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- Title
Elastic behavior of a red blood cell with the membrane's nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion.
- Authors
Tsubota, Ken-ichi; Wada, Shigeo; Liu, Hao
- Abstract
Direct numerical simulations of the mechanics of a single red blood cell (RBC) were performed by considering the nonuniform natural state of the elastic membrane. A RBC was modeled as an incompressible viscous fluid encapsulated by an elastic membrane. The in-plane shear and area dilatation deformations of the membrane were modeled by Skalak constitutive equation, while out-of-plane bending deformation was formulated by the spring model. The natural state of the membrane with respect to in-plane shear deformation was modeled as a sphere ( $$\alpha =0$$ ), biconcave disk shape ( $$\alpha =1$$ ) and their intermediate shapes ( $$0<\alpha <1$$ ) with the nonuniformity parameter $$\alpha $$ , while the natural state with respect to out-of-plane bending deformation was modeled as a flat plane. According to the numerical simulations, at an experimentally measured in-plane shear modulus of $$2.5\times 10^{-6}\,\hbox {N}/\hbox {m}$$ and an out-of-plane bending rigidity of $$2.0\times 10^{-19}\,\hbox {N}\cdot \hbox {m}$$ of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for $$\alpha >0.22$$ and cupped otherwise; (ii) the experimentally measured fluid shear stress at the transition between tumbling and tank-treading motions under shear flow was reproduced for $$0.05<\alpha <0.34$$ ; (iii) the elongation deformation of the RBC during tank-treading motion from the simulation was consistent with that from in vitro experiments, irrespective of the $$\alpha $$ value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for $$0.22<\alpha <0.34$$ . The condition $$0.05<\alpha <0.22$$ precludes a biconcave discoid shape at equilibrium (i); however, it gives appropriate fluid shear stress at the motion transition under shear flow (ii), suggesting that a combined effect of $$\alpha $$ and the natural state with respect to out-of-plane bending deformation is necessary for understanding details of the RBC mechanics at equilibrium. Our numerical results demonstrate that moderate nonuniformity in a membrane's natural state with respect to in-plane shear deformation plays a key role in RBC mechanics.
- Subjects
ERYTHROCYTE deformability; ELASTICITY (Physiology); SHEAR flow; SHEARING force; BENDING moment
- Publication
Biomechanics & Modeling in Mechanobiology, 2014, Vol 13, Issue 4, p735
- ISSN
1617-7959
- Publication type
Article
- DOI
10.1007/s10237-013-0530-z