Controllability of Voltage- and Calcium-Driven Alternans in a Cardiac Ionic Model

Laura Munoz1, Mark Ampofo1, Elizabeth Cherry2
1Rochester Institute of Technology, 2Georgia Institute of Technology


Abstract

Motivation: Electrical alternans, a beat-to-beat alternation in cardiac action potential duration, can precede dangerous abnormal rhythms. Alternans may arise from different mechanisms, including instabilities in membrane-potential dynamics (voltage-driven alternans) or intracellular calcium dynamics (calcium-driven alternans). Some studies indicated that the effectiveness of alternans suppression strategies may depend on the alternans mechanism. We recently examined mechanistic influences on alternans controllability within a map model, but low dimensionality of the model limited the analysis to a small number of strategies.

Aims: Here, we aimed to examine the impact of different mechanisms on alternans controllability within a higher-dimensional model, the Shiferaw, Sato, and Karma (SSK) ionic model, which allowed examination of a wider range of control strategies.

Methods: For each mechanism under consideration, we numerically linearized the SSK system about its fixed point for a period of 350ms, which produced alternans in the model, and estimated eigenvalues of the resulting Jacobian. Linear stability analysis indicated the presence of a dominant alternans eigenvalue. To determine the ability of a control strategy to suppress alternans, we computed modal controllability measures for the alternans eigenvalue, where each strategy corresponded to perturbing one of the dynamical variables periodically.

Results: For voltage-driven alternans, the predicted best control strategies involved perturbing the slow delayed rectifier K+ activation gate or the L-type Ca2+ voltage-dependent inactivation gate. For calcium-driven alternans, the best strategies were to perturb the cytosolic Ca2+ concentration or the average junctional SR calcium concentration of compartments not being drained (cj’). Perturbing cj’ was the best common approach for suppressing either type of alternans, although the more practical strategy of perturbing voltage was still a viable control approach for either mechanism.

Conclusions: The best strategy for suppressing alternans within the SSK model varied depending on the type of alternans, although some common strategies were indicated by the controllability measure.