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

## TL;DR

This paper models how cells move together in changing environments, focusing on interactions that influence their collective behavior.

## Contribution

The novel contribution is extending non-local PDE models to time-dependent domains, enabling more realistic simulations of cell migration.

## Key findings

- The model successfully simulates aggregating cellular populations on changing domains.
- Numerical simulations demonstrate the impact of contact inhibition of locomotion in neural crest cell invasion.
- The approach highlights challenges in modeling and simulating collective cell migration in dynamic environments.

## Abstract

We extend the formulation of a non-local PDE model of collective cell migration involving attracting or repelling cellular interactions to the case of time-dependent spatial domains as present, for instance, in modelling developmental processes from embryology. We restrict to a spatially one-dimensional setting, as is appropriate for the modelling of neural crest cell invasion, and focus on the case of spatially homogeneous domain change as this already highlights many of the modelling and numerical challenges. The approach is illustrated and numerical simulations are presented and discussed for a model of an aggregating cellular population and for a simple model of neural crest cell invasion accounting for contact inhibition of locomotion.