Author ORCID Identifier

0000-0001-6546-0401

Document Type

Dissertation

Date of Award

5-31-2026

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Casey Diekman

Second Advisor

Victor Victorovich Matveev

Third Advisor

James MacLaurin

Fourth Advisor

Guiling Wang

Fifth Advisor

Tim Rumbell

Abstract

Mathematical models of biological rhythms and excitable systems can provide insights into mechanisms underlying cardiac electrical dynamics. However, estimating the parameters of these models from experimental observations is often difficult due to noise, heterogeneity, and unobserved variables. For example, in an electrocardiogram (ECG) recording, information about the electrical properties of different regions of the heart is compressed into a single voltage trace. Additionally, variability within these signals may contain important information about population heterogeneity, regional differences in electrophysiology, and time-dependent modulation.

This dissertation develops, explores, and evaluates methods that perform feature-based distributional inference for complex nonlinear dynamical systems. The objective is to augment pointwise parameter estimates by matching distributions of a feature space described by biophysically-inspired summary statistics. These methods are applied to two different models of the cardiac conduction system.

This research aims to provide a framework for mechanistic inference in settings where capturing the variability in models is essential to answer the core scientific question. In cardiac electrophysiology, this includes understanding how distributions of model parameters explain differences in ECG behavior between individuals and across their physiological states. In particular, this dissertation studies circadian regulation as a motivating application of these methods. Using feature-based inference to compare day and night ECG recordings over a 24-hour period, these frameworks demonstrate how distributional inference can be used to reveal the biophysical mechanisms responsible for observable differences in ECG morphology.

These results highlight important tradeoffs between iterative and amortized posterior density estimation techniques. Understanding these tradeoffs is essential for determining which method is preferred under different computational and feature budgets. These methods were used to identify that circadian variation of certain model parameters that represent pacemaker function and coupling can explain the day-night differences observed in patient ECG data. Finally, an ionic conductance-based 1D strand cardiac tissue model capable of pseudo-ECG generation was developed, providing a vessel to further investigate circadian regulation of cardiac dynamics on the cellular scale.

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