The effect of domain growth on spatial correlations

Robert Ross, Christian Yates, Ruth E. Baker

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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.
Original languageEnglish
Pages (from-to)334-345
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Early online date12 Sept 2016
Publication statusPublished - 15 Jan 2017


  • Domain growth
  • spatial correlations
  • mean-field model
  • ODEs


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