Mathematical models for cell migration: a nonlocal perspective

Li Chen, Kevin Painter, Christina Surulescu, Anna Zhigun

Research output: Contribution to journalSpecial issuepeer-review

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Abstract

We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality occurring in advection terms, used to characterise 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, nonlocal chemotaxis), but we also shortly address spatially nonlocal source terms. Following a brief introduction and motivation, we give a systematic classification of available PDE models with respect to the type of featured nonlocalities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects.
Original languageEnglish
JournalPhilosophical Transactions of the Royal Society B
Early online date27 Jul 2020
DOIs
Publication statusEarly online date - 27 Jul 2020

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