In vitro investigations of red blood cell phase separation in a complex microchannel network

Figures

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  FIG. 1.. Microfluidic device. Schematic of the microfluidic device (top) and magnified microscope images (bottom). The device had a single inlet and a single outlet and embedded a network composed of 49 hexagonal elements. The general direction of flow was from left to right. All the microchannels had a width W=10μm, a height H=8μm, and a length L=85μm. The image at the bottom right represents a typical microscope field of view of 512×512pixels.

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  FIG. 2.. Schematic of the experimental setup. A reservoir containing 10 ml RBC suspension was connected to the inlet of the microchannel. The outlet was at atmospheric pressure. The flow was driven by the hydrostatic pressure difference between the fluid level in the reservoir and the outlet. The hydrostatic pressure difference was controlled by setting the reservoir height via a linear-motion stage (ΔP=ρ×g×Δh).

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  FIG. 3.. Microfluidic network. Upper half of the microfluidic device (left). Red arrows indicate the direction of blood flow. Blue arrows indicate the direction of plasma flow in RBC-free vessels. Green dots represent diverging bifurcations. The path along I, II, III, and IV features a series of diverging and converging bifurcations, studied in Sec. III C 2. The inset (right) shows an example of a diverging bifurcation. Region of interests (ROIs) for the parent vessel and for the daughter branches are marked in red. The width of the ROI (WROI) is 10μm, while the length (LROI) is 78μm for all vessels of the bifurcation.

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  FIG. 4.. Computation of the plasma flow rate by mass balance. The magnitude and direction of plasma flow were evaluated by computing the mass balance for each of the two bifurcations sharing the RBC-free vessel.

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  FIG. 5.. Method validation: (a) Velocity measurement. Comparison between Particle-Tracking Velocimetry (PTVlab) and Line Scan Method (LSM). Mean velocity data from a sample of 11 diverging bifurcations for the high velocity experiment were compared. (b) Mass balance. Verification of the RBC flux conservation for all diverging bifurcations considered in this study for low (orange) and high velocity experiment (blue). QrbcP is the RBC flux in the parent vessel, while Qrbc1+Qrbc2 is the sum of the RBC fluxes in the daughter branches.

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  FIG. 6.. Hematocrit maps. Hematocrit distribution illustrated by the time-averaged pixel intensity of the video frames for the low velocity experiment (a) and for the high velocity experiment (b). The color intensity is monotonically related to the hematocrit of each branch: black denotes Ht=0, while red indicates Ht=Ht,max. The pixel intensity was normalized with respect to the maximum intensity found for each experiment. Magnified images of bifurcation III (c) and IV (d) are displayed for the high velocity experiment.

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  FIG. 7.. (a) Mean hematocrit. Time-averaged hematocrit in the function of the y-coordinate in the network (see Fig. 3) for either low (orange) and high velocity (blue) experiments. (b) RBC flux. Mean RCB flux in the parent vessels of all considered diverging bifurcations in function of the y-coordinate. Data are represented as mean (dots) and standard deviation (solid lines). Dotted lines are linear interpolations.

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  FIG. 8.. Phase separation results. Blood flow fraction vs RBC flux fraction data for low (orange) and high (blue) velocity experiments. Circles represent data from this study. The green continuous line is the empirical law by Pries et al.42 The dashed line is the identity line representing the proportional separation of blood and RBC (no phase separation). Data in the blue shaded regions indicate an inversion of the Zweifach-Fung effect.10,52 Data in the gray regions were sampled from bifurcations with one RBC-free daughter branch (see Figs. 3 and 4).

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  FIG. 9.. (a) Phase separation results. Blood flow fraction-RBC flux fraction data for the bifurcations I, II, III, and IV for low (orange) and high (blue) velocity experiments (extracted from Fig. 8). For all cases, data are sampled from the daughter branch closer to the upper half of the parent vessel [0<y∗<0.5, gray regions in the inset of panel (a) and in panel (b)]. The green continuous line is the empirical law from Pries et al.42 The dashed line is the identity line representing the proportional separation of blood and RBC (no phase separation). Data in the blue shaded regions indicate the inversion of the Zweifach-Fung effect.10,52 (b) Normalized RBC line density. Samples of normalized line density along the normalized width of the microchannels (y∗=y/WROI) for the parent vessels of the diverging bifurcations I, II, III, and IV (see Fig. 3). Continuous orange lines and blue lines represent low velocity and high velocity experiments, respectively.

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  FIG. 10.. Root Mean Square Error (RMSE). RMSE between our data [low velocity (a) and high velocity data (b)] and the original phase separation law proposed by Pries et al.42 in the function of the parameters α and β. The filled circle represents the RMSE between the data present in this study and the original Pries’ phase separation law. The triangle represents the RMSE between the data presented in this study and Pries’ phase separation corrected according to the Bayesian posthoc analysis by Rasmussen et al.43

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  FIG. 11.. Optical density profiles. Optical density profiles for the low velocity experiment computed for the parent vessels of the diverging bifurcations I, II, III, and IV following Roman et al.47

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  FIG. 12.. RBC velocity ratio. Ratio between the RBC velocity in the lateral direction (Uy,rbc) and the magnitude of the RBC velocity (Urbc) for the low (orange) and high (blue) velocity experiment.