Effect of fractional blood flow on plasma skimming in the microvasculature

Although redistribution of red blood cells at bifurcated vessels is highly dependent on flow rate, it is still challenging to quantitatively express the dependence of flow rate in plasma skimming due to nonlinear cellular interactions. We suggest a plasma skimming model that can involve the effect of fractional blood flow at each bifurcation point. To validate the model, it is compared with in vivo data at single bifurcation points, as well as microvascular network systems. In the simulation results, the exponential decay of the plasma skimming parameter $M$ along fractional flow rate shows the best performance in both cases.

Figure 1

Plots of plasma skimming parameter $M$ against fractional blood flow and illustrations of RBC redistribution in two cases. Here $Q_1/Q_0$ denotes the fractional blood flow between the largest daughter vessel and parent vessel. (a)–(c) Without using the fractional blood flow model, there is negligible change in RBC redistributions at bifurcation since $M$ is set as a constant. (d)–(f) When including the effect of fractional blood flow, both hemoconcentration and hemodilution after plasma skimming become more significant.

Figure 2

Ratio of hematocrit between parent and daughter vessels ($H_i/H_0$) against fractional blood flow ($Q_i/Q_0$) at single bifurcation for comparing fractional blood flow model with the model developed by Gould and Linninger [26] and experimental data [24]. Two cases of geometries stated in Table 1 are considered. Significant amplifications in both hemoconcentration and hemodilution are produced by using fractional blood flow model, accurately matching the experimental data.

Figure 3

Ratio of hematocrit between parent and daughter vessels ($H_i/H_0$) against fractional blood flow ($Q_i/Q_0$) at a single bifurcation for different $k$ values. The second case stated in Table 1 is considered. The plots clearly show the high sensitivity of $k$ and that $k=4$ gives the best match with the experimental data [24].

Figure 4

Computational model of the microvascular network and the corresponding hemodynamic calculations.

Figure 5

Comparison of hemodynamic characteristics at the microvascular network level between (a)–(c) Gould and Linninger's model and (d)–(f) the fractional flow model. Vessel diameters are asymmetrically decreased from 40 to $6\mu \mathrm{m}$. The pressure drop between the root vessel to capillary ends is set to 47 mm Hg. Flow velocity and pressure data are compared with two sets of in vivo experimental data [34, 35]. Also shown is the relative hematocrit distribution along with vessel diameters for the microvascular network model. The systemic hematocrit $H_{\mathrm{sys}}$ is set to 0.45. Black triangles represent in vivo experimental data [36]. The initial hematocrit at the root vessel is varied from 0.3 to 0.45.