Deformational strain energy and erythrocyte shape.
Analyses of erythrocyte deformation commonly assume the discocytic shape to be unstressed and hence to be without strain energy. This assumption is based on micropipet experiments and a theoretical disparity between observed and requisite curvature rigidity. The polynomial description of Evans and Fung and strain energy expressions introduced by Zarda et al. have been used to explore the dependence of erythrocyte strain energy on unstressed surface curvature and elastic moduli. As unstressed membrane curvature is varied from flatness to curvatures greater than that of the sphered erythrocyte, the strain energy is found to fall to a value about two-thirds that of the sphered cell. This value occurs for a cell with a thickness, surface area and volume comparable to those of observed erythrocytes assuming a curvature elastic modulus of 1.5 X 10(-11) ergs and an extensional elastic modulus of 6.6 X 10(-3) ergs cm-1. The erythrocyte so characterized has a slightly smaller diameter than that of the measured erythrocyte as does a cell similar in thickness to the expanded cell studied by Evans and Fung. A cup-shaped erythrocyte with similar surface area and volume has a slightly greater strain energy than the standard discocyte when its unstressed curvature is that of a sphered cell. Its strain energy falls below that of the discocyte as its unstressed curvature approaches flatness. Curvature strain energy was found to be concentrated in the dimple of the erythrocyte, the effect being more striking when unstressed curvature was greater. Extensional strain energy, lower in density, was concentrated at the equator. The basis for current emphasis on the unstressed discocyte is reviewed. While no clear conclusion can be reached, the alternative model presented here is attractive in explaining cup-shaped erythrocyte formation but requires a rather high resistance to curvature deformation. Until conclusive evidence is developed both the unstressed and the present discocyte models should be evaluated in examining erythrocyte deformation and adhesive behavior.
McMillan
D E
DE
Mitchell
T P
TP
Utterback
N G
NG
D001696:Biomechanical Phenomena; D004548:Elasticity; D004907:Erythrocyte Deformability; D004910:Erythrocyte Membrane / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D013314:Stress, Mechanical