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Modelling and Simulation of Collective Cell Migration with Non-Local Interactions on Time-Dependent Spatial Domains.

Alf Gerisch1

  • 1Research Group Numerical Analysis and Scientific Computing, Department of Mathematics, Technische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany. gerisch@mathematik.tu-darmstadt.de.

Bulletin of Mathematical Biology
|March 24, 2026
PubMed
Summary
This summary is machine-generated.

This study models collective cell migration in changing environments. It addresses challenges in developmental biology and neural crest cell invasion using a non-local partial differential equation model.

Keywords:
Collective cell migrationComputational complexityNon-local interactionNumerical simulationPDE modelTime-dependent domain

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Area of Science:

  • Mathematical Biology
  • Developmental Biology
  • Cellular Dynamics

Background:

  • Collective cell migration is crucial for embryonic development and tissue repair.
  • Existing models often assume static spatial domains, limiting their applicability to dynamic biological processes.
  • Understanding cell movement in changing environments requires advanced modeling techniques.

Purpose of the Study:

  • To extend a non-local partial differential equation (PDE) model of collective cell migration to time-dependent spatial domains.
  • To investigate the challenges associated with modeling cell migration in dynamic environments, particularly in a one-dimensional setting.
  • To simulate and analyze cellular population dynamics in scenarios relevant to embryology and neural crest cell invasion.

Main Methods:

  • Developed a non-local PDE model incorporating cell-cell interactions (attraction/repulsion).
  • Adapted the model to accommodate spatially homogeneous, time-dependent domain changes.
  • Performed numerical simulations to analyze model behavior for aggregating populations and neural crest cell invasion.

Main Results:

  • The extended PDE model successfully captures collective cell migration in time-varying spatial domains.
  • Simulations demonstrate the model's ability to represent both simple aggregation and complex invasion dynamics, including contact inhibition of locomotion.
  • The study highlights significant modeling and numerical challenges inherent in dynamic domain scenarios.

Conclusions:

  • The non-local PDE framework provides a robust approach for modeling collective cell migration in dynamic environments.
  • This extended model offers valuable insights into developmental processes and diseases involving cell invasion.
  • Further research can explore more complex domain changes and biological scenarios.