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

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.