Investigation of shear rates of rolling adhesion on leukocytes with bending of microvilli

An advanced leukocyte model based on a lattice-Boltzmann lattice-spring model (LLM) and an adhesive dynamics (AD) is presented. In principle, the model can deal with not only extensional and compressional but also bending deformation of microvilli of of leukocytes. In this work, the model is applied to investigate how different flow shear rates affect bending deformation of the microvilli and related physical properties. It is demonstrated that at each given flexural stiffness, adhesive bond force, rolling velocity, contact area, number of bonds, and bending deformation increase as the shear rate increases. At each given shear rate, the bending angles of microvilli increase as the flexural stiffness decreases. Therefore, the adhesive bond force, contact area, and number of bonds increase and result in a decrease in cell rolling velocity. The degree of the decrease depends on both shear rate and flexural stiffness. In addition, a bonding and debonding process for individual microvilli is observed and explored from a bending angular point of view.

Figure 1

A microvillus is modeled by a spring with its end fixed at the base node $i$ on the cell surface. The tip node $j$ can be extended or compressed with respect to the base node $i$. In addition, the vector ${\mathbf{r}}_{ji}$ can be bent with respect to vector ${\mathbf{r}}_{ki}$ to have a bending angle ${\theta }_{kij}$, where the node $k$ is always located on the extension portion of the line connecting the mass center $C_M$ to the base node $i$.

Figure 2

Simulation configuration.

Figure 3

The comparisons between the present simulation results and those of the previously published data from other groups for (a) the translational velocity, (b) the deformation index $(L/H)$, and (c) the contact area.

Figure 4

The instantaneous velocity as a function of time at the shear rates of (a) $100{\text{s}}^{-1}$ and (b) $400{\text{s}}^{-1}$. The magnified drawings represent the instantaneous velocity within a 1-s period.

Figure 5

The simulation results of (a) the average translational velocity, (b) number of bonds, and (c) the contact area as a function of a shear rate at two different levels of the flexural stiffness of microvilli. The shear rate is varied from $\gamma =100{\text{s}}^{-1}$ to $400{\text{s}}^{-1}$ at each level of flexural stiffness.

Figure 6

The simulation results of the deformation index at two different levels of the flexural stiffness of microvilli at the shear rates from $100{\text{s}}^{-1}$ to $400{\text{s}}^{-1}$.

Figure 7

The instantaneous velocity at microvillus flexural stiffness of (a) $K_{exp}$ and (b)$10K_{exp}$ at the shear rate of $\gamma =300{\text{s}}^{-1}$. The magnified drawing presents the instantaneous velocity in a 0.1-s period.

Figure 8

The simulation results of the Y component of the total adhesive bond force as a function of shear rate at two different levels of flexural stiffness.

Figure 9

The simulation results of the angular distribution of the microvilli at two different levels of the microvillus flexural stiffness at shear rates of (a) $100{\text{s}}^{-1}$, (b) $200{\text{s}}^{-1}$, (c) $300{\text{s}}^{-1}$, and (d) $400{\text{s}}^{-1}$.

Figure 10

The bending angle as a function of time for (a) the single microvillus initially located near the center of the contact area at $\gamma =400{\text{s}}^{-1}$ and (b) the single microvillus initially located near the center of the contact area at $\gamma =100{\text{s}}^{-1}$. The stiffness of the microvillus is fixed at the experimental value.