Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.

Figure 1

The multiscale computational framework for simulating blood-borne nanoparticle partitioning through microvasculatures. The method directly and concurrently resolves the dynamics of microscale cells and nanoscale particles and molecules suspended in blood plasma through complex microvascular networks, where open BCs are prescribed.

Figure 2

Demonstration of the particulate suspension inflow and outflow boundary condition (PSIO-BC). The schematic illustration of the PSIO-BC applied to a NP-RBC bidisperse suspension flowing through a two-generation microvascular bifurcation (a). The time course of the particle number simulated in the bifurcation (b), where at equilibrium the particle number becomes quasiconserved.

Figure 3

Schematics for the general particulate inflow and outflow boundary condition (PSIO-BC). The particle array represents the array storing the particle information according to the particle index, which increases from 1 to $N_{\max }$ from left to right. Here, for example, $N_{\max }=5$ at time $t$.

Figure 4

Demonstration of three reconstructed microvascular bifurcations of physiologic relevance.

Figure 5

The benchtop microscale particle image velocimetry ($\mu \mathrm{PIV}$) system (left), the chick chorioallantoic membrane microvasculature model (middle), and the grayscale visualization of the flow field of a selected region of interest (right).

Figure 6

Normalized axial flow velocity plotted against vessel radial locations for a tubular flow with or without red blood cells, computed with the P-BC or the PSIO-BC.

Figure 7

(a) Comparisons of the mean velocity distribution between the experiment and simulation through a CAM vascular bifurcation. The velocity contour for the simulation is an snapshot after the system reaches equilibrium (i.e., the number of particles reach plateau). (b) The radial distribution of the mean axial velocity at the A-A cross section annotated in (a). The asymmetry of the experimental curve may be related to the noncircular shape of the actual cross-sectional area.

Figure 8

(a) Snapshots of RBC-NP suspension flow through symmetric bifurcations under the various suspension flow flux partition ratio, ${\eta }_Q^F$. (b) Particle flow partition ratios, ${\eta }_Q^p$, plotted against the suspension flow partition ratio, ${\eta }_Q^F$, for symmetric microvascular bifurcations. The inset shows the results without the presence of RBCs.

Figure 9

(a) Snapshots of RBC-NP suspension flow through asymmetric bifurcations under various suspension flow flux partition ratio, ${\eta }_Q^F$. (b) Particle partition ratio, ${\eta }_Q^p$, plotted against suspension flow partition ratio, ${\eta }_Q^F$, for asymmetric microvascular bifurcations. The inset shows the results without the presence of RBCs.

Figure 10

(a–b) The cell distribution, NP trajectories, and a cross section of interest within an asymmetric microvascular bifurcation. (c) The contours of the $y$ velocity component at the cross section adjacent to the bifurcation junction. The left column shows the case without the presence of RBCs. The other six columns corresponds to six time points when a RBC sliding towards the upper branch. The black dashed line denotes the zero velocity line, which shows the flow separatrix that divides the flow entering two daughter branches.