Narrow Results

Computer simulation is applied to study the role of cellular coupling, dispersion of refractoriness as well as both of them, in the mechanisms underlying cardiac arrhythmias. We first assumed that local ischemia mainly induces cell to cell dispersion in the coupling resistance (case 1), refractory period (case 2) or both (case 3). Numerical experiments, based on the van Capelle and Durrer model, showed that vortices could not be induced in these conditions. In order to be more realistic about coronary circulation we simulated a patchy dispersion of cellular properties, each patch corresponding to the zone irrigated by a small coronary artery. In these conditions, a single activation wave could give rise to abnormal activities. Probabilities of reentry, estimated for the three cases cited above, showed that a severe alteration of the coupling resistance may be an important factor in the genesis of reentry. Moreover, use of isochronal maps revealed that vortices were both stable and sustained with an alteration of coupling alone or along with reductions of action potential duration. Conversely, simulations with reduction of the refractoriness alone induced only transient patterns.

A parametric study of composite strips leads to systems of partial differential equations, coupled through interface conditions, that are naturally solved in Laplace transform space. Because of the complexity of the solutions in transform space and the potential variations due to geometry and materials, a systematic approach to inversion is necessarily numerical. The Dubner-Abate-Crump (DAC) algorithm is the standard in such problems and is implemented. The presence of discontinuous wavefronts in the problems considered leads to Gibbs phenomenon; which, in turn, overestimates the values of maximum stress. These errors are mitigated by use of Lanczos' σ-factors, which combine naturally with the DAC algorithm.