Applications of level set methods in computational biophysics

Emmanuel Maitre (1) , Thomas Milcent (1) , Georges-Henri Cottet (1) , Annie Raoult (2) , Yves Usson (3)

1 EDP - Equations aux Dérivées Partielles
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 RFMQ

We describe in this paper two applications of Eulerian level set methods to fluid-structure problems arising in biophysics. The first one is concerned with three-dimensional equilibrium shapes of phospholipidic vesicles. This is a complex problem which can be recast as the minimization of the curvature energy of an immersed elastic membrane, under a constant area constraint. The second deals with isolated cardiomyocyte contraction. This problem corresponds to a generic incompressible fluid-structure coupling between an elastic body and a fluid. By the choice of these two quite different situations, we aim to bring evidences that Eulerian methods provide efficient and flexible computational tools in biophysics applications.

Mots clés: level set methods; fluid structure interaction; biological vesicles; cell dynamics

Domaines: Analyse numérique [math.NA]

Emmanuel Maitre, Thomas Milcent, Georges-Henri Cottet, Annie Raoult, Yves Usson. Applications of level set methods in computational biophysics. Mathematical and Computer Modelling, 2009, 49 (11-12), pp.2161-2169. ⟨10.1016/j.mcm.2008.07.026⟩. ⟨hal-00177593v3⟩