Mathematical modeling and simulation of active matter and biological materials

Abstract

In this thesis, we will study the invasion of breast cancer into the tissue. This process involves many cellular and extracellular processes tightly coupled between them. In particular, in this work we focus on the mechanics of the extra-cellular matrix that forms part of this tissue and exhibits a mechanosensitive nature that is essential to understand the motility and invasion of cancer. We will focus on the mechanics of the collagen network, more precisely on a model for an elastic material that can account for different types of collagen networks, with varying concentration and properties. In order to capture the large deformations of the extracellular matrix, we need to go beyond linear elasticity and use a hyperelastic model. This study will be done using a C++ library called Hipelife, dedicated to the solving of finite element problems.