The effect of domain growth on spatial correlations

Authored by Robert J H Ross, C A Yates, R E Baker

Date Published: 2017

DOI: 10.1016/j.physa.2016.09.002

Sponsors: United Kingdom Engineering and Physical Sciences Research Council (EPSRC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Mathematical models describing cell movement and proliferation are important tools in developmental biology research. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner. (C) 2016 Elsevier B.V. All rights reserved.

Tags

Dynamics Dispersal patterns Mechanisms Cell-migration Stochastic-model Neural crest migration Growing domains Mean-field Individual-based modelling Domain growth Moment-closure approximations Spatial correlations Migratory and proliferative cell populations Pair density functions