Dynamics of rotating vortices in the Beeler-Reuter model of cardiac tissue

Cardiac muscle is a highly nonlinear active medium which may undergo rotating vortices of electrical activity. We have studied vortex dynamics using a detailed mathematical model of cardiac muscle based on the Beeler-Reuter equations. Specifically, we have investigated the dependence of vortex dynamics on parameters of the excitable cardiac cell membrane in a homogeneous isotropic medium. The results demonstrate that there is a transition from the vortex with circular core that is typical of most excitable media, including the Belousov-Zhabotinsky reaction, to a vortex with linear core that has been observed in heart muscle during so-called reentrant arrhythmias. The transition is not direct but goes through the well-known sequence of nonstationary quasiperiodic rotating vortices. In the parameter space there are domains of different types of vortex dynamics. Such domains include regions where: (1) vortices can not be generated, (2) vortices occur readily, and (3) vortices arise but have a short lifetime. The results provide testable predictions about dynamics associated with initiation, maintenance and termination of cardiac arrhythmias.