Abstract
Cellular calcium transient alternans are beat-to-beat alternations in the peak cytosolic calcium concentration exhibited by cardiac cells during rapid electrical stimulation or under pathological conditions. Calcium transient alternans promote action potential duration alternans, which have been linked to the onset of life-threatening ventricular arrhythmias. Here we use a recently developed physiologically detailed mathematical model of ventricular myocytes to investigate both stochastic and deterministic aspects of intracellular calcium dynamics during alternans. The model combines a spatially distributed description of intracellular calcium cycling, where a large number of calcium release units are spatially distributed throughout the cell, with a full set of ionic membrane currents. The results demonstrate that ion channel stochasticity at the level of single calcium release units can influence the whole-cell alternans dynamics by causing phase reversals over many beats during fixed frequency pacing close to the alternans bifurcation. They also demonstrate the existence of a wide range of dynamical states. Depending on the sign and magnitude of calcium-voltage coupling, calcium alternans can be spatially synchronized or desynchronized, in or out of phase with action potential duration alternans, and the node separating out-of-phase regions of calcium alternans can be expelled from or trapped inside the cell. This range of states is found to be larger than previously anticipated by including a robust global attractor where calcium alternans can be spatially synchronized but out of phase with action potential duration alternans. The results are explained by a combined theoretical analysis of alternans stability and node motion using general iterative maps of the beat-to-beat dynamics and amplitude equations.