Multiscale analyses of tissue growth and front propagation

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• Reuben O'Dea (Nottingham)
• Thursday 04 December 2014, 16:00-17:00
• Muirhead 122.

If you have a question about this talk, please contact Alexandra Tzella.

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 key 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 Applied Mathematics Seminar Series series.

This talk is included in these lists:

• Applied Mathematics Seminar Series
• Muirhead 122
• School of Mathematics events

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