Clinical Hemorheology and Microcirculation 1 (2014) 1–13
DOI 10.3233/CH-141909
IOS Press
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Influence of erythrocyte aggregation at
pathological levels on cell-free marginal
layer in a narrow circular tube
Bumseok Namgunga , Hiromi Sakaib and Sangho Kima,∗
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Department of Biomedical Engineering and Department of Surgery, National University of Singapore,
Singapore
b
Department of Chemistry, School of Medicine, Nara Medical University, Nara, Japan
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Abstract. Human red blood cells (RBCs) were perfused in a circular micro-tube (inner diameter of 25 ␮m) to examine the dynamic
changes of cell-free marginal region at both physiological (normal) and pathophysiological (hyper) levels of RBC aggregation.
The cell-free area (CFA) was measured to provide additional information on the cell-free layer (CFL) width changes in space
and time domains. A prominent enhancement in the mean CFL width was found in hyper-aggregating conditions as compared
to that in non-aggregating conditions (P < 0.001). The frequent contacts between RBC and the tube wall were observed and the
contact frequency was greatly decreased when the aggregation level was increased from none to normal (P < 0.05) and to hyper
(P < 0.001) levels. In addition, the enhanced aggregation from none to hyper levels significantly enlarged the CFA (P < 0.01).
We concluded that the RBC aggregation at pathophysiological levels could promote not only the CFL width (one-dimensional
parameter) but also the spatiotemporal variation of CFA (two-dimensional parameter).
Keywords: Plasma layer, red blood cell, hemodynamic, microcirculation
1. Introduction
Reduction in tube hematocrit with narrowing the tube diameter (Fåhraeus effect [12]) contributes to
a decrease in apparent viscosity due to formation of cell-free layer (CFL) (Fåhraeus-Lindqvist effect
[13]) [1, 9, 37]. The CFL can be formed in microcirculation, and its roles have been highlighted in many
previous studies. The CFL play a significant role in modulating wall shear stress [24, 42], regulating the
oxygen (O2 ) releasing rate [38], and attenuating the nitric oxide (NO) scavenging by RBCs [5, 6, 20].
In addition, temporal variations of the CFL width may enhance the NO bioavailability in small arterioles
by elevating the wall shear stress [26]. A subsequent study highlighted that the effect of CFL width
variations on the NO bioavailability might become more pronounced by RBC aggregation [27]. Since
the CFL formation is mainly attributed to the axial accumulation of RBCs induced by the cells migration
towards the flow center, the formation can be promoted by RBC aggregation. It is of note that the mean
peak NO concentration could be decreased at pathological levels of aggregation since the reduction of the
∗
Corresponding author: Sangho Kim, PhD, Department of Biomedical Engineering, National University of Singapore 9
Engineering Drive 1, Block EA #03-12 Singapore 117575. Tel.: +65 6516 6713; Fax: +65 6872 3069; E-mail: [email protected].
1386-0291/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
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wall shear stress due to formation of the thick CFL would result in the overall decrease in NO production
[7]. The change in the shear stress may also alter NO originating from RBC as reported in a previous
study [40].
Our previous in vivo study [28] reported that under hyper-aggregating conditions, the CFL width in the
rat cremaster muscle arterioles was significantly (P < 0.05) increased at reduced flow rates (PSR (mean
velocity / tube diameter) = 57.3 ± 45.8 s−1 ) compared to that obtained under normal flow conditions
(144.7 ± 89.5 s−1 ). The pathological elevation in RBC aggregation is an important diagnostic indicator
highly correlating with an inflammatory state [2], and is clinically related to human diseases such as
sepsis [4], hypertension [31], diabetes mellitus [8], and HIV infection [17].
Although the clinical relevance of CFL has been highlighted in many previous studies, limited information is available on its dynamic response to the RBC aggregation change. Our previous in vivo studies
[19, 28, 29] provided some information on how RBC aggregation can influence the CFL width. However,
such information has been limited to temporal variations of CFL at a specific location. For the application
of CFL width changes to diagnostic purpose, the characteristics of CFL width change will need to be
quantified under an in vitro condition since the in vivo flow environment would be different from that in
vitro. In addition, simple statistical analyses such as mean CFL width and its standard deviation would
be insufficient to completely quantify the dynamic changes in the CFL width since the CFL width varies
spatially and temporally.
Therefore, the present study performed in vitro experiments by perfusing human RBCs in a circular
micro-tube with diameter of 25 ␮m. The experiments were carried out at both physiological and pathophysiological levels of RBC aggregation seen in humans to better understand the significance of CFL
changes by RBC aggregation. The spatiotemporal variation in CFL was quantified by various analysis
techniques.
2. Materials and methods
2.1. Blood sample preparation
Human whole blood in 7.5% K2 -EDTA solution (I-DNA Biotechnology, Singapore) was centrifuged
(Sigma 2–6, Gottingen, Germany) and washed with Phosphate Buffer Saline (PBS, Hanks). The buffy
coat was gently removed after the first centrifugation, and the collected packed RBCs were rewashed
three times more before resuspending them in a medium. The level of RBC aggregation was varied by
resuspending the packed RBCs in dextran-PBS solutions with different concentrations. The suspending media were prepared by dissolving Dextran 500 (Avg. MW = 450–550 kDa, Pharmacosmos A/S,
Denmark) in PBS at desired concentrations of 7.5 and 12.5 mg/mL for normal and hyper aggregation
conditions, respectively. The packed RBCs were then added to the media at a hematocrit of 40%. The
RBC aggregation levels of the blood samples were quantified by the Myrenne aggregometer (MA-1,
Myrenne GmbH, Roetgen, Germany) in terms of M index at physiological (M = 12–16) and pathological
(M > 20) levels seen in humans [28]. For non-aggregating conditions (M = 0.0), no dextran was used.
2.2. Experimental setup
Fig. 1 shows the schematic diagram of our experimental setup. The micro-tubes used in the present
study were purchased from Hirakawa Hewtech Co. (Ibraki, Japan), which is made of fluorinated ethylene
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Fig. 1. Schematic diagram of experimental setup.
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propylene (FEP) copolymer. The tube with inner diameter of 25 ␮m and length of 150 mm was assembled
with a chamber that consists of top and bottom acrylic plates (thickness = 1 mm) with a sealing rubber
frame, and one end of the tube was connected to a reservoir. The tube was completely immersed in
the distilled water inside the chamber which was placed on the stage of an inverted microscope (IX71,
Olympus, Japan) with a 40X objective (UPlanSApo 40x, Olympus, Japan) and a long working distance
condenser (WI-UCD, Olympus, Japan).
To avoid unexpected image distortion induced by a difference in refractive index (RI) between fluid
and micro-tube, we have matched the RI of FEP tube with that of dextran-PBS solutions (fluid inside the
tube) and distilled water (fluid outside the tube) (see Table 1). Thus, as a result, we did not encounter any
discernible image distortion during image acquisition.
The micro-tube was pre-flushed with autologous plasma to minimize adhesion of RBCs to the inner
surface of the tube. A polytetrafluoroethylene (PTFF) coated small magnetic stirring bar (2 x 2 mm,
Big Science Inc., USA) was inserted into the reservoir and it was continuously stirred to prevent RBC
sedimentation. A syringe pump (KDS 210, Holliston, USA) was used to control flow rates. The blood
Table 1
Refractive indices (RIs) of the fluid and FEP tube
Materials
FEP tube
Distilled water
PBS
Dextran 500 + Saline (5 mg/mL)
Dextran 500 + Saline (20 mg/mL)
Dextran 500 + Saline (50 mg/mL)
RI
Ref.
1.338
1.333
1.334
1.339
1.341
1.346
Petzold et al.[30]
Hecht et al.[16]
Schoch et al.[34]
Xu et al.[41]
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flow in the tube was recorded with a high-speed video camera (FASTCAM 1024PCI, Photron, USA)
at 3000 frame/s for 1 s with a resolution of 512 x 512 pixels. A blue filter (B-390, HOYA, Japan) with
peak transmittance at 394 ± 4 nm and spectral bandpass of 310-510 nm was used to enhance the contrast
between RBCs and background. Seven experiments per each aggregating condition were performed at
room temperature of 21◦ C.
2.3. CFL width and cellular velocity measurements
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The CFL width was defined as the distance between the inner wall of the tube and the edge of the
RBC core. Thus, the CFL width is one-dimensional information. In contrast, the cell-free area (CFA) was
defined as the area occupied by the CFL along the tube, thus providing two-dimensional information on the
spatiotemporal variation of CFL along the flow direction. The detailed procedure of determining the CFL
width can be found in our previous studies [25]. The spatial resolution of the CFL width measurement
in the present study was 0.5 ␮m. Since RBC aggregation is a shear-dependent reversible feature, we
do not expect to see discernible effect of RBC aggregation on the CFL width change in high shear
conditions. Therefore, the velocity at the outer edge of RBC core (edge velocity (Vedge )) in the present
study (Vedge = 2.7 mm/s) was adjusted to be similar to that (2.8 ± 1.3 mm/s) used to simulate pathological
flow conditions in our previous arteriolar flow study [28]. The Vedge of the RBC core was obtained by
manually tracking the outermost cells across 10 digitalized frames [18]. Centerline velocity (Vcenter ) of
the tube flow was measured by adopting the image correlation method on sequentially extracted images
from the high-speed video recording [11, 39]. Mean velocity (Vmean ) was estimated by dividing the
Vcenter with a correction factor of 1.6 [3].
2.4. Persistency of CFL
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The persistency of the CFL width pattern along downstream was characterized by using the crosscovariance which has commonly been used to find the similarity of two sequences. The CFL width data
were obtained at two points along the length of the tube on each side of the tube. The first analysis
line for the CFL width measurement was established at a distance of 80 mm from the inlet of the tube
and considered as the baseline. The second analysis line was then placed at a distance 0.5D, 1.0D,
1.5D, or 2.0D from the baseline (0.0D) where D represents the inner diameter of the tube. The CFL
width over a time period of 1 s from each position of the second line was cross-correlated against the
baseline measurement. Based on this approach, the 3000 sequential variations of the CFL width at each
analysis line were treated as a time-dependent continuous signal. The correlation length was determined
as described in a previous study by Kim et al. [19]. In brief, the correlation values were fitted by the
exponential equation of y = e−kx . The correlation length is defined as the downstream distance from the
baseline where the normalized correlation coefficient falls to 1/e (0.368).
2.5. cell-free layer (CFA) determination
To better illustrate the spatiotemporal variation of the CFL width, the CFA was determined in a particular
region of interest (ROI). It was achieved by adopting our previous image analysis technique [25] for the
CFL width measurement. Flow image in the ROI that has a length of 4.0D was cropped, and the cropped
sequential images over the time period (1 s) were then subjected to the minimum thresholding method
[25] to obtain binary images. The CFA was determined by counting the number of pixels in the area with
no RBCs near the tube wall, and it was normalized by the total area of the ROI.
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2.6. Statistical analysis
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Fig. 2. Mean (a) and standard deviation (b) of the cell-free layer width in different aggregating conditions. SD represents standard
deviation. ∗ P < 0.05 and ∗∗ P < 0.001.
All statistical comparisons were performed with a statistical software package (Prism 6.0, GraphPad).
One-way ANOVA with Tukey’s Post-Hoc test was used to determine significance of difference among
the three different aggregating groups. All data are reported as means ± SD (standard deviation). For all
statistical tests, P < 0.05 was considered to be statistically significant.
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3. Results
3.1. Systemic parameters
The aggregation index (M) was 15.7 ± 1.3 and 24.6 ± 4.6 for normal-aggregating and hyperaggregating conditions respectively, whereas it was 0.0 for the non-aggregating condition. Hematocrit
of all blood samples was 40 ± 1%, and there was no significant difference among the three aggregating groups. The edge velocity (Vedge ) was 2.7 ± 0.8, 2.7 ± 0.5 and 2.6 ± 0.4 mm/s for non-aggregating,
normal-aggregating, and hyper-aggregating groups, respectively. There was no significant difference in
Vedge among the three aggregating groups. Volumetric flow rate and Reynolds number in all experiments were approximately 0.07 ± 0.01 ␮L/min and 0.01, respectively. Representative values of density
(1 g/cm3 ) and viscosity (0.05 dyn·s/cm2 ) were used for estimation of the Reynolds number as also reported
previously [35]. The driving pressure estimated from the flow rates and the reference viscosity was
0.76 ± 0.16 atm.
3.2. Effect of RBC aggregation on mean and SD of the CFL widths
Fig. 2 shows the mean and SD of the CFL widths from the five analysis lines in the three aggregating conditions. As shown in the figure, the mean CFL width increased with elevating the aggregation
level (Fig. 2(a)). The mean CFL widths in the normal-aggregating (1.7 ± 0.5 ␮m) and hyper-aggregating
(2.0 ± 0.5 ␮m) conditions were significantly larger (P < 0.05 and P < 0.001, respectively) than that in the
non-aggregating condition. On the other hand, the SD of the CFL width appeared to be independent of the
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Fig. 3. (a) Typical microscopic image of contact between red blood cell and tube wall. (b) Contact frequency results for three
aggregating conditions. ∗ P < 0.05 and ∗∗ P < 0.001.
aggregation level (Fig. 2(b)). We found no significant difference in the SD among the three aggregating
groups.
3.3. Persistency of the CFL width variation
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The correlation length was used to examine the persistency of the CFL width variation along
downstream. No statistical difference was found between the non-aggregating (48.0 ± 5.5 ␮m) and
normal-aggregating (47.2 ± 3.0 ␮m) conditions. Similarly, the correlation length in the hyper-aggregating
(50.8 ± 5.0 ␮m) condition was not significantly different from that in either non-aggregating or normalaggregating condition, confirming that aggregation has no effect on the persistency of CFL width variation.
3.4. Effect of RBC aggregation on RBC-wall contact frequency
Interestingly, we observed that a number of RBCs were in contact with the tube wall while flowing
(Fig. 3(a)). To examine whether this RBC-wall contact can be influenced by the RBC aggregation, the
number of zero values of the CFL width during its measurement (1 s) was compared under the three
aggregating conditions. In the measurement, we assumed that the zero CFL width represents the instant
contact between RBC and the tube wall. Fig. 3(b) shows the contact frequency results normalized by
the total number of observations (3000 data). The contact frequency decreased with increasing the level
of aggregation. Significant decreases in the contact frequency were found under the normal-aggregating
(P < 0.01) and hyper-aggregating (P < 0.001) conditions as compared with that in the non-aggregating
condition.
3.5. Effect of RBC aggregation on CFA
Fig. 4(a) shows two-dimensional visualization of CFL changes at different time points. The figure
illustrates two distinct regions (RBC core and CFA) in the ROI. The CFA varied with time and RBCs
occasionally made contact with the tube wall. The CFA on each side of the wall (top and bottom) appeared
to be asymmetric, and thus the degree of asymmetry was examined by comparing the CFA on the two
sides as follows:
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Fig. 4. (a) Visualization of cell-free area (CFA) in a hyper-aggregating condition at a particular time. Gray and white regions
represent the red blood cell core and CFA, respectively. (b) Asymmetry of CFA on the two sides of the tube wall in three
aggregating conditions.
CFAtop − CFAbottom In
CFAtop + CFAbottom
× 100%
(1)
The asymmetry of CFA seemed to be decreased by elevating the aggregation level (non-aggregation:
19.1% −→ normal: 15.2% −→ hyper: 14.8%) as shown in Fig. 4(b).
A typical example of time-dependent normalized CFA (NCFA) variation over 1 s is shown in Fig. 5(a).
The NCFA at higher levels of aggregation seemed to be greater than that at lower aggregation levels
(none < normal < hyper). However, the NCFA difference among the three aggregating conditions varied
with time, thus all NCFAs were integrated over 1 s for the statistical comparison (Fig. 5(b)). The results
showed that the mean NCFA in hyper-aggregating conditions were significantly greater than that in nonaggregating conditions (P < 0.01). Although no statistical difference was found between none and normal
aggregating conditions or normal and hyper aggregating conditions, there seemed to be an increasing
trend of the mean NCFA with elevating the aggregation level.
To obtain further detailed information on the NCFA, probability of the NCFA was analyzed. The
probability was obtained by normalizing the frequency of NCFA value over 1 s. Fig. 6(a) shows a typical
example of the probability distribution of the NCFA of which data correspond to those in Fig. 5(a), and
definitions for the probability distribution is described in Fig. 6(b). As expected, the distribution was
shifted to greater values as the aggregation level increased from none to hyper. All distributions did not
follow the normal distribution. As shown in Fig. 6(c), both left and right tail widths from the mean NCFA
appeared to have an increasing trend with elevating the aggregation level. However interestingly, there
was a significant increase only in the right tail width in hyper-aggregating conditions compared to that
in non-aggregating conditions (P < 0.05).
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Fig. 5. (a) Time-dependent normalized cell-free area (NCFA) change in three aggregating conditions. (b) Time integration of
the NCFA over 1 s. ∗ P < 0.01.
Fig. 6. (a) Probability distribution of normalized cell-free area (NCFA) obtained from the data shown in figure 5a. (b) Definition
of left and right tail widths in the probability distribution. (c) Aggregation effect on the left and right tail widths. ∗ P < 0.05.
4. Discussion
4.1. Effect of RBC aggregation on the mean CFL width and its SD
The prominent increase in the CFL width with elevating the aggregation level in the present study
is supported by previous in vivo and in vitro studies [1, 28]. Our earlier in vivo study [28] showed
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that the prominent CFL width can be formed in arterioles under pathological aggregating conditions
(M = 21.6 ± 4.8). A similar effect was found in the present in vitro study in hyper-aggregating conditions
(M = 24.6 ± 4.6) (Fig. 2(a)). The mean CFL width results obtained in this study confirmed that pathological
elevation of the aggregation level could lead to a prominent enhancement in the mean CFL width.
However, relatively thin CFL widths (mean ± SEM) were found in the present study (9.7 ± 0.8%,
13.7 ± 1.1% and 16.6 ± 1.1% for non-aggregating, normal-aggregating and hyper-aggregating conditions, respectively) compared to previous in vivo results (15.7 ± 0.9%, 18.3 ± 0.9% and 20.6 ± 0.9%)
[28], which were all normalized by radius of tube or vessel. A thicker CFL width can provide a more
marginal space for RBCs to move, in particular for RBCs positioned near the vessel (or tube) wall. Such
cell movements would result in a greater irregularity of the interface between CFL and RBC core. Unlike
the previous in vivo study, no statistical change in the SD of the CFL width found in the present study
would suggest that the aggregation effect on dynamic characteristics of the interface could be diminished
in the in vitro tube flow (Fig. 2(b)). A possible reason for the discrepancy in the mean CFL width between
in vivo and in vitro can be the elasticity difference between the tube and vessel walls. As reported in
an earlier study by Maeda et al. [22], the CFL width ( 3.5 ␮m) in an elastic micro-vessel with diameter
of 25 ␮m was 20% greater than that ( 2.8 ␮m) in a hardened micro-vessel. The micro-tube wall in the
present study would be more rigid than the arteriolar wall, the difference in the wall elasticity may also
contribute to the greater mean CFL width in arterioles compared to that in micro-tubes.
4.2. Persistency of CFL variation
In
The correlation length of the CFL width formed in arterioles (ID = 10 – 50 ␮m) of the rat cremaster
muscle has been reported to be 32 ± 5.6 and 30 ± 4.0 ␮m at PSR (Vmean / D, where D = inner diameter)
of 288.2 ± 150.5 and 220.3 ± 123.4 s−1 for non-aggregating and normal-aggregating conditions respectively, at 42% systemic haematocrit [19]. Thus, the in vivo correlation length appeared to be independent
of aggregating condition. The outermost RBCs would be subjected to higher shear stresses than those in
the core region, which further lower the potential aggregation effect on the persistency of CFL variation.
A relatively short correlation length ( 16 ␮m) was found in a 25-␮m arteriole of the cat momentum
at a high PSR of 124 s−1 [36]. On the other hand, relatively greater correlation lengths (49 ± 5.1 ␮m)
were obtained in the present study as compared with those reported in the previous in vivo study [19].
This greater correlation length would be due to the different flow environment such as significantly nonuniformity of inner surface in arterioles as compared to micro-tubes. Relatively smoother surface of inner
wall in the micro-tube could potentially contribute to the greater correlation length in the tube flow.
4.3. RBC-wall contact frequency
The distinct attenuation of the contact frequency in the presence of RBC aggregates was expected
since we found a significant increase (P < 0.05 in normal-aggregating conditions, P < 0.001 in hyperaggregating conditions) in the CFL width due to aggregation compared with non-aggregating conditions
(Fig. 2(a)). The elevation in RBC aggregation might form more compact aggregates in the core, resulting
in the increase of CFL width. The distance increase between outer edge of cells and inner tube wall could
reduce the chance of instantaneous contact between RBCs and the tube wall. In addition, the compact
forming RBC aggregates could mitigate perturbation and collision among RBCs, which in turn leads to
a reduction in the RBC-wall contact frequency.
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However, the RBC-wall contact frequency may not be measurable under in vivo situation. In particular,
most of in vivo results with RBC aggregation showed that the RBC-wall contact was seldom observed
due mainly to the presence of glycocalyx layer on endothelial cells [19, 28]. The current CFL width
measurement relies on bright filed image, thus the transparent glycoclayx layer is not detectable, in
particular in arterioles if present [18]. The glycocalyx thickness has been reported to be ∼0.38 ␮m
in arterioles with diameter of ∼20–70 ␮m [33]. Therefore, with existence of the glycocalyx layer in
arterioles, the direct contact between RBC and the endothelium should be absence.
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4.4. Effect of RBC aggregation on CFA
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To quantify the spatiotemporal characteristics of CFL width changes, we provided the time-dependent
CFA as a more comprehensive parameter than the CFL width. The asymmetry of CFA on the opposite
sides of the tube wall (Fig. 4) was also observed in a previous in vivo study [19]. This study reported that
the CFL width was substantially different on the opposite sides of vessel wall without RBC aggregation,
but the symmetry of CFL widths appeared to be recovered after inducing the aggregation. A similar
trend was found for the CFA with and without aggregation in the present study (Fig. 4(b)). This might
be due to non-uniform distribution of RBCs in the core [10], and the non-uniformity could be attenuated
by compact formation of RBCs (aggregation) in the core. Therefore, RBC aggregation could potentially
promote the symmetry recovery of CFA by enhancing the axial alignment of cells. However, under the
high shear condition used in this study, aggregates could form only in the very center of the flow stream
where shear stress is lowest. Thus, the asymmetry of CFA is most likely due to lateral movements of
RBC column and random positioning of un-aggregated cells near the tube wall. Moreover, there was
no significant attenuation in the asymmetry of CFA in comparing hyper-aggregating (14.8 ± 6.8%) and
normal-aggregating conditions (15.2 ± 6.1 %). This may imply that the elevation of aggregation level
from the normal to hyper-levels could not dominantly influence the non-uniformity of RBC core.
The NCFA result in Fig. 5(b) provides the time- and space-independent trend of the CFA and its corresponding result is shown in Fig. 6(c). The increase in tail width (Fig. 6(c)) indicates that the NCFA can
vary widely, which implies that temporal changes of the CFA can be promoted with elevating the aggregation level. In addition, the significant (P < 0.05) increase in the right tail width from non-aggregating
to hyper-aggregating conditions suggests that the tendency of the CFL to extend into the RBC core away
from its mean can be significantly enhanced by aggregation. This phenomenon would be important in
hemodynamics since the thicker CFL width due to the presence of RBC aggregates may result in a greater
inward radial deviation of the CFL width into the RBC core, potentially leading to discontinuity of the
RBC core.
4.5. Potential influences on CFL
Axial migration of RBCs toward the flow center induced by tank-treading motion promotes formation
of CFL [15, 23]. The migration and deformation of the RBCs are largely influenced by fluid shear
stress acting on the cell membrane, thus a change in the CFL width can be expected with elevating the
suspending medium viscosity. The viscosity of the dextran solutions in the present study were 1.03 ± 0.02,
1.44 ± 0.01, and 1.65 ± 0.01 cP for non-aggregating, normal-aggregating and hyper-aggregating groups,
respectively. However, a previous study [14] observed that the frequency of RBC tank-treading motion
increased linearly with the shear rate but this relation was weakly enhanced by increasing the suspending
medium viscosity. Since the flow condition was not significantly different among the three aggregating
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Fig. 7. Mean difference between cell-free layer widths measured at 3 cm and 8 cm away from the inlet.
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groups in the present study, presumably, the thicker CFL width in hyper-aggregating conditions could be
partially affected by the viscosity increase of the suspending medium.
The RBC sedimentation in the flow can significantly influence the CFL width, in particular under
reduced flow conditions. The PSR in the present study under all aggregating conditions was 83 ± 17 s−1 .
The shear rates used in this study were much greater than those reported in an in vitro study by Reinke et
al. [32] where they reported a significant effect of RBC sedimentation on CFL formation in capillary tubes
with diameter of 30.2-132.3 ␮m and length of 38–73 mm at pseudoshear rates < 10 s−1 using Dextran 250
mediated aggregating blood. To examine the potential sedimentation effect, we compared the CFL width
results at a location closer to the tube inlet with those at the current measurement location (8 cm away from
the inlet). The shortest distance from the inlet at which we can take the CFL width measurement was 3 cm
due to technical limitations of our experimental setup. As shown in Fig. 7, the CFL widths measured at two
different locations (3 and 8 cm away from the inlet) were compared under the three different aggregating
conditions. Although a slightly decreasing trend was seen with aggregation level, no statistical difference
in the CFL width was found between results at the two locations regardless of aggregating condition,
indicating that there would be no significant effect of the cell sedimentation on our results.
4.6. Effect of aggregation on tube hematocrit
The proportional relation between the CFL width and the extent of RBC aggregation may not be
explained solely by formation of compact aggregates in RBC core. Previous observations in the microvascular network with RBC aggregation have revealed that the local hematocrit and flow resistance were
decreased during induced RBC aggregation [21]. Thus, the increase of the CFL width with RBC aggregation in this study might be due partly to the reduction in tube hematocirt by the screening effect of
aggregates at the tube entrance. However, although the RBC aggregates screening could partly contribute
to our results, its effect would not be significant since we continuously stirred the blood sample in the
reservoir to prevent sedimentation of cells and formation of aggregates. Thus, we do not expect such
a significant screening effect of aggregates at the tube entrance which could result in a considerable
reduction in tube hematocrit.
5. Conclusion
The RBC aggregation at hyper-levels significantly increased (P < 0.001) the mean CFL width but
showed no effect on its SD. The RBC-wall contact frequency was significantly attenuated with increasing
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the level of aggregation, which would be due mainly to the thicker CFL width by aggregation. The
persistency of CFL variation seemed to be independent of aggregating condition. The enhancement in
RBC aggregation from none to hyper-levels significantly enlarged CFA. In addition, asymmetry of CFA on
the two sides of the tube wall appeared to be attenuated by RBC aggregation, but no further enhancement
of the symmetry recovery was found in hyper-aggregating conditions compared to normal-aggregating
conditions.
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Acknowledgments
References
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This work was supported by FRC Grant R-397-000-155-112 from MOE Academic Research Fund,
Singapore and Grant-in-Aid for Scientific Research (Challenging Exploratory Research, 24650301) from
Japan Society for the Promotion of Science.
In
[1] C. Alonso, A.R. Pries and P. Gaehtgens, Time-dependent rheological behavior of blood at low shear in narrow vertical
tubes, Am J Physiol 265 (1993), H553–561.
[2] R.B. Ami, G. Barshtein, D. Zeltser, Y. Goldberg, I. Shapira, A. Roth, G. Keren, H. Miller, V. Prochorov, A. Eldor, S.
Berliner and S. Yedgar, Parameters of red blood cell aggregation as correlates of the inflammatory state, Am J Physiol
Heart Circ Physiol 280 (2001), H1982-1988.
[3] M. Baker and H. Wayland, On-line volume flow rate and velocity profile measurement for blood in microvessels, Microvasc
Res 7 (1974), 131-143.
[4] O.K. Baskurt, A. Temiz and H.J. Meiselman, Red blood cell aggregation in experimental sepsis, J Lab Clin Med 130
(1997), 183-190.
[5] A.R. Butler, I.L. Megson and P.G. Wright, Diffusion of nitric oxide and scavenging by blood in the vasculature, Biochim
Biophys Acta 1425 (1998), 168-176.
[6] X. Chen, D. Jaron, K.A. Barbee and D.G. Buerk, The influence of radial RBC distribution, blood velocity profiles, and
glycocalyx on coupled NO/O2 transport, J Appl Physiol 100 (2006), 482-492.
[7] S. Cho, B. Namgung, H.S. Kim, H.L. Leo and S. Kim, Effect of erythrocyte aggregation at pathological levels on NO/O2
transport in small arterioles, Clin Hemorheol Microcirc (2014), DOI: 10.3233/CH-141837.
[8] Y.I. Cho, M.P. Mooney and D.J. Cho, Hemorheological disorders in diabetes mellitus, J Diabetes Sci Technol 2 (2008),
1130-1138.
[9] G.R. Cokelet and H.L. Goldsmith, Decreased hydrodynamic resistance in the two-phase flow of blood through small
vertical tubes at low flow rates, Circ Res 68 (1991), 1-17.
[10] B. Das, P.C. Johnson and A.S. Popel, Effect of nonaxisymmetric hematocrit distribution on non-Newtonian blood flow in
small tubes, Biorheology 35 (1998), 69-87.
[11] J.B. Dixon, A.A. Gashev, D.C. Zawieja, J.E. Moore, Jr. and G.L. Cote, Image correlation algorithm for measuring
lymphocyte velocity and diameter changes in contracting microlymphatics, Ann Biomed Eng 35 (2007), 387-396.
[12] R. Fahraeus, The suspension stability of the blood, Physiol Rev 9 (1929), 241-274.
[13] R. Fahraeus and T. Lindqvist, The viscosity of the blood in narrow capillary tubes, American Journal of Physiology 96
(1931), 562-568.
[14] T.M. Fischer, Tank-tread frequency of the red cell membrane: Dependence on the viscosity of the suspending medium,
Biophys J 93 (2007), 2553-2561.
[15] H.L. Goldsmith, The Microcirculatory Society Eugene M. Landis Award lecture. The microrheology of human blood,
Microvasc Res 31 (1986), 121-142.
[16] E. Hecht and A. Zajac 2001. Optics, Fourth Edition, Addison-Wesley.
[17] A. Kim, H. Dadgostar, G.N. Holland, R. Wenby, F. Yu, B.G. Terry and H.J. Meiselman, Hemorheologic abnormalities
associated with HIV infection: Altered erythrocyte aggregation and deformability, Invest Ophthalmol Vis Sci 47 (2006),
3927-3932.
B. Namgung et al. / Variation of cell-free layer width
13
In
Pr
es
s
[18] S. Kim, R.L. Kong, A.S. Popel, M. Intaglietta and P.C. Johnson, A computer-based method for determination of the cell-free
layer width in microcirculation, Microcirculation 13 (2006), 199-207.
[19] S. Kim, R.L. Kong, A.S. Popel, M. Intaglietta and P.C. Johnson, Temporal and spatial variations of cell-free layer width in
arterioles, Am J Physiol Heart Circ Physiol 293 (2007), H1526-1535.
[20] K.A. Lamkin-Kennard, D. Jaron and D.G. Buerk, Impact of the Fahraeus effect on NO and O2 biotransport: A computer
model, Microcirculation 11 (2004), 337-349.
[21] H.H. Lipowsky, Microvascular rheology and hemodynamics, Microcirculation 12 (2005), 5-15.
[22] N. Maeda, Y. Suzuki, J. Tanaka and N. Tateishi, Erythrocyte flow and elasticity of microvessels evaluated by marginal
cell-free layer and flow resistance, Am J Physiol 271 (1996), H2454-2461.
[23] G. Mchedlishvili and N. Maeda, Blood flow structure related to red cell flow: A determinant of blood fluidity in narrow
microvessels, Jpn J Physiol 51 (2001), 19-30.
[24] B. Namgung, P.K. Ong, P.C. Johnson and S. Kim, Effect of cell-free layer variation on arteriolar wall shear stress, Ann
Biomed Eng 39 (2011), 359-366.
[25] B. Namgung, P.K. Ong, Y.H. Wong, D. Lim, K.J. Chun and S. Kim, A comparative study of histogram-based thresholding
methods for the determination of cell-free layer width in small blood vessels, Physiol Meas 31 (2010), N61-N70.
[26] P.K. Ong, S. Jain and S. Kim, Modulation of no bioavailability by temporal variation of the cell-free layer width in small
arterioles, Ann Biomed Eng 39 (2011), 1012-1023.
[27] P.K. Ong, S. Jain and S. Kim, Temporal variations of the cell-free layer width may enhance NO bioavailability in small
arterioles: Effects of erythrocyte aggregation, Microvasc Res 81 (2011), 303-312.
[28] P.K. Ong, S. Jain, B. Namgung, Y.I. Woo and S. Kim, Cell-free layer formation in small arterioles at pathological levels
of erythrocyte aggregation, Microcirculation 18 (2011), 541-551.
[29] P.K. Ong, B. Namgung, P.C. Johnson and S. Kim, Effect of erythrocyte aggregation and flow rate on cell-free layer formation
in arterioles, Am J Physiol Heart Circ Physiol 298 (2010), H1870-1878.
[30] A.M. Petzold, V.M. Bedell, N.J. Boczek, J.J. Essner, D. Balciunas, K.J. Clark and S.C. Ekker, SCORE imaging: Specimen
in a corrected optical rotational enclosure, Zebrafish 7 (2010), 149-154.
[31] S.M. Razavian, M. Del Pino, A. Simon and J. Levenson, Increase in erythrocyte disaggregation shear stress in hypertension,
Hypertension 20 (1992), 247-252.
[32] W. Reinke, P. Gaehtgens and P.C. Johnson, Blood viscosity in small tubes: Effect of shear rate, aggregation, and sedimentation, Am J Physiol 253 (1987), H540-547.
[33] M.D. Savery and E.R. Damiano, The endothelial glycocalyx is hydrodynamically relevant in arterioles throughout the
cardiac cycle, Biophys J 95 (2008), 1439-1447.
[34] R.L. Schoch, L.E. Kapinos and R.Y. Lim, Nuclear transport receptor binding avidity triggers a self-healing collapse
transition in FG-nucleoporin molecular brushes, Proc Natl Acad Sci U S A 109 (2012), 16911-16916.
[35] T.W. Secomb and A.R. Pries 2007. Basic priniciple of hemodynamics. Handbook of Hemorheology and Hemodynamics.
IOS Press.
[36] J. Silva and M. Intaglietta, The correlation of photometric signals derived from in vivo red blood cell flow in microvessels,
Microvasc Res 7 (1974), 156-169.
[37] M. Soutani, Y. Suzuki, N. Tateishi and N. Maeda, Quantitative evaluation of flow dynamics of erythrocytes in microvessels:
Influence of erythrocyte aggregation, Am J Physiol 268 (1995), H1959-1965.
[38] N. Tateishi, Y. Suzuki, I. Cicha and N. Maeda, O(2) release from erythrocytes flowing in a narrow O(2)-permeable tube:
Effects of erythrocyte aggregation, Am J Physiol Heart Circ Physiol 281 (2001), H448-456.
[39] K. Tsukada, H. Minamitani, E. Sekizuka and C. Oshio, Image correlation method for measuring blood flow velocity in
microcirculation: Correlation ‘window’ simulation and in vivo image analysis, Physiol Meas 21 (2000), 459-471.
[40] P. Ulker, F. Gunduz, H.J. Meiselman and O.K. Baskurt, Nitric oxide generated by red blood cells following exposure
to shear stress dilates isolated small mesenteric arteries under hypoxic conditions, Clin Hemorheol Microcirc 54 (2013),
357-369.
[41] X. Xu, R.K. Wang, J.B. Elder and V.V. Tuchin, Effect of dextran-induced changes in refractive index and aggregation on
optical properties of whole blood, Physics in medicine and biology 48 (2003), 1205-1221.
[42] O. Yalcin, P. Ulker, U. Yavuzer, H.J. Meiselman and O.K. Baskurt, Nitric oxide generation by endothelial cells exposed to
shear stress in glass tubes perfused with red blood cell suspensions: Role of aggregation, Am J Physiol Heart Circ Physiol
294 (2008), H2098-2105.