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A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor

  • A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed. The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion equation for the extracellular proton concentration on the macroscale. In a more general context the existence and uniqueness of solutions for local and nonlocal SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both, in its local version and the case with nonlocal path dependence. Numerical simulations are performed to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.

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Author:Peter E. Kloeden, Stefanie Sonner, Christina Surulescu
Document Type:Preprint
Language of publication:English
Publication Date:2015/06/19
Year of Publication:2015
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2015/06/22
Tag:intra- and extracellular proton dynamics; multiscale model; nonlocal sample dependence; partial differential equations; stochastic differential equations; tumor acidity
Number of page:22
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Fxx Equations and systems with randomness [See also 34K50, 60H10, 93E03] / 34F05 Equations and systems with randomness [See also 34K50, 60H10, 93E03]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R60 Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 13.02.2015