Asymptotic analysis and analytical solutions of a model of cardiac excitation.

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Asymptotic analysis and analytical solutions of a model of cardiac excitation.

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dc.contributor.author Biktashev, V. N. en_US
dc.contributor.author Suckley, R. en_US
dc.contributor.author Elkin, Y. E. en_US
dc.contributor.author Simitev, R. D. en_US
dc.date.accessioned 2012-09-28T17:58:18Z en_US
dc.date.accessioned 2013-03-20T12:24:42Z
dc.date.issued 2008 en_US
dc.description.abstract We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble in J. Physiol. 160:317-352, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an "Archetypal Model" with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable "caricature" of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the "caricature" right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model. en_US
dc.identifier.citation Vol. 70 (2), pp. 517 - 554 en_US
dc.identifier.doi 10.1007/s11538-007-9267-0 en_US
dc.identifier.uri http://hdl.handle.net/10036/3777 en_US
dc.language.iso eng en_US
dc.publisher Springer Verlag en_US
dc.relation.url http://dx.doi.org/10.1007/s11538-007-9267-0 en_US
dc.subject Action Potentials en_US
dc.subject Animals en_US
dc.subject Anisotropy en_US
dc.subject Computer Simulation en_US
dc.subject Evoked Potentials, Motor en_US
dc.subject Humans en_US
dc.subject Ion Channel Gating en_US
dc.subject Models, Cardiovascular en_US
dc.subject Myocytes, Cardiac en_US
dc.subject Nonlinear Dynamics en_US
dc.subject Purkinje Fibers en_US
dc.subject Reference Standards en_US
dc.subject Reproducibility of Results en_US
dc.title Asymptotic analysis and analytical solutions of a model of cardiac excitation. en_US
dc.date.available 2012-09-28T17:58:18Z en_US
dc.date.available 2013-03-20T12:24:42Z
dc.identifier.issn 0092-8240 en_US
exeter.contacts.depositing-owner-email Biktashev, Vadim <V.N.Biktashev@exeter.ac.uk> en_US
exeter.contacts.depositing-owner-email Biktashev, Vadim <V.N.Biktashev@exeter.ac.uk> en_US
exeter.contacts.owner-email Biktashev, Vadim <V.N.Biktashev@exeter.ac.uk> en_US
exeter.contacts.owner-email Biktashev, Vadim <V.N.Biktashev@exeter.ac.uk> en_US
exeter.place-of-publication United States en_US
dc.description The original publication is available at www.springerlink.com - http://link.springer.com/article/10.1007/s11538-007-9267-0 en_US
dc.description Journal Article en_US
dc.description Copyright © Springer en_US
dc.identifier.journal Bulletin of Mathematical Biology en_US


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