We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Mathematical models for cell migration: A non-local perspective / Chen, L.; Painter, K.; Surulescu, C.; Zhigun, A.. - In: PHILOSOPHICAL TRANSACTIONS - ROYAL SOCIETY. BIOLOGICAL SCIENCES. - ISSN 0962-8436. - ELETTRONICO. - 375:1807(2020), p. 20190379. [10.1098/rstb.2019.0379]

Mathematical models for cell migration: A non-local perspective

Painter K.;
2020

Abstract

We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2867020