Indeterminacy of spatiotemporal cardiac alternans

Abstract

Cardiac alternans, a beat-to-beat alternation in action potential duration (at the cellular level) or in ECG morphology (at the whole heart level), is a marker of ventricular fibrillation, a fatal heart rhythm that kills hundreds of thousands of people in the US each year. Investigating cardiac alternans may lead to a better understanding of the mechanisms of cardiac arrhythmias and eventually better algorithms for the prediction and prevention of such dreadful diseases. In paced cardiac tissue, alternans develops under increasingly shorter pacing period. Existing experimental and theoretical studies adopt the assumption that alternans in homogeneous cardiac tissue is exclusively determined by the pacing period. In contrast, we find that, when calcium-driven alternans develops in cardiac fibers, it may take different spatiotemporal patterns depending on the pacing history. Because there coexist multiple alternans solutions for a given pacing period, the alternans pattern on a fiber becomes unpredictable. Using numerical simulation and theoretical analysis, we show that the coexistence of multiple alternans patterns is induced by the interaction between electrotonic coupling and an instability in calcium cycling.

Spatiotemporal intracellular calcium dynamics during cardiac alternans

“…This bistability leads to a nonuniqueness of the dynamically selected state for negative coupling that has been noted in previous studies of coupled cells and tissue. [33][34][35] The analysis of the weak negative coupling limit makes it possible here to obtain a simple analytical prediction of the condition for bistability and the results will also hold for two coupled cells in this limit.…”

Estimating eigenvalues of dynamical systems from time series with applications to predicting cardiac alternans

“…Further, alternans of the Shiferaw-Fox model have been studied by numerous authors (Sato et al 2006;Weiss et al 2006;Zhao 2008;Tolkacheva & Zhao 2012). This model is based on the physiology of canine dogs whose rest heart rates are between 60 and 160 beats per minute.…”

“…The Shiferaw-Fox model can vary different parameters to describe different mechanisms of alternans: voltage-driven, positive Ca to APD coupling and negative Ca to APD coupling (Sato et al 2006;Zhao 2008;Tolkacheva & Zhao 2012;Lemay et al 2012). Our first model analyses time series from negative Ca to APD coupling (where alternans occurs at a BCL of 397 ms) while a second looks at time series from positive Ca to APD coupling (where alternans occurs at a BCL of 315 ms).…”

Nonlinear Dynamics in Cardiology

“…Finally, bistability between different phase-locked rhythms of low periodicity [in particular between alternans (2:2) and regular beating (1:1) and between block (2:1) and regular beating] is recurrently observed in cardiac cells (38, 39), small tissues (11), whole hearts (39, 40), and mathematical cell (38, 41, 42) and tissue models (42, 43). At the level of the whole heart, bistability can also manifest between alternans with different spatiotemporal patterns (39).…”

“…At the level of the whole heart, bistability can also manifest between alternans with different spatiotemporal patterns (39). Indeed, in simulated tissue models, multistability between a range of different spatial alternans patterns can occur (42, 43), suggesting prudence should be taken when performing such simulations and interpreting their outcomes.…”