Narrow Results

The transient deformation of red blood cells (RBCs) in a shear flow is studied by a three-dimensional numerical model proposed by the present authors. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to be the same to the fluid outside. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the present results show that the cells carry out a swinging motion, in which periodic inclination-oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rate decreasing, the swinging amplitude of the cell increases, and finally triggers a transition to tumbling motion.

Cell deformation and adhesion under shear flows play an important role in both cell migration in vivo and capture based microfluidic devices in vitro. Adhesion dynamics of captured cell (e.g., firm adhesion, cell rolling and cell detachment) under steady shear flows have been studied extensively. However, cell adhesion under accelerating flows is common both in vivo and in vitro, and dynamics of cell adhesion under accelerating flows remains unknown. As such, we used a mathematical model based on the front tracking method and investigated the effect of flow acceleration on deformation and adhesion dynamics of captured cells, including cell deformation index, cell shape evolution, the velocities of cell center, contact time and wall shear stress for cell rolling and detachment by using a series of parameter values for leukocyte. The results showed that the cell presented three dynamics states (i.e., firm adhesion, rolling and detachment) with increasing wall shear stress under uniform flows. Wall shear stresses were < 0.56 Pa and > 1.12 Pa for firm adhesion and detachment, respectively. The wall shear stresses were at the range 1.48–1.63 Pa (higher than 1.12 Pa) when cell left the bottom surface of the channel under flow accelerations (a = 0.975–1.625 m/s²). The minimum of deformation index under accelerating flow was smaller than that under uniform flow. In conclusion, the flow acceleration promotes the deformation and adhesion of captured cells. These findings could further the understanding of cell migration in vivo and promote the development of capture based microfluidic devices in vitro.

This paper presents a dissipative particle dynamics (DPDs) method for investigating the movement and deformation of biconcave shape red blood cells (RBCs) with the worm-like chain (WLC) bead spring. First, the stretching of a RBC is modeled and the obtained shape evolution of the cell agrees well with experimental results. Second, the movement and deformation of a RBC in shear flows are investigated and three typical modes (tumbling, intermittent and tank-treading) are observed. Lastly, an illustrating example of multi-RBCs in Poiseuille flow in a tube is simulated. We conclude that the presented DPD method with WLC spring can effectively model the movement and deformation of bioconcave cells.

A biological cell exhibits viscoelastic behavior mainly because its components (membrane and cytoplasm) are viscoelastic, and this is clearly seen when it is stretched and released. The present work numerically studied the shape recovery of a red blood cell (RBC) based on a viscoelastic model at the meso-scale using Dissipative Particle Dynamics (DPD) method. In this model, the RBC membrane is represented by a triangular network of worm-like chains, while the cytoplasm is replaced by a system of DPD particles. This viscoelastic model is validated by examining the stretching deformation of an RBC and comparing with the existing experimental data. Viscoelastic properties of the RBC are then analyzed by stretching an RBC under a 20 pN stretching force, and allowing it to relax. The time to recover its shape upon removal of the stretching force is measured to be 111 and 92.6ms for an RBC with and without cytoplasm, and the corresponding membrane viscosity is $6.67\times 10^{-4}$ and $5.56\times 10^{-4}$$\mathrm{\text{Poise}}\cdot \mathrm{\text{cm}}$, respectively. These values, for an RBC with cytoplasm, are closer to experimental data than those for an RBC without cytoplasm, lending support to the model with cytoplasm. Finally, parametric studies are conducted on the membrane elastic and bending moduli. The results show that the shape recovery time decreases with increasing the membrane elastic and bending moduli.