Spatially Discordant Alternans in Cardiac Tissue

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Abstract
Spatially discordant alternans, where the action potential duration (APD) and intracellular calcium transient (Cai) alternate with opposite phase in different regions of tissue, is known to promote wave break and reentry. However, this phenomenon is not completely understood. It is known that alternans at the cellular level can be caused by dynamical instabilities arising from either membrane voltage (Vm) attributable to steep APD restitution or to calcium (Ca) cycling. Here, we used a mathematical model of intracellular Ca cycling, coupled with membrane ion currents, to investigate the dynamics of Vm and Cai transient alternans in an isolated cell, in two electrotonically coupled cells, and in 1D spatially homogeneous tissue. Our main finding is a novel instability mechanism in which the bidirectional coupling of Vm and Cai can drive the Cai transient of two neighboring cells to be out of phase. This instability is manifested in cardiac tissue by the dynamical formation of spatially discordant alternans. In this case, Cai transient alternans can reverse phase over a length scale of one cell, whereas APD alternans reverses phase over a much longer length scale set by the electrotonic coupling. We analyze this mechanism in detail and show that it is a robust consequence of experimentally established properties of the bidirectional coupling between Ca cycling and Vm dynamics. Finally, we address the experimental relevance of these findings and suggest physiological conditions under which these patterns can be observed.