title: Conditions for propagation and block of excitation in an asymptotic model of atrial tissue.
abstract: Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction of the models. Earlier results have shown that the asymptotics of cardiac equations are nonstandard. Here we apply such a novel asymptotic method to an ionic model of human atrial tissue to obtain a reduced but accurate model for the description of excitation fronts. Numerical simulations of spiral waves in atrial tissue show that wave fronts of propagating action potentials break up and self-terminate. Our model, in particular, yields a simple analytical criterion of propagation block, which is similar in purpose but completely different in nature to the "Maxwell rule" in the FitzHugh-Nagumo type models. Our new criterion agrees with direct numerical simulations of breakup of reentrant waves.
authors.affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom.
authors.forename: Radostin D
authors.initials: RD
authors.lastname: Simitev
authors.forename: Vadim N
authors.initials: VN
authors.lastname: Biktashev
mesh_terms: D000200:Action Potentials; D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D006325:Heart Atria / Q000473:pathology*; D006329:Heart Conduction System; D006352:Heart Ventricles / Q000473:pathology; D006801:Humans; D007477:Ions; D008955:Models, Cardiovascular; D015233:Models, Statistical; D008962:Models, Theoretical; D032342:Muscle Cells / Q000473:pathology; D015203:Reproducibility of Results; D013997:Time Factors
chemical_list: D007477:Ions