Search Advanced

Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 743-759. doi: 10.3934/mbe.2013.10.743
Previous Article Next Article

Calcium waves with mechano-chemical couplings

  • 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: 01 June 2012 Accepted: 29 June 2018 Published: 01 April 2013

  • MSC : Primary: 35K57, 35C07; Secondary: 35Q92.

  • As follows from experiments, waves ofcalcium concentration in biological tissuescan be easily excited by a local mechanical stimulation.Therefore the complete theory of calcium waves should alsotake into account couplingbetween mechanical and chemical processes.In this paper we consider the existenceof 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 (forthe calcium and buffers concentrations) and equations for thebalance of mechanical forces.

    Citation: Bogdan Kazmierczak, Zbigniew Peradzynski. Calcium waves with mechano-chemical couplings[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 743-759. doi: 10.3934/mbe.2013.10.743

    Related Papers:

  • As follows from experiments, waves ofcalcium concentration in biological tissuescan be easily excited by a local mechanical stimulation.Therefore the complete theory of calcium waves should alsotake into account couplingbetween mechanical and chemical processes.In this paper we consider the existenceof 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 (forthe calcium and buffers concentrations) and equations for thebalance of mechanical forces.


    加载中
    [1] Acta Physiol. Scand., 181 (2004), 359-366.
    [2] Nonlinear Analysis TM & A, 26 (1996), 1621-1642.
    [3] Circ. Res., 27 (1970), 105-119.
    [4] Journal of Cell Science, 117 (2004), 2203-2214.
    [5] Advances in Physics, 53 (2004), 255-440.
    [6] Nonlinear Analysis: Theory, Methods and Applications, 36 (1999), 45-62.
    [7] Am. J. Physiol. (Heart Circ. Physiol.), 290 (2006), 2498-2508.
    [8] Proc. Natl. Acad. Sci. USA, 88 (1991), 9883-9887.
    [9] Biol. Cell, 99 (2007), 75-184.
    [10] J. Biological Chemistry, 278 (2003), 4082-4086.
    [11] Journal of Mathematical Biology, 62 (2011), 1-38.
    [12] Nonlinearity, 21 (2008), 71-96.
    [13] Mathematical Models and Methods in Applied Sciences, 18 (2008), 883-912
    [14] Nonlinear Analysis: Theory, Methods and Applications, 55 (2003), 467-491.
    [15] Springer-Verlag, 1998.
    [16] 2nd edition, Springer-Verlag, Berlin, 1993.
    [17] J. Diff. Equat., 20 (1984), 225-256.
    [18] Arch. Mech., 62 (2010), 423-440.
    [19] Archive of Applied Mechanics, 74 (2005), 827-833.
    [20] Arch. Mech., 64 (2012), pp. 477-509
    [21] Journal of Biomechanics, 29 (1996), 461-467.
    [22] SIAM J. Appl. Math., 58 (1998), 1178-1192.
    [23] J. Wiley and Sons, New York, 1958.
    [24] AMS, Providence 1994.
    [25] Am. J. Physiol. Gastrointest. Liver Physiol., 276 (1999), 1204-1212.
  • Reader Comments
  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
2.6 3.9

Metrics

Article views(1564) PDF downloads(462) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog