Elastic properties of the red blood cell membrane that determine echinocyte deformability

Abstract

The natural biconcave shape of red blood cells (RBC) may be altered by injury or environmental conditions into a spiculated form (echinocyte). An analysis is presented of the effect of such a transformation on the resistance of RBC to entry into capillary sized cylindrical tubes. The analysis accounts for the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending, the latter corresponding to different area strains in the two leaflets of the bilayer. The shape transformation is assumed to be driven by the equilibrium area difference (delta A(0), the difference between the equilibrium areas of the bilayer leaflets), which also affects the energy of deformation. The cell shape is approximated by a parametric model. Shape parameters, skeleton shear deformation, and the skeleton density of deformed membrane relative to the skeleton density of undeformed membrane are obtained by minimization of the corresponding thermodynamic potential. Experimentally, delta A(0) is modified and the corresponding discocyte-echinocyte shape transition obtained by high-pressure aspiration into a narrow pipette, and the deformability of the resulting echinocyte is examined by whole cell aspiration into a larger pipette. We conclude that the deformability of the echinocyte can be accounted for by the mechanical behavior of the normal RBC membrane, where the equilibrium area difference delta A(0) is modified.

Modeling the flow of dense suspensions of deformable particles in three dimensions

“…However, most of these models either simulate acute deformation of a single red blood cell (e.g. [6][7][8][9][10]), or model multiple red blood cells (RBCs), but with significant restrictions on, for example, deformability and shape (e.g., [11,12]) or the number of spatial dimensions (e.g., [11,13]). Other than these examples, numerical studies generally ignore the particulate nature of blood, and models of mesoscale blood dynamics which explicitly account for blood cells are lagging far behind the experimental data.…”

“…We use the popular midlink bounceback method which has been carefully evaluated by a number of workers (e.g., [35][36][37]). The f i 's on a boundary node at position x w are subject to a specular reflection, taken to occur at the midpoint of the appropriate lattice link c i , ( 7 ) This simple rule was generalized by Ladd [38] to moving boundaries with velocity u 0 by replacing the evolution expressed in Eq. (1) with ( 8 ) Moving walls are implemented using this approach.…”

Red blood cell shape and deformability in the context of the functional evolution of its membrane structure

“…The three layers of the RBC membrane are the two layers of its bilayer part and the spectrin skeleton. The RBC membrane is characterized by some specific features [12,13]. The area compressibility moduli of the two layers of the bilayer are much larger than that of the skeleton (represented in terms of the spring model in Fig.…”

“…The RBC membrane is thus assumed to attain the shape that requires the smallest increase of the sum of the bending energy of its bilayer and the elastic energy of its skeleton. Analyses based on a minimal model of the RBC membrane elasticity, that describes its main functional requirements and emphasizes the complementary roles of the bilayer and the skeleton, predicted the echinocyte as a possible minimum energy shape [12,13].…”

Stress-free state of the red blood cell membrane and the deformation of its skeleton

“…The mapping function, which defines from which point on the undeformed surface the bond reached the point s, is introduced as s 0 (s) [13,14] and it is derived by variational calculation. It is to be pointed out that because spring constant k appears in the expression of the skeleton energy as a constant factor, the variationally obtained mapping function does not depend on its magnitude and therefore also not on the corresponding extension and shear moduli.…”