Cardiac alternans has emerged in recent years both as an important marker of long-term susceptibility to life-threatening arrhythmias, and as a possible mechanistic trigger of these arrhythmias. Although the importance of alternans is widely recognized, the mechanisms underlying alternans at the cellular level remain poorly understood, and the selection of available algorithms from which future medical devices may choose in order to terminate alternans is small. In this computational modeling study, a number of aspects of alternans were explored using a variety of mathematical models of cardiac myocytes. In the first part of this study, the effects of alternans and the concomitant alternation in short-term cardiac memory on the dynamic restitution curve were explored. It was found that the interaction of alternans and memory could result in a dynamic restitution curve that is not unique. To address this, a constant-memory restitution protocol was developed, one that enables unique, constant-memory restitution curves to be obtained. In the second part of this study, a new model-independent control method for suppressing alternans was developed. When applied to model cells exhibiting alternans, the cellular rhythm converged to a non-alternating period-1 rhythm over as wide, and in some cases a wider, range of feedback proportionality constant values relative to existing methods. In the third part of this study, the role of action potential morphology in alternans was investigated. It was found that the morphology of the action potential has a significant effect on the stability of the calcium handling system, with small changes in morphology resulting in a transition from no alternans to alternans. Finally, in the fourth part of this study, a method to probe the contributions of voltage and calcium to the mechanism of alternans was developed. This new approach makes it possible to quantify, for the first time, the relative contributions of voltage- and calcium-dependent coupling to cellular rhythm instabilities such as alternans. Using this method, it was found that voltage- and calcium-dependent coupling exhibit varying degrees of influence on action potential stability across cell models.
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