Nonlinear modeling for predicting red blood cell morphological transformations

A nonlinear model, based on the area difference elasticity theory, has been developed to predict the sequence of stomatocyte–discocyte–echinocyte transformation in red blood cells. This model coarsely grains the cell membrane into a triangular network, accounting for the shear deformation of membrane skeleton, the area dilation, volume variation, bending deformation, and area difference deformation of lipid bilayer. It exhibits linear behavior under small deformations and transits to nonlinear behavior under large deformations, mirroring the biomechanical response of the cell that is susceptible to small deformations but significantly resists large deformations. The model parameters are calibrated by determining the biconcave equilibrium shape from an ellipsoidal stress-free configuration. After calibration, the model is utilized to predict the stomatocyte–discocyte–echinocyte transformation and is compared with the previously published experimental observations and the numerical results. It has been shown that the equilibrium shapes of a red blood cell are achieved in a self-equilibrium of spring lengths, as well as the balance between the triangle areas and surface area, and the interplay among dihedral curvature and area differences. The nonlinear model is believed to be capable of predicting the deformation behavior of red blood cells in diverse shape-transforming scenarios, such as in microvascular circulation and microfluidic devices.