Direction-dependent turning leads to anisotropic diffusion and persistence

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning r...

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Bibliographic Details
Published in:European journal of applied mathematics 2022-08, Vol.33 (4), p.729-765
Main Authors: LOY, N., HILLEN, T., PAINTER, K. J.
Format: Article
Language:English
Subjects:
Anisotropy
Applied mathematics
Cell adhesion & migration
Collagen
Domains
Enhanced diffusion
Micropatterning
Transport equations
Velocity
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Summary:Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792521000206