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Multiscale analyses of tissue growth and front propagation

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If you have a question about this talk, please contact Mustapha Amrani.

Free Boundary Problems and Related Topics

The derivation of continuum models which represent underlying discrete or microscale phenomena is emerging as an important part of mathematical biology: integration between subcellular, cellular and tissue-level behaviour is crucial to understanding tissue growth and mechanics. I will consider the application of a multiscale method to two problems on this theme.

Firstly a new macroscale description of nutrient-limited tissue growth, which is formulated as a microscale moving-boundary problem within a porous medium, is introduced. A multiscale homogenisation method is employed to enable explicit accommodation of the influence of the underlying microscale tissue structure, and its evolution, on the macroscale dynamics.

A challenging consideration in continuum models of tissue is the accommodation of (spatially-discrete) cell-signalling events, a feature of which being the progression of moving fronts of cell-signalling activity across a lattice. New (continuum) analyses of monotone waves in a discrete diffusion equation are presented, and extended to modulated fronts exhibited in cell signalling models.

This talk is part of the Isaac Newton Institute Seminar Series series.

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