Aspiration of a nonlinear elastic spherical membrane

The goal of this research is to construct a mathematical model of the micromechanical experiment: an aspiration of spherical cells. Such experiment is often used to study properties of cells and their membranes. In our model the cell is considered as a fluid-filled membrane with solid-like behavior. The membrane is modeled by a hyperelastic isotropic momentless shell. The action of the internal environment is considered in two ways: a constant internal pressure and a constant internal volume. Usually the aspiration process is controlled directly by a suction pressure in a micropipette. In this paper it is also considered a model of aspiration with control by motion of a syringe piston.