On the study of tumour growth influenced by self-driven inhmogeneities

Salvatore di Stefano (Politecnico di Torino)

Thursday 17th January, 2019 14:00-15:00 Maths 116

Abstract

The understanding of the ensamble of physical events accompanying the onset and evolution of tumour growth is central in some branches of mathematical modelling. In particular, the complexity of the causes entailing the growth of a tumour can be addressed by following different approaches. In particular, if we refer to the Continuum Mechanics framework, a multi-scale investigation is required, in order to create a bridge among the scales of observation at which phenomena of different nature occur. The description of a tumour tissue is based on the Theory of Porous Media. In particular, we assume that the tumour tissue is a biphasic porous medium, in which the solid phase, accounting for two families of cells, is saturated with an interstitial fluid, which transports biological molecules within the tissue, such as nutrients. By specifying suitable sources and sinks terms, growth consists on gain or loss of mass. The redistribution of the tissue's mass leads to a rearrangement of its internal structure, and this induces the production and development of material inhomogeneities, which may influece the growth of the tissue itself. The purpose of this talk is to present a multi-scale mathematical model describing the growth of a tumour in the avascular stage, with the aim of sudying the interplay among growth-induced inhomogeneities and mechanical and chemical processes. For this seminar, we will refer to the work ¹ "Self-induced growth through evolving material inhomogeneities", by Salvatore Di Stefano, Ariel Ramírez-Torres, Raimondo Penta and Alfio Grillo.

1 S., Di Stefano, A., Ramírez-Torres, R., Penta, A., Grillo. Self-influenced growth through evolving material inhomogeneities. International Journal of Non-Linear Mechanics (2018), 106, 174-187.

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