Dynamics of scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from ischaemic boundary is one of major causes of ischemia-reperfusion arrhythmias, though exact mechanisms remain poorly understood. We used asymptotic theory of spiral waves drift based on response functions to compute specific forces acting on scroll waves in the vicinity of ischaemic border. The model included macroscopic gradients of cell-to-cell coupling and of cell excitability, and microscopic heterogeneity of individual cells, with Beeler-Reuter-Pumir explicit, albeit simplified, description of ionic currents. The quantitative interplay of specific forces explained formation of vortices, their drift together with recovering boundary, transient pinning to local inhomogeneities followed by penetration into bulk of healthy tissue. Likelihood of vortex escape into better coupled tissue depended on the border zone recovery speed. Direct numerical simulations confirmed the theoretical predictions for evolution of vortices.