Related Experiment Video
Updated: Feb 19, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
Published on: April 16, 2017
Incompressible Limit of a Mechanical Model for Tissue Growth with Non-Overlapping Constraint
Sophie Hecht1, Nicolas Vauchelet2
1Francis Crick Institute, 1 Midland Rd, Kings Cross, London NW1 1AT, UK - Imperial College London, South Kensington Campus London SW7 2AZ, UK (sophie.hecht15@imperial.ac.uk).
Abstract:
A mathematical model for tissue growth is considered. This model describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that such cell population model converges at the incompressible limit towards a Hele-Shaw type free boundary problem. The novelty of this work is to impose a non-overlapping constraint. This constraint is important to be satisfied in many applications. One way to guarantee this non-overlapping constraint is to choose a singular pressure law. The aim of this paper is to prove that, although the pressure law has a singularity, the incompressible limit leads to the same Hele-Shaw free boundary problem.
Related Concept Videos
Modeling with Differential Equations
Hooke's Law
Growth Models with Integration: Problem Solving
Generalized Hooke's Law
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

