title: Applications of parameter inference and modelling in cardiac single-cell action potential models
Creators: name: Aldawoud, Antesar Mohammed
Publisher: name: University of Glasgow
Year: 2024

description: Cardiac electrophysiological modelling has long been a valuable tool for exploring both normal and abnormal heart rhythms, playing a crucial role in diagnosing heart conditions and developing effective therapies. This thesis focuses on single-cell cardiac electrophysiology, with particular attention to the variability in action potential (AP) and its impact on anti-arrhythmic treatments. The primary goal is to investigate this common issue in cardiac electrical excitation models and understand its implications for anti-arrhythmic therapies. To achieve this, a variety of action potential models, ranging from complex to simplified, are employed to provide an analysis.

Firstly, a method is presented that uses an asymptotic approximation of action potential duration (APD) in a simplified model to study ion-channel block dynamics. This approach involves determining the specific properties of each myocyte based on the parameter values of a selected model. Drug effects on ion conductance are quantified using a multiplicative factor, and a mathematical formula is developed to approximate APD. This formula is then used to establish model parameters as functions of APD and drug-induced changes in APD for each heart cell. Additionally, two protocol-related parameters are calibrated using an adaptive-domain approach based on optimal excitability. This precise formulation allows for direct assessment of the conditions required to maintain a constant APD or its variations. It also enables predictions about the proportion of excitable cells after drug application, as well as insights into stimulus periods and dose-response relationships, consistent with experimental data.

Subsequently, a regression method is developed to predict drug responses in cardiac electrophysiology models by assessing how alterations in ion channel conductances affect model outputs. The method focuses on predicting changes in action potential duration (APD) following drug administration. The Ordinary Least Squares regression model provided accurate predictions, effectively capturing the relationship between drug-induced changes in ion channel conductances and APD. In addition to the standard regression model, an advanced approach is employed by incorporating nonlinear terms to capture the complex relationships between conductances and physiological biomarkers. These nonlinear predictors enable the model to account for interactions and dependencies that linear models often overlook. The enhanced model unables more accurate predictions of the effects of ionic conductances.

Finally, a method is introduced to reproduce action potential variability observed in experimental rabbit cardiomyocytes using Gaussian process emulators and rejection sampling. The method accurately captures variations in APD and correlates them with changes in ionic conductances across a population of models. By utilizing rejection sampling in combination with GP emulation, large populations of models are efficiently generated, enabling the study of the interactions between ionic conductances, action potentials, and drug effects without requiring extensive computational resources.

This thesis enhances the understanding of cardiac electrophysiology by addressing variability in action potential and its implications for anti-arrhythmic treatments. It proposes an integrated approach combining modelling and experimentation, offering new insights into the complex dynamics of cardiac function.