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

Anne Dietrich; Niklas Kolbe; Nikolaos Sfakianakis; Christina Surulescu

doi:10.1137/21M1412104

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

Anne Dietrich, Niklas Kolbe, Nikolaos Sfakianakis^*, Christina Surulescu

^*Corresponding author for this work

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	685-713
Number of pages	29
Journal	Multiscale Modeling and Simulation
Volume	20
Issue number	2
DOIs	https://doi.org/10.1137/21M1412104
Publication status	Published - 24 Jun 2022

Keywords

Glioma invasion
Multiscale modeling
Flux-limited PDE
Receptor binding

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10.1137/21M1412104

Dietrich_2022_MMS_Multiscale-modeling_VoR
Copyright © 2022 Society for Industrial and Applied Mathematics. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1137/21M1412104.
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1 Working paper

Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs
Dietrich, A., Kolbe, N., Sfakianakis, N. & Surulescu, C., 7 Oct 2020.
Research output: Working paper

Cite this

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title = "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.",

keywords = "Glioma invasion, Multiscale modeling, Flux-limited PDE, Receptor binding",

author = "Anne Dietrich and Niklas Kolbe and Nikolaos Sfakianakis and Christina Surulescu",

note = "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.",

year = "2022",

month = jun,

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doi = "10.1137/21M1412104",

language = "English",

volume = "20",

pages = "685--713",

journal = "Multiscale Modeling and Simulation",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Multiscale modeling of glioma invasion

T2 - from receptor binding to flux-limited macroscopic PDEs

AU - Dietrich, Anne

AU - Kolbe, Niklas

AU - Sfakianakis, Nikolaos

AU - Surulescu, Christina

N1 - 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.

PY - 2022/6/24

Y1 - 2022/6/24

N2 - 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.

AB - 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.

KW - Glioma invasion

KW - Multiscale modeling

KW - Flux-limited PDE

KW - Receptor binding

U2 - 10.1137/21M1412104

DO - 10.1137/21M1412104

M3 - Article

SN - 1540-3459

VL - 20

SP - 685

EP - 713

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

IS - 2

ER -

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

Abstract

Keywords

UN SDGs

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Research output

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

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