Asymptotic properties of mathematical models of excitability

Nonlinear Sciences – Pattern Formation and Solitons

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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.

Rate now

     

Profile ID: LFWR-SCP-O-38386

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.