Applications of level set methods in computational biophysics

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 evidence that Eulerian methods provide efficient and flexible computational tools in biophysics applications.