Curvature dependence of propagating velocity for a simplified calcium model

Wenjun Zhang, James Sneyd, Je Chiang Tsai

Research output: Contribution to journalArticle

Abstract

It is known that the relation between curvature and wave speed plays a key role in the propagation of two-dimensional waves in an excitable model. For typical excitable models (e.g., the FitzHugh-Nagumo (FHN) model), such a relation is believed to obey the linear eikonal equation, which states that the relation between the normal velocity and the local curvature is approximately linear. In this paper, we show that for a caricature model of intracellular calcium dynamics, although its temporal dynamics can be investigated by analogy with the FHN model, the curvature relation does not obey the linear eikonal equation even in the limiting case. Hence, this caricature calcium model may be an unexpected excitable system, whose wave propagation properties cannot be always understood by analogy with the FHN model.

Original languageEnglish
Pages (from-to)1442-1462
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume74
Issue number5
DOIs
Publication statusPublished - 2014 Jan 1

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Keywords

  • Calcium dynamics
  • Eikonal equation
  • FitzHugh-Nagumo model
  • Waves

ASJC Scopus subject areas

  • Applied Mathematics

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