Semi-analytical modeling and simulation of human red blood cell deformation under non-linear strain

The study of red blood cell (RBC) deformability remains an active area of research due to its linkage to health and normal physiological functions of RBCs in the circulatory system. In the present study, we use a semi-analytical approach analogous to optical tweezers or extensional flow experiments to investigate the deformation of the RBCs. The axial and transverse diameters of the RBCs subjected to axial stretching under non-linear strain are found in good agreement with the reported optical tweezers experiment and simulation results for the applied stretching force in the range ~ 10–90 pN. Our results reveal that the linear elastic behaviour of the cell membrane is valid only for small axial deformations of the RBC up to ~ 10 µm for the applied force less than 20 pN. The results also demonstrate the utility of the non-linear Hencky strain to account for the hyperelastic behaviour of the cell membrane over a significantly wide range of axial deformation up to ~ 14 µm for the applied force range of ~ 90 pN. The colour-coded mapping of local membrane curvatures and their quantitative distributions gives intuitive insights into the variation of the membrane bending energy distribution over the RBC surface in the normal and axially stretched states under non-linear strain. Analysis of the curvature bending energy of the RBC subjected to axial stretching suggests that the non-linear strain and the spontaneous curvature should be the essential considerations to ensure the membrane bending energy within the limit of 10–100 eV for the biomechanical deformation of the RBC.