Erythrocyte Shape Simulation by Optimization of a Closed Fluid Lamina

Abstract

Abstract In our earlier work the morphology of red blood cells (RBC) was examined in terms of the mean mean curvature (MMC) of their cell membranes. A simulation of the different geometries of these shapes showed that the MMC increases from the sphero-stomatocyte to the sphero-echinocyte via the discocyte. We extend this work by using a free energy function based on curvature elasticity, curvature homogeneity and volume and area constraints in conjunction with two different simulation methods: a gradient relaxation method and a Metropolis Monte Carlo method based on importance sampling. The problem with conventional methods of simulation is that they lead to the trapping of the cell shape in a local minimum. Rather than processing the new shape after calculating each point on the surface, the new shape is only processed once every point on the old surface has been calculated. The RBC membrane is treated in the simulations as a single fluid lamina exhibiting viscoelastic characteristics. In the simulations...