BIOPHYSICAL THEORY AND MODELING |
Conditions for propagation and block of excitation in an asymptotic model of atrial tissue
Radostin D. Simitev 1 and Vadim N. Biktashev 1*
1 University of Liverpool
* To whom correspondence should be addressed. E-mail: vnb{at}liv.ac.uk.
Submitted on August 14, 2005
Revised on September 21, 2005
Accepted on 12 December 2005
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Abstract |
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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 non-standard. Here we apply such a novel asymptotic method to an ionic model of human atrial tissue in order 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 break-up of re-entrant waves.
Key Words:
conduction, excitation, mathematical model, refractoriness
