Modeling multiple taxis : tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
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We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.
Kolbe , N , Sfakianakis , N , Stinner , C , Surulescu , C & Lenz , J 2021 , ' Modeling multiple taxis : tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence ' , Discrete and Continuous Dynamical Systems - Series B , vol. 26 , no. 1 , pp. 443-481 . https://doi.org/10.3934/dcdsb.2020284
Discrete and Continuous Dynamical Systems - Series B
Copyright © 2021 American Institute of Mathematical Sciences. 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 author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.3934/dcdsb.2020284.
DescriptionN. Kolbe gratefully acknowledges the support by the International Research Fellowship of the Japanese Society for the Promotion of Science. C. Surulescu was partially supported by the Federal Ministry of Education and Research BMBF, project GlioMaTh 05M2016.
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