Investigation of membrane mechanics using spring networks: application to red-blood-cell modelling

In recent years a number of red-blood-cell (RBC) models have been proposed using spring networks to represent the RBC membrane. Some results predicted by these models agree well with experimental measurements. However, the suitability of these membrane models has been questioned. The RBC membrane, like a continuum membrane, is mechanically isotropic throughout its surface, but the mechanical properties of a spring network vary on the network surface and change with deformation. In this work spring-network mechanics are investigated in large deformation for the first time via an assessment of the effect of network parameters, i.e. network mesh, spring type and surface constraint. It is found that a spring network is conditionally equivalent to a continuum membrane. In addition, spring networks are employed for RBC modelling to replicate the optical tweezers test. It is found that a spring network is sufficient for modelling the RBC membrane but strain-hardening springs are required. Moreover, the deformation profile of a spring network is presented for the first time via the degree of shear. It is found that spring-network deformation approaches continuous as the mesh density increases.