Monday. Oct. 28, 2019, McAllister 106, 2:30–3:30 pm
Vincenzo Capasso
ADAMSS (Interdisciplinary Centre for ADvanced Applied Mathematical and Statistical Sciences)
Universita ́ degli Studi di Milano La Statale
Email: vincenzo.capasso@unimi.it
TITLE
Tumour driven angiogenesis; from a stochastic model to its mean-field approximation.
ABSTRACT:
In the field of Life Sciences it it very common to deal with extremely com- plex systems, from both analytical and computational points of view, due to the unavoidable coupling of different interacting structures. As an example, angiogenesis has revealed to be an highly complex, and extremely interesting biomedical problem, due to the strong coupling between the kinetic param- eters of the relevant branching – growth – anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting un- derlying biochemical fields, at the macroscale. Here an original conceptual stochastic model of tumor driven angiogenesis will be presented, for which it has been shown that it is possible to reduce complexity by taking advantage of the intrinsic multiscale structure of the system; one may keep the stochas- ticity of the dynamics of the vessel tips at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. A rigorous proof is given of the so called “propagation of chaos”, which leads to a mean field approximation of the stochastic relevant measures associated with the vessel dynamics, and consequently of the underlying TAF field.