The Role of Physiology, Geometry and Mechanics in Some Cardiac Arrhythmias

Abstract

Chapter 1: We start with a brief introduction about the history and modern perspective, of cardiac literature, some description of the models we use for the electrophysiology simulations. Chapter 2 Focal arrhythmias, which arise from delayed afterdepolarizations (DADs), are observed in various pathophysiological heart conditions; these can lead to arrhythmias and sudden cardiac death. A clear understanding of the interplay of electrophysiological factors of cardiac myocytes, which lead to DADs, can suggest pharmacological targets that can eliminate DAD-induced arrhythmias. Therefore, we carry out multiscale investigations of two mathematical models for human-ventricular myocytes, namely, the ten Tusscher-Panfilov 06 (TP06) model and the HuVEC15 model from Himeno, et al., at the levels of single myocytes, one- and two-dimensional (1D and 2D) tissue, and anatomically realistic bi-ventricular domains using phase-field method. By using continuation analysis, we uncover steady- to oscillatory-state transitions in the Ca2+ concentrations and show the key parameters that affect this transition, in these models. We also show that the frequencies and amplitudes of the DADs are key features that can be used to classify the three types of DADs ovserved in these models. By carrying out detailed parametersensitivity analyses, we identify the electrophysiological parameters, in the myocyte models, that most affect these key features. We discuss the implications of our results for some DAD-induced ventricular arrhythmias, which we examine in detail in Chapter 3. Chapter 3: The calcium-overload conditions linked to abnormal calcium releases, can occur primarily in the following two phases of the action potential (AP): (a) triggered or late calcium release (LCR) during the plateau phase; (b) spontaneous calcium release (SCR) during the diastolic interval (DI). Experimental and numerical studies of LCRs and SCRs have suggested that these abnormal calcium releases can lead to triggered excitations and thence to life-threatening ventricular arrhythmias. We explore using a detailed in-silico investigation of the ten Tusscher-Panfilov (TP06) model for cardiac myocyte physiology, how the coexistence of LCRs and SCRs in one-, two-, and threedimensional (1D, 2D, and 3D) domains, with clumps of DAD-capable myocytes can lead to conduction block, complex spatiotemporal patterns like spiral and scroll waves. Chapter 4: Delayed afterdepolarizations (DADs), which occur during the diastolic phase of a cardiomyocyte action potential (AP), are frequently observed under specific pathophysiological conditions. The synchronization of DAD-capable myocytes can effectively overcome the inherent source-sink mismatch with adjacent normal myocytes, so it is an important mechanism for the genesis of premature ventricular contractions (PVCs). Our study elucidates the role of mechano-electrical feedback in modulating this critical source-sink requirement and its interplay with diffusional anisotropy in cardiac tissue. We combine the TP06 electrophysiological model for human ventricular myocytes with cardiac-tissue-mechanics models and account for spontaneous calcium releases (SCRs) and the randomness associated with these and with the disordered arrangement of DAD myocytes in a clump. In a cable-and 2D domains we demonstrate how mechanical contraction of the domain, influences the source-size requirement for the formation of PVCs. Chapter 5: Spiral waves, observed during cardiac arrhythmias, has a characteristic rotating wavefront encircling a central core with a phase singularity (spiral tip). While typically exhibiting circular trajectories, under certain conditions, these spirals can exhibit non-circular drifting patterns. This study investigates the influence of geometrical factors, such as size, curvature, and topology, on spiral wave dynamics. Employing an in-silico approach with a simple two-variable model, we explore spiral wave drift behaviour due to geometrical features such as topology, curvature and domain to wavelength size ratio. Chapter 6: We use our experience of finite-element modelling (used in Chapters 4 and 5) to develop algorithms and computer programs that address the spatiotemporal evolution of spiral or scroll waves in anatomically realistic ventricular geometries. Our approach includes cardiac-tissue mechanics, electrophysiology, electromechanics, mechano-electrical feedback in an optimised approach, for which we use the library deal.ii, an open-source, fast, parallel, scalable, and extensively documented library.