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Using Pair Approximation Methods to Analyze Behavior of a Probabilistic Cellular Automaton Model for Intracellular Cardiac Calcium Dynamics
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Robert J Rovetti\inst{1,}
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\inst{1}Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045 \\
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rrovetti@lmu.edu
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Pair approximation and quartet approximation methods are applied to a probabilistic cellular automaton model (PCA) designed to model physiological calcium dynamics in cardiac myocytes. The update rules of the PCA have a unique two-stage (split-step) structure, resulting in multiple pathways by which the lattice sites can transition to the next state. A method for systematically addressing the resulting combinatorial complexity in applying the approximation methods is presented. Observed macroscopic features of the PCA (periodicity in the activation fraction, and spatial clustering) obtained by simulation are compared to those predicted by the two approximation methods as well as by a mean-field analysis. We show that the second-order quartet approximation is able to accurately predict the onset of both periodic behavior and spatial clustering.
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