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SUMMARY:Multiscale analyses of tissue growth and front propagation - O'Dea
 \, R (University of Nottingham)
DTSTART:20140624T092000Z
DTEND:20140624T095000Z
UID:TALK53131@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The derivation of continuum models which represent underlying 
 discrete or microscale phenomena is emerging as an important part of mathe
 matical biology: integration between subcellular\, cellular and tissue-lev
 el behaviour is crucial to understanding tissue growth and mechanics. I wi
 ll consider the application of a multiscale method to two problems on this
  theme. \n\nFirstly a new macroscale description of nutrient-limited tissu
 e growth\, which is formulated as a microscale moving-boundary problem wit
 hin a porous medium\, is introduced. A multiscale homogenisation method is
  employed to enable explicit accommodation of the influence of the underly
 ing microscale tissue structure\, and its evolution\, on the macroscale dy
 namics. \n\nA challenging consideration in continuum models of tissue is t
 he accommodation of (spatially-discrete) cell-signalling events\, a featur
 e of which being the progression of moving fronts of cell-signalling activ
 ity across a lattice. New (continuum) analyses of monotone waves in a disc
 rete diffusion equation are presented\, and extended to modulated fronts e
 xhibited in cell signalling models.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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