Multiscale modeling of glioma invasion : from receptor binding to flux-limited macroscopic PDEs
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 nonnegativity 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.
Citation
Dietrich , A , Kolbe , N , Sfakianakis , N & Surulescu , C 2022 , ' Multiscale modeling of glioma invasion : from receptor binding to flux-limited macroscopic PDEs ' , Multiscale Modeling and Simulation , vol. 20 , no. 2 , pp. 685-713 . https://doi.org/10.1137/21M1412104
Publication
Multiscale Modeling and Simulation
Status
Peer reviewed
ISSN
1540-3459Type
Journal article
Description
Funding: The work of the first and fourth authors was supported by the German Federal Ministry of Education and Research (BMBF) through project GlioMaTh 05M2016. The work of the third author was supported by the Postdoctoral Fellowship for Research in Japan (Standard) of the Japan Society for the Promotion of Science.Collections
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