Growing Avascular Tumours as Elasto-Plastic Bodies by the Theory of Evolving Natural Configurations

Keywords

Code:
52/2015
Title:
Growing Avascular Tumours as Elasto-Plastic Bodies by the Theory of Evolving Natural Configurations
Date:
Wednesday 30th September 2015
Author(s):
Giverso, C.; Scianna, M.; Grillo, A.
Download link:
Abstract:
The aim of this article is to propose a simple way of describing a tumour as a linear elastic material from a reference configuration that is continuously evolving in time due to growth and remodelling. The main assumption allowing this simplification is that the tumour mass is a very ductile material, so that it can only sustain moderate stresses while the deformation induced by growth, that can actually be quite big, mainly induces a plastic reorganisation of malignant cells. In mathematical terms this means that the deformation gradient can be split into a volumetric growth term, a term describing the reorganisation of cells, and a term that can be approximated by means of the linear strain tensor. A dimensionless analysis of the importance of the different terms also allows to introduce a second simplification consisting in the decoupling of the equations describing the growth of the tumour mass from those describing the flow of the interstitial fluid.
This report, or a modified version of it, has been also submitted to, or published on
Mechanics Research Communications, 68:31-39