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

TL;DR

This study uses detailed numerical simulations of canine and human ventricular models to analyze how variations in potassium and calcium currents influence spiral and scroll wave dynamics, revealing that combined changes in these currents are crucial for wave stability.

Contribution

It provides a comprehensive stability diagram showing the combined effects of $I_{Kr}$ and $I_{CaL}$ on wave dynamics in realistic ventricular geometries, highlighting differences between models.

Findings

Wave stability depends mainly on simultaneous changes in $I_{Kr}$ and $I_{CaL}$.

3D geometry enhances scroll wave stability compared to 2D.

Transitions between wave states require coordinated modulation of both currents.

Abstract

We conduct a systematic,direct-numerical-simulation study,in mathematical models for ventricular tissue,of the dependence of spiral-and scroll-wave dynamics on $G_{Kr}$, the maximal conductance of the delayed rectifier Potassium current($I_{Kr}$) channel,and the parameter $\gamma_{Cao}$,which determines the magnitude and shape of the current $I_{CaL}$ for the L-type calcium-current channel,in both square and anatomically realistic,whole-ventricle simulation domains using canine and human models. We use ventricular geometry with fiber-orientation details and employ a physiologically realistic model for a canine ventricular myocyte. We restrict ourselves to an HRD-model parameter regime, which does not produce spiral- and scroll-wave instabilities because of other,well-studied causes like a very sharp action-potential-duration-restitution (APDR) curve or early after depolarizations(EADs) at the single-cell level. We find that spiral- or scroll-wave dynamics are affected predominantly by a simultaneous change in $I_{CaL}$ and $I_{Kr}$,rather than by a change in any one of these currents;other currents do not have such a large effect on these wave dynamics in 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 domain supports the confinement of the scroll waves and makes them more stable compared to their spiral-wave counterparts in 2D domain. We have also carried out a comparison of our HRD results with their counterparts for the human-ventricular TP06 model and have found important differences. In both these models,to make a transition,(from broken-wave to stable-scroll states or vice versa) we must simultaneously increase $I_{Kr}$ and decrease $I_{CaL}$;a modification of only one of these currents is not enough to effect this transition.