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Mathematical models for cell migration: a non-local perspective.

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Summary

This review covers non-local continuous models for cell migration, focusing on their role in embryonic development and cancer invasion. It highlights spatial non-localities in advection and source terms, and associated mathematical challenges.

Keywords:
cell–cell and cell–tissue adhesionclasses of non-local modelshaptotaxisintegro-differential equationsmathematical challengesnon-local and local chemotaxis

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Area of Science:

  • Mathematical Biology
  • Cellular Dynamics
  • Developmental Biology

Background:

  • Collective cell migration is crucial in embryogenesis and cancer metastasis.
  • Non-local continuous models capture long-range interactions influencing cell movement.
  • Understanding these models is key to addressing biological processes and diseases.

Purpose of the Study:

  • To review recent advancements in non-local continuous models for cell migration.
  • To emphasize the role of spatial non-localities in advection and source terms.
  • To classify partial differential equation (PDE) models and discuss mathematical challenges.

Main Methods:

  • Review of existing literature on non-local continuous models.
  • Classification of PDE models based on non-locality types.
  • Analysis of mathematical challenges, particularly analytical aspects.

Main Results:

  • Detailed review of non-local continuous models for migration.
  • Emphasis on spatial non-localities in advection (motility bias) and source terms.
  • Systematic classification of PDE models and discussion of analytical challenges.

Conclusions:

  • Non-local continuous models offer valuable insights into collective cell migration.
  • Spatial non-localities in advection and source terms are critical features.
  • Further mathematical analysis is needed to fully understand these complex biological systems.