the mathematics of growth & remodeling of soft biological tissues

miniworkshop, mathematisches forschungsinstitut oberwolfach, 08/31/08-09/06/08, organizers: ellen kuhl, davide ambrosi, krishna garikipati

abstract biology is becoming the most attractive field of application of mathematics. the discoveries that have characterized the biological sciences in the last decades have become the most fertile matter for application of classical mathematical methods, while they offer a natural environment where new theoretical questions arise. ``mathematical biology has born many years ago and has developped along directions that now constitute its traditional background: population dynamics and reaction-diffusion equations. nowadays mathematical biology is differentiating into several branches, essentially depending on the specific spatial scale size under consideration: molecular scale (i.e. dna transcription, protein folding and cascades), cellular scale (i.e. motility, aggregation and moprhogenesis) and macroscale (i.e. tissue mechanics). currently one of the most attractive scientific topics is the mathematics of growth and remodelling of soft biological tissues. this area, located at the crossroads of biology, mathematics and continuum mechanics, concerns the statement and analysis of the equations that characterize the mechanics, growth and remodelling of systems like arteries, tumors and ligaments, studied at the macroscopic scale. these are open continuous systems that pose new challenging questions, which go beyond the standard mechanics that is traditionally devoted to closed systems. past initiatives in oberwolfach have been devoted to the interaction between biology and mathematics in a broad sense. a minisymposium in oberwolfach focusing on ``the mathematics of growth and remodelling of soft biological tissues would be the occasion to bring together established researchers on this topic with newer entrants to the field.