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

Yusuke Asai, Shunichi Ishida, Hironori Takeda, Gakuto Nakaie, Takuya Terahara, Yasutoshi Taniguchi, Kenji Takizawa, Yohsuke Imai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number104081
JournalJournal of Fluids and Structures
Publication statusPublished - 2024 Mar


  • Fluid-structure interaction
  • Helfrich bending energy
  • Isogeometric analysis
  • Lattice Boltzmann method
  • Membrane strain
  • Red blood cell

ASJC Scopus subject areas

  • Mechanical Engineering


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