Partitioning of red blood cell aggregates in bifurcating microscale flows

Abstract

Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.

Figure 1. A schematic representation of the flow system.

A pressure system was used to drive the flow entering the parent branch (P). The outlet left (L) and right (R) daughter branches led to the open reservoirs, the height of which was adjusted to provide the desired pressure drop, and thereby control the flow ratio. A magnetic stirrer was used in the inlet reservoir to avoid sedimentation and aggregation of cells in the samples. Regions of interest are shown as white, dashed rectangles. The velocity field and streamlines derived from an aggregating case with Q*~0.13 is shown in the right panel. The vector and streamline density is reduced by half for clarity of presentation. The red lines are the lines that separate the flow to the different daughter branches. The dimensionless quantities y* and y* are the x and y coordinates normalised by the channel width (100 μm).

Figure 2. Representative cases of original and processed images.

Top: (a) the original image and (b) the processed image of a non-aggregating sample (PBS) for Q*~0.5. Bottom: (c) original and (d) processed images of an aggregating sample (D2000) for Q*~0.2. The size of the detected structures is shown in colour-scale for a qualitative comparison; the size is normalised with the maximum size detected in the aggregating case. The origin of the global coordinate system is shown in panel (a).

Figure 3. A schematic explanation of the key parameters quantified in the present study, A, Ac, A*, and .

Images shown are magnified sections from representative processed images.

Figure 4

(a) Aggregate size (A*) distribution in the entire channel for the non-aggregating case (PBS) and for Q*~0.5 obtained from 400 images (k = 208479). The mean value is 1.06[0.50′, 1.08]. (b) detected edge area A* distribution for the aggregating case (D2000) obtained for Q*~0.5 and from 400 images (k = 73164). The mean value is 1.90[0.50′, 1.91]. The dotted line indicates the maximum area of one RBC. (c) distribution of all detected structures (A*) at Q*~0.5 in the parent and (d) daughter branches. Intensity-based haematocrit profiles (H(I*)) calculated as in Sherwood et al. (dashed line, linear function), and in Sherwood et al. (solid lines, non-linear function) are superimposed; in the present case the haematocrit profiles are scaled for the purpose of comparison.

Figure 5

(a) Ensemble average () and values based on 400 images against Q* for the PBS case. (b) Ensemble averaged values () with pooled standard deviation for the D2000 case. (c) Ensemble averaged values (PBS) obtained by normalising by the values in parent branch (the standard deviation of (n = 400) is also shown). The lower limit in the data of in (a) was 0.5 due to noise reduction in the data. (d) Ensemble averaged () values of aggregate size plotted against Q* (D2000 cases); the data is normalised by the values in the parent branch. Data below Q* = 0.5 correspond to the right daughter branch and above Q* = 0.5 to the left daughter branch. The standard deviation of is also included. (e) Size-flow parameter F_A* = Q*A* against Q* as an index of the flow preference of different aggregate size.

Figure 6

(a) Spatial distributions for two different A* ranges (3 < A* < 5 and 7 < A* < A*_max) in the aggregating case (D2000, parent branch), and for all flow rates tested in this study (Q ~0.35 ± 0.5 μl/h). (b) Spatial distributions of RBC aggregates of three different sizes throughout the bifurcating microchannel geometry. A* ~7 is shown in blue triangles (▴), A*~ 5 is shown in red squares (▪) and A*~3 in black circles (⚬). The flow ratio in the left daughter branch is ~0.87 (Q* = 0.13 in the right daughter). The red flow streamlines define the flow separating lines in the parent branch. Selected aggregates are shown for clarity of presentation.

Figure 7

(a) Spatial distribution of a specific aggregate size (A*~4) in the parent branch; the vertical solid line represents the x* axis location of the mean value of A* calculated from the data falling below the 5^th percentile of the distribution (denoted as x*_A*). (b) Location of the flow-split line on x* axis (x*_fs) (black, filled circles) against Q*. The location of x*_A* is plotted in the same graph for specific A* values (1 to 7, coloured lines).