Impulse patterning and relaxation propagation in excitable media

C. Elphick, E. Meron, J. Rinzel, E. A. Spiegel

Research output: Contribution to journalArticle

Abstract

Wavetrains of impulses in homogeneous excitable media relax during propagation toward constant-speed patterns. Here we present a study of this relaxation process. Starting with the basic reaction-diffusion or cable equations, we derive kinematics for the trajectories of widely spaced impulses in the form of ordinary differential equations for the set of times at which impulses arrive at a given point in space. Stability criteria derived from these equations allow us to determine the possible asymptotic forms of propagating trains. When the recovery after excitation is monotonic, only one stable train exists for a given propagation speed. In the case of an oscillatory recovery, however, many stable trains are possible. This essential difference between monotonic and oscillatory recoveries manifests itself in qualitatively distinct relaxational behaviors.

Original languageEnglish (US)
Pages (from-to)249-268
Number of pages20
JournalJournal of Theoretical Biology
Volume146
Issue number2
DOIs
StatePublished - Sep 21 1990

Fingerprint

Excitable Media
Patterning
Biomechanical Phenomena
Impulse
Recovery
Propagation
Monotonic
Propagation Speed
Stability criteria
Relaxation processes
Reaction-diffusion
kinematics
Cable
Stability Criteria
Ordinary differential equations
trajectories
Kinematics
Cables
Ordinary differential equation
Excitation

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Applied Mathematics
  • Modeling and Simulation
  • Statistics and Probability
  • Medicine(all)

Cite this

Impulse patterning and relaxation propagation in excitable media. / Elphick, C.; Meron, E.; Rinzel, J.; Spiegel, E. A.

In: Journal of Theoretical Biology, Vol. 146, No. 2, 21.09.1990, p. 249-268.

Research output: Contribution to journalArticle

Elphick, C. ; Meron, E. ; Rinzel, J. ; Spiegel, E. A. / Impulse patterning and relaxation propagation in excitable media. In: Journal of Theoretical Biology. 1990 ; Vol. 146, No. 2. pp. 249-268.
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