Numerical Studies of Spiral- and Scroll-wave Dynamics in Cardiac Tissue: (1) Spiral- and Scroll-Wave Turbulence; (2) Spiral- and Scroll-Wave dynamics in Anatomically and Physiologically realistic Mathematical Models for Canine and Human Ventricular Tissue

Abstract

A summary of the main results of our studies is given below. In most of our work, we use three mathematical models for cardiac myocytes, namely, the Panfilov model, the Aliev-Panfilov model, and the Hund-Rudy-Dynamic (HRD) canine-ventricular model for our simulations. The first two are two-variable models; the HRD model is a realistic multi-variable complicated model with 45 variables; in a few cases we also employ the TP06 human-ventricular model. The equations for the first two models are given in Chapter 2. The full descriptions of the HRD model and the TP06 model equations are given in Appendices A and B, respectively. In Appendix C, we give a brief explanation of the phase-field method that we have used in our DNS’s to handle boundary conditions.