Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: Effects of the constitutive law and membrane modeling.

Despite research spanning several decades, the exact value of the shear modulus Gs of the erythrocyte membrane is still ambiguous, and a wealth of studies, using measurements based on micropipette aspirations, ektacytometry systems and other flow chambers, and optical tweezers, as well as application of several models, have found different average values in the range 2-10μN/m. Our study shows that different methodologies have predicted the correct shear modulus for the specific membrane modeling employed, i.e., the variation in the shear modulus determination results from the specific membrane modeling. Available experimental findings from ektacytometry systems and optical tweezers suggest that the dynamics of the erythrocyte membrane is strain hardening at both moderate and large deformations. Thus the erythrocyte shear modulus cannot be determined accurately using strain-softening models (such as the neo-Hookean and Evans laws) or strain-softening/strain-hardening models (such as the Yeoh law), which overestimate the erythrocyte shear modulus. According to our analysis, the only available strain-hardening constitutive law, the Skalak et al. law, is able to match well both deformation-shear rate data from ektacytometry and force-extension data from optical tweezers at moderate and large strains, using an average value of the shear modulus of Gs=2.4-2.75μN/m, i.e., very close to that found in the linear regime of deformations via force-extension data from optical tweezers, Gs=2.5±0.4μN/m. In addition, our analysis suggests that a standard deviation in Gs of 0.4-0.5μN/m (owing to the inherent differences between erythrocytes within a large population) describes well the findings from optical tweezers at small and large strains as well as from micropipette aspirations.