Introduction



19051501140Ehi-Egharevba, O, Boyle, F Computational Haemodynamics Research Group, Department of Mechanical Engineering,Technological University Dublin, Dublin, IrelandOsayomwanbor.EhiEgharevba@TUDublin.ie00Ehi-Egharevba, O, Boyle, F Computational Haemodynamics Research Group, Department of Mechanical Engineering,Technological University Dublin, Dublin, IrelandOsayomwanbor.EhiEgharevba@TUDublin.ie01047750spring network modelling of red blood cells 00spring network modelling of red blood cells IntroductionBlood is a two-phase suspension in which 55-58% is plasma and 42-45% cellular elements. Red Blood Cells (RBCs) account for over 99% of cellular elements in blood flow with one cubic millimetre of blood containing approximately 5,000,000 cells. The main role of RBCs is to supply tissues with oxygen and to transport waste carbon dioxide back to the lungs. The microcirculatory network which contains the smallest blood vessels like capillaries is the main site of exchange between blood and tissue. Micro-haemodynamic studies involving length scales similar to capillaries show many interesting phenomena like the Fahraeus and Fahraeus-Lindqvist effects [1], RBC rouleaux aggregates and cell free layers [2]. These phenomena greatly affect blood viscosity and oxygen transport. Due to scale and ethical limitations, it is important to develop accurate numerical models for investigating blood microcirculatory flows in order to supplement experimental work.The RBC membrane is a composite structure composed of a phospholipid bilayer attached to an underlying cytoskeleton. The composite membrane has a thickness of 9-10 nm so for a length scale of microns, the membrane can be treated as a two-dimensional (2D) viscoelastic interface embedded in a three-dimensional (3D) space. Following this, RBCs are typically modelled numerically under two distinct approaches: a continuum approach and a discrete approach. The RBC membrane is modelled as a thin elastic sheet in the continuum approach where RBC model energy is postulated through strain-deformation relationships. This approach has been successfully deployed to model known micro-haemodynamic phenomena but inherent difficulties in representing membrane viscosity and thermal fluctuations limit their usage for more complex flow scenarios. Discrete numerical approaches model the composite nature of the RBC membrane using spring networks, but current models are either 2D, neglect membrane viscosity or are incapable of simulating complex RBC morphologies like echinocytes.In this work, a 3D numerical spring network model of an RBC is developed (see Figure 1) using worm-like-chain springs. The numerical model accurately captures the mechanics of biological RBCs. RBC elastic deformation is validated against the optical tweezers experiment of Mills et al [3] while creep and cell relaxation experiments are used to validate viscoelasticity. Following the formulations of Chen [4] a curvature-based model of bending is also employed for simulating complex RBC morphologiesMODELLING TECHNIQUESWorm-like chain springs are used to construct 2D and 3D meshes comprised of hexagonal spring networks. Accurate mechanics is enforced through force calculations from the negative gradient of the Helmholtz free energy. The Helmholtz free energy of the spring network is a summation of the RBC component energies such as volume and area constraint, shear, bending and membrane viscosity i.e.Etotal=Evolume+Earea+Eshear+Ebending+EviscFollowing a numerical time integration scheme, the position of the spring network RBC can be updated to capture transient response due to enforced boundary conditions. Figure 1Spring network model of a red blood cell constructed with worm-like chain springs. The image on the left is an undeformed discocytic cell while the image on the right is the same red blood cell subjected to optical tweezers loading. Elastic deformation was validated against the optical tweezers experiment of Mills et al [3] while creep and relaxation experiments were used to validate viscoelastic response. References[1] Goldsmith et al., The American journal of physiology, 253:1005-1015,1989.[2] Popel et al., Annual Review of Fluid Mechanics, 37:43-69, 2005.[3] Mills et al., Mechanics & Chemistry of Biosystems, 1:169-180,2004.[4] Chen et al., Journal of Biomechanical Engineering, 139:121009-121009-11, 2017. ................
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