Analysis and applications of models of single-cell cardiac electrical excitation

Noor Aziz, Muhamad Hifzhudin Bin (2021) Analysis and applications of models of single-cell cardiac electrical excitation. PhD thesis, University of Glasgow.

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For over a century, cardiac electrophysiology modelling has been widely used for studying various problems of normal or abnormal heart rhythm, which is essential for understanding the disease mechanisms, provide accurate diagnoses and develop a new treatment. This thesis focuses on several analysis and applications of models in single-cell cardiac electrical excitation. In particular, I aim to study some typical challenges present in cardiac electrophysiology modelling, which is, variability in action potentials (AP) and their effects on cardiac anti-arrhythmic drugs, mechanisms of cardiac alternans and efficient numerical solver. To address the problems, I use various action potential models initially a range of biophysically detailed models, then focusing on a single simplified model.

This thesis consists of two main parts, excluding the part for background and introductory materials. The first and most important part, in terms of effort and time spent, is devoted to the investigation of action potential variability in a population of rabbit ventricular myocytes and their effects on cardiac anti-arrhythmic drugs. To determine the distributions of ion channel conductance values that capture the electrophysiological heterogeneity measured in large populations of cells, I apply the experimentally-calibrated population of models introduced by Britton et al. (2013), constructing from randomly varied ion conductances combinations. The model population is further used to quantitatively predict the range of response to the application of hERG and L-type calcium channel blocks. I implement the methodologies on three different AP models to study the capability of the cell models in predicting the drug effects. The models are a rabbit AP model by Shannon et al. (2004) and two human AP models by Ten Tusscher et al. (2004) and O’Hara et al. (2011). The AP responses following channel blocks are compared and analysed.

The second part of the thesis covers the analysis and application of a simplified ionic cardiac model. The model used is a modified version of caricature Noble model by Biktashev et al. (2008). Our first task is to propose the model as a generic model of cardiac electrophysiology by using a parameter estimation method. The model’s parameters are adjusted so that it can reproduce AP morphologies of various cell types. In particular, the model is fitted to three different AP models which are Purkinje model by Noble (1962), ventricular model by Luo and Rudy (1991) and atrial model by Courtemanche et al. (1998). The action potential duration restitution curve of targeted models are also reproduced. The similar model template now can be used for various regions of the heart by changing the parameter values. Furthermore, the modified caricature Noble model is fitted to experimental measurements of healthy and failing myocytes by McIntosh et al. (2000). I analyse the difference between parameter values from fitting works intending to find the physiological meaning for AP differences shown in experimental recordings. Parameter fitting of modified caricature Noble model demonstrates that it can replace other more complicated models, and it can also be used as a prototype to look for cardiac alternans and to construct an efficient numerical method.

The modified caricature Noble model is further used to develop an efficient numerical method for simulation of cardiac action potential model by taking into account the asymptotic solutions of the system. In order to achieve this, I implement the heterogenous multiscale method proposed by Weinan and Engquist (2003). The proposed method exhibits better stability and efficiency compared to other numerical solvers. The drawbacks of the method are also explained. Finally, the application of the model is extended by utilising it to study the mechanisms of cardiac alternans. The objective is to determine parameters and variables in the model that are responsible for generating action potential duration alternans. Using the slow-slow-time system of the model, an explicit discrete restitution map is derived and their equilibrium branches and bifurcations are studied. The bifurcations of equilibria of these maps are studied to identify regions in the parameter space of the model where normal response and alternans exhibit. Also, using the full system of the model, a framework formulated in terms of a boundary value problem is developed, which can be used to construct various branches of the action potential duration restitution map. At the end of the work, I perform some numerical simulations by fitting the caricature Noble model to models of normal response and alternans. The differences in parameter values are analysed and used to understand the onset of alternans. Importantly, the result shows that the magnitude of time-dependent potassium current can induce or suppress alternans.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Cardiac electrophysiology Action potential Variability
Subjects: Q Science > QA Mathematics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Supervisor's Name: Simitev, Dr Radostin
Date of Award: 2021
Depositing User: Mr Muhamad Hifzhudin Bin Noor Aziz
Unique ID: glathesis:2021-81912
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 11 Jan 2021 16:50
Last Modified: 12 Jan 2021 15:04
Thesis DOI: 10.5525/gla.thesis.81912

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