Author:
Kumar Pawan,Li Jing,Surulescu Christina
Abstract
AbstractGliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .
Funder
Deutscher Akademischer Austauschdienst
Bundesministerium für Bildung und Forschung
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Modelling and Simulation
Reference60 articles.
1. Alfonso JCL, Köhn-Luque A, Stylianopoulos T, Feuerhake F, Deutsch A, Hatzikirou H (2016) Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights. Sci Rep 6:37283
2. Banerjee S, Khajanchi S, Chaudhuri S (2015) A mathematical model to elucidate brain tumor abrogation by immunotherapy with t11 target structure. PLOS ONE 10(5):e0123611
3. Bartel P, Ludwig FT, Schwab A, Stock C (2012) pH-taxis: directional tumor cell migration along pH-gradients. Acta Physiologica 204(Suppl. 689):113
4. Bellomo N (2008) Modeling complex living systems. Birkhäuser, Boston
5. Böttger K, Hatzikirou H, Chauviere A, Deutsch A (2012) Investigation of the migration/proliferation dichotomy and its impact on avascular glioma invasion. Math Model Nat Phenom 7:105–135
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