Mathematics Colloquia and Seminars

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Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms of the formation of SDA are not completely understood. In this study, we show a novel mechanism for the formation of SDA in the case where the cellular instability to alternans is caused by intracellular Ca cycling. We use a multi-scale computational model of the action potential (AP) and intracellular Ca cycling to study the formation of SDA at the cell, multi-cell, and tissue scales We show that SDA is formed, following a decrease in pacing cycle length (CL), in the case when Ca transient alternans develops over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). During this accumulation time, fine scale patterns of out-of-phase Ca alternans can form due to small subcellular fluctuations, which break the symmetry between opposite alternans phase. These patterns coarsen in time due to Ca diffusion and electrotonic coupling, and evolve toward a final steady state pattern displaying SDA. We identify a novel mechanism for SDA, which is a direct consequence of beat-to-beat variations of Ca cycling on the sarcomere scale, and diffusive coupling via both Ca and voltage in tissue. We argue that this mechanism is robust and is likely to underlie a wide range of experimentally observed patterns of SDA.