Electrical waves in mathematical models of human ventricular tissue effects of different modeling formalisms electrophysiological factors and heterogeneities on ventricular arrhythmias and the termination of these arrhythmias via a deep learning approach

Abstract

Sudden cardiac death (SCD) remains one of the significant causes of mortality in industrialized and developing countries. SCD is often caused by life-threatening cardiac arrhythmias like ventricular tachycardia and ventric- ular fibrillation, which are associated with the formation of spiral, broken- spiral (two dimensions), and scroll waves (in three dimensions) of electrical activation in cardiac tissue. To understand, and eventually control, such arrhythmias, it is important to carry out in vivo, ex vivo, in vitro, and in silico studies; the last of these has become increasingly important over the past three decades. In this thesis, I have carried out several in silico stud- ies of state-of-the-art mathematical models for cardiac tissue which focus mainly on four themes: (I) The effects of subcellular ion-channel modeling on electrical-wave dynamics in cardiac tissue; in particular, I have carried out a detailed comparison of wave dynamics in Hodgkin-Huxley and Markov- state formalisms for the Sodium (Na) channel in some mathematical models for human cardiac tissue. (II) The frequency and tip-trajectory of spiral waves and its dependence on electrophysiological parameters in a realistic mathematical model for human-ventricular tissue with and without fibrob- lasts. (III) The arrhythmogenicity of cardiac fibrosis and its dependence on the lacunarity parameter and Betti numbers of patterns of fibrotic tis- sue. (IV) The efficient elimination of pathological spiral and broken-spiral waves via a deep-learning-assisted detection and termination of spiral- and broken-spiral waves in mathematical models for cardiac tissue. In Chapter 2 we investigate the effects of different subcellular model- ing formalsims for an ion-channel and on its properties, the action-potential of a single cell, and spiral and scroll waves in two- and three-dimensional human ventricular tissue. In particular, we compare and contrast the ex- citation properties of cardiac myocytes and cardiac tissue modelled by (a) a Hodgkin-Huxley-model (...