Fluid dynamics modeling of cell and membrane deformations
We propose a realistic model of cell and membrane deformations based on fluid mechanics. We focus on the blebbing process, a key mechanism of motility for several cell types. It is seen as a rupture of symmetry in the surface tension forces affecting the membrane of the cell. It produces sudden protrusions in regions where the tension forces vanish, inducing large displacements of cell material and whole-cell movement. We describe the cell and the external medium as fluids subject to Stokes equations, and the cell membrane as an interface defined by an advected level set function and subject to surface tension. We setup a numerical implementation in two dimensions using finite elements and show that the model successfully produces whole-cell movement, without involving substrate adhesion nor specific organelles. This work paves the way for further studies on the shape and dynamics of the blebs, in direct relation with live cell imaging.