title: Unidirectional pinning and hysteresis of spatially discordant alternans in cardiac tissue.
abstract: Spatially discordant alternans is a widely observed pattern of voltage and calcium signals in cardiac tissue that can precipitate lethal cardiac arrhythmia. Using spatially coupled iterative maps of the beat-to-beat dynamics, we explore this pattern's dynamics in the regime of a calcium-dominated period-doubling instability at the single-cell level. We find a novel nonlinear bifurcation associated with the formation of a discontinuous jump in the amplitude of calcium alternans at nodes separating discordant regions. We show that this jump unidirectionally pins nodes by preventing their motion away from the pacing site following a pacing rate decrease but permitting motion towards this site following a rate increase. This unidirectional pinning leads to strongly history-dependent node motion that is strongly arrhythmogenic.
authors.affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA. skardal@colorado.edu
authors.forename: Per Sebastian
authors.initials: PS
authors.lastname: Skardal
authors.forename: Alain
authors.initials: A
authors.lastname: Karma
authors.forename: Juan G
authors.initials: JG
authors.lastname: Restrepo
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D002118:Calcium / Q000378:metabolism; D006329:Heart Conduction System / Q000502:physiology*; D008955:Models, Cardiovascular; D012849:Sinoatrial Node / Q000502:physiology
chemical_list: D002118:Calcium