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

Abstract

Summary 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.

PyOIF: Computational tool for modelling of multi-cell flows in complex geometries

“…We have investigated the inclination angle in [ 39 ] and confirmed that our model corresponds to the experimental measurements of the inclination angle reported in [ 40 ]. Further, in [ 34 ] we performed computational experiments of tank-treading frequency also reproducing the experimental results and thus validating the model.…”

“…The correspondence is however not direct. The linking of PyOIF elastic parameters to the mechanical properties of cell membrane is described in detail in [ 34 ]. We use values (in lattice units) …”

“…The calibration of RBC elastic parameters was done using the cell stretching experiment described in [ 33 ]. The detailed procedure of calibration and discussion about suitable values of parameters are available in [ 34 ].…”

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension

“…We work with an RBC model that we previously developed and introduced in [ 17 , 18 ]. The model consists of two principal components: the fluid and elastic objects immersed in it.…”

“…In this work, we employ a novel approach to taking the viscosity contrast into account. We extend the existing red blood cell model based on lattice-Botzmann method (LBM) for governing the fluid and spring network for governing the elasticity of cell membrane [ 17 , 18 ]. We include dissipative particles (DPs) inside the cell as a coarse-grained hemoglobin model to increase the viscosity of the resulting suspension inside the cell.…”