Alfio Grillo, Salvatore Di Stefano – DISMA - Politecnico di Torino - THE ROLE OF INHOMOGENEITIES IN THE MECHANICS OF TUMOR GROWTH
The study of tumor growth is a largely investigated research topic, because of its implication on public health. In
this sense, mathematical modelling can give some important contributions to understand the complexity of the
phenomena that occur for the onset and development of tumors. To address this problem, an interdisciplinary
approach is required in order to identify the role played, at different scales of observation, by mechanical and
chemical factors.
Within the Continuum Mechanics framework that we adopted, a tumor tissue is described as a soft porous medium,
saturated with an interstitial fluid, that transports nutrients and other biological macromolecules and species.
Growth is conceived as the result of two processes: one relies on the mass transfer among the different constituents,
taken into account through sources and sink terms, and one is featured with the changes of the internal
structure of the tumor, described by means of a growth tensor. Since such tensor is, in general, non-integrable
and incompatible, it induces a non-Euclidean metric, which allows to define a Levi-Civita connection. The scalar
curvature associated to such connection is an indicator of the material inhomogeneities produced by growth.
The aim of this talk is to present a mathematical model describing the growth of a tumor in the avascular stage,
trying to answer the following question: If a tissue finds itself in a grown configuration, what is the influence of
growth-induced inhomogeneities on the evolution of the tumor?
The content of this seminar is extracted from the work “Self-induced growth through evolving material inhomogeneities”,
by Salvatore Di Stefano, Ariel Ramírez-Torres, Raimondo Penta and Alfio Grillo, submitted to International
Journal of Nonlinear Mechanics.
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