Red Blood Cell Membrane Mechanics Using Discrete Exterior Calculus (DEC) and Optimization

Abstract

In this study, a novel algorithm for computing red blood cell (RBC) geometry was developed as the first step of a quantitative model for RBC-ATP release. This model relied on the developing coordinate-invariant computational framework of discrete exterior calculus (DEC). The algorithm for the first time in literature was formulated in an implicit manner, utilized a Lie-derivative based vertex drift contribution to ensure the mesh was well-behaved throughout deformation, and was able to obtain RBC equilibrium geometries in an efficient manner. This algorithm was shown to be highly stable, quantified through tracking the RBC membrane energy. Equilibrium geometries were shown to agree with literature in in vivo observations, and qualitatively reproduced phenomena seen in in vivo experiments where RBCs are subjected to solutions of varying osmolarity. This DEC algorithm will be applied in future work to fluid–structure interactions of RBCs, and has application to a multitude of open cell biology problems.