TY - JOUR

T1 - A computational model of red blood cells using an isogeometric formulation with T-splines and a lattice Boltzmann method

AU - Asai, Yusuke

AU - Ishida, Shunichi

AU - Takeda, Hironori

AU - Nakaie, Gakuto

AU - Terahara, Takuya

AU - Taniguchi, Yasutoshi

AU - Takizawa, Kenji

AU - Imai, Yohsuke

N1 - Publisher Copyright:
© 2024 Elsevier Ltd

PY - 2024/3

Y1 - 2024/3

N2 - 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 T-splines. 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 Gs=4.0×10−6 N/m, and the bending modulus is estimated to be EB=4.5×10−19 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.

AB - 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 T-splines. 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 Gs=4.0×10−6 N/m, and the bending modulus is estimated to be EB=4.5×10−19 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.

KW - Fluid-structure interaction

KW - Helfrich bending energy

KW - Isogeometric analysis

KW - Lattice Boltzmann method

KW - Membrane strain

KW - Red blood cell

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U2 - 10.1016/j.jfluidstructs.2024.104081

DO - 10.1016/j.jfluidstructs.2024.104081

M3 - Article

AN - SCOPUS:85184522311

SN - 0889-9746

VL - 125

JO - Journal of Fluids and Structures

JF - Journal of Fluids and Structures

M1 - 104081

ER -