A computational model of red blood cells using an isogeometric formulation with T-splines and a lattice Boltzmann method

The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high -order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with Tsplines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid-structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be ������s = 4.0 x 10-6 N/m, and the bending modulus is estimated to be ������B = 4.5 x 10-19 J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.