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We conduct a systematic,direct-numerical-simulation study,in mathematicalmodels for ventricular tissue,of the dependence of spiral-and scroll-wavedynamics on $G_{Kr}$, the maximal conductance of the delayed rectifierPotassium current($I_{Kr}$) channel,and the parameter $\gamma_{Cao}$,whichdetermines the magnitude and shape of the current $I_{CaL}$ for the L-typecalcium-current channel,in both square and anatomicallyrealistic,whole-ventricle simulation domains using canine and human models. Weuse ventricular geometry with fiber-orientation details and employ aphysiologically realistic model for a canine ventricular myocyte. We restrictourselves to an HRD-model parameter regime, which does not produce spiral- andscroll-wave instabilities because of other,well-studied causes like a verysharp action-potential-duration-restitution (APDR) curve or early afterdepolarizations(EADs) at the single-cell level. We find that spiral- orscroll-wave dynamics are affected predominantly by a simultaneous change in$I_{CaL}$ and $I_{Kr}$,rather than by a change in any one of thesecurrents;other currents do not have such a large effect on these wave dynamicsin this parameter regime of the HRD model.We obtain stability diagrams in the$G_{Kr} -\gamma_{Cao}$ plane.In the 3D domain,the geometry of the domainsupports the confinement of the scroll waves and makes them more stablecompared to their spiral-wave counterparts in 2D domain. We have also carriedout a comparison of our HRD results with their counterparts for thehuman-ventricular TP06 model and have found important differences. In boththese models,to make a transition,(from broken-wave to stable-scroll states orvice versa) we must simultaneously increase $I_{Kr}$ and decrease $I_{CaL}$;amodification of only one of these currents is not enough to effect thistransition.

Spiral- and scroll-wave dynamics in mathematical models for canine and human ventricular tissue with varying Potassium and Calcium currents