Two-Dimensional Simulation of Red Blood Cell Deformation and Lateral Migration in Microvessels

Abstract

A theoretical method is used to simulate the motion and deformation of mammalian red blood cells (RBCs) in microvessels, based on knowledge of the mechanical characteristics of RBCs. Each RBC is represented as a set of interconnected viscoelastic elements in two dimensions. The motion and deformation of the cell and the motion of the surrounding fluid are computed using a finite-element numerical method. Simulations of RBC motion in simple shear flow of a high-viscosity fluid show "tank-treading'' motion of the membrane around the cell perimeter, as observed experimentally. With appropriate choice of the parameters representing RBC mechanical properties, the tank-treading frequency and cell elongation agree closely with observations over a range of shear rates. In simulations of RBC motion in capillary-sized channels, initially circular cell shapes rapidly approach shapes typical of those seen experimentally in capillaries, convex in front and concave at the rear. An isolated RBC entering an 8-mum capillary close to the wall is predicted to migrate in the lateral direction as it traverses the capillary, achieving a position near the center-line after traveling a distance of about 60 mum. Cell trajectories agree closely with those observed in microvessels of the rat mesentery.

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

“…Unlike RBCs, for vesicles we can vary their intrinsic characteristic parameters (e.g., size, degree of deflation, and nature of internal fluid). Despite the simplicity of their structure, vesicles have exhibited many features observed for red blood cells: equilibrium shapes [21], tank-treading motion [3,22], lateral migration [15,23,24], or slipperlike shapes [25,26]. Capsules (a model system incorporating shear elasticity) have also revealed some common features with vesicles [27,28].…”

“…We use large systems (in lattice units) because of the higher resolution required to extract the results shown below. Previous works done in 2D dealing with vesicles (also for red blood cells) have demonstrated that the dynamics in the third dimension is not relevant, even in confined geometries [23,24,29]. Vesicle dynamics under shear has been extensively studied in the literature.…”

Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads

“…Beside the above mentioned partitioning mechanisms, basically relying on a flow rate unbalance, several studies have investigated the possibility of exploiting particle deformability for their separation in bifurcations [17][18][19]. The capability of sorting particles based on their mechanical properties is of primary importance in medicine, since cell deformability is a clinical indicator of a wide range of diseases, e.g., malaria [20] and leukemia [21].…”

“…In the last decade, Secomb et al [17,18] Elastic beads were studied with finite element approach by Trofa et al [26], hinting at the possibility of their sorting based on their elastic moduli in a T-shaped microchannel.…”

Formation of the three-dimensional geometry of the red blood cell membrane

“…In recent years, particle methods were used to model rbc behaviour in microvessels [5,6,7], since the motion, deformation and the fluid structure interacion of rbcs are easily modelled. In reality, the motion and deformation of the rbcs are highly three dimensional, as they exhibit three dimensional deformations in microvessels [8]. Therefore, simplified two dimensional models are not enough to capture the actual behaviour of rbcs in microvessels.…”