Asymptotic properties of mathematical models of excitability.

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Asymptotic properties of mathematical models of excitability.

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dc.contributor.author Biktasheva, I. V. en_US
dc.contributor.author Simitev, R. D. en_US
dc.contributor.author Suckley, R. en_US
dc.contributor.author Biktashev, V. N. en_US
dc.date.accessioned 2012-09-28T17:57:19Z en_US
dc.date.accessioned 2013-03-20T12:43:56Z
dc.date.issued 2006 en_US
dc.description.abstract We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics. en_US
dc.identifier.citation Vol. 364 (1842), pp. 1283 - 1298 en_US
dc.identifier.doi 10.1098/rsta.2006.1770 en_US
dc.identifier.other 080V042T0000K322 en_US
dc.identifier.uri http://hdl.handle.net/10036/3774 en_US
dc.language.iso eng en_US
dc.publisher Royal Society en_US
dc.relation.url http://dx.doi.org/10.1098/rsta.2006.1770 en_US
dc.subject Action Potentials en_US
dc.subject Animals en_US
dc.subject Computer Simulation en_US
dc.subject Heart Conduction System en_US
dc.subject Humans en_US
dc.subject Models, Cardiovascular en_US
dc.subject Models, Neurological en_US
dc.subject Myocytes, Cardiac en_US
dc.title Asymptotic properties of mathematical models of excitability. en_US
dc.date.available 2012-09-28T17:57:19Z en_US
dc.date.available 2013-03-20T12:43:56Z
dc.identifier.issn 1364-503X 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 England en_US
dc.description Copyright © 2006 The Royal Society en_US
dc.description Journal Article en_US
dc.identifier.journal Philosophical Transactions A: Mathematical, Physical and Engineering Sciences en_US


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