Constitutive Models for Tumour Classification

Abstract

The aim of this paper is to formulate new mathematical models that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumours. We present preliminary results of a tri-phasic model and numerical simulations of the effect of cellular adhesion forces on the mechanical properties of biological tissues.

We pursued the following three approaches:
(i) the simulation of the time-harmonic linear elastic models to examine coarse scale effects and adhesion properties,
(ii) the investigation of a tri-phasic model, with the intent of upscaling this model to determine effects of electro-mechanical coupling between cells,
and (iii) the upscaling of a simple cell model as a framework for studying interface conditions at malignant cells.
Each of these approaches has opened exciting new directions of research that we plan to study in the future.