Applied Math Distinguished Lecture | José Carrillo, Cell-cell Adhesion micro-and macroscopic models via Aggregation-Diffusion systems

MC 5501 

Speaker

José Carrillo  | University of Oxford, Mathematical Institute

Title

Cell-cell Adhesion micro-and macroscopic models via Aggregation-Diffusion systems

Abstract

We discuss microscopic and continuum cell-cell adhesion models and their derivation based on the underlying microscopic assumptions. We will derive these macroscopic limits via mean-field assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. Asymptotic models are obtained via Cahn-Hilliard approximations. The new models are able to capture both qualitatively and quantitatively experiments. We also review some of the applications of these models in other areas of tissue growth in developmental biology. We will analyse the mathematical properties of the resulting aggregation-diffusion, Cahn-Hilliard and reaction-diffusion systems based on variational tools.