Author ORCID Identifier
https://orcid.org/0009-0002-9052-8169
Defense Date
2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Systems Modeling and Analysis
First Advisor
Cheng Ly
Second Advisor
Laura Ellwein Fix
Abstract
Understanding complex physiological systems requires mathematical frameworks that can capture underlying dynamics and support reliable inference from real-world data. This dissertation presents a series of studies that illustrate the roles of mathematical modeling, parameter identifiability, and statistical inference in respiratory and neural physiology.
In the first two chapters, we investigate parameter identifiability through sensitivity analysis and subset selection in two distinct nonlinear respiratory mechanics models tailored to preterm infant physiology. These models describe dynamic airflow and pressure signals under a range of adverse clinical scenarios; the first captures the effects of a highly compliant chest wall and thoracoabdominal asynchrony, while the second examines the impact of mechanical ventilation and surfactant replacement therapy on pulmonary function. Model calibration using clinical data enables the inference of underlying physiological parameters and provides a patient-specific characterization of respiratory health.
In the last two chapters, we investigate parameter estimation through frequentist and Bayesian approaches in statistical, probabilistic models of human visual and motor pathways. The third chapter employs time-series autoregressive models to predict human electroencephalogram (EEG) responses to randomly alternating visual stimuli, with parameter estimation performed using likelihood-based methods. The fourth chapter uses Bayesian firing rate estimation techniques and criticality analysis to model continuous representations of single-unit basal ganglia spiking activity, ultimately delineating healthy and Parkinsonian behavior.
Together, these studies demonstrate how principled approaches to modeling, identifiability, and statistical inference can link observable data to interpretable and predictive representations of complex physiological systems, particularly in settings characterized by limited, noisy, or indirect measurements.
Rights
© Richard R. Foster
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
5-7-2026
Included in
Applied Statistics Commons, Computational Neuroscience Commons, Dynamic Systems Commons, Longitudinal Data Analysis and Time Series Commons, Other Physiology Commons, Probability Commons