“The Hele-Shaw asymptotics for fluid models of tumor growth”

by Benoit Perthame, Laboratoire J.-L. Lions (UPMC)

ABSTRACT: The growth of solid tumors can be described at a number of different scales from the cell to the organ scales. For a large number of cells, the ‘fluid mechanical’ approach has been advocated recently by many authors in mathematics or biophysics. Several levels of mathematical descriptions are commonly used, including only elastic effects, nutrients, active movement, surrounding tissue, vasculature remodeling and several other features.
We will focuss on the links between two types of models. The `microscopic’ description is at he cell population density level and a more macroscopic, description is based on a free boundary problem close to the classical Hele-Shaw equation. Asymptotic analysis is a tool to derive these Hele-Shaw free boundary problems from cell density systems in the stiff pressure limit. This modeling also opens other questions as circumstances in which instabilities develop.
This work is a collaboration with F. Quiros and J.-L. Vazquez (Universidad Autonoma Madrid), M. Tang (SJTU) and N. Vauchelet (LJLL)

”Seminar @ ISC-PIF, 2:00pm room 1.1′