V.N. Biktashev 
& A.V. Holden 
September 28, 1997
Institute for Mathematical Problems in Biology,
Pushchino, Moscow Region, 142292, Russia
Department of Physiology, University of Leeds, Leeds LS2 9JT, UK
Author to whom correspondence should be addressed
The vulnerability to re-entrant wave propagation, its characteristics (period, meander and stability), the effects of rotational transmural anisotropy, and the control of re-entrant waves by small amplitude perturbations and large amplitude defibrillating shocks are investigated theoretically and numerically for models based on high order, stiff biophysically derived excitation equations.
The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviours can be described by solutions of reaction-diffusion equation excitable medium models, in which the reaction terms come from the results of voltage clamp analyses of cell excitation processes -- membrane currents and pumps, intra- and extracellular ion accumulation and intracellular sequestration processes, and the diffusion coefficient tensor is obtained from the propagation velocity and scaled muscle fibre orientation. Numerical solution of such biophysical detailed models will allow the screening of putative antiarrhythmic agents, by computing their effects on vulnerability to re-entry, and the specification of means of pharmacologically modifying meander, to enhance the self-termination of re-entry. Quantitative aspects of defibrillation, by extinguishing propagating waves of excitation by a single shock, or by resonant drift induced by appropriately timed small amplitude perturbations, can be computed.