... 17
Figure 3 Lumbar Vertebra (Anatomist90, Wikipedia.com) ........................................................ 18
Figure 4 Abdominal Muscles (SEER Training Module) ............................................................. 20
Figure 5 SEMG and motion sensors attached to back muscles and vertebrae respectively .......... 26
Figure 6 SEMG sensors attached to abdominal muscles............................................................. 27
Figure 7 Sine Curve .................................................................................................................. 30
Figure 8 Time series for flexion-extension against 5 lb resistance .............................................. 30
Figure 9 FFT of a periodic sine curve ........................................................................................ 32
Figure 10 FFT of experimental motion data ............................................................................... 32
Figure 11 Example of standard phase space ............................................................................... 39
Figure 12 Pseudo phase space plot of experimental data ............................................................ 40
Figure 13 Identifying qualifying neighbors from (a) point 1 and (b) point 2 ............................... 43
Figure 14 Plot of Correlation Sum vs. Radius ............................................................................ 47
Figure 15 Sketch showing geometric increase in number of points within circle of radius ? for
uniformly spaced points (after Berg? et al. 1984: Fig. VL. 36). (a) One-dimensional attractor
(line). (b) Two-dimensional attractor (plane) ............................................................................. 48
Figure 16 Idealized plot of Correlation Sum vs. Radius for increasing Embedding Dimension ... 49
Figure 17 Muscle Recruitment for ES Left muscle during FE under 5 lb resistance .................... 50
Figure 18 ROM results for FE ................................................................................................... 52
Figure 19 ROM results for LB .................................................................................................. 53
ix
Figure 20 ROM results for ROT ................................................................................................ 53
Figure 21 Phase Plane plots for FE data against 0 lb, 5 lb, 10 lb and 15 lb respectively for
participant 1 (left to right; top to bottom)................................................................................... 55
Figure 22 Phase Plane plot of a perfectly periodic (sine wave) time series data .......................... 56
Figure 23 FFT for FE data against 0 lb, 5 lb, 10 lb and 15 lb respectively for participant 1 (left to
right; top to bottom) .................................................................................................................. 57
Figure 24 FFT of sine wave....................................................................................................... 58
Figure 25 ApEn results for FE ................................................................................................... 58
Figure 26 ApEn results for LB .................................................................................................. 59
Figure 27 ApEn results for ROT................................................................................................ 59
Figure 28 CoD results for FE .................................................................................................... 61
Figure 29 CoD results for LB .................................................................................................... 61
Figure 30 CoD results for ROT ................................................................................................. 61
Figure 31 ES Left ? Mean and Median Frequencies (Left and Right) ......................................... 64
Figure 32 ES Right - Mean and Median Frequencies (Left and Right) ....................................... 65
Figure 33 LD Left - Mean and Median Frequencies (Left and Right) ......................................... 65
Figure 34 LD Right - Mean and Median Frequencies (Left and Right) ....................................... 65
Figure 35 MF Left - Mean and Median Frequencies (Left and Right) ........................................ 66
Figure 36 MF Right - Mean and Median Frequencies (Left and Right) ...................................... 66
Figure 37 ES Right - Mean and Median Frequencies (Left and Right) ....................................... 68
Figure 38 EO Right - Mean and Median Frequencies (Left and Right) ....................................... 68
Figure 39 LD Right - Mean and Median Frequencies (Left and Right) ....................................... 68
Figure 40 MF Right - Mean and Median Frequencies (Left and Right) ...................................... 69
Figure 41 ES Left - Mean and Median Frequencies (Left and Right) ......................................... 70
Figure 42 ES Right - Mean and Median Frequencies (Left and Right) ....................................... 70
Figure 43 LD Left - Mean and Median Frequencies (Left and Right) ......................................... 70
x
Figure 44 LD Right - Mean and Median Frequencies (Left and Right) ....................................... 71
Figure 45 MF Left - Mean and Median Frequencies (Left and Right) ........................................ 71
Figure 46 MF Right - Mean and Median Frequencies (Left and Right) ...................................... 71
Figure 47 ROM, ApEn and CoD results for participant 1 during LB .......................................... 75
Figure 48 Mean and Median Frequency results for ES Left muscle for participant 3 during
ROT ......................................................................................................................................... 76
Figure 49 Mean and Median Frequency results for ES Right muscle for participant 3 during
ROT ......................................................................................................................................... 77
Figure 50 User Report Options .................................................................................................. 94
Figure 51 Orthopedic Angle Selection ....................................................................................... 94
Figure 52 Forceplate Data ......................................................................................................... 95
Figure 53 EMG Data 1 .............................................................................................................. 95
Figure 54 EMG Data 2 .............................................................................................................. 96
Figure 55 EMG Data 3 .............................................................................................................. 96
xi
List of Abbreviations
ROM ? Range of Motion
ApEn ? Approximate Entropy
CoD ? Correlation Dimension
SEMG ? Surface Electromyography
FE ? Flexion Extension
LB ? Lateral Bending
ROT ? Rotation
ES ? Erector Spinae
MF ? Multifidus
LD ? Latissimus Dorsi
IO ? Internal Obliques
EO ? External Obliques
RA ? Rectus Abdominis
1
CHAPTER 1
INTRODUCTION
1.1 Low Back Pain (LBP) ?
LBP is the second most common cause of disability in US adults (Centers for
Disease Control and Prevention) and a common reason for lost work days (Stewart W.F.,
2003). When persons of all ages are considered, back pain was the second leading cause
for absenteeism in the United States, accounting for approximately 25 percent of all lost
workdays in 2009 (Devereaux M., 2009). The condition is also costly, with total costs
estimated to be between $100 and $200 billion annually in 2006, two-thirds of which are
because of decreased wages and productivity (Katz J. N., 2006). More than 80 percent of
the population will experience an episode of LBP at some time during their lives (Rubin
D. I., 2007). For most, the clinical course is benign, with 95 percent of those afflicted
recovering within a few months of onset (Carey T. S. et. al, 1995). Some however, will
not recover and will develop chronic LBP (i.e., pain that lasts for 3 months or longer).
Recurrences of LBP are also common, with the percentage of subsequent LBP episodes
ranging from 20 percent to 44 percent within 1 year for working populations to lifetime
2
recurrences of up to 85 percent (van Tulder M., 2002). The use of health care services for
chronic LBP has increased substantially over the past two decades. Multiple studies using
national and insurance claims data have identified greater use of spinal injections (Weiner
D. K., 2006). Surgery (Deyo R. A., 2005) and opioid medications (Luo X, 2004) ?
treatments most likely to be used by individuals with chronic LBP. Studies have also
documented increases in medication prescription and visits to physicians, physical
therapists, and chiropractors (Feuerstein M, 2004). Because individuals with chronic LBP
are more likely to seek care (IJzelenberg W, 2004) and to use more health care services
(Carey T. S. et. al., 1995), relative to individuals with acute LBP, increases in health care
use are likely driven more by chronic than by acute cases. Increased health care use for
chronic LBP could be a function of (1) increased prevalence of chronic LBP; (2)
increased proportion of those with chronic LBP who seek care; (3) increased use by those
who seek care, or (4) some combination of these factors (Thorpe K. E. et. al., 2004). The
documented increase in use of services is often assumed to be because of increased health
care seeking or use by those who seek care.
A large number of studies have focused on chronic LBP, but they have not
revealed a complete understanding of this condition (Bergman, S. 2007). In order to
apprehend this condition, researchers are now focusing on the effect of LBP on trunk
movements. Kinematic and kinetic quantities are assumed to be periodic or pseudo
periodic based on body characteristics and personal ability to control the lumbar spine.
With neuromuscular and musculoskeletal pathologies or injuries, these movements may
not be periodic and may result in increased instability of the lumbar spine (Papadakis,
N.C. et. al., 2009).
3
1.2 Stability of Spine -
Local dynamic stability of the spine is defined as the sensitivity of the system to
small perturbations, such as the natural stride to stride variations present during
locomotion. A study done by Manohar Panjabi explains the factors responsible for
stability and normal functioning of the spine. The vertebrae, discs, and ligaments
constitute the passive subsystem. All muscles and tendons surrounding the spinal column
that can apply forces to the spinal column constitute the active subsystem. The nerves
and central nervous system comprise the neural subsystem, which determines the
requirements for spinal stability by monitoring the various transducer signals, and
directs the active subsystem to provide the needed stability. A dysfunction of a
component of any one of the subsystems may lead to one or more of the following three
possibilities: (a) an immediate response from other subsystems to successfully
compensate, (b) a long-term adaptation response of one or more subsystems, and (c) an
injury to one or more components of any subsystem. It is conceptualized that the first
response results in normal function, the second results in normal function (but with an
altered spinal stabilizing system) and the third leads to overall system dysfunction,
producing, for example, low back pain (LBP). In situations where additional loads or
complex postures are anticipated, the neural control unit may alter the muscle
recruitment strategy, with the temporary goal of enhancing the spine stability beyond
the normal requirements (Panjabi M. M.).
4
1.3 Variability ?
Variation, as mentioned in the definition of stability, is inherent within all
biological systems and can be characterized as the normal changes that occur in motor
performance across multiple repetitions of tasks. For example, a man performs similar
repetitive movement while rowing a boat. But, his hands do not follow exactly the same
trajectory each and every time. For various reasons, there is some change in trajectory
every time. This change in trajectory is known as variation. Until recently, variability was
interpreted as the result of random processes (Leon Glass, ?From Clocks to Chaos: The
Rhythms of Life?). However, recent literature from a number of scientific domains has
shown that many phenomena previously described as noisy are actually the result of non
linear interactions and have a deterministic origin (Gleick, J. 1987. Chaos: Making a new
Science, Amato, I. 1992. Chaos breaks out at NIH, but order may come of it). Thus, one
can get important information regarding the system?s behavior by examining the ?noisy?
component of the measured signal.
1.4 Quantification of Variability ?
In the past years a lot of effort has gone into correctly quantifying the variability
in various biological systems. The magnitude of the variability is the measure of stability
of that biological system. There are numerous methods and quantities for representing
variability. The variability in kinematic, kinetic, and temporal variables can be computed
using both traditional and non-traditional approaches. Traditional methods originate from
descriptive statistics, while non-traditional methods are those that use techniques from the
5
study of non-linear dynamical systems to isolate chaotically deterministic variability from
other variability components contained within the movement process.
The traditional methods include range, variance, standard deviation (SD), etc.
These methods are known as discrete methods. Range is simply the difference between
the greatest and the least values and is computed by subtracting the least value from the
greatest value. Variance is a measure of variability that uses the sum of the squared
deviations between the individual values and the sample mean divided by the
approximate degrees of freedom for the sample, while SD is merely square root of
variance. Although variance and SD are computed similarly, variance is used less often in
variability studies because units of variance are squared, making the interpretation of
variability somewhat harder than that of SD ( Fitzgerald, G.K. et. al., 1983).
Collectively, the discrete methods provide a thorough description of the
variability of the discrete variables across multiple performance trials. A literature survey
shows that hundreds of studies have been conducted where these discrete methods have
been applied in the analysis of various human physiological phenomena, such as human
gait and heart rate analysis. Let us take a look at some of the recent studies done related
to human lumbar spine motion and gait analysis. In 2008, Hsu et. al. measured the range
of motion (ROM) of the spine in healthy individuals by using an electromagnetic tracking
device to evaluate the functional performance of the spine. The authors used the Flock of
Birds electromagnetic tracking device with four receiver units attached to C-7, T-12, S-1,
and the mid-thigh region. Forward/backward bending, bilateral side bending, and axial
rotation of the trunk were performed in 18 healthy individuals. The average ROM was
calculated after three consecutive measurements. The results showed that the thoracic
6
spine generated the greatest angle in axial rotation and smallest angle in backward
bending. The lumbar spine generated the greatest angle in forward bending and smallest
angle in axial rotation. The hip joints generated the greatest angle in forward bending and
smallest angle in backward bending. Additionally, 40 percent of forward-bending motion
occurred in the lumbar spine and 40 percent occurred in the hip joints. Approximately 60
percent of backward bending occurred in the lumbar spine; 60 percent of axial rotation
occurred in the thoracic spine; and 45 percent of side bending occurred in the thoracic
spine (Chien-Jen Hsu et. al., 2008)
In 2010, Shrawan Kumar studied the muscle activation in combined rotation and
flexion of the torso in varying degree of asymmetries of the trunk. Nineteen normal
young subjects (seven males and 12 females) were stabilized on a posture-stabilizing
platform and instructed to assume a ?exed and right rotated posture. A combination 20
degrees, 40 degrees and 60 degrees of rotation, and 20 degrees, 40 degrees and 60
degrees of ?exion resulted in nine postures. These postures were assumed in a random
order. The subjects were asked to exert their maximal voluntary isometric contraction
(MVC) in the plane of rotation of the posture assumed for a period of five seconds. The
surface EMG from the external and internal obliques, rectus abdominis, latissimus dorsi
and erector spinae at the 10th thoracic and third lumbar vertebral levels was recorded.
The abdominal muscles had the least response, at 40 degrees of ?exion; the dorsal
muscles had the highest magnitude.
With increasing right rotation, the left external oblique continued to decrease its
activity. The ANOVA revealed that rotation and muscles had a significant main effect on
normalized peak EMG (p < 0.02) in both genders. There was a significant interaction
7
between rotation and ?exion in both genders (p < 0.02) and rotation and muscle in
females. The erector spinae activity was highest at 40 degrees ?exion, because of greater
mechanical disadvantage and having not reached the state of ?exion?relaxation. The
abdominal muscle activity declined with increasing asymmetry, because of the
decreasing initial muscle length. The EMG activity was significantly more affected by
rotation than by ?exion (p < 0.02) (Shrawan Kumar, 2010).
In 2010, Desai et. al. conducted a study in which they applied discrete methods to
analyze variability in trunk muscle activation and other physiological parameters for
subjects with and without LBP. The group with LBP and the control group each had 10
participants. Bilateral trunk muscle activity was measured using surface
electromyography (EMG); whole body balance was measured by quantifying the
dispersion of the centre of pressure (CoP); lumbar range of motion (LROM) was
measured with single-axis inclinometers. Individuals with LBP had adaptive recruitment
patterns during the side-bridge and modified push-up exercises. CoP dispersion and
LROM were not different between the groups for any exercise. The labile surface did not
change the difference between groups, and only increased muscle activity during the
side-bridge (p < 0.05). The labile surface increased LROM (p = 0.35) and CoP dispersion
(p < 0.001) during the quadruped, decreased LROM during squats (p = 0.05), and
increased CoP dispersion during push-ups (p = 0.04) (Imtiaz Desai, 2010).
1.5 Nonlinear Methods to Quantify Variability ?
Traditionally, physicians in the medical field use linear models for prediction and
problem solving. However, biological systems, including those of humans, are complex
8
adaptive systems, characterized by multiple interconnected and interdependent parts
(Harbourne, R.T. et. al., 2009). These are highly non-linear systems with inherent
variability in all healthy organisms. There is growing understanding that linear models
are limited in many cases and are certainly not the best models for understanding the
nonlinear human system (Stergiou, N. 2004). Professionals in different medical fields,
such as biomechanics, epidemiology, etc., are now turning to nonlinear tools for solving
such complex systems. Some of these nonlinear methods are Lyapunov Exponents,
Approximate Entropy, and Correlation Dimension. Lyapunov Exponent calculates the
rate at which adjacent trajectories converge or diverge in reconstructed state space.
Approximate Entropy calculates the predictability of a given time series. Correlation
dimension is used to quantify chaos in a given time series. Detailed explanation of these
non-linear methods has been provided in Chapter 3.
In 2006, Granata and England used non-linear tools to estimate control of
dynamic stability during repetitive flexion and extension movements of the lumbar spine.
There were 20 healthy subjects who performed repetitive trunk flexion and extension
movements at 20 and 40 cycles per minute. Maximum lyapunov exponents describing the
expansion of the kinematic state-space were calculated from the measured trunk
kinematics to estimate stability of the dynamic system.
Repeated trajectories from fast paced movements diverged more quickly than
slower movement, indicating that local dynamic stability is limited in fast movements.
Movements in the mid-sagittal plane showed higher multi-dimensional kinematic
divergence than asymmetric movements. Non-linear dynamic systems analyses were
successfully applied to empirically measured data (Kevin P. Granata et. al., 2006).
9
The local dynamic stability of trunk movements was assessed by Graham et. al. in
2011 during repetitive lifting using non-linear Lyapunov analysis. The goal was to assess
how varying the load-in-hands affects the neuromuscular control of lumbar spinal
stability. Thirty healthy participants (15M, 15F) performed repetitive lifting at 10 cycles
per minute for three minutes under two load conditions: zero load and 10 percent of each
participant?s maximum back strength. Short and long-term maximum finite-time
Lyapunov exponents, describing responses to infinitesimally small perturbations, were
calculated from the measured trunk kinematics to estimate the local dynamic stability of
the system.
The findings indicated improved dynamic spinal stability when lifting the heavier
load, meaning that as muscular and moment demands increased, so too did participants?
abilities to respond to local perturbations. These results support the notion of greater
spinal instability during movement with low loads because of decreased muscular
demand and trunk stiffness, and should aid in understanding how lifting various loads
contributes to occupational low back pain (Ryan B. Graham et. al., 2011).
In 2009, Kavanagh studied lower trunk motion and speed dependence during
walking. He used another nonlinear tool, Approximate Entropy, to do so. The primary
purpose of this study was to examine how gait speed influences a healthy individual's
lower trunk motion during over-ground walking. Thirteen healthy subjects (23 ? 3 years)
performed five straight-line walking trials at self-selected slow, preferred, and fast
walking speeds. Accelerations of the lower trunk were measured in the anterior-posterior
(AP), vertical (VT), and mediolateral (ML) directions using a triaxial accelerometer.
10
The results showed that the value of Approximate Entropy decreased as the
walking velocity increased. The main finding of this study was that walking at speeds
slower than preferred primarily alters lower trunk accelerations in the frontal plane.
Despite greater amplitudes of trunk acceleration at fast speeds, the lack of regularity and
repeatability differences between preferred and fast speeds suggested that features of
trunk motion are preserved between the same conditions (Justin J. Kavanagh, 2009).
Correlation Dimension is another non-linear parameter that can be used to study
the stability of a physiological system. In 2003, Buzzi et. al. investigated the nature of
variability present in a time series generated from gait parameters of two different age
groups via a non-linear analysis. Twenty females, 10 younger (20?37 years old) and 10
older (71?79 years old) walked on a treadmill for 30 consecutive gait cycles. Time series
from selected kinematic parameters of the right lower extremity were analyzed using
nonlinear dynamics. The largest Lyapunov exponent and the correlation dimension of all
the time series were calculated.
The elderly exhibited significantly larger Lyapunov exponents and correlation
dimensions for all parameters evaluated, indicating local instability. The non-linear
analysis revealed that fluctuations in the time series of certain gait parameters are not
random, but display a deterministic behavior (Ugo H. Buzzi, 2003).
1.6 Objectives of the Study ?
From the above illustration described in the previous section, we understand that
bio-mechanists and scientists are increasingly starting to employ non-linear analysis
methods to study dynamic behavior of various biological systems. But, despite the
11
advantages that non-linear tools offer, it also has certain limitations. Some of them are
mentioned below ?
1. Non-linear measurement techniques require mathematical equations and
software to evaluate time series data; as a result they must be carried out in a research
environment.
2. There is a lack of understanding of variability and complexity in most medical
fields.
3. Translation of non-linear measures to clinical problems requires concurrent use
of linear tools to make associations and determine clinical meaning.
4. Most of these measures require multiple repetitions or cycles of a movement
(Harbourne, R.T et. al., 2009).
Thus, even now the best option remains to study the biological systems using both
linear and non-linear methods given the advantages and disadvantages of both. Also, in
spite of all the work that has been done previously, plenty of scope for future research
remains to better understand the characteristics of biological systems.
In 2008, Lee et. al. studied the effects of trunk exertion force and direction on
postural control of the trunk during unstable sitting. Seat movements were recorded while
subjects maintained a seated posture on a wobbly chair against different exertion forces
(0N, 40N, and 80N) and exertion directions (trunk flexion and extension). Postural
control of the trunk was assessed from kinematic variability and non-linear stability
analyses (stability diffusion exponent and maximum finite-time Lyapunov exponent).
12
Kinematic variability and non-linear stability estimates increased as exertion force
increased. The study showed that trunk exertion force and exertion direction affect
postural control of the trunk (Hyun Wook Lee et. al. 2008).
In one of the previously mentioned studies, Hsu et. al. measured the range of
motion (ROM) of the spine in healthy individuals by using an electromagnetic tracking
device to evaluate the functional performance of the spine (Chien-Jen Hsu et. al., 2008).
Also, Granata and England used non-linear tools to estimate control of dynamic stability
during repetitive flexion and extension movements of lumbar spine (Kevin P. Granata et.
al., 2006). In 2005, Lamoth et. al. studied the effects of chronic low back pain on trunk
coordination and back muscle activity during walking. The study included 19 individuals
with non-specific LBP and 14 healthy controls. Gait kinematics and Erector Spinae (ES)
activity were recorded during treadmill walking at (1) a self-selected (comfortable)
velocity, and (2) sequentially increased velocities from 1.4 up to maximally 7.0 km/h.
The angular movements of the thorax, lumbar and pelvis were recorded in three
dimensions. ES activity was recorded with pairs of surface electrodes.
Rotational amplitudes were not significantly different between the LBP and
control participants. In the LBP participants, the pattern of ES activity was affected in
terms of increased (residual) variability, timing deficits, amplitude modifications and
frequency changes. The gait of the LBP participants was characterized by a more rigid
and less variable kinematic coordination in the transverse plane, and less tight and more
variable coordination in the frontal plane, accompanied by poorly coordinated activity of
the lumbar ES (Claudine J. C. Lamoth et. al., 2006).
13
During this literature survey, it was noticed that more research can be done in low
back motion and muscle recruitment pattern during the standing position. The effect of
increasing load resistance on various trunk motions such has flexion extension, lateral
bending and rotation has not yet been investigated. These types of motions are a common
occurrence in places such as gymnasiums of warehouses where heavy lifting is required.
We may get some valuable insight in characteristics of motion lumbar vertebrae and
recruitment of related muscles during these motions.
We have attempted to do this in this particular exercise. The objectives of this
study are ?
1. Develop a test procedure to measure and record data for lumbar motion and trunk
muscle recruitment.
2. Identify particular muscle groups recruited for specific types of low back motions.
3. Analysis of variability of motion and strength generation of low back muscles
using traditional discrete and non-linear techniques.
4. Try and suggest the most suitable method to analyze and study these motions.
14
CHAPTER 2
ANATOMY OF HUMAN SPINE
2.1 The Vertebral Column ?
The human spine is composed of 26 individual bony masses, 24 of those are
bones called vertebrae. The vertebrae are stacked one on top of the other and form the
main part of the spine running from the base of the skull to the pelvis. At the base of the
spine, there is a bony plate called the sacrum which is made of five fused vertebrae. The
sacrum forms the back part of the pelvis. At the bottom of the sacrum is a small set of
four partly fused vertebrae, the coccyx or tailbone. Adding the fused and partly fused
bones of the sacrum and coccyx to the 24 vertebrae, the spine has 33 bones all together.
The spine is labeled in three sections: the cervical spine, the thoracic spine and the
lumbar spine. Starting from the top, there are seven cervical vertebrae, 12 thoracic
vertebrae, and five lumbar vertebrae.
15
The spinal vertebrae are separated from each other by intervertebral discs. These
discs are made of collagen fibers and cartilage. They provide padding and shock
absorption for the vertebrae. Each pair of vertebrae creates a movable unit.
The spinal cord runs within the vertebral canal formed by the back parts of the
vertebrae. Thirty-one pairs of nerves branch out from the spinal cord through the
vertebrae, carrying messages between the brain and every part of the body.
Aging, diseases, accidents and muscular imbalances can cause compression and
thinning of the intervertebral discs. This results in pressure on the spinal nerves and wear
on the bony vertebrae, and these conditions are common sources of back pain.
Figure 1 The Human Spine (Uwe Gille, Wikipedia.com)
16
There are four natural curves in the spine. We usually speak in terms of the three
that comprise the cervical, thoracic, and lumbar portions of the spine; but, as you can see,
the sacrum and coccyx form a curved section as well.
The spinal curves provide architectural strength and support of the spine. They
distribute the vertical pressure on the spine, and balance the weight of the body. If the
spine were absolutely straight, it would be more likely to buckle under the pressure of the
weight of the body.
When all the natural curves of the spine are present, the spine is a neutral position.
This is its strongest position and usually the safest to exercise in. When we have perfect
posture the curves of the spine are helping us balance. We are meant to walk and stand in
the neutral spine position (Marguerite Ogle, About.com).
2.1.1 Thoracic Vertebrae ?
In vertebrates, thoracic vertebrae compose the middle segment of the vertebral
column, between the cervical vertebrae and the lumbar vertebrae. In humans, they are
intermediate in size between those of the cervical and lumbar regions; they increase in
size as one proceeds down the spine, the upper vertebrae being much smaller than those
in the lower part of the region. They are distinguished by the presence of facets on the
sides of the bodies for articulation with the heads of the ribs, and facets on the transverse
processes of all, except the 11th and 12th, for articulation with the tubercles of the ribs.
The cervical vertebrae run into the cranium.
17
Figure 2 Thoracic Vertebra (Anatomist90, Wikipedia.com)
First thoracic vertebra ?
The first thoracic vertebra has, on either side of the body, an entire articular facet
for the head of the first rib, and a demi-facet for the upper half of the head of the second
rib. The body is like that of a cervical vertebra, being broad, concave, and lipped on
either side. The superior articular surfaces are directed upward and backward; the spinous
process is thick, long, and almost horizontal. The transverse processes are long, and the
upper vertebral notches are deeper than those of the other thoracic vertebrae. The thoracic
spinal nerve 1 (T1) passes out underneath it (Anatomist90, Wikipedia.com).
2.1.2 Lumbar Vertebrae ?
The lumbar vertebrae are the largest segments of the movable part of the vertebral
column, and are characterized by the absence of the foramen transversarium within the
18
transverse process, and by the absence of facets on the sides of the body. They are
designated L1 to L5, starting at the top.
Each lumbar vertebra consists of a vertebral body and a vertebral arch. The
vertebral arch, consisting of a pair of pedicles and a pair of laminae, encloses the
vertebral foramen (opening) and supports seven processes (Wikipedia.com).
Figure 3 Lumbar Vertebra (Anatomist90, Wikipedia.com)
2.2 Low Back Musculature ?
In this study, six muscle groups have been used to collect Electromyography
(EMG) data. Let us take a look at the muscle groups and their location in the human
body.
19
2.2.1 Erector Spinae ?
A deep muscle of the back; it arises from a tendon attached to the crest along the
centre of the sacrum (the part of the backbone at the level of the pelvis, formed of five
vertebrae fused together). When it reaches the level of the small of the back, the erector
divides into three columns, each of which has three parts. The muscle system extends the
length of the back and functions to straighten the back and to rotate it to one side or the
other (Britannica.com)
2.2.2 Multifidus ?
The multifidus muscle consists of a number of fleshy and tendinous fasciculi,
which fill up the groove on either side of the spinous processes of the vertebrae, from the
sacrum to the axis. The multifidus is a very thin muscle. Deep in the spine, it spans three
joint segments, and works to stabilize the joints at each segmental level. The stiffness and
stability makes each vertebra work more effectively, and reduces the degeneration of the
joint structures (Wikipedia.com).
2.2.3 Latissimus Dorsi ?
The latissimus dorsi, meaning 'broadest muscle of the back' (Latin latus meaning
'broad', latissimus meaning 'broadest' and dorsum meaning the back), is the larger, flat,
dorso-lateral muscle on the trunk, posterior to the arm, and partly covered by the
trapezius on its median dorsal region.
20
The latissimus dorsi is responsible for extension, adduction, transverse extension
(also known as horizontal abduction), flexion (from an extended position), and (medial)
internal rotation of the shoulder joint. It also has a synergistic role in extension and lateral
flexion of the lumbar spine (Wikipedia.com).
2.2.4 Internal Obliques ?
The internal oblique muscle (of the abdomen) is the intermediate muscle of the
abdomen, lying just underneath the external oblique and just above (superficial to) the
transverse abdominal muscle.
Its fibers run perpendicular to the external oblique muscle, beginning in the
thoracolumbar fascia of the lower back, the anterior two-thirds of the iliac crest (upper
part of hip bone) and the lateral half of the inguinal ligament. The muscle fibers run from
these points superiomedially (up and towards midline) to the muscle's insertions on the
inferior borders of the 10th through the 12th ribs and the linea alba (abdominal midline
seam).
Figure 4 Abdominal Muscles (SEER Training Module)
21
2.2.5 External Obliques ?
The external oblique muscle (of the abdomen) (also external abdominal oblique
muscle) is the largest and the most superficial (outermost) of the three flat muscles of the
lateral anterior abdomen. The external oblique is situated on the lateral and anterior parts
of the abdomen. It is broad, thin, and irregularly quadrilateral, its muscular portion
occupying the side, its aponeurosis the anterior wall of the abdomen. In most humans
(especially females), the oblique is not visible, due to subcutaneous fat deposits and the
small size of the muscle.
The external oblique functions to pull the chest downwards and compress the
abdominal cavity, which increases the intra-abdominal pressure as in a valsalva
maneuver. It also has limited actions in both flexion and rotation of the vertebral column.
One side of the obliques contracting can create lateral flexion. It also contributes to
compression of abdomen.
2.2.6 Rectus Abdominis ?
The rectus abdominis muscle, also known as the "six pack" is a paired muscle
running vertically on each side of the anterior wall of the human abdomen (and in some
other animals). There are two parallel muscles, separated by a midline band of connective
tissue called the linea alba (white line). It extends from the pubic symphysis/pubic crest
inferiorly to the xiphisternum/xiphoid process and lower costal cartilages (5?7)
superiorly.
22
The rectus abdominis is an important postural muscle. It is responsible for flexing
the lumbar spine, as when doing a "crunch" The rib cage is brought up to where the
pelvis is when the pelvis is fixed, or the pelvis can be brought towards the rib cage
(posterior pelvic tilt) when the rib cage is fixed, such as in a leg-hip raise. The two can
also be brought together simultaneously when neither is fixed in space.
In 2010, Shin et. al. used the lumbar erector spinae muscles to record data
during EMG activity analysis of low back extensor muscles during cyclic flexion-
extension (Shin et. al., 2010). The same muscle group was used by Mathieu et. al. in their
study of EMG and kinematic analysis of trunk flexion-extension in free space (Mathieu
et. al. 2000). Dickstein et. al. studied EMG activity of lumbar erector spinae (ES),
latissimus dorsi (LD), rectus abdominis (RA), and external oblique (EO) muscles in their
study of trunk flexion-extension of post-stroke hemiparetic subjects (Dickstein et. al.,
2004).
Ten channels of EMG data were collected from bipolar surface electrodes over
the right and left sides of the erector spinae, rectus abdomini, latissimus dorsi, external
abdominal obliques, and internal abdominal oblique muscles by Marras and Granata in
their study of spine loading during trunk lateral bending motion (Marras et. al., 1997).
Similarly, for trunk rotation Joseph K.-F Ng et. al. collected data from rectus
abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum and
multifidus muscles in their study of EMG activity of trunk muscles and torque output
during isometric axial rotation exertion (Joseph K.-F Ng, 2002).
In this study of ours, we are trying to see if meaningful data can be obtained from
the six muscle groups that we are studying under the given laboratory conditions.
23
CHAPTER 3
METHODS AND TECHNIQUES USED
3.1 Experimental Protocol ?
During the literature review it was noticed that there was still scope for analysis of
low back exertions in the standing position. Flexion-extension, lateral bending, and
rotation motions were selected because these are the motions that are repeated plenty of
times in day to day routines and hence can affect daily activities to a larger extent.
It was decided that data will be collected for the three motion types against no
load and resistances of 5 lbs., 10 lbs. and 15 lbs. to study the effect of increasing loads on
stability of low back spine. The participant performed flexion-extension, lateral bending
and rotation at no load at first. After the first set of data acquisition, the participant
repeated the same exercises against resistances of 5 lbs., 10 lbs. and 15 lbs. The weights
for resistance were attached to a rope which was passed over a pulley away from the
body of the participant. The participants performed 10 repetitions of each exercise with
the rope held close to their chest.
24
Approvals were obtained from Institutional Review Boards (IRB) of both Auburn
University (Protocol Number ? 09-344 M41001) and Palmer College of Chiropractic, IA
(IRB Assurance Number - 2008G116). Following the IRB approvals, the participants
were recruited through word of mouth. The following were the inclusion and exclusion
criteria for the participants:
Inclusion Criteria ?
1. Participant must be an adult (over 18 years old) and capable of reading and
understanding English language.
2. Participant should not have any musculoskeletal injury related to spine, hands or
legs in the past 12 months.
3. Participant should not have a pacemaker or any non-removable metal object on
them.
4. Participant should not experience any pain in the range of motion while
performing the motions mentioned in the testing protocol.
Exclusion Criteria ?
The participants were additionally screened for neurological or dermatitis-related
symptoms by certified clinicians before they performed the biomechanical tests. The
screening was based on questionnaires, physical tests and visual observation. If the
participants exhibited those symptoms they were excluded.
25
3.2 Sample Size ?
A biomedical study, to be successful, has to have a well-defined problem,
an appropriate population, and a reliable procedure and instruments, among other
resources. In addition to these, an adequate sample size is one of the most critical
parameters to be considered. It must be big enough that it does not waste resources on an
inconclusive study, and short enough that it can yield useful results in a timely manner.
Sample size is of the utmost importance in experiments involving human or animal
subjects for ethical issues. In an over-populated experiment, an unnecessary number of
participants are exposed to potentially hazardous tests, while under-populated studies
expose subjects to potentially hazardous tests without advancing the research knowledge
(Lenth, R.V. 2001).
Finally, the study must be of adequate size, which would be relative to the goal of
the study. The present study is a preliminary study, and time and cost are the main
constraints. Keeping this in mind, a sample size of ten subjects was considered adequate
for this study. 10 males subjects were recruited through word of mouth, though data was
only recorded from 9 participants as sensors could not be attached properly to one of the
participants. The demographics of the participants were as follows:
Age (yrs) Height (cm) Weight (kg)
Mean 43.22222 Mean 176.4444 Mean 76.68889
SD 17.41248 SD 11.04662 SD 10.1228
Table 1 Demographics
26
3.3 Data Acquisition ?
Two types of motion data were obtained for this study, motion data and EMG
data. The motion data was obtained using the Liberty 24/8 (Polhemus, Vermont, USA)
system. Motion data was recorded at 120 samples per second using motion sensors
attached to T1, L3, L5 and S1 vertebrae. A fourth order butterworth filter with low pass
frequency of 20 Hz was used to filter the motion data. The EMG data was recorded at
1200 samples per second using DELSYS Bagnoli - 12 Channel EMG System. The EMG
signals were amplified 1000 times and band passed between 20 Hz and 500 HZ (Lee et.
al., 2007; Okubo et. al, 2010). Frequencies less than 20 Hz eliminate noise due to wire
sway, whereas frequencies over 500 Hz eliminate noise due to surface contact between
the electrodes and the skin (M. B. I. Raez et. al., 2006). Motion Monitor 7.0 software
(Innovative Sports Training, Inc.) was used to collect both Motion and EMG data.
Figure 5 SEMG and motion sensors attached to back muscles and vertebrae respectively
27
Figure 6 SEMG sensors attached to abdominal muscles
SEMG sensor positions were initially marked using body markers. The skin was
then prepared using alcohol prep pads and skin abrasive. The skin was initially cleaned
using alcohol prep pads to remove any oil present on the surface of the skin. The skin was
then gently abraded using skin abrasive to remove any dead cells, which may affect EMG
signals, from the surface of the skin. The skin was cleaned again using alcohol prep pads
to remove any dead cell debris from the skin. The sEMG sensors were also cleaned using
alcohol prep pads to remove any dirt from their surfaces. The sensors were then attached
to the skin using double sided tape. As mentioned in the table above, EMG data was
obtained from 6 muscles, namely Multifidus, Erector Spinae, Latissimus Dorsi, Internal
Obliques, External Obliques and Rectus Abdominis. The locations for the placement of
sEMG sensors were determined based on previous studies. (Sridhar Poosapadi Arjunan
et. al., 2009; Rafael F Escamilla et. al., 2006).
The motion sensors were attached at T1, L3, L5 and S1 vertebrae. The locations
of these vertebrae were found using a palpation technique. The skin was cleaned using
alcohol prep pads to remove any oil present on the surface of the skin. The motion
sensors were attached to the skin using double-sided tape.
28
Table 2 EMG sensor placement
Once the sensors were attached the participant was asked to wear a harness and
anti-vibration gloves for safety. The participant was asked to hold the rope to which the
weight was attached close to the chest and then stand in an upright position with his feet
in a comfortable position. The chosen position of the feet was marked and was kept
constant throughout the data acquisition process. Once the data acquisition started, the
participants were asked to hold the neutral position for 2 seconds, then asked to perform
10 repetitions of the three exertions as described above, and then asked to hold the neutral
position for 2 seconds again before the data acquisition ended. The data was then
Muscle Side Amplifier
Ch. No.
(Sensor
No.)
A/D
Board
Channel
No.
Location
Erector
Spinae
Left 1 0 6 Over the largest muscle mass
found by palpation and 4 cm
from midline of the spine at
the third lumbar vertebrae.
Righ
t
2 0 7
Rectus
Abdominus
Left 3 0 8 3 cm from the midline of the
abdomen and 2 cm above the
umbilicus.
Righ
t
4 0 9
External
Oblique
Left 5 0 10 10 cm from the midline of the
abdomen and 4 cm above the
ilium at an angle of 45?.
Righ
t
6 0 11
Internal
Oblique
Left 7 0 12 4 cm above the ilium in the
lumbar triangle at an angle of
45?.
Righ
t
8 0 13
Multifidus Left 11 1 0 Bilaterally at the level of L5
and aligned parallel between
the line of the posterior-
superior iliac spine (PSIS) and
the interspinous space of L1
and L2.
Righ
t
12 1 1
Latissimus
Dorsi
Left 9 0 14 Positioned obliquely
(approximately 25? from
horizontal in the inferomedial
direction) 4 cm below the
inferior angle of the scapula.
Righ
t
10 0 15
29
exported from motion monitors using the preference file created (Appendix). The data
was exported twice, once for motion data and then for EMG data.
3.4 Motion Data Analysis ?
After exporting the data, the data was separated from Excel files to form
individual data files for FE, LB and ROT data for 0 lb, 5 lb, 10 lb and 15 lb respectively.
Data for the first and the last two seconds when the participant was stationary was
eliminated. Data analysis was carried out on these data files.
3.4.1 Time series ?
The motion data obtained is nothing but a time series. A time series is a collection
of observations made sequentially through time. Examples occur in a variety of fields
ranging from engineering to economics. Examples include daily stock market prices or
pressure readings from pressure gauges at some factories (Chatfield Chris, ?The Analysis
of Time Series: An Introduction?). The best way to see how a physical quantity changes
with time is to plot a graph.
30
Figure 7 Sine Curve
Figure 8 Time series for flexion-extension against 5 lb resistance
3.4.2 Range of Motion (ROM) ?
ROM tells us the limits between which a person can carry out a particular type of
exercise. The flexibility of the spine represents the functional performance of the trunk
31
mobility. For most spinal surgeries, spinal flexibility is regarded as an important part of
preoperative evaluation and postoperative functional outcome assessment (McGregor A.
H. et. al. 2004, Nissan M. et. al. 1999). Analysis of spinal ROM may improve our
understanding the severity of some spinal disorders, such as progression of ankylosing
spondylitis and the surgical effect of multiple-level discectomy or laminectomy. The
information derived from changes in spinal ROM is also useful in investigating the
development of adjacent-segment instability after fusion procedures (Chou WY et. al.
2002, Lu WW et. al. 1999).
In our study the ROM was studied for flexion-extension, lateral bending and
rotation motions. As mentioned before, the participants were asked to perform these three
exercises against no load and resistances of 5 lbs, 10 lbs and 15 lbs. The participants were
asked to move in their comfortable range of motion without exerting too much force on
their lower back muscles. The data was obtained as described previously and analyzed for
changes in ROM. A customized MATLAB program was used to study the ROM. The
time series data obtained after repetitive trunk FE, LB and ROT was plotted first. The
peaks and valleys of the plot were identified and the highest and lowest points were
selected. The difference between a successive highest and lowest point was ROM for that
particular movement cycle. The average of ROM of a particular time series data was the
average of all the ROM values of individual movement cycles.
32
3.4.3 Classification of time series as periodic or chaotic ?
The non-linear methods that we are going to apply calculate the chaos in a
dynamic system. Before we do this, we have to make sure that the system that we have is
indeed chaotic. This can be done using Fast Fourier Transformation (FFT) and Phase
Plane plots (L. F. P. Franca et. al. 2001). As is well known, the FFT of a chaotic signal
presents continuous spectra over a limited range and the energy is spread over a wider
bandwidth. On the other hand, FFT of a periodic signal presents discrete spectra, where a
finite number of frequencies contribute for the response (Mullin T. 1993, Moon F. C.
1992).
Figure 9 FFT of a periodic sine curve
Figure 10 FFT of experimental motion data
33
From the above FFT plots we can see that the experimental data contains
continuous spectra over a limited range, as opposed to FFT of the sine wave which
returns a single frequency. This is an indication that our data might be chaotic.
3.4.4 Approximate Entropy (ApEn) ?
Entropy is a statistical concept, which was first introduced by Shanon and Weaver
in 1963 as a measure of uncertainty or variability. Similarly, ApEn is a specific method to
determine complexity that can quantify the regularity or predictability of a time series
(Pincus, 1994). Predictability and regularity are inversely proportional to complexity. The
more predictable and regular the time series, the less would be the complexity, and vice
versa. Approximate Entropy measures the logarithmic probability that a series of data
points a certain distance apart will exhibit similar relative characteristics on the next
incremental comparison within the state space (Pincus, 1994). Data points that exhibit
greater possibilities of remaining the same distance apart upon comparison will result in
lower ApEn values, while those with large differences in distance between them will
result in higher ApEn values.
In order to mathematically define ApEn, we need to form a time series of data u
(1), u (2) ????. u (N). These are N raw data values from measurements taken at
equally spaced points in time. We then fix m, an integer, and r, a positive real number.
The input parameter m is the length of compared runs, and r is the tolerance that specifies
a filtering level. The first step is to form a sequence of vectors x(1), x(2)??.. x(N - m +
1) in Rm, real m-dimensional space, defined by x(i ) = [u(i)?.. u(I + m - 1)]. The second
step is to use the sequence x(1), x(2)?.. x(N - m + 1) to construct for each I, 1 ? i ? N - m
+ 1, Cim(r) = (number of x(j) such that d[x(i), x(j)]? r)/(N - m+1). We must define d[x(i),
34
x(j)] for vectors x(i) and x(j). We follow the Takens modification of formula by defining
d[x, x*] = max ?u(a) - u*(a)?, where the u(a) are the m scalar components of x. d
represents the distance between the vectors x(i) and x(j), given by the maximum
difference in their respective scalar components. Next we define ?m(r) = (N - m + 1)-1
?i=1N-m+1 In Cim(r), where In is natural logarithm. Lastly we define Approximate Entropy
as:
ApEn (m, r, N) = ?m(r) - ?m+1(r)
As seen above, calculation of ApEn requires selection of two parameters: m, the
number of observation windows to be compared, and r, the tolerance factor. In order to
compare the results, these parameters, along with the data length, must be kept the same
for all calculations (Pincus and Goldberger, 1994).
Typically m = 2 or 3; r depends greatly on the application (Pincus et. al, 1991).
This choice of m is made to ensure that the conditional probabilities, defined in the
equation below for fixed m and r, are reasonably estimated from the N input data points.
Theoretical calculations indicate that reasonable estimates of these probabilities, for fixed
m and r chosen as discussed below, are achieved with between 10m and 30m points,
analogous to findings of Wolf et al. (Pincus et. al, 1991).
The number of input points for ApEn computations ranges typically from 50 to
5,000 points (Stergiou, 2003; Pincus, 1994; Pincus et. al, 1991). Using fewer than 50 data
points yields less meaningful results, especially for m = 2 or 3, while using more than
5,000 points will result in unacceptably long computational time (Pincus et. al, 1991). For
noiseless, theoretically described systems, such as Henon maps and logistic maps, it has
been shown that if entropy (A) ? entropy (B), then ApEn (m, r) (A) ? ApEn (m, r) (B) and
35
vice versa. Moreover, for both theoretical and experimental systems, if ApEn (m1, r1) (A)
? ApEn (m1, r1) (B), then ApEn (m2, r2) (A) ? ApEn (m2, r2) (B) and vice versa. This
ability of ApEn to preserve the order is a relative property and is an important utility of
ApEn (Pincus et al, 1991). Considering this, one should not conclude that for the same
systems, ApEn (m1, r1) (A) ? ApEn (m2, r2) (B), as ApEn values differ with different m
and r values. The strength of ApEn is its ability to compare systems.
As explained above there are two critical parameters (m and r) that need to be set
in order to achieve reasonable results while using ApEn. Different m and r values would
result in different results. ApEn (2, 0.1) may be different form ApEn (3, 0.01) values.
This leads to the question of which one should be chosen. ?r? is effectively a filter level
and in order to eliminate the effect of noise in the ApEn calculation, ?r? must be chosen
such that its value is above most of the noise. In order to achieve reasonable results the
magnitude of noise should rarely reach ?r?.
Another key factor in choosing the value of r is that it should be large enough to
achieve numerically stable conditional probability estimates in equation (A) above
(Pincus et. al, 1991). If the ?r? value is small, one gets unstable conditional probability
estimates, while larger ?r? values result in detailed system information being lost due to
filter coarseness. In the current study a value of 2 was used for m and r was 0.2 (Pincus
1990; Pincus 1994; Stergiou, 2004).
3.4.5 Calculation of ApEn ?
Consider a time series SN, consisting of N number of sample size. To compute
ApEn we must choose two input parameters, m and r. We denote a pattern of m time
series, beginning at measurement i within SN, by the vector pm(i). Two patterns, pm(i) and
36
pm(j), are said to be similar if the difference between any pair of corresponding
measurements in the patterns is less than r ? i.e, if
|N(i+k)-N(j+k)|< r, for k=0 to m
Now consider the set Pm of all patterns of length m (i.e., pm(1),pm(2),? pm(N-
m+1)), within SN. So we may define Cim(r) = nim(r)/ (N-m+1) where nim(r) is the number
of patterns in Pm that are similar to pm(i)(provided similarity criterion ?r?). The quantity
Cm(r) is the fraction of length m that is identical to the pattern of the same length that
begins at interval i. We can calculate Cim(r) for each pattern in Pm, and we define Cm(r) as
the mean of these Cim(r) values. The quantity Cm(r) expresses the prevalence of repetitive
patterns of length m in SN. Finally, we define approximate entropy of SN, for patterns of
length m and similarity criterion r, as
ApEn(m,r)=In[Cm(r)/Cm+1(r)]
Thus, if we find similar patterns in a time series, ApEn estimates the logarithmic
likelihood that the next intervals after each of the patterns will differ.
3.4.6 Correlation Dimension (CoD) ?
The correlation dimension presently is the most popular measure of dimension.
It's much like the information dimension but is slightly more complex. The information
dimension usually is based on spreading a grid of uniformly sized compartments over the
trajectory like a quilt. That's like moving the measuring device over the object by equal,
incremental lengths. Analysis for the correlation dimension could also be done with that
approach. Instead, however, the usual technique is to center a compartment on each
successive datum point in turn, regardless of how many points a region has and how far
apart the points may be.
37
Many types of exponent dimension are essentially impossible to compute in
practice, either because they apply to some unattainable limit (such as ?? 0) or they are
computationally very inefficient. The correlation dimension avoids those problems. Also,
for a given dataset, it probes the attractor to a much finer scale than, say, the box-
counting dimension. Two data points that plot close together in phase space are highly
correlated spatially. (One value is a close estimate of the other.) However, depending on
the trajectory's route between them, those same two points can be totally unrelated with
regard to time. (The time associated with one point may be vastly and unpredictably
different from the time of the other.) The correlation dimension only tests points for their
spatial interrelations; it ignores time. (That's also true of the information dimension, but
for other reasons it acquired a different name) (Garnett P. Williams, 1997).
Before we go to the measuring procedure for the CoD, we need to understand
some basic concepts, namely Phase Space Plots, Time Delay and Embedding Dimension.
3.4.7 Phase Plane Plots ?
We'll begin by setting up the arena or playing field. One of the best ways to
understand a dynamical system is to make those dynamics visual. A good way to do that
is to draw a graph. Two popular kinds of graph show a system's dynamics. One is the
ordinary time-series graph that we've already discussed (Fig. 1.1). Usually, that's just a
two-dimensional plot of some variable (on the vertical axis, or ordinate) versus time (on
the horizontal axis, or abscissa).
Right now we're going to look at the other type of graph. It doesn't plot time
directly. The axis that normally represents time therefore can be used for some other
variable. In other words, the new graph involves more than one variable (besides time). A
38
point plotted on this alternate graph reflects the state or phase of the system at a particular
time (such as the phase of the Moon). The space on the new graph has a special name:
phase space or state space.
The phase space includes all the instantaneous states the system can have. As a
complement to the common time-series plot, a phase space plot provides a different view
of the evolution. Also, whereas some time series can be very long and therefore difficult
to show on a single graph, a phase space plot condenses all the data into a manageable
space on a graph.
Chaos theory deals with two types of phase space: standard phase space (my
term) and pseudo phase space. The two types differ in the number of independent
physical features they portray (e.g. temperature, wind velocity, humidity, etc.) and in
whether a plotted point represents values measured at the same time or at successive
times (Garnett P. Williams, 1997).
3.4.8 Standard Phase Space ?
Standard phase space (hereafter just called phase space) is the phase space defined
above: an abstract space in which coordinates represent the variables needed to specify
the state of a dynamical system at a particular time. On a graph, a plotted point neatly and
compactly defines the system's condition for some measuring occasion, as indicated by
the point's coordinates (values of the variables). For example, we might plot a baby's
height against its weight. Any plotted point represents the state of the baby (a dynamical
system!) at a particular time, in terms of height and weight. The next plotted point is the
same baby's height and weight at one time interval later, and so on. Thus, the succession
39
of plotted points shows how the baby grew over time. That is, comparing successive
points shows how height has changed relative to weight, over time, t.
Figure 11 Example of standard phase space
3.4.9 Pseudo Phase Space ?
Each axis on a standard phase space graph represents a different variable (e.g. Fig.
12). In contrast, our graph of the one-dimensional map plots two successive
measurements (xt+1 versus xt) of one measured feature, x. Because xt and xt+1 each have a
separate axis on the graph, chaosologists (those who study chaos) think of xt and xt+1 as
separate variables ("time-shifted variables") and of their associated plot as a type of phase
space. However, it's not a real phase space because the axes all represent the same feature
(e.g., stock price) rather than different features. Also, each plotted point represents
sequential measurements rather than a concurrent measurement. Hence, the graphical
space for a one-dimensional map is really a pseudo phase space. Pseudo phase space is an
imaginary graphical space in which the axes represent values of just one physical feature,
taken at different times (Garnett P. Williams, 1997).
40
Figure 12 Pseudo phase space plot of experimental data
3.4.10 Time Lag ?
To properly reconstruct a state space, it is essential to quantify an appropriate time
delay and embedding dimension for the investigated time series. Investigation of the
characteristics of the state space is a powerful tool for examining a dynamic system
because it provides information that is not apparent by just observing the time series
(Abarbanel, 1996; Baker and Gollub, 1996). To reconstruct the state space, a state vector
was created from the time series. This vector was composed of mutually exclusive
information about the dynamics of the system (Eq. (1)).
y(t) = [x(t), x(t-T1), x(t-T2)????] (1)
where y(t) was the reconstructed state vector, x(t) was the original data, and x(t ? Ti) was
time delay copies of x(t). The time delay (Ti) for creating the state vector was determined
by estimating when information about the state of the dynamic system at x(t) was
different from the information contained in its time-delayed copy. If the time delay was
41
too small then no additional information about the dynamics of the system would be
contained in the state vector. Conversely, if the time delay was too large then information
about the dynamics of the system may be lost, and this can result in random information
(Abarbanel, 1996; Baker and Gollub, 1996). Selection of the appropriate time delay was
performed by using an average mutual information algorithm (Eq. (2); Abarbanel, 1996).
Ix(t), x(t+T) = ? P(x(t), x(t+T))log2 (2)
where T was the time delay, x(t) was the original data, x(t + T) was the time delay data,
P(x(t), x(t + T)) was the joint probability for measurement of x(t) and x(t + T), P(x(t))
was the probability for measurement of x(t), and P(x(t + T)) was the probability for
measurement of x(t + T). The probabilities were constructed from the frequency of x(t)
occurring in the time series. Average mutual information was iteratively calculated for
various time delays and the selected time delay was at the first local minimum of the
iterative process (Abarbanel, 1996; Stergiou et al., 2004). This selection was based on
previous investigations that have determined that the time delay at the first local
minimum contains sufficient information about the dynamics of the system to reconstruct
the state vector (Abarbanel, 1996).
3.4.11 Embedding Dimension ?
Embedding dimension is the number of variables required to define a given
dynamic system. The minimum embedding dimension in the reconstruction producer was
estimated using an algorithm proposed by Kennel et al. (1992). The algorithm is based on
the idea that in the passage from dimension d to d + 1, one can differentiate between
points on the orbit that are true neighbors and those that are false. A false neighbor is a
point in the data set that is identified as a neighbor solely because of viewing the attractor
42
in an embedding space that is too small. When the point in the data has achieved a large
enough embedding space, all neighbors of every attractor point in the multivariate phase
space will be true neighbors.
3.4.12 Measuring Correlation Dimension ?
The procedure for getting the correlation dimension involves not only lag but also
the embedding dimension?the number of pseudo phase space axes. For any given
practical problem, there is no way to determine the correct embedding dimension in
advance. It depends on the attractor's true dimension in regular phase space, and that
value is what we're trying to find. The correct embedding dimension emerges only after
the analysis.
Once the lag is specified, the procedure usually begins with an embedding
dimension of two (two-dimensional pseudo phase space). First, situate the measuring cell
such that its center is a datum point in the pseudo phase space. Next, count the number of
data points in the cell. After that, center the cell on the reconstructed trajectory's next
point (in the ideal approach) and make a new count. Keep repeating that same procedure,
systematically moving the cell's center to each successive point on the trajectory. (Some
people choose center points at random to get a representative sample of the attractor,
instead of going to every point on the trajectory.) Let's look at an example with just five
data points (Garnett P. Williams, 1997).
43
Figure 13 Identifying qualifying neighbors from (a) point 1 and (b) point 2
Next we center our circle on point 2, keeping the same radius as before (Fig. 14).
Within the circle at its new location, points 1 and 3 now qualify. (As before, the reference
point doesn't count.) Keeping that same radius and systematically centering the circle on
each point, in turn, we count the qualifying points within each circle. Once through the
entire dataset with the same radius, we add up the total number of qualifying points for
that radius. For example, Figure 14 has a total of eight points for the radius indicated.
(We get two points when the circle is centered at point 1, two more when it is on point 2,
two again at point 3, and one point each for centering on points 4 and 5.) Having obtained
the total for the radius chosen, we now work only with that total rather than with the
numbers pertaining to any particular point. I'll refer to that total (eight in this example) in
a general way as the "total number of points within radius ? " or the "total number of
qualifying points."
The total number of points defining the trajectory (i.e., the size of the basic-
dataset) obviously influences the total count for a given radius. For instance, the count of
qualifying points for a given radius is much smaller for a trajectory made up of ten points
than for a trajectory of 10,000 points. For comparison purposes, therefore, we normalize
each count of qualifying points, to account for the total available on the trajectory. That
44
means dividing each total of qualifying points by some maximum reference constant.
That constant here is the maximum number of total points obtainable by applying the
circling-and-counting procedure to each point throughout the dataset, for a given radius.
The normalized result is the correlation integral or correlation sum, C? , for the
particular radius:
C? =
=
(3)
in which N is the total number of points in the dataset (i.e., on the trajectory).
A special version of the ratio that defines the correlation sum (3) comes from
considering the limit as N becomes large. When N is very large, the 1 in N-1 becomes
negligible. For all practical purposes, N-1 then becomes simply N. The quantity N(N-1)
(the denominator in the definition of correlation sum) therefore becomes N(N) or N2.
Thus, in the limit of infinitely large N we can define the correlation sum (3) as:
C? = (4)
In the technical literature, Equation 24.2 often appears in an imposing symbol
form, as follows:
C? = (5)
The xi in Equation 5 stands for a point on which we center our measuring device
(e.g., our circle). xj is each other point on the trajectory (each point to which we'll
measure the distance from the circle's center point xi). For each center point, the absolute
distance between xi and xj is |xi - xj|. The distance formula gives that absolute distance.
45
The next thing Equation 5 says to do is to subtract that distance from radius e. In
symbols, that means computing ? - |xi - xj|. If the answer is negative, then the measured
distance |xi-xj| is greater than ?. That means point xj is beyond the circle of radius ? and
therefore doesn't qualify for our count. On the other hand, if ? - |xi - xj| is positive, then |
xi-xj | is smaller than ?, and the point xj is within the circle.
We now have to devise a way to earmark the qualifying points (the points within
the circle). (In the highly unlikely event that the distance to a point equals the radius, we
can count it or not, as long as we're consistent throughout the analysis.) Equation 5's next
ingredient (to the left of the distance symbols) is G. G is an efficient way to label each
qualifying point ? that is, each point for which ? - |xi - xj| is positive (>0). In another
sense, G acts as a sort of gatekeeper or admissions director. (The technical literature gives
it the imposing name of the Heaviside function.) It lets all qualifying points into the
ballgame for further action and nullifies all others. If ?-|xi-xj| is positive, the point xj has to
be counted, as just explained. For all those cases the computer program assigns a value of
1 to the entire expression G (? - |xi - xj|). If, instead, ? - |xi - xj| is negative, the point xj is
beyond the radius of the measuring device. For those cases, the computer program
assigns a value of 0 to G (? - |xi - xj|).
Normalization is the equation's final job. As explained above, that's done by
dividing the total number of qualifying points by the total number of available points.
Strictly, the total number of available points is N (N-1). Hence, we'd multiply the counted
total by 1/ [N (N-1)]. Equation 5 uses the approximation (per Eq. 4) and so multiplies by
1/N2, with N2 being the total number of available points or pairs on the trajectory in the
abstract limit where N becomes infinitely large. And that's all there is to Equation 5.
46
Having determined the correlation sum for our first radius, we next increase the
radius and go through the entire dataset with the new radius. The larger radius catches
more points than the smaller radius did. That is, the new radius yields a larger total
number of qualifying points (numerator in Eq. 3). The normalization constant N2 depends
only on the size of the basic dataset and so is constant regardless of the radius ?. Hence,
the larger ? yields a larger correlation sum.
The idea is to keep repeating the entire procedure, using larger and larger radii.
Each new radius produces a larger and larger total of qualifying points and a larger
correlation sum. We end up with a dataset of successively larger radii and their associated
correlation sums. Those radii and correlation sums apply only to the two-dimensional
pseudo phase space in which we've been working. We now have to go to a three-
dimensional pseudo phase space (an embedding dimension of three) and compute a
similar dataset (or, rather, tell our computer to do it). All computed distances with the
distance formula now involve three coordinates instead of two. Once the radii and
associated correlation sums for three-dimensional pseudo phase space are assembled, we
move on to four embedding dimensions, then five, and so on. A typical analysis involves
computing a dataset for embedding dimensions of up to about ten. You might get by with
fewer, or you might need more, depending on what a plot of the data shows. That plot is
the next step.
For each embedding dimension, the correlation sum is plotted against the radius.
Except for tail regions at the ends of the distribution, data for a given embedding
dimension tend to plot as a straight line (a power law) on log paper (Fig. 14) (Garnett P.
Williams, 1997).
47
Figure 14 Plot of Correlation Sum vs. Radius
Figure 15, involving the special case of uniformly distributed phase space points,
shows the reason for the power law. One center point is enough to demonstrate the
power-law relation. For a given embedding dimension and center point, we choose a
radius and count the number of qualifying points (N?). Using the same center point, we
then repeat for larger and larger radii. A plot of such data (not included here) shows that
N? ? ? dimension, which is a power law. For instance, data for the one dimensional case
(Fig. 16 (a)) follow the relation N? ? ?1. In the two-dimensional case (Fig. 16 (b)), the
data adhere to the rule N? ? ?2, and so on. Also, that proportionality doesn?t change if we
deal with a correlation sum rather than just N?. The numerator in the correlation sum just
increases by a constant multiplier that equals the number of center points; the
denominator, based on the size of the dataset, is also a constant.
48
Figure 15 Sketch showing geometric increase in number of points within circle of radius ? for uniformly spaced
points (after Berg? et al. 1984: Fig. VL. 36). (a) One-dimensional attractor (line). (b) Two-dimensional attractor
(plane)
Why does Figure 14 have tail regions where the power law no longer holds? The
general idea is the same as we discussed for the information dimension. As we increase
our measuring radius ?, it eventually becomes so large that it starts to catch nearly all the
available points. That is, it catches fewer and fewer new points. The numerator in
Equation 4 (total number of points within radius ?) then increases at a lesser rate than at
smaller radii. The plotted data then depart from a power law, and the relation becomes
flatter (upper end of curve in Fig. 14). The radius finally becomes so large that it catches
all possible points, no matter where it's centered. Thereafter, the total number of points
remains constant at the maximum available in the data. The numerator and denominator
in Equation 4 then are equal, and the correlation sum becomes 1 (its maximum possible
value).
A tail region also occurs at small radii. The reason is that, in practice, data include
noise and aren't uniformly distributed. Some small radius marks the beginning of a zone
where measuring errors (noise) are of the same magnitude as true values. We can then no
longer distinguish between the two. Furthermore, qualifying points become very scarce at
small radii. In fact, even with noiseless data, our radius is eventually so small that it
49
doesn't catch any points. All of these features lead to unreliable statistics. The result is
that the plotted relation at the smallest radii might curve away from the straight line, in
either direction (Fig. 15).
We have, then, a scaling region (middle segment of plotted line), just as we found
on a related plot when deriving the information dimension.
Figure 16 Idealized plot of Correlation Sum vs. Radius for increasing Embedding Dimension
The slope of the scaling region gives us the value of the CoD for that particular
embedding dimension. Fig. 16 shows us the plots of correlation sum vs. measuring radius
for successive embedding dimensions. As we can see from Fig. 16, the slope of the
scaling region for the successive embedding dimensions tends to saturate to one
particular value. This value of the slope is our CoD for the given time series (Garnett P.
Williams, 1997).
50
3.5 EMG Data Analysis ?
3.5.1 Identifying muscle activation ?
EMG data was acquired from 6 muscle groups using 12 channels of DELSYS
sEMG sensors. The first step was to identify the muscles recruited for each type of low
back exertion. This was done by plotting the EMG signals as a time series and then
observing the nature of the graph. Below you can see the nature of the raw and RMS
value graphs for ES Left muscle under 5 lb resistance during FE. It can be observed that
there is a spike in muscle activity during FE motion and decrease in muscle activity when
the participant is in neutral position.
Figure 17 Muscle Recruitment for ES Left muscle during FE under 5 lb resistance
51
If a muscle is not recruited, then the spike in muscle activity is absent throughout
the motion indicating that the muscle is not getting exerted under motion.
3.5.2 Mean and Median Frequency of SEMG signals ?
The next step was to calculate the mean and median frequencies of the recorded
sEMG signals. The median frequency is the frequency at which 50% of the total power
within the epoch is reached. Mean frequency is the frequency at which the average power
within the epoch is reached (BIOPAC Systems Inc., Application notes). Previous
research has shown that the mean and median frequencies decrease with fatigue induced
in muscles (Bilodeau et. al., 2003; Mannion et. al., 1997). It would be interesting to see
how the mean and median frequencies in the muscles under consideration vary with
increase in resistance to motion. The mean and median frequencies were calculated using
customized MATLAB programs in the Biomechanics et. al. Toolbox (BEAT) created by
Ian Kremenic and Ali Sheikhzadeh from the Nicholas Institute of Sports Medicine and
Athletic Trauma. The mean was calculated as the ratio of sum of product of signal
amplitude and frequency to sum of amplitudes, whereas the median frequency was
calculated as the frequency which divides the area under the amplitude vs frequency
graph in two equal parts.
52
CHAPTER 4
RESULTS
Traditional (ROM) and non-traditional (ApEn and Cod) methods were used to
study low back motion during FE, LB and ROT under resistance of 0 lb, 5 lb, 10 lb and
15 lb. Muscle activation under the same exertions was studied using mean and median
frequency analysis.
4.1 ROM Results ?
The ROM results for all nine participants for flexion-extension, lateral bending,
and rotation for exercises against no load and against resistances of 5 lb, 10 lb and 15 lb
have been plotted in graphs 1(a), 1(b), and 1(c) respectively.
Figure 18 ROM results for FE
53
Figure 19 ROM results for LB
Figure 20 ROM results for ROT
One factor ANOVA test revealed that the ROM did not change significantly (p >
0.05) as the resistance increased from zero to 15 lb during all three types of exercise.
54
SUMMARY
Groups Count Sum Average Variance
Column 1 9 248.2337 27.58152 87.75713
Column 2 9 233.7492 25.97214 94.77536
Column 3 9 225.004 25.00045 101.5264
Column 4 9 209.7471 23.30524 105.3682
ANOVA
Source of
Variation SS df MS F P-value F crit
Between Groups 86.55527 3 28.85176 0.296351 0.827739 2.90112
Within Groups 3115.417 32 97.35677
Total 3201.972 35
Table 3 One factor ANOVA test on ApEn results for FE
Exercise p-value
Flexion - Extension 0.8277
Lateral Bending 0.716
Rotation 0.0907
Table 4 p-values for ROM results
4.2 Phase Plane Plots ?
Phase Plane Plots were plotted to give a general idea of the dynamics of the
system. The original time series was plotted against a lagged time series using time delay
calculated by first minimum of average mutual information method. Below are the phase
plane plots plotted for Participant 1 during FE, LB and ROT motion against 0 lb, 5 lb, 10
lb and 15 lb resistance.
55
Figure 21 Phase Plane plots for FE data against 0 lb, 5 lb, 10 lb and 15 lb respectively for participant 1 (left to
right; top to bottom)
From the above plots we can see that the trajectory follows a specific pattern with
limited divergence. This indicates variability in the dynamic system. These plots can be
compared to phase plane plots of perfectly periodic time series (sine wave).
56
Figure 22 Phase Plane plot of a perfectly periodic (sine wave) time series data
Fig. 21 shows the Phase Plane plot of a sine wave. We can see that the trajectories
overlap perfectly. The nature of the graph is ellipsoid because of the time delay value
selected. This means that there is no variability in the data.
4.3 Fast Fourier Transformation (FFT) ?
As mentioned in the previous chapter, one of the ways of detecting chaos in a
synamical system is to take FFT of the given data. FFT of a chaotic signal presents
continuous spectra over a limited range and the energy is spread over a wider bandwidth.
On the other hand, FFT of a periodic signal presents discrete spectra, where a finite
number of frequencies contribute for the response (Mullin T. 1993, Moon F. C. 1992).
57
Figure 23 FFT for FE data against 0 lb, 5 lb, 10 lb and 15 lb respectively for participant 1 (left to right; top to
bottom)
We can see from above FFT plots that the experimental data recorded during FE
for the participant consists of frequencies over a wide spectrum. This is an indication that
the data that we have might be chaotic. We can compare this to a sine wave, which is an
example of non chaotic data, which consists of a single frequency.
58
Figure 24 FFT of sine wave
4.4 Approximate Entropy (ApEn) Results ?
ApEn results were calculated using the algorithm developed by Pincus (Pincus,
1994). Below are the results for ApEn of experimental data recorded during FE, LB and
ROT against 0 lb, 5 lb, 10 lb and 15 lb resistance.
Figure 25 ApEn results for FE
59
Figure 26 ApEn results for LB
Figure 27 ApEn results for ROT
One factor ANOVA tests revealed that the ApEn values did not change
significantly (p > 0.05) as the resistance increased from zero to 15 lb during all the three
types of exercises.
60
SUMMARY
Groups Count Sum Average Variance
Column 1 9 2.6096 0.289956 0.001987
Column 2 9 2.7531 0.3059 0.004959
Column 3 9 2.5042 0.278244 0.005593
Column 4 9 2.6835 0.298167 0.005934
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.003781 3 0.00126 0.272894 0.844479 2.90112
Within Groups 0.147779 32 0.004618
Total 0.151559 35
Table 5 One factor ANOVA test on ApEn results for FE
Exercise p-value
Flexion ? Extension 0.8444
Lateral Bending 0.8371
Rotation 0.2034
Table 6 p-values for ApEn results
4.5 Correlation Dimension (CoD) Results ?
CoD for the motion data was calculated using an algorithm developed by
Grassberger and Procaccia (1983). Below are the results for CoD of experimental data
recorded during FE, LB and ROT against 0 lb, 5 lb, 10 lb and 15 lb resistance.
61
Figure 28 CoD results for FE
Figure 29 CoD results for LB
Figure 30 CoD results for ROT
62
The ANOVA tests revealed that the CoD did not change significantly (p > 0.05)
as the resistance increased from zero to 15 lb during all the three types of exercised. The
p-values for FE, LB and ROT data sets came out to be 0.9734, 0.5668 and 0.6328
respectively.
SUMMARY
Groups Count Sum Average Variance
Column 1 9 17.83 1.981111 0.003436
Column 2 9 17.83 1.981111 0.002536
Column 3 9 17.94 1.993333 0.007075
Column 4 9 17.86 1.984444 0.002678
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.0009 3 0.0003 0.076312 0.972327 2.90112
Within Groups 0.1258 32 0.003931
Total 0.1267 35
Table 7 One factor ANOVA test on CoD results for FE
Exercise p-value
Flexion - Extension 0.9723
Lateral Bending 0.5668
Rotation 0.6328
Table 8 p-values for CoD results
63
4.6 EMG Frequency Analysis Results ?
EMG signals were recorded from six muscle groups, namely Erector Spinae,
Multifidus, Latissimus Dorsi, Internal Obliques, External Obliques and Rectus
Abdominis. After the signals were recorded and processed, they were plotted to identify
the muscles recruited by each participant for each type of low back exertion. It was
interesting to note that not all the participants recruited the same muscles for the same
type of low back exertion. The following table shows details about which muscle was
recruited by how many participants for each type of low back exertion.
Muscle No. of participants who used that muscle for that motion
Flexion-Extension Lateral Bending Rotation ES Left 9 4 9
ES Right 9 9 9
EO Left 6 5 6
EO Right 6 9 6
IO Left 3 4 4
IO Right 3 4 3
RA Left 4 2 1
RA Right 4 2 1
LD Left 9 5 9
LD Right 9 9 9
MF Left 9 3 9
MF Right 9 9 9
Table 9 Muscle recruitment during FE, LB and ROT by number of participants.
Thus we can see that during FE, ES Left, ES Right, LD Left, LD Right, MF Left
and MF Right were recruited by all the participants while the remaining muscles were
not. Similarly, during LB, ES Right, EO Right, LD Right and MF Right were recruited by
64
all the participants. During ROT motion, ES Left, ES Right, LD Left, LD Right, MF Left
and MF Right were recruited by all the participants.
For comparison purposes, the data from the muscles that were used by all the
participants for that particular type of motion was used. Below are the results of mean
and median frequency calculations for data obtained from muscles that were recruited by
all the participants during FE, LB an ROT. After the mean and median frequency were
calculated, One Factor ANOVA analysis with significance level of ? = 0.05 was
conducted to see if the mean and median frequency varied significantly with increase in
resistance to motion.
4.6.1 Mean and Median Frequency during Flexion ? Extension motion ?
Figure 31 ES Left ? Mean and Median Frequencies (Left and Right)
65
Figure 32 ES Right - Mean and Median Frequencies (Left and Right)
Figure 33 LD Left - Mean and Median Frequencies (Left and Right)
Figure 34 LD Right - Mean and Median Frequencies (Left and Right)
66
Figure 35 MF Left - Mean and Median Frequencies (Left and Right)
Figure 36 MF Right - Mean and Median Frequencies (Left and Right)
67
Muscle Mean value of Mean Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Left 135.58 (4.85) 137.5 (4.4) 138.04 (4.01) 139.99 (5.29)
ES Right 139.85 (6.67) 141.50 (5.37) 142.83 (4.87) 142.21 (5.68)
LD Left 132.42 (4.30) 133.49 (4.64) 130.35 (4.74) 128.02 (4.51)
LD Right 129.44 (5.40) 127.22 (6.49) 125.21 (6.26) 122.9 (6.46)
MF Left 161.79 (3.60) 162.36 (4.20) 163.39 (4.28) 161.63 (4.35)
MF Right 162.75 (4.92) 166.49 (5.68) 167.73 (5.14) 166.71 (5.13)
Table 10 Mean values of Mean Frequencies with increasing loads during FE
Muscle Mean value of Median Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Left 94.36 (5.97) 96.85 (5.47) 98.29 (4.91) 101.19 (6.31)
ES Right 99.06 (8.23) 100.38 (6.52) 101.85 (6.28) 103.02 (7.13)
LD Left 89.05 (4.79) 91.89 (4.98) 58.52 (5.54) 87.67 (5.05)
LD Right 85.57 (5.60) 86.65 (4.90) 87.29 (5.20) 85.75 (5.36)
MF Left 122.79 (4.48) 124.32 (4.80) 125.57 (5.10) 124.45 (5.04)
MF Right 121.54 (6.26) 126.96 (6.91) 130.22 (6.37) 129.95 (6.29)
Table 11 Mean values of Median Frequencies with increasing loads during FE
68
4.6.2 Mean and Median Frequency during Lateral Bending motion ?
Figure 37 ES Right - Mean and Median Frequencies (Left and Right)
Figure 38 EO Right - Mean and Median Frequencies (Left and Right)
Figure 39 LD Right - Mean and Median Frequencies (Left and Right)
69
Figure 40 MF Right - Mean and Median Frequencies (Left and Right)
Muscle Mean value of Mean Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Right 161.60 (7.73) 157.62 (5.00) 155.75 (4.09) 152.00 (5.15)
EO Right 138.85 (5.53) 142.00 (7.48) 141.21 (5.95) 139.01 (6.72)
LD Right 139.62 (7.05) 133.80 (6.02) 127.74 (5.37) 124.14 (4.99)
MF Right 190.37 (6.43) 188.28 (5.16) 184.77 (5.81) 181.60 (5.23)
Table 12 Mean values for Mean Frequencies with increasing loads during LB
Muscle Mean value of Median Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Right 117.9 (10.4) 111.56 (7.57) 112.01 (6.87) 109.94 (7.39)
EO Right 88.38 (5.91) 95.07 (8.35) 92.78 (6.29) 92.13 (6.87)
LD Right 93.42 (6.01) 89.38 (4.42) 86.18 (4.03) 85.00 (4.10)
MF Right 155.53 (8.67) 152.10 (6.53) 147.71 (8.09) 145.10 (7.64)
Table 13 Mean values for Median Frequencies with increasing loads during LB
70
4.6.3 Mean and Median Frequency during Rotation motion ?
Figure 41 ES Left - Mean and Median Frequencies (Left and Right)
Figure 42 ES Right - Mean and Median Frequencies (Left and Right)
Figure 43 LD Left - Mean and Median Frequencies (Left and Right)
71
Figure 44 LD Right - Mean and Median Frequencies (Left and Right)
Figure 45 MF Left - Mean and Median Frequencies (Left and Right)
Figure 46 MF Right - Mean and Median Frequencies (Left and Right)
72
Muscle Mean value of Mean Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Left 164.10 (5.89) 160.31 (5.12) 158.69 (4.71) 156.52 (4.59)
ES Right 163.16 (6.05) 162.58 (5.29) 160.89 (4.78) 158.64 (4.43)
LD Left 137.78 (6.30) 137.31 (6.34) 128.55 (6.00) 126.33 (5.44)
LD Right 141.58 (7.93) 130.95 (5.92) 128.95 (5.70) 127.04 (5.90)
MF Left 179.88 (5.87) 180.76 (4.71) 178.91 (4.62) 176.00 (4.53)
MF Right 177.65 (9.50) 179.28 (6.75) 182.40 (6.18) 175.94 (7.77)
Table 14 Mean values of Mean Frequencies with increasing loads during ROT
Muscle Mean value of Median Frequencies in Hz (S.D.)
NL 5 lb 10 lb 15 lb
ES Left 124.44 (8.91) 122.91 (6.66) 122.41 (5.90) 120.21 (5.44)
ES Right 121.80 (9.43) 124.67 (6.95) 122.73 (6.35) 121.08 (5.83)
LD Left 95.23 (6.98) 96.62 (5.28) 90.66 (5.61) 88.75 (5.15)
LD Right 98.19 (6.25) 93.77 (6.15) 89.16 (4.86) 90.77 (5.56)
MF Left 144.96 (8.63) 148.41 (6.30) 146.91 (6.38) 143.60 (6.11)
MF Right 143.46 (12.95) 146.24 (8.46) 151.77 (7.84) 143.65 (9.70)
Table 15 Mean values of Median Frequencies with increasing loads during ROT
73
CHAPTER 5
DISCUSSION
The aim of this exercise was to develop test protocols for analysis of low back
exertions in standing position. Traditional (ROM) and non-linear (ApEn and CoD)
techniques were employed for analysis of low back motion while analysis of EMG data
was done using mean and median frequency calculations.
The ROM, while giving accurate measures of motor variability within the system,
is not explanatory of the underlying neural processes of human movement. The nonlinear
measures helped us to understand the motor variability within a system, and not just to
provide a measure of the amount of variability that is present. Furthermore, as stated
previously, traditional linear tools can mask the true structure of motor variability, since a
few strides are averaged to generate a ??mean?? picture of the subject?s gait. In this
averaging procedure, the temporal variations of the gait pattern may be lost. On the
contrary, nonlinear techniques focus on understanding how variations in the gait pattern
change over time (Dingwell and Cusumano, 2000; Hausdorff et al., 1997). This is the
reason for using both traditional and non-linear tools to analyze low back motion in our
74
case. The ROM does not describe the effect of increasing resistance on motion. It does
not take into account the chaos in the dynamic motion of low back. Non-linear methods
will help us better understand the dynamics of low back motion.
Motion and EMG data was recorded from nine healthy participants using the
protocols approved by the IRB?s of Auburn University, AL and Palmer College of
Chiropractic, IA. One of the participants could not be used for data acquisition as the
sensors could not be attached to the participant?s lower back because of perspiration.
Following data exporting and data reduction, motion data was analyzed using ROM,
ApEn and CoD techniques. The values of ApEn and CoD results were similar to results
obtained in some of the other studies conducted on healthy participants to study
variability. Newell et. al. in their study of dimensional constraints on limb movement
found out that the approximate entropy values increased from an average of 0.2 to 0.3 as
participants went from gait with vision to gait without vision aid. Buzzi et. al. studied
effect of aging on variability during gait and found out that CoD values for young people
were 2.3 as compared to 2.7 for old people for variation in knee angle. Both traditional
and non-linear methods were thus applied successfully to the human physiological data
obtained.
Statistical analysis revealed that variability did not change significantly as the
resistance to FE, LB and ROT increased from zero to 15 lb. It must be noted that the aim
of this exercise was to develop test protocol to analyze low back exertion. The sample
size used for this study was relatively small and statistical analysis results may not be
enough to generalize the results for entire healthy population. The protocol needs to be
fine tuned before it can be applied to a large scale study. Statistical analysis on results of
75
a much larger population will then give a correct estimate of effect of increasing loads on
variability in motion of low back spine.
Though the overall results suggested that variability remained constant as the
resistance to motion increased, there were some exceptions. One of them is discussed
below.
Figure 47 ROM, ApEn and CoD results for participant 1 during LB
In the graphs above, you can see the results for ROM, ApEn and CoD for
participant 1 (Age ? 59 yrs, Height ? 164 cm, Weight ? 66.2 kg). It can be noticed that as
the resistance to lateral bending increases, the ROM falls sharply. This means that the
participant found it difficult to cope with the increase in resistance. However, the values
for ApEn and CoD do not change with increase in load. This means that even though the
ROM decreased, the regularity of the repetition cycles did not change significantly. The
age of the participant was significantly higher than the average age (43.2 yrs) of all the
76
participants. This may have been one of the reasons for decrease in ROM with increasing
resistance. Thus you can see that to totally analyze motion, both traditional and non-
linear tools are necessary.
Mean and median frequencies of recorded EMG signals were calculated to see the
effect of increasing loads on muscle fatigue. As explained earlier, it was noticed that
muscle fatigue typically results in decrease in the mean and median frequencies.
Statistical analysis revealed that mean and median frequencies did not change
significantly with increase in load. This means muscle fatigue was not induced in the
participants due to increasing loads. This may be one of the reasons; variability in motion
was not affected by increasing loads, as the muscles were able to provide the required
neuro-muscular response to the increasing loads. However, as mentioned before, this is
only the protocol development stage of the study and more testing will be needed before
this conclusion can be generalized for the entire healthy population. As with the motion
analysis results, there were some outliers in the EMG results also. A couple of them are
discussed below.
Figure 48 Mean and Median Frequency results for ES Left muscle for participant 3 during ROT
77
It can be seen that the mean and median frequencies for participant 3 (Age ? 24
yrs, Height ? 181 cm, Weight ? 80 kg) decrease as the resistance to motion increases.
This means that fatigue is getting induced in the muscles of participant 3 as the load
increases. This is not consistent with other results and hence may be considered an
outlier. The reason might be less endurance when it comes to dealing with increasing
resistance. This is a surprising result, as younger participants are expected to have higher
muscle endurance.
Figure 49 Mean and Median Frequency results for ES Right muscle for participant 3 during ROT
Fig. 49 shows us the mean and median frequency results for ES Right muscle of
participant 5 (Age ? 51 yrs, Height ? 160 cm, Weight ? 63 kg) during ROT. The overall
results show that mean and median frequencies either remained constant or decreased
slightly as the resistance to motion increased. However, in this case, the mean and
median frequencies increased as the resistance to motion increases. This may happen if
the participant uses the leg muscles to compensate for the increase in effort required to
overcome the increase in resistance. The age of this participant is higher than the average
age (43.2) of all the participants. Thus he might have needed his leg muscles to deal with
the increasing resistance to motion. In this case the participant does not use only his back
78
muscle which may lead to them relaxing, resulting in increase in mean and median
frequencies.
As mentioned before test methods need to be improved before using them in a
larger study. Some of the recommendations to improve the protocol are listed below ?
1. It was observed that the rotation data did not truly reflect the motion of
participants because the skin was stretched during rotation. This can be minimized by
applying a stiff plastic plate to the skin before the motion sensors are applied.
2. The participants were also asked to perform the exertions at their comfortable
speeds. This may have allowed them to compensate for the increase in resistance to
motion. It would be interesting to see the results if the participants are asked to perform
these exertions under two different fixed speeds or under higher resistance. It has been
previously reported that variability is less for slower trunk movements as compared to
rapid ones. In this study healthy participants were asked to perform repetitive trunk
flexion and extension movements at 20 and 40 cycles per second. Maximum Lyapunov
exponents describing the expansion of the kinematic state-space were calculated from the
measured trunk kinematics to estimate stability of the dynamic system. The values of the
Maximum Lyapunov exponent were more for rapid movements than for slow movements
(Granata et. al., 2006).
3. Another limitation of the study might be the fact that participants were able to use
their leg muscle to compensate for the increase in load resistance. It was necessary to
leave the legs unconstrained to simulate real world conditions. Before the data recording
started, the participants were instructed to move only their upper body, from the waist up
and perform the three types of exertions. However, it was observed that some of the
79
participants still used their leg muscle to compensate for increasing loads. To remedy this
participants can be given a practice session to get better acquainted to the exercises.
Once the protocol had been developed, the next step would be to apply the
protocol to larger sample sizes of healthy participants as well as patients with LBP. It has
been shown previously that LBP affects trunk co-ordination and muscle activity during
walking (Lamoth et. al., 2005). It will be interesting to see the effect of LBP on FE, LB
and ROT exertions under increasing loads. If LBP affects variability significantly, then
these exercises will be characterized by different values of ROM, ApEn and CoD.
When a patient under goes rehabilitation for LBP, then convergence of these
values towards values for these parameters for healthy subjects may suggest that the
treatment is working. Hence, this sort of variability analysis can be used as a diagnostic
tool during rehabilitation. However, before this can be done, a solid database needs to be
created by testing more healthy subjects, as nine subjects is not enough to generalize
movement characteristics of entire healthy population. This should be followed by testing
of patients with LBP to establish the difference in movement characteristics.
80
CHAPTER 6
CONCLUSION
Collectively, the results of kinematic analysis during FE, LB and ROT revealed
that variability in motion does not change under gradual increase in resistance to motion.
The findings of the traditional method (ROM) used were supported by non-linear analysis
(ApEn and CoD) of motion. Thus, both traditional and non-linear methods were applied
successfully to analyze motion. Also, the increasing resistance to motion did not induce
enough fatigue in muscles of participants which might have helped the participants to
provide required neuromuscular response to increasing loads. The measurements during
rotation should be improved by attaching the sensors to prevent sliding over the skin.
Future studies should be undertaken to increase the challenges by either increasing the
load, or by asking the subjects to increase the speed. Studies recruiting larger number of
subjects should be undertaken. These will ultimately lead to studies involving low back
pain subjects and possible tools for diagnosing low back pain using motion
measurements.
81
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87
APPENDIX
A. Auburn University IRB Approval Document ?
88
89
90
B. Palmer College of Chiropractic, IA IRB Approval Document ?
91
92
93
94
C. Motion Monitor Preference File Settings ?
Figure 50 User Report Options
Figure 51 Orthopedic Angle Selection
95
Figure 52 Forceplate Data
Figure 53 EMG Data 1
96
Figure 54 EMG Data 2
Figure 55 EMG Data 3
97
D. Literature Review Summary Sheets ?
Study Title
Health
Status and
number of
participan
ts
Gender
Age in
years
(SD)
Weight
in kg
(SD)
Height
in cm
(SD) Males
Female
s
Cavanaug
h et. al.
2007
Approximate entropy detects the effect
of
a secondary cognitive task on postural
control in healthy young adults: a
methodological report
Healthy -
30 15 15 21.7 (2.3) 71 (13.3) 173 (11)
Kavanagh
et. al 2006
Lumbar and cervical erector
spinae fatigue elicit compensatory
postural responses to assist in
maintaining head stability during
walking
Healthy - 8 8 0 23 (4) 77 (12) 181 (9)
Kavanagh
et. al 2009
Lower trunk motion and speed-
dependence
during walking
13 7 6 23 (3) 71 (11) 171 (11)
Fell et. al.
2000
Nonlinear analysis of continuous ECG
during
sleep II. Dynamical measures
Healthy -
12 12 0 27.3 (4.2)
Not
Clear
Not
Clear
Lee et. al.
2010
Non-linear Analysis of Single
Electroencephalography (EEG) for
Sleep-Related Healthcare Applications
Healthy - 4 4 0 27.5 Not Clear Not Clear
Newell et.
al. 2000
Dimensional constraints on limb
movements Healthy - 8 8 0 Not Clear
Not
Clear
Not
Clear
Buzzi et.
al. 2003
Nonlinear dynamics indicates aging
a?ects
variability during gait
Healthy
young - 10
Healthy
older - 10
0 20
25.1 (5.3)
74.6
(2.55)
63.93
(6.53)
64.07
(9.69)
170 (4.9)
159 (5.3)
Demographics Summary
98
Study Title Rate of data collection Duration r, m ApEn
Cavanaugh et.
al. 2007
Approximate entropy
detects the effect of
a secondary cognitive
task on postural
control in healthy
young adults: a
methodological
report
100 Hz Not Clear r = 0.2 m= 2
No significant interaction
was
found between cognitive
task and sensory
condition for ApEn-AP
and ApEn-ML
Kavanagh et.
al 2006
Lumbar and cervical
erector spinae fatigue
elicit
compensatory
postural responses to
assist in maintaining
head stability during
walking
Motion - 250 Hz
EMG - 1000 Hz
Time required to
walk 30 m level
walkway at
comfortable speed.
r = 0.2
m = 1
ApEn values did not
show significant change
when data obtained after
fatigue induced in neck
and trunk region were
compared.
Kavanagh et.
al 2009
Lower trunk motion
and speed-
dependence
during walking
512 Hz
Time required to
walk 30 m level
walkway at
comfortable speed.
r = 0.2
m = 1
ApEn values increased as
the walking speed
increased. The increase in
value ranged from 0.15 to
0.24 depending on axis of
inclinometer.
Newell et. al.
2000
Dimensional
constraints on limb
movements
100 Hz 2 minutes r = 0.25 m = 2
ApEn values increased as
the subjects went from
preferred with vision to
random and no vision
type of motion. The
increase was in the range
of 0.2 to 0.3.
Approximate Entropy Studies Summary