Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-08-12
Nonlinear Sciences
Pattern Formation and Solitons
15 pages, 8 figures, to appear in Phil Trans Roy Soc London A
Scientific paper
10.1098/rsta.2006.1770
We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic timescales 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 break-ups and self-termination of re-entrant waves in excitable media with Courtemanche et al. (1998) kinetics.
Biktashev Vadim N.
Biktasheva Irina V.
Simitev Radostin D.
Suckley Rebecca
No associations
LandOfFree
Asymptotic properties of mathematical models of excitability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Asymptotic properties of mathematical models of excitability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic properties of mathematical models of excitability will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-38386