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

Fingerprint

Calcium
Curvature
FitzHugh-Nagumo
Eikonal Equation
Linear equations
Wave propagation
Analogy
Linear equation
Model
Excitable Systems
Wave Speed
Wave Propagation
Limiting
Propagation

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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

In: SIAM Journal on Applied Mathematics, Vol. 74, No. 5, 01.01.2014, p. 1442-1462.

Research output: Contribution to journalArticle

@article{4ce0338ad6ae4ba6be7d304247c43749,
title = "Curvature dependence of propagating velocity for a simplified calcium model",
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.",
keywords = "Calcium dynamics, Eikonal equation, FitzHugh-Nagumo model, Waves",
author = "Wenjun Zhang and James Sneyd and Je-Chiang Tsai",
year = "2014",
month = "1",
day = "1",
doi = "10.1137/14095964X",
language = "English",
volume = "74",
pages = "1442--1462",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",

}

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 -