MACROSCOPIC FEATURES. d) Biological SystemsSOME THEORETICAL SHAPES OF RED BLOOD CELLS

Helfrich, W.; Deuling, H.J.

doi:10.1051/jphyscol:1975155

Cited by 29 publications

(21 citation statements)

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“…However, starting from the same volume, oblate and prolate spheroids will evolve into a biconcave discoid and a dumbbell respectively as volume is reduced, with a dumbbell shape having lower energy and thus being a more stable shape; this is the opposite of what one is looking for. Helfrich et al [17][18][19] suggested the need for a spontaneous curvature having a negative value such that a biconcave shape is stable. In these and many subsequent treatments, the spontaneous curvature was assumed to be constant over the entire surface and treated as a free parameter that can be chosen in order to fit the RBC shape.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a single red blood cell in simple shear flow

2015

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This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number Ca) is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high Ca such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low Ca such as rolling, tumbling, kayaking, and flip-flopping.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a single red blood cell in simple shear flow

2015

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“…Canham [9] proposed an incompressible shell model and argued that the biconcave discoidal shape should be the result of minimizing the curvature energy for the given surface area and volume of the red blood cell. Although the dumbbell-like shape has the same curvature energy as the biconcave discoid within this model, the former configuration has never been observed in any experiment [10].…”

Section: Introductionmentioning

confidence: 94%

Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model

Ouyang

2014

Advances in Colloid and Interface Science

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Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solutions to these equations and their corresponding configurations are demonstrated.

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“…18 On the other hand, workers in the field of mechanics tried to explain the deformation of RBCS with a thin-shell theory, but were unable to define the state of zero stress. 19 Furthermore, the assumption of solid shell is inconsistent with the kind of caterpillar motion of the red blood cells along the wall of the blood vessel.…”

Section: Helfrich's Approachmentioning

confidence: 99%