Spring-network model of red blood cell: From membrane mechanics to validation

Red blood cell membrane is highly elastic and proper modeling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. Inseparable and often some of the most difficult parts of modeling process are verification and validation. In this work, we present a revised model, which uses a spring network to represent the cell membrane immersed in a fluid and has been successfully used in blood flow simulations. We demonstrate the validation steps by first deriving the theoretical relations between the bulk properties of elastic membranes-shear modulus and area compressibility modulus-and parameters of the model that enter the nonlinear stretching and local area conservation computational moduli. We verify the theoretically derived relations using computer simulations of deformable triangular mesh. We calibrate the model by performing a computational version of the optical tweezers experiment. And finally, we validate the modeled cell behavior by investigating the cell rotation frequency when it is subjected to shear flow and cell deformation in narrow channels. The supplementary material contains an extensive dataset that can be used for setting different elastic properties for each cell in simulations of dense suspensions, while still conforming to the biological data. This work contains a complete model development process: From modelling of basic mechanical concepts (the spring network) and advanced biomechanical concepts (such as elasticity of the membrane), through calibration process towards the final stage of model validation.