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
LJK - Laboratoire Jean Kuntzmann
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 RFMQ
TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
Abstract : 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.
Keywords : level set methods fluid structure interaction biological vesicles cell dynamics
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Emmanuel Maitre, Thomas Milcent, Georges-Henri Cottet, Annie Raoult, Yves Usson. Applications of level set methods in computational biophysics. Mathematical and Computer Modelling, Elsevier, 2009, 49 (11-12), pp.2161-2169. ⟨10.1016/j.mcm.2008.07.026⟩. ⟨hal-00177593v3⟩

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