### 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 language | English |
---|---|

Pages (from-to) | 1442-1462 |

Number of pages | 21 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 74 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*74*(5), 1442-1462. https://doi.org/10.1137/14095964X

**Curvature dependence of propagating velocity for a simplified calcium model.** / Zhang, Wenjun; Sneyd, James; Tsai, Je-Chiang.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 74, no. 5, pp. 1442-1462. https://doi.org/10.1137/14095964X

}

TY - JOUR

T1 - Curvature dependence of propagating velocity for a simplified calcium model

AU - Zhang, Wenjun

AU - Sneyd, James

AU - Tsai, Je-Chiang

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Calcium dynamics

KW - Eikonal equation

KW - FitzHugh-Nagumo model

KW - Waves

UR - http://www.scopus.com/inward/record.url?scp=84919785812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919785812&partnerID=8YFLogxK

U2 - 10.1137/14095964X

DO - 10.1137/14095964X

M3 - Article

VL - 74

SP - 1442

EP - 1462

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -