Inverse Functional Modeling for Drug Dissolution Profiles: A Statistical Framework for Curve-Based Formulation Design

Abstract

This work establishes a statistically reliable framework for reverse engineering drug formulations from a target dissolution profile, formulated as an inverse functional problem. Dissolution profiles describe the rate at which a drug is released from a dosage form and serve as a primary \textit{in vitro} surrogate for product performance. Although regulatory evaluation commonly relies on scalar summaries such as the $f_2$ factor, dissolution behavior is inherently functional and reflects structured relationships between formulation variables and release dynamics.

The reverse engineering problem is formulated as an inverse mapping from formulation predictors to curve-valued responses under sampling noise and model-form uncertainty. By representing dissolution profiles as continuous functions of time, the framework enables dimension reduction, regression modeling, and optimization based on the entire trajectory. Parametric models and functional approaches based on spline smoothing and functional principal component analysis are integrated within a unified curve-space optimization architecture, with a reference-anchored extension to stabilize inverse estimation.

Applications to extended-release datasets demonstrate the behavior of the framework under real experimental conditions. To generalize beyond specific datasets, the framework is further evaluated through simulation studies spanning multiple mechanistic generating processes, including controlled structural misspecification. A formulation recovery error metric is introduced to assess inverse identification accuracy alongside curve-level discrepancy measures.

The results characterize when parametric efficiency is achieved under structural alignment and when functional representations provide greater robustness under heterogeneity or model mismatch. Collectively, this work provides a regulatorily grounded and general framework for curve-based dissolution modeling and formulation design when the underlying release mechanism is uncertain.