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Quantitative Biology > Tissues and Organs

arXiv:2010.03277 (q-bio)
[Submitted on 7 Oct 2020 (v1), last revised 13 Apr 2021 (this version, v2)]

Title:Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs

Authors:Anne Dietrich, Niklas Kolbe, Nikolaos Sfakianakis, Christina Surulescu
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Abstract:We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered angiogenesis. The multiscale procedure links single-cell and mesoscopic dynamics with population level behavior, leading on the macroscopic scale to flux-limited glioma diffusion and multiple taxis. We verify the non-negativity of regular solutions (provided they exist) to the obtained macroscopic PDE-ODE system and perform numerical simulations to illustrate the solution behavior under several scenarios.
Comments: 28 pages, 7 figures
Subjects: Tissues and Organs (q-bio.TO); Analysis of PDEs (math.AP); Cell Behavior (q-bio.CB)
MSC classes: 35Q92 (Primary), 92C17, 92C50 (Secondary)
Cite as: arXiv:2010.03277 [q-bio.TO]
  (or arXiv:2010.03277v2 [q-bio.TO] for this version)
  https://doi.org/10.48550/arXiv.2010.03277

Submission history

From: Niklas Kolbe [view email]
[v1] Wed, 7 Oct 2020 08:58:44 UTC (1,689 KB)
[v2] Tue, 13 Apr 2021 11:04:32 UTC (13,007 KB)
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