Two-dimensional simulation of red blood cell motion near a wall under a lateral force

Abstract

The motion of a red blood cell suspended in a linear shear flow adjacent to a fixed boundary subject to an applied lateral force directed towards the boundary is simulated. A two-dimensional model is used that represents the viscous and elastic properties of normal red blood cells. Shear rates in the range of 100 s−1 to 600 s−1 are considered, and the suspending medium viscosity is 1 cP. In the absence of a lateral force, the cell executes a tumbling motion. With increasing lateral force, a transition from tumbling to tank-treading is predicted. The minimum force required to ensure tank-treading increases non-linearly with the shear rate. Transient swinging motions occur when the force is slightly larger than the transition value. The applied lateral force is balanced by a hydrodynamic lift force resulting from the positive orientation of the long axis of the cell with respect to the wall. In the case of cyclic tumbling motions, the orientation angle takes positive values through most of the cycle, resulting in lift generation. These results are used to predict the motion of a cell close to the outer edge of the cell-rich core region that is generated when blood flows in a narrow tube. In this case, the lateral force is generated by shear-induced dispersion, resulting from cell-cell interactions in a region with a concentration gradient. This force is estimated using previous data on shear-induced dispersion. The cell is predicted to execute tank-treading motions at normal physiological hematocrit levels, with the possibility of tumbling at lower hematocrit levels.

Hemodynamics

“…The eventual thickness of the cell-free layer is governed by the balance between these two effects (97). Although detailed numerical simulations of multiple suspended particles are able to predict formation of the layer (22), the underlying mechanical processes remain incompletely understood and are currently an active area of research (31,37,75). …”

Modeling Stem Cell Myogenic Differentiation

“…They include analyses of spreading on patterned substrates1, alignment under cyclic load23, mechanotransduction under applied shear forces4, deformation under 3-D flow forces5, force generation with 3-D tissue6, etc. However, the modeling of stem cell mechanobiology, where mechanotransduction converges with cell differentiation, remains less developed.…”

Prediction of noninertial focusing of red blood cells in Poiseuille flow

“…For ${\stackrel{false¯}{y}}_0=-1\text{to}-2$, initial tumbles result in migration towards the wall before a stable tank-treading motion is reached. In this case, a tumbling cell generates a lift directed towards the wall, in the opposite direction to that generated by cells closer to the wall [22, 23]. The phase-plane type plots in Figure 3 shows trajectories converging a fixed point where the center of mass position is $\overline{y}\ast \approx -2.2$, and the orientation angle is θ *≈0.12.…”

“…If the cell is placed initially too far from a solid boundary, the cell migrates towards the centerline. If the cell is sufficiently close to the solid boundary, tumbling motions are inhibited, resulting in a tank-treading motion [23]. A cell placed in a shear flow near a boundary in a 20- μ m channel would migrate and tumble [23].…”

“…If the cell is sufficiently close to the solid boundary, tumbling motions are inhibited, resulting in a tank-treading motion [23]. A cell placed in a shear flow near a boundary in a 20- μ m channel would migrate and tumble [23]. Results from the expanded Poiseuille flow simulations indicate that the curvature of the flow has the effect of restricting the cell’s motion to a region near the solid boundary.…”