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A multiscale model for pH-tactic invasion with time-varying carrying capacities

  • We propose a model for acid-mediated tumor invasion involving two different scales: the microscopic one, for the dynamics of intracellular protons and their exchange with their extracellular counterparts, and the macroscopic scale of interactions between tumor cell and normal cell populations, along with the evolution of extracellular protons. We also account for the tactic behavior of cancer cells, the latter being assumed to biase their motion according to a gradient of extracellular protons (following [2,31] we call this pH taxis). A time dependent (and also time delayed) carrying capacity for the tumor cells in response to the effects of acidity is considered as well. The global well posedness of the resulting multiscale model is proved with a regularization and fixed point argument. Numerical simulations are performed in order to illustrate the behavior of the model.

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Author:Christina Surulescu, Gülnihal Meral, Christian Stinner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-37578
Document Type:Preprint
Language of publication:English
Publication Date:2014/03/17
Year of Publication:2014
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2014/03/18
Tag:multiscale models; pH-taxis; reaction-diffusion-taxis equations; time-delayed carrying capacities; tumor cell migration
Number of page:21
Source:IMA Journal of Applied Mathematics 80, No. 5, 1300-1321 (2015)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K57 Reaction-diffusion equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q92 PDEs in connection with biology and other natural sciences
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C17 Cell movement (chemotaxis, etc.)
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012