Modeling of Stresses and Strains in Cell Membranes Subjected to Micro-Injection

Abstract

This work is concerned with the determination of stresses and strains in cell membranes subjected to micro-injections. For that purpose, a suitable variational statement of the problem is developed within a continuum mechanics approach to the analysis of cell membrane geometry and physics. In this setting, the cell membrane is regarded as an axially symmetric surface in the three-dimensional Euclidean space providing a stationary value of the bending energy functional under the constraint of fixed total area. The Euler-Lagrange equations and the natural boundary conditions associated with the foregoing variational problem are derived, analyzed and used to express the stresses and moments in the membrane. Several examples of such surfaces representing possible shapes of cell membranes subjected to micro injection are determined numerically.