Blood flow and cell-free layer in microvessels

Abstract

Blood is modeled as a suspension of red blood cells using the dissipative particle dynamics method. The red blood cell membrane is coarse-grained for efficient simulations of multiple cells, yet accurately describes its viscoelastic properties. Blood flow in microtubes ranging from 10 to 40 μm in diameter is simulated in three dimensions for values of hematocrit in the range of 0.15-0.45 and carefully compared with available experimental data. Velocity profiles for different hematocrit values show an increase in bluntness with an increase in hematocrit. Red blood cell center-of-mass distributions demonstrate cell migration away from the wall to the tube center. This results in the formation of a cell-free layer next to the tube wall corresponding to the experimentally observed Fahraeus and Fahraeus-Lindqvist effects. The predicted cell-free layer widths are in agreement with those found in in vitro experiments; the results are also in qualitative agreement with in vivo experiments. However, additional features have to be taken into account for simulating microvascular flow, e.g., the endothelial glycocalyx. The developed model is able to capture blood flow properties and provides a computational framework at the mesoscopic level for obtaining realistic predictions of blood flow in microcirculation under normal and pathological conditions.

Figure 1

Sample trajectories of individual RBCs (left) as flow develops and a snapshot of RBCs (right) in Poiseuille flow in a tube of a diameter D = 20 μm after steady state is achieved. H_t = 0.45. x is the coordinate along the cylinder axis.

Figure 2

Typical velocity profiles of blood flow in tubes of diameters D = 10 μm (left) and D = 40 μm (right) for different H_t values employing “repulsion” EV interactions. Dashed lines show the corresponding parabolic profiles of the Newtonian plasma with no cells present for the same pressure gradients. Dotted lines indicate the corresponding CFL thicknesses. H_t is the tube hematocrit, r is the radial axis, and v(r) is the axial flow velocity.

Figure 3

Center-of-mass distributions of RBCs in tubes of D = 10 μm (left) and D = 40 μm (right) for different H_t values with “repulsion” EV interactions. Dotted lines denote the corresponding CFL thicknesses. H_t is the tube hematocrit and r is the radial axis.

Figure 4

Number density profiles of the suspending solvent normalized by their average in tubes of diameters 10 μm (left) and 40 μm (right) for different RBC volume fractions using “repulsion” EV interactions. Dotted lines denote the corresponding CFL thicknesses. H_t is the tube hematocrit and r is the radial axis.

Figure 5

Discharge hematocrits for various RBC volume fractions and tube diameters in comparison with the approximation in equation (12). “Repulsion” (left) and “reflection” (right) EV interactions are employed. H_t is the tube hematocrit.

Figure 6

H_d for different RBC volume fractions and tube diameters obtained by the “wall force” method that utilize a net repulsion of cells from the wall. H_t is the tube hematocrit.

Figure 7

Relative apparent viscosity obtained with “repulsion” (left) and “reflection” (right) EV interactions in comparison with experimental data [28] for various H_t values and tube diameters. H_t is the tube hematocrit.

Figure 8

Relative apparent viscosity obtained with the “wall force” setup in comparison with experimental data [28] for different H_t values and tube diameters. H_t is the tube hematocrit.

Figure 9

An example of a CFL edge (left) and CFL thickness distribution (right) for H_t = 0.45 and D = 20 μm. x is the coordinate along the cylinder axis and δ is the CFL thickness.

Figure 10

CFLs obtained in blood flow simulations employing the “repulsion” and “reflection” EV interactions (left) and the “wall force” setup in comparison with experimental data [20,22,30] (right) for various H_t values and tube diameters. H_t is the tube hematocrit and H_d is the discharge hematocrit.

Figure 11

Spatial variations of the CFL thickness (SD) (left) and CFLs for different shear rates at H_t = 0.45 (right) for various H_t values and tube diameters. In vivo experimental data [20] for H_t = 0.42 are included in the left plot for comparison. H_t is the tube hematocrit, D is the tube diameter, and γ̄ is the mean shear rate.