Coupled Cell Model of Border Zone Arrhythmias

Abstract

Border zones between normal and ischemic tissue have been implicated as a cause of arrhythmic cardiac activity. A variety of experiments with coupled cells and strips of tissue has been designed to understand the arrhythmogenic effects of border zone currents. In this paper, we use systems of differential equations to model an ischemic (depolarized) cell (or region) coupled to a normal cell under a variety of conditions. For two ionic models (reduced Hodgkin--Huxley and Luo--Rudy I), we find the boundary in parameter space between oscillatory and nonoscillatory solutions. We find that there are regions in parameter space for which the ischemic cell (region) is stable and inexcitable when uncoupled, but when coupled to a normal, excitable cell the cells oscillate. We state a general principle that relates the oscillation of a forced single cell to oscillations of the coupled system. Furthermore, in modeling drug-modified experimental dynamics we are able to reproduce early after depolarization (EAD)--like phenomena, which has implications in locating oscillations in the drug-free experiment. Finally, we describe a mechanism by which oscillations in the transmembrane potential may be encountered during reperfusion.