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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.
Biomech Model Mechanobiol 2014; 13(4):735-46BM

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 ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], 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 [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] 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 [Formula: see text]; (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 [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] 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 [Formula: see text] 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.

Authors+Show Affiliations

Department of Mechanical Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba, 263-8522, Japan, tsubota@faculty.chiba-u.jp.No affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article
Research Support, Non-U.S. Gov't

Language

eng

PubMed ID

24104211

Citation

Tsubota, Ken-Ichi, et al. "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." Biomechanics and Modeling in Mechanobiology, vol. 13, no. 4, 2014, pp. 735-46.
Tsubota K, Wada S, Liu H. 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. Biomech Model Mechanobiol. 2014;13(4):735-46.
Tsubota, K., Wada, S., & Liu, H. (2014). 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. Biomechanics and Modeling in Mechanobiology, 13(4), pp. 735-46. doi:10.1007/s10237-013-0530-z.
Tsubota K, Wada S, Liu H. 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. Biomech Model Mechanobiol. 2014;13(4):735-46. PubMed PMID: 24104211.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - 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. AU - Tsubota,Ken-Ichi, AU - Wada,Shigeo, AU - Liu,Hao, Y1 - 2013/10/09/ PY - 2012/09/06/received PY - 2013/09/17/accepted PY - 2013/10/10/entrez PY - 2013/10/10/pubmed PY - 2015/9/22/medline SP - 735 EP - 46 JF - Biomechanics and modeling in mechanobiology JO - Biomech Model Mechanobiol VL - 13 IS - 4 N2 - 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 ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], 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 [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] 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 [Formula: see text]; (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 [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] 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 [Formula: see text] 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. SN - 1617-7940 UR - https://www.unboundmedicine.com/medline/citation/24104211/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_ L2 - https://dx.doi.org/10.1007/s10237-013-0530-z DB - PRIME DP - Unbound Medicine ER -