An isogeometric analysis formulation for red blood cell electro-deformation modeling

Nicola A.Nodargi, Josef Kiendl, Paolo Bisegna, Federica Caselli, Laura De Lorenzis

An isogeometric analysis formulation for simulating red blood cell (RBC) electro-deformationis presented. Electrically-induced cell deformation experiments are receiving increasing attention as an attractive strategy for single-cell mechanical phenotyping. As the RBC structure consists in a very thin biological membrane enclosing a nearly-incompressible fluid, (i) a surface shell kinematic model and (ii) the imposition of the shell enclosed-volume conservation constraint are proposed within the isogeometric analysis framework. With regard to the electro-deformation, an accurate evaluation of the electric-field induced forces is achieved by the Maxwell stress tensor approach. A staggered fixed-point iteration scheme is then proposed for performing the electro-mechanical coupling, in order to use reliable mechanical and electrical problem solvers sequentially. Supported by the comparison with experimental results and reference solutions, numerical simulations concerning the large deformation of a RBC by optical tweezers and an in silico electro-deformation experiment prove the accuracy and the effectiveness of the proposed formulation.

DOI

A quasi-continuum model for human erythrocyte membrane based on the higher order Cauchy–Born rule

Xiangyang Wang, Xu Guo, Zheng Su

A nanoscale quasi-continuum (QC) model for exploring the mechanical properties of human erythrocyte/red blood cell (RBC) membranes is presented in this paper. The so-called higher order Cauchy–Born rule (HCB rule) is utilized as the linkage between the deformation of the spectrin network/cytoskeleton and that of the corresponding equivalent continuum. By incorporating the second order deformation gradients into kinematic description, the resulting QC model can capture the curvature effect of nanoscale membranes accurately in a geometrically consistent way. Based on the proposed QC model, a variationally consistent meshless computational scheme is developed for simulating the finite deformation of human erythrocyte/RBCs. The obtained deformation and wrinkling patterns are in good agreement with those from the existing experiments.

DOI