Density-dependent quiescence in glioma invasion: instability in a simple reaction–diffusion model for the migration/proliferation dichotomy

DOI10.1080/17513758.2011.590610zbMath1448.92064OpenAlexW1983769407WikidataQ36758634 ScholiaQ36758634MaRDI QIDQ3304445

Arnaud Chauvière, Kara Pham, Vittorio Cristini, Haralambos Hatzikirou, Xiangrong Li, John S. Lowengrub, Helen M. Byrne

Publication date: 3 August 2020

Published in: Journal of Biological Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17513758.2011.590610

zbMATH Keywords

travelling wave solutionstumour invasiondiffusion-driven instabilityspatio-temporal heterogeneitycell migration/proliferationgo-or-grow

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Traveling wave solutions (35C07) Pathology, pathophysiology (92C32)

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Cites Work

• Unnamed Item
• Unnamed Item
• Simulating the impact of a molecular `decision-process' on cellular phenotype and multicellular patterns in brain tumors
• Identification of intrinsic \textit{in vitro} cellular mechanisms for glioma invasion
• Evolutionary game theory in an agent-based brain tumor model: exploring the `genotype-phenotype' link
• Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method
• 'Go or Grow': the key to the emergence of invasion in tumour progression?
• A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism
• Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour
• Transport equations with resting phases
• MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW
• Nonlinear modelling of cancer: bridging the gap between cells and tumours

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