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A Computational Model for Single Cell Migration and Chemotaxis: Coupling Bulk and Membrane Bound Processes

Presented by: 
John Mackenzie University of Strathclyde
Tuesday 15th September 2015 - 15:30 to 16:15
INI Seminar Room 1
Co-authors: Michael Nolan (University of Strathclyde), Grant McDonald (University of Strathclyde), Matt Neilson (Beatson Institute for Cancer Research), Robert Insall (Beatson Institute for Cancer Research)

In this talk I will present details about a moving mesh finite element method for the approximate solution of partial differential equations on an evolving bulk domain in two dimensions, coupled to the solution of partial differential equations on the evolving domain boundary. Problems of this type occur frequently in the modelling of eukaryotic cell migration and chemotaxis - for these applications the bulk domain is either the intracellular or extracellular region and the domain boundary is the cell membrane. Fundamental to the success of the method is the robust generation of bulk and surface meshes for the evolving domains. For this purpose we use a moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known solutions which indicate second-order spatial and temporal accuracy. The method is then applied to a model of the two-way interaction of a migrating cell with an external chemotactic field.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons