Two-dimensional simulation of the deformation of a model endothelial cell in a laminar flow

In this work a numerical simulation of the deformation of a model endothelial cell (EC) in a laminar flow was presented. The EC was considered as a two-dimensional isotropic elastic material with a less deformable nucleus. It was supposed that identical cells were aligned in a regular way to form an infinite monolayer. Thus the flow near the monolayer would be periodic and the authors could consider only the flow above one cell by imposing periodic boundary conditions into numerical computations. The equations governing the flow and the equilibrium of the cell were solved by using the finite element method. An interface between the computations of the fluid flow and the solid deformation was created such that the flow induced stresses on the cell surface could be used as solid boundary conditions and that deformed cell shape could be introduced into flow computation. The numerical results showed that cell deformation under flow depends largely on Reynolds number and the Young´s modulus of the cell and the nucleus. The distributions of mechanical stresses on cell surface were modified compared to a non deformable cell. The maximum values of shear stress and pressure were lowered. This modeling indicates that it would be interesting to study eventual correlation between the distribution of mechanical stresses and that of biological receptors which could allow a better understanding of the leukocyte adhesion on endothelium