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

Abstract

a b s t r a c t a r t i c l e i n f oIn 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.

A novel strain energy relationship for red blood cell membrane skeleton based on spectrin stiffness and its application to micropipette deformation

“…Such elastic behavior is entirely the consequence of the mechanical properties of its membrane. There is a longstanding quest to properly describe these properties (Evans 1973; Skalak et al 1973; Zarda et al 1977; Stokke et al 1986; Markin and Kozlov 1988; Hochmuth and Waugh 1987; Mohandas and Evans 1994; Discher et al 1998; Li et al 2005; Mukhopadhyay et al 2002; Lim et al 2002; Kuzman et al 2004; Pivkin and Karniadakis 2008; Zhu and Asaro 2008; Fedosov et al 2010; Peng et al 2010; Hartmann 2010; Li et al 2013; Chen and Boyle 2014). Understanding that the membrane bilayer constrains the surface area of the cell to be constant inspired early formulations involving a two-dimensional, locally incompressible skeleton.…”

How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics?

“…This reveals the simplistic nature of these experimental data, which was also pointed out by Dimitrakopoulos (2012). Despite this observation, optical tweezers data continue to be used as a way to validate numerical models of the RBC membrane (Li et al 2005;Dao et al 2006;Pivkin and Karniadakis 2008;Le et al 2009;Fedosov et al 2010aFedosov et al , b, 2014Klöppel and Wall 2011;Chen and Boyle 2014;Farutin et al 2014;Sinha and Graham 2015), notably to probe the accuracy of solvers dedicated to the study of the RBC dynamics under flow. However, a proper validation test case needs to be selective to discriminate between appropriate and inappropriate models.…”

“…So far, there is no universal model to describe the mechanical behavior of the RBC membrane. The local elasticity of the RBC membrane is generally described using either continuum models (Le et al 2009;Klöppel and Wall 2011;Farutin et al 2014;Sinha and Graham 2015) or network models (Li et al 2005;Dao et al 2006;Pivkin and Karniadakis 2008;Fedosov et al 2010aFedosov et al , b, 2014Chen and Boyle 2014), which can be complemented with other global models to treat the quasi-incompressibility of the lipid bilayer (Pivkin and Karniadakis 2008;Fedosov et al 2010a, b). Detailed experi-mental investigations of the RBC mechanics are nonetheless needed in order to: (1) characterize and validate a numerical model of the RBC membrane and (2) once validated, determine the mechanical parameters of the model.…”

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

“…It has been shown in previous studies that through a careful design of the spring network and the selection of appropriate elastic constants the mechanics of several elastic membranes can be exactly reproduced [17,52,53]. Here we would like to note that the derivation of the interaction potential approach is not unique to our work and variants of this method have already been used previously to predominantly study red blood cells [52][53][54][55]. In this work we show that this approach can be used for large scale flows with dispersed drops/bubbles and also biological membranes with full fluid-structure interaction, for example flow in heart ventricles with valves.…”