Calcium waves with mechano-chemical couplings

Bogdan Kazmierczak; Zbigniew Peradzynski

doi:10.3934/mbe.2013.10.743

Article Contents

2013, Volume 10, Issue 3: 743-759. Doi: 10.3934/mbe.2013.10.743

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Calcium waves with mechano-chemical couplings

Bogdan Kazmierczak^1, and
Zbigniew Peradzynski^2,

1.
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw
2.
Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw

Received: May 31, 2012

Revised: October 31, 2012

Published: March 2013

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Abstract

As follows from experiments, waves of calcium concentration in biological tissues can be easily excited by a local mechanical stimulation. Therefore the complete theory of calcium waves should also take into account coupling between mechanical and chemical processes. In this paper we consider the existence of travelling waves for buffered systems, as in [22], completed, however, by an equation for mechanical equilibrium and respective mechanochemical coupling terms. Thus the considered, coupled system consists of reaction-diffusion equations (for the calcium and buffers concentrations) and equations for the balance of mechanical forces.

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Mathematics Subject Classification: Primary: 35K57, 35C07; Secondary: 35Q92.

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