DOI:10.1111/j.1549-8719.2011.00114.x
Original Article
Cell-Free Layer Formation in Small Arterioles at
Pathological Levels of Erythrocyte Aggregation
PENG KAI ONG, SWATI JAIN, BUMSEOK NAMGUNG, YEON I. WOO AND, SANGHO KIM
Division of Bioengineering & Department of Surgery, National University of Singapore, Singapore
Address for correspondence: Sangho Kim, Ph.D., Division of Bioengineering, Faculty of Engineering, National University of Singapore, 9 Engineering
Drive 1, Block EA #03-12, 117576 Singapore. E-mail: [email protected]
Received 8 March 2011; accepted 14 May 2011.
ABSTRACT
Objective: To test our hypothesis that an elevation in the
aggregation level of red blood cells found in human pathological
conditions will significantly enhance cell-free layer formation in
small arterioles.
Methods: Visualization of arteriolar blood flow in rat cremaster
muscle was carried out in both normal and reduced flow
conditions before and after Dextran 500 infusion to simulate
physiological and pathological levels of red blood cell aggregation
in humans.
Results: Both normalized mean (p < 0.0001) and SD (p < 0.002)
of the layer width were significantly enhanced after hyperaggregation induction in reduced flow conditions (mean
pseudoshear rate = 57.3 ± 7.2 ⁄ sec). Normalized mean and SD of
the layer width generally increased with decreasing vessel radius
and this effect was most pronounced with hyper-aggregation in
reduced flow conditions. The threshold pseudoshear rate at which
the layer formation became more pronounced when compared
with non-aggregating condition was higher with hyper-aggregation
(217 ⁄ sec) than normal-aggregation induction (139 ⁄ sec).
Conclusion: Our
findings confirmed the formation of a
prominent cell-free layer in the arterioles under higher shear
conditions at pathological aggregation levels and this effect
became more pronounced in smaller arterioles in normalizing the
layer to the vessel radius.
words:
plasma layer, red
microcirculation, wall shear stress
Key
blood
cell
aggregation,
used: ANOVA, Analysis of Variance; CFD,
Cumulative Frequency Distribution; ESL, Endothelial Surface
Layer; ID, Inner Diameter; ip, intraperitoneal; NO, Nitric Oxide;
SD, Standard Deviation.
Abbreviations
Please cite this paper as: Ong, Jain, Namgung, Woo and Kim (2011). Cell-Free Layer Formation in Small Arterioles at Pathological Levels of Erythrocyte
Aggregation. Microcirculation 18(7), 541–551.
INTRODUCTION
Blood flow in arterioles can be characterized by the formation of a plasma layer (cell-free layer) adjacent to the luminal vessel wall [14,31]. This phenomenon is the
consequence of the phase separation of red blood cells and
plasma near the vessel wall, as red blood cells tend to
migrate toward the vessel center [9,18]. The extent of phase
separation is determined by various interactive forces
exerted on the red blood cells, which are influenced by
blood rheological properties [17,41]. The dispersive hydrodynamic forces between the red blood cells tend to attenuate the cell-free layer formation, whereas the attractive
forces between the cells induced by high molecular weight
polymers, such as Dextran 500, promote axial migration of
the cells through aggregates formation and enhance the
layer formation. The balance of these forces determines the
overall radial migration behavior of the red blood cells in
the flow stream with respect to the vessel wall, which in
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
turn defines the characteristics of the layer. Due to the
dynamic positioning of the red blood cells, the layer width
can vary in both the spatial and temporal domains.
One of the most distinctive rheological characteristics of
human red blood cells is their ability to form aggregates
depending on the flow environment. This blood property
has been linked to pathophysiology in numerous diseases
found in humans. In many clinical studies [2,5,6,12,16,
26,29], an intensification of red blood cell aggregation was
suggested to play a role in hypertension, sepsis, nephrotic
syndrome, diabetes mellitus type II, and cardiac syndrome
X through a reduction in microvascular blood flow following the augmentation of blood viscosity. These diseases are
thus often characterized by tissue necrosis and ischemia at
the microcirculatory level. A few of these studies [5,16]
have, however, speculated that modifications in cell-free
layer characteristics due to altered levels of aggregation
may contribute to the impaired functioning at the tissue
level. To ascertain the pathophysiological role of the cell-
541
P.K. Ong et al.
free layer in microcirculatory functions, it would be imperative to acquire quantitative information on the layer width
characteristics in the presence of rheological abnormalities
in red blood cell aggregation. There has been a lack of
detailed information regarding the temporal characteristics
of the layer width in arteriolar blood flow under pathological levels of red blood cell aggregation, despite recent suggestions [19,29] on its possible physiological importance.
Therefore, an objective of this study would be to tackle this
deficiency by providing dynamic quantitative information
on the cell-free layer in the arterioles at aggregation levels
relevant to pathological conditions in humans.
Another notable deficiency in most previous studies
[14,25,34] on the effect of aggregation on the cell-free layer
formation is their lack of hemo-rheological relevance to
humans. Our recent study [25] in small arterioles has
reported that, when the aggregation levels were elevated to
those seen in healthy humans, a significant augmentation
in the layer width was observed only under extremely low
shear conditions (pseudoshear rate = 17.1 ± 6.1 ⁄ sec). We
tested the hypothesis that, at pathological aggregation levels
of red blood cells, the layer formation can be significantly
enhanced at substantially high pseudoshear rates (>>17.1
± 6.1 ⁄ sec). To test this hypothesis, arteriolar blood flow
visualization in the rat cremaster muscle was carried out
before and after aggregation induction in both normal and
reduced flow conditions. The levels of red blood cell aggregation were adjusted to those observed in human blood
under physiological and pathological conditions.
MATERIALS AND METHODS
Animal Preparation
A total of 13 male Sprague–Dawley rats weighing between
195 and 250 g were utilized in this study. All animal handling and care procedures were in accordance with National
University of Singapore Guidelines and Ethics on Animal
Experimentation. The animal was anesthetized using
50 mg ⁄ kg ip pentobarbital sodium before the start of the
surgery, and additional doses were administered throughout
the experiment when needed. The animal was placed on a
heating pad to maintain the body temperature at 37C during the surgery. A tracheal tube was inserted into the trachea
to assist in ventilation. The jugular vein was catheterized for
administration of Dextran 500 (average molecular weight,
460 kDa; Sigma-Aldrich, Singapore) dissolved in saline
(6%) and anesthetics, while the femoral artery was catheterized for blood withdrawals and arterial pressure measurements. All catheters used were filled with a solution of
heparinized saline (30 IU ⁄ mL) to prevent clotting of blood.
An in vivo metrics 1.5-mm ID pneumatic cuff (OC2; Kent
Scientific Corporation, Torrington, CT, USA) was placed
around the abdominal aorta to control blood flow in the
542
cremaster muscle. The muscle was continuously irrigated
with Plasma-Lyte A (Injection pH 7.4; Baxter, Deerfield, IL,
USA) during its exposure. The connective tissue was cleared,
and the muscle was separated from the testis with the nerves
and the blood supply intact. The animal was then placed on
a Plexiglas plate and its muscle, which was bathed in
Plasma-Lyte A and covered with polyvinyl film (Saran; SC
Johnson & Son, Singapore), was secured to a transparent
platform for observation. The temperature of the muscle
was maintained at 35C using heating coils attached underneath the plate of muscle attachment and a probe was placed
near the muscle for temperature monitoring.
Hematocrit, Aggregation and Pressure Measurements
A blood sample (0.1 mL) was withdrawn from the femoral
artery for both hematocrit and aggregation measurements.
The hematocrit was determined using a microhematocrit
centrifuge (Sigma 1–14 Microcentrifuge; Sartorius AG,
Weender Landstrasse, Goettingen, Germany) while the level
of aggregation was measured using a photometric rheoscope
(Myrenne Aggregometer; Myrenne, Roetgen, Germany).
Arterial pressure was continuously recorded using a physiological data acquisition system (MP100; BIOPAC Systems,
Goleta, CA, USA).
Adjustment of Aggregation Levels
Red blood cell aggregation was elevated to physiological
and pathological levels (normal- and hyper-aggregating
conditions) found in humans by infusion of Dextran 500
dissolved in saline (60 mg ⁄ mL). A total of 200 mg ⁄ kg of
body weight was infused over the course of one to two
minutes to achieve normal levels of aggregation, while a
total of 250 mg ⁄ kg of body weight was administered to
induce hyper-levels of aggregation. On the assumption that
the blood volume constitutes 5.5% of the body weight, the
infusion of the Dextran 500. Solution would produce the
plasma-dextran concentrations of 0.63% and 0.78% in
the normal-aggregating and hyper-aggregating rats, respectively. The degree of red blood cell aggregation determined
using the aggregometer was presented in terms of the M
index based on the 10-second setting where M is a function
of the degree of aggregation. Previous studies have reported
M values of between 12 and 16 [16,39] and >20 [5,12] for
human blood in physiological and pathological conditions,
respectively. Therefore, experiments were performed on rats
under non-aggregating conditions (M = 0), normal-aggregating physiological conditions (M = 12–16), and hyperaggregating pathological conditions (M > 20).
Experimental Protocol
The rat was mounted on the microscopic stage and allowed
to stabilize over a period of 10 minutes, after which an
arterial blood sample was withdrawn for measurements of
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Plasma Layer in Hyper-Aggregating Blood Flow
aggregation and hematocrit levels. An unbranched arteriole
with an ID of 15–60 lm was selected for the study based
on the criteria of stable flow, clear focus, and good contrast
of the image. An intravital microscope (BX51; Olympus,
Shinjuku-Ku, Tokyo, Japan) was used in conjunction with
a water-immersion objective (40X; Olympus) and a long
working distance condenser, which have numerical apertures of 0.7 and 0.35, respectively. A blue filter (model no.
B390; HOYA, Machida-Shi, Tokyo, Japan) with peak transmission at 394 nm and spectral bandpass of 310–510 nm
was used to enhance contrast between the red blood cells
and background. The microscope was focused on the equatorial plane of the arteriole and a high-speed video camera
(Fastcam-1024PCI; Photron, San Diego, CA, USA) was utilized to record the blood flow in the arteriole at a framing
rate of 3000 ⁄ sec for a time period of one second. To
achieve reduced flow conditions, the pressure in the pneumatic cuff was increased using an air-filled syringe to lower
the arterial pressure to 60 mmHg, which was then maintained by manual adjustment. The reduced arterial pressure
was designed to be higher than that (40 mmHg) used in
our earlier study [25] so that higher pseudoshear rates
could be simulated to distinguish the effects of hyperaggregation from those of normal-aggregation. Recording
of blood flow was repeated for the reduced flow condition,
after which the cuff pressure was released for the arterial
pressure to return and stabilize to normal levels. The above
protocol was repeated after the administration of Dextran
500 to elevate the red blood cell aggregation to either normal or hyper levels.
Cell-Free Layer Width Measurement
The cell-free layer width was defined by the distance
from the outer edge of the red blood cell core to the inner
wall of the vessel. Thus, red blood cells are not present in this
layer. A detailed description of the layer width measurement
can be found in our previous studies [22,24]. This measurement technique is capable of measuring the thickness of a
temporally varying cell-free layer as opposed to a cell-poor
layer that is based on conventional methods [34,36], as the
red blood cell is excluded from every layer width measurement at individual time points. The spatial resolution of this
layer measurement was 0.42 lm with the current microscopic system. In this study, the mean or temporal variation
(SD) of the layer widths was the averaged magnitude on
both sides of the vessel. As a strong proportional relationship
between the vessel radius and the layer width was apparent
in previous studies [13,17,30], to eliminate the effects of
varying vessel radius on the layer formation in the present
study, the layer width characteristics were normalized to
their vessel radius. This analysis also provides an indication
of the proportion of the vessel lumen occupied by the layer.
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Cellular Velocity and Pseudoshear Rate
The centerline velocity (Vc) in the vessel was obtained by
performing the image correlation method on sequentially
extracted images from the high-speed video recording
[7,38]. The mean velocity (Vmean) was determined using a
correction factor of 1.6 [1]. On the other hand, the edge
cellular velocity (Vedge) of the blood core was obtained by
manually tracking movements of outermost red blood
cells across 10 digitalized frames using an image analysis
software (SigmaScan Pro 4.0; Jandel Scientific, San Rafael,
_ used in this study
CA, USA) [13]. Pseudoshear rate ðcÞ
was determined based on Vmean using the relationship:
c_ ¼ Vmean =D, where D is vessel diameter.
Statistical Analysis and Data Interpretation
Statistical tests including regression fits of the experimental
data were carried out using a statistical software package
(Prism 4.0; GraphPad, La Jolla, CA, USA). The two-tailed
unpaired t-test was used to determine differences between
parameters for normal and reduced arterial pressures. To
compare experimental and physiological parameters for
three or more groups, one-way ANOVA with post Bonferroni tests were used to determine the significance of statistical difference. All the physiological and rheological data
have been reported as mean ± SD. For all statistical data
analyses, p < 0.05 was considered statistically significant.
RESULTS
Systemic Parameters
Normal mean arterial pressures for non-aggregating, normal-aggregating, and hyper-aggregating rats were 99.8 ±
10.9, 98.6 ± 8.8, and 94.0 ± 9.6 mmHg, respectively. After
flow reduction, the corresponding mean arterial pressures
were 61.8 ± 5.5, 62.0 ± 5.5, and 60.1 ± 5.9 mmHg. Systemic hematocrit was 47.0 ± 2.3%, 46.0 ± 2.7%, and
46.0 ± 2.2% for non-aggregating, normal-aggregating, and
hyper-aggregating rats, respectively. No significant differences were found in the mean arterial pressures or hematocrits between the different aggregating groups. The
aggregation index, M-value, was 0.0 before aggregation
induction. After normal-aggregation and hyper-aggregation
inductions, respective M values became 13.1 ± 2.7 and
21.6 ± 4.8, which simulated both healthy and pathological
levels of aggregation in human blood [2,12,16]. At normal arterial pressures, mean c_ in the arterioles was
170.5 ± 102.6, 167.6 ± 99.3, and 144.7 ± 89.5 ⁄ sec under
non-aggregating, normal-aggregating, and hyper-aggregating
conditions, respectively. After reduction in arterial pressures, the corresponding mean c_ was 74.6 ± 53.4,
70.3 ± 48.7, and 57.3 ± 45.8 ⁄ sec. No significant differences
were found between the mean c_ of the different aggregating
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P.K. Ong et al.
Table 1. Systemic parameters
Aggregating
condition
Arterial pressure (mmHg)
Pseudoshear rate (/sec)
Normal
Reduced
Normal
Reduced
Hematocrit (%)
M-value
Non
Normal
Hyper
99.8 ± 10.9
98.6 ± 8.8
94.0 ± 9.6
61.8 ± 5.5
62.0 ± 5.5
60.1 ± 5.9
170.5 ± 102.6
167.6 ± 99.3
144.7 ± 89.5
74.6 ± 53.4
70.3 ± 48.7
57.3 ± 45.8
47.0 ± 2.3
46.0 ± 2.7
46.0 ± 2.2
0.0
13.1 ± 2.7
21.6 ± 4.8
5
(18.0 ± 0.9%), although this increment was statistically
insignificant. Conversely, in reduced flow conditions, the
increase in normalized mean width from non-aggregating
condition was found to be significant (p < 0.0001) after
hyper-aggregation induction. Accordingly, normalized mean
width was 15.7 ± 0.9%, 18.3 ± 0.9%, and 20.6 ± 0.9% for
non-aggregating, normal-aggregating, and hyper-aggregating
conditions, respectively. A significant increase (p < 0.05) in
normalized mean width was also found after flow reduction
ðc_ ¼ 144:7 89:5/sec ! 57:3 45:8/secÞ during hyperaggregation induction, which was not seen in normal-aggregating condition.
Normalized SD of the cell-free layer width in the three
aggregating conditions before and after flow reduction is
shown in Figure 1B. No significant differences were found
among the three aggregating conditions under normal flow
conditions. However, at reduced flow rates, the hyperaggregating condition (11.0 ± 1.0%) showed a significant
increase (p < 0.002) in normalized SD from the non-aggregating condition (9.2 ± 0.9%). Unlike the normalized mean
width, no significant augmentation in the normalized SD
was obtained after flow reduction during hyper-aggregation
induction.
0
Effect of Vessel Radius on Normalized Mean and
SD of the Layer Width
40
A
Normalized mean (%)
35
Non-aggregation
Normal-aggregation
Hyper-aggregation
30
*
25
***
20
15
10
5
0
Normal flow
Normalized SD (%)
20
Reduced flow
B
15
**
10
Normal flow
Reduced flow
Figure 1. (A, B) Mean and SD of the cell-free layer width normalized
by vessel radius. *p < 0.05, **p < 0.002, ***p < 0.0001.
conditions for both normal and reduced flow conditions.
The systemic parameters are summarized in Table 1.
Effect of Aggregation and Flow Rate on Normalized Mean and SD of the Cell-Free Layer Width
Figure 1 shows the mean and SD of the cell-free layer
width normalized by vessel radius for the three different
aggregating conditions at both normal and reduced flow
rates. In normal flow conditions, as shown in Figure 1A,
an increase in normalized mean width from non-aggregating (16.0 ± 0.8%) and normal-aggregating (16.2 ± 0.8%)
conditions was found under hyper-aggregating condition
544
The effect of vessel radius on normalized mean and SD of
the cell-free layer width is shown in Figure 2. An exponential decay function (y = Ae)Bx) was utilized as it provided a
better fit than linear regression for all conditions. In accordance, an increase in both normalized mean and SD of the
layer width was generally observed with decreasing vessel
radius irrespective of the flow and aggregating conditions.
Under normal flow conditions, the slopes of the exponential fits for normalized mean width were very similar for
the different aggregating conditions (B = 0.018, 0.02, and
0.02 for non-aggregating, normal-aggregating, and hyperaggregating conditions, respectively). Upon the reduction
of flow, the slope of the exponential fit associated with
the hyper-aggregating condition (B = 0.032) became 146%
and 33% greater than those (0.013 and 0.024) of the nonaggregating and normal-aggregating conditions, respec-
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Plasma Layer in Hyper-Aggregating Blood Flow
Non-aggregation
Normal-aggregation
Hyper-aggregation
A
30
20
10
0
0
10
20
30
40
Normalized mean (%)
Normalized mean (%)
40
B
30
20
10
0
40
10
0
C
35
30
Normalized SD (%)
Normalized SD (%)
35
20
30
40
30
40
Radius (µm)
Radius (µm)
25
20
15
10
5
0
D
30
25
20
15
10
5
0
0
10
20
30
40
Radius (µm)
0
10
20
Radius (µm)
Figure 2. (A, B) Relationship between normalized mean width and vessel radius at normal and reduced arterial pressures, respectively. An
exponential curve (y = 21.4e)0.017x; R2 = 0.06) is used to fit data points from all aggregating groups at normal arterial pressure while individual
exponential fits are utilized for the different aggregating conditions at reduced arterial pressure (y = 19.8e)0.013x; R2 = 0.03 for non-aggregation,
y = 27.9e)0.024x; R2 = 0.09 for normal-aggregation and y = 35.9e)0.032x; R2 = 0.20 for hyper-aggregation). (C, D) Relationship between normalized
SD and vessel radius at normal and reduced arterial pressures, respectively. At normal arterial pressure, an exponential fit (y = 24.9e)0.066x; R2 = 0.48)
is used to fit data points from all aggregating groups, whereas at reduced arterial pressure, individual exponential curve fits are utilized for the nonaggregating (y = 15.8e)0.038x; R2 = 0.16), normal-aggregating (y = 22.6e)0.055x; R2 = 0.24), and hyper-aggregating (y = 34.9e)0.083x; R2 = 0.43)
,
, and
represent the exponential fits for the non-aggregating, normal-aggregating, and hyper-aggregating
conditions. In (B, D),
conditions, respectively.
tively. As a result, the discrepancy in normalized mean
widths between the aggregating and the non-aggregating
conditions enlarged with decreasing vessel radius, and this
effect became more pronounced under hyper-aggregating
conditions than under normal-aggregating conditions. As
apparent in Figure 2B, the normalized mean widths for the
entire range of vessel radii were consistently larger under
hyper-aggregating condition than those in non-aggregating
and normal-aggregating conditions.
As shown in Figure 2C,D, similar effects of vessel radius
were observed on normalized SD. The slopes of exponential
fits for all aggregating conditions did not significantly differ
from one another in normal flow conditions. However,
after flow reduction, an augmentation in the slope was
obtained with increasing aggregation level. The slope of the
exponential fit associated with the hyper-aggregating condition (B = 0.083) was 118% and 51% greater than those
(0.038 and 0.055) in the non-aggregating and normalaggregating conditions, respectively.
Effect of Pseudoshear Rate on Normalized Mean
and SD of the Layer Width
As shown in Figure 3, linear regression was used to evaluate the relationship between the normalized mean or SD of
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
the layer width and the corresponding c_ for the different
aggregating conditions. In the case of normalized mean
layer width (Figure 3A), no significant relationship was
found for the non-aggregating condition as the slope of its
linear regression fit ()0.004) was not significantly different
from zero. Despite the large scattering of data points for
both normal-aggregating and hyper-aggregating conditions,
the slopes of their regression fits ()0.028 for normal-aggregating condition and )0.031 for hyper-aggregating condition) were statistically significant (p < 0.05), indicating a
small but significant increase in normalized mean layer
_ The intercepts of their regression
width with decreasing c.
fits with that of the non-aggregating condition was used to
provide a threshold c_ at which the cell-free layer formation
might become more pronounced after aggregation induction. The threshold c_ was higher under hyper-aggregating
conditions (217 ⁄ sec) than under normal-aggregating conditions (139 ⁄ sec). On the other hand, no significant relationship between the normalized SD of the layer width and c_
was found in the three aggregating conditions (Figure 3B).
It was expected as no significant effect of flow reduction
was observed for the normalized SD of the layer width
under all aggregating conditions (Figure 1B). In addition,
the y-intercept of the linear regression fit associated with
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P.K. Ong et al.
Normalized mean (%)
50
A
Non-aggregation
Normal-aggregation
Hyper-aggregation
40
30
20
10
0
100
0
Normalized SD (%)
40
200
300
400
200
300
400
.
γ (/sec)
B
30
20
10
0
0
100
.
γ (/sec)
Figure 3. (A) Relationship between normalized mean layer width and
_ Linear regression fits are used to depict this
pseudoshear rate c.
relationship for the non-aggregating (y = )0.004x + 16.2, R2 = 0.003),
normal-aggregating (y = )0.028x + 19.6, R2 = 0.07), and hyperaggregating (y = )0.031x + 22.1, R2 = 0.11) groups. (B) Relationship
_ Linear regression fits are used to
between normalized SD and ðcÞ.
describe this relationship for the non-aggregating (y = )0.0001x + 8.8,
R2 = 0.001), normal-aggregating (y = )0.0034x + 9.2, R2 = 0.001) and
,
hyper-aggregating (y = )0.0103x + 11.0, R2 = 0.018) groups.
and
represent the linear fits for the non-aggregating, normalaggregating, and hyper-aggregating conditions, respectively.
the hyper-aggregating condition (11.0) was significantly
(p < 0.05) larger than that obtained with the non-aggregating condition (8.8). This would indicate a pronounced augmentation of normalized SD from the non-aggregating
_
condition by hyper-aggregation induction, regardless of c.
Histogram and CFD of the Layer Widths
To provide a more comprehensive view of the cell-free
layer width characteristics, all the temporal variation data
of the layer width were grouped according to their normalized distances (by vessel radius) away from the vessel wall
in the form of histograms and CFDs. This is beneficial as
the layer width distribution may not be adequately
described by their mean value and SD due to their
non-Gaussian characteristics [25]. Figure 4A,B present
546
histograms of the layer widths at normal and reduced arterial pressures, respectively, for the three aggregating conditions. For the histogram analyses, the layer widths were
divided into bins of normalized distance 5%. A normalized
distance of 0% indicates the position of the luminal vessel
wall, while a normalized distance of 100% refers to the
location of the vessel center. The various key distribution
parameters of the histograms are provided in Table 2.
When the aggregation tendency was enhanced from nonaggregating to hyper-aggregating levels, a distinct augmentation in median, 25th, and 75th percentiles was observed
for both flow conditions. However, such an increase was
more pronounced under reduced flow conditions as compared with normal flow conditions. This shift of the layer
widths toward magnitudes of larger normalized distances
away from the vessel wall became even more obvious when
a CFD plot was used as shown in Figure 4C,D. Under normal flow conditions (Figure 4C), CFD for non-aggregating
and normal-aggregating conditions appeared to be almost
identical and the layer widths were all found within a normalized distance of 60% from the vessel wall. With
hyper-aggregation induction, 25% increase in this distance was observed. On the other hand, under reduced
flow conditions (Figure 4D), CFD for the three aggregating
conditions appeared different from one another and even
greater penetration of the layer widths toward the vessel
center was observed for the hyper-aggregating condition
compared with normal flow conditions. All the layer widths
for the hyper-aggregating condition were found within a
normalized distance of 85% from the vessel wall, a 13%
increase compared with that under normal flow conditions.
DISCUSSION
The salient finding of the present study was the significant
enhancement of the cell-free layer formation in the arterioles at pathological aggregation (hyper-aggregation) levels
of red blood cells at relatively high pseudoshear rates
(57.3 ± 45.8 ⁄ sec), which was previously not found at physiological aggregation (normal-aggregation) levels. In addition, this effect became more pronounced in smaller
arterioles in normalizing the mean layer width with vessel
radius.
Effect of Aggregation and Flow Rate on the Layer
Characteristics
A previous study by Kim et al. [14] has reported no significant effect of red blood cell aggregation at physiological
levels (M = 13.7 ± 1.1) on the mean and SD of the cell-free
layer width at normal arterial pressures (PA = 112 ±
7 mmHg ðc_ ¼ 220:3 123:4/secÞ. This finding was in
agreement with that obtained in the present study where
no significant changes in normalized mean and SD of the
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Plasma Layer in Hyper-Aggregating Blood Flow
25
A
Non-aggregation
Normal-aggregation
Hyper-aggregation
15
Cumulative frequency (%)
Cumulative frequency (%)
C
80
60
40
Non-aggregation
Normal-aggregation
Hyper-aggregation
20
0
0
20
40
60
80
100
Normalized distance from wall (%)
95
10
0
90
85
75
80
65
70
60
55
50
45
40
35
30
Normalized distance from wall (%)
Normalized distance from wall (%)
100
25
0
10
0
90
95
80
85
70
75
60
65
45
50
55
0
35
40
0
20
25
30
5
5
5
20
10
5
10
15
10
10
15
B
20
15
0
Frequency (%)
20
Frequency (%)
25
D
100
80
60
40
20
0
0
20
40
60
80
100
Normalized distance from wall (%)
Figure 4. (A, B) Histograms of the cell-free layer widths at normal and reduced arterial pressures, respectively. (C, D) CFD of the layer widths at
normal and reduced arterial pressures, respectively.
Table 2. Distribution parameters for normalized layer widths in
Figure 4
Normal flow
Mean
Median
25%
75%
Reduced flow
Mean
Median
25%
75%
Nonaggregation
Normalaggregation
Hyperaggregation
16.0
13.5
7.0
21.6
16.0
14.3
7.4
22.2
17.9
17.8
7.8
25.4
16.0
14.3
6.7
22.2
18.7
16.7
8.7
25.8
20.9
18.6
10.3
28.6
All units in (%).
layer width were found under similar aggregating and flow
conditions. In addition, our study revealed that hyperaggregation induction had no significant effect on the layer
formation at normal arterial pressures. This would suggest
that the high shear conditions in the arterioles associated
with normal arterial pressures were unfavorable for prominent aggregates formation to promote axial migration of
the red blood cells even at the hyper-aggregation levels.
However, the small increase (11%) in normalized mean
width from the non-aggregating condition, although not
significant (p = 0.07), might suggest a slight enhancement
of the layer formation after hyper-aggregation induction.
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Studies [8,20] have reported flow reduction in the arterioles at hyper-aggregation levels higher than those in this
study. McHedlishvili et al. [20] have observed that blood
flow velocity in arterioles (ID 14–26 lm) of the rat mesentery slows down by 50% after the intravascular administration of Dextran 500 dissolved in saline (10%), which
produces an estimated plasma-dextran concentration of
0.87%. An even greater reduction of flow (75%) was
found by Durussel et al. [8] in arterioles (ID 50 lm) of
the rat cremaster muscle when excessive amount of Dextran 500 was infused (approximately sevenfold higher in
plasma-dextran concentration than in this study). These
declines in blood flow in the arterioles are accompanied by
the observations of large aggregates in the flow stream. As
compared with the above studies [8,20], blood flow was
decreased by a modest extent (19%) in the present study
after the pathological induction of aggregation at reduced
arterial pressures, which was expected due to the lesser
amount of dextran infusion. Due to flow dependence of
red blood cell aggregation, the reduction in flow after the
hyper-aggregation induction might have synergistically contributed to the significant enhancement of the layer formation by promoting aggregates formation.
Effect of Vessel Radius on the Layer Characteristics
The inverse relationship between the normalized mean
layer width and the vessel radius for non-aggregating and
normal-aggregating conditions at normal flow rates was in
agreement with those previously obtained from in vitro and
in vivo experiments [14,28] or predicted from computa-
547
P.K. Ong et al.
tional studies [10,33]. We further showed that the inverse
relationship was also applicable to the hyper-aggregating
condition. Based on the exponential curve fit of the combined data points from different aggregating conditions,
the present study revealed an increase in normalized mean
width from 13.0% to 18.8% with decreasing vessel radius
from 29.5 to 7.7 lm at normal arterial pressures. A similar
relationship that was independent of aggregation was found
in arterioles of the same tissue type by Kim et al. [14] at
normal arterial pressures. In their study, a comparable
change in magnitudes of normalized mean widths
(11.0% fi 17.7%) was obtained for the same change in
vessel radius. However, normalized mean widths predicted
using a computational model by Sharan and Popel [33]
were relatively smaller, ranging from 7% to 14%, probably because parameters (i.e., apparent blood viscosity) used
in their model were obtained from in vitro glass tube
experiments with perfusion of human blood cells. The
comparison between in vivo and in vitro results on the cellfree layer would be limited by different experimental conditions such as tube wall rigidity, mechanical properties of
blood cells, existence of ESL, and so on. It should be noted
that our cell-free layer measurements include the thickness
of the ESL which was found to be 0.38 lm in arterioles
10–35 lm in radius [30]. By considering this thickness
of ESL in all vessels, the ESL would contribute to
26%—10% of normalized mean layer width (18.8%–
13.0%) for the range of vessel radii (7.7–29.5 lm) examined in the current study in normal flow conditions.
The present study provided information on the effect
of vessel radius on the layer formation at pathological
hyper-aggregation levels under reduced flow conditions. In
accordance, a more pronounced exponential increase of
normalized mean width with decreasing vessel radius was
found in the hyper-aggregating condition as compared with
the non-aggregating and normal-aggregating conditions.
This finding was in agreement with results reported in a
previous study [34] where the slope of linear regression
curves used to depict the relationship between normalized
mean layer width and vessel radius (10–20 lm) also
increased with an elevation of the aggregation level by
Dextran 70 infusion (0 fi 4 g ⁄ dL).
Combining the findings on normalized mean and SD of
the layer width shown in Figure 2, the cell-free layer
seemed to play a more significant physiological role in the
smaller vessels than bigger ones as the layer width characteristics were found to be superior in the former. However,
to assess the overall functional implication of the layer, it
would be necessary to consider opposing influences
imposed by the layer width characteristics. For instance,
potential reduction in effective blood viscosity by the presence of the layer with finite thickness may be counteracted
by converse increase of the viscosity implicated with the
548
temporal and spatial variations of the layer [33]. Such an
effect is thus expected to become more pronounced after
flow reduction, in particular at pathological aggregation
levels.
Effect of Pseudoshear Rate on the Layer Formation
Reinke et al. [28] have reported a shift in the pseudoshear
rate for prominent layer formation in small glass tubes
(ID = 30.2–132.3 lm) to higher values when the aggregation tendency of the human red blood cells perfusate was
intensified (M = 28 ± 2) by the addition of Dextran 250.
This effect appeared pertinent to cell-free layer formation
in the arterioles as well, as our present study showed that
prominent arteriolar cell-free layer formation could take
place at a higher threshold pseudoshear rate under the
hyper-aggregating condition than under the normal-aggregating condition (Figure 3A). The stronger attractive forces
between red blood cells induced by the higher concentration of Dextran 500 used to simulate hyper-aggregation as
opposed to normal-aggregation could overcome the larger
magnitudes of shear-induced dispersive forces at higher
pseudoshear rates, increasing the possibility of aggregates
formation at these flow conditions that can potentially lead
to a more prominent layer formation through enhanced
red blood cell axial migration.
Physiological Significance
The prominent cell-free layer formation found under hyperaggregating condition could lower overall flow resistance in
small arterioles by attenuating the effective blood viscosity
near the vessel wall [28]. The reduction in flow resistance
by an increase in the layer width can be estimated based on
the change in relative apparent blood viscosity (lrel) using a
two-phase model developed previously [33]. By assuming
that the viscosity in the cell-free layer is equivalent to that
of the plasma, the lrel can be given as follows:
" !
#1
1
4
4
ð1 WÞ þ 1 ð1 WÞ
ð1Þ
lrel ¼
lc
lp
where llc represents the ratio between the blood core viscosp
ity (lc) and the plasma viscosity (lp) which is obtained
from a previous study [27]. W denotes the normalized
mean cell-free layer width. On the basis of the above analysis, we found that an increase in normalized mean layer
width (14.0% fi 15.8%, vessel radius [R] = 26.7 lm)
from the non-aggregating state after hyper-aggregation
induction in reduced flow conditions was capable of reducing lrel by 4.3% (1.71 fi 1.63). This effect became
enhanced with decreasing vessel radius. Accordingly, lrel
was attenuated by 14.6% (1.57 fi 1.34) for
R = 10.2 lm ðW ¼ 17:4% ! 25:9%Þ.
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
Plasma Layer in Hyper-Aggregating Blood Flow
A reduction in the wall shear stress could also occur
which attenuates the production of NO, possibly leading to
vasoconstriction [11]. This effect can be supported by several experimental studies [3,40], where a diminished
expression of NO synthesizing mechanisms in arterioles or
glass capillaries was found after aggregation induction. In
addition, an experimental study [35] has suggested that the
cell-free layer may form a resistive barrier to the diffusion
of oxygen from the red blood cells to the tissues, possibly
leading to tissue atrophy at the microcirculatory level.
On the other hand, the dynamic characteristics of the
cell-free layer width could modulate physiological
responses. Sharan and Popel [33] have theoretically shown
that variations in the layer width could lead to additional
viscous dissipation, hence diminishing the reduction of
flow resistance that is expected from the lubricating presence of the cell-free layer. This effect is likely to be more
pronounced after hyper-aggregation induction than normal-aggregation induction especially at reduced flow rates
as the increase in normalized SD from non-aggregating
condition was greater in the former (18.9%) than in the
latter (11.4%). Our previous study [21] has also shown that
wall shear stress in small arterioles could be enhanced by
the temporal variations in the layer width at physiological
aggregation levels (M = 9.9 ± 1.4) and very low edge
pseudoshear rates ðc_ edge ¼ 9:2 0:6/secÞ where the c_ edge
was defined based on the Vedge on either side of the blood
core using the relationship: c_ edge ¼ Vedge =R. To examine
the relative importance of this effect under hyper-aggregating condition compared with other aggregating conditions,
we selectively regrouped the arterioles for each aggregating
condition to have a narrow range of c_ edge . After regrouping, mean c_ edge in the selected vessels (ID = 37.7 ± 1.3 lm)
was 37.1 ± 5.8, 35.8 ± 10.4 and 34.3 ± 8.8 ⁄ sec for the nonaggregating, normal-aggregating, and hyper-aggregating
conditions, respectively. The coefficient of variation (Cv)
was introduced to quantify the temporal variability of the
layer as follows:
Cv ¼ CFLSD =CFLmean
ð2Þ
where CFLSD and CFLmean refer to the SD and mean of the
cell-free layer width on either side of the vessel, respectively.
Based on the analysis method for wall shear stress determination reported in our earlier study [18], Figure 5 compares the wall shear stress values obtained with (s*) and
without (s) consideration of the temporal variations in the
layer width. The wall shear stress for a particular layer
width (W) was obtained by the product of the wall shear
rate and the plasma viscosity (1.3 cP) [37], where wall
shear rate can be derived using Vedge ⁄ W by assuming a linear velocity gradient in the cell-free layer. s* was obtained
by averaging the individual wall shear stress values derived
ª 2011 John Wiley & Sons Ltd, Microcirculation, 18, 541–551
2.5
Non-aggregation
Normal-aggregation
Hyper-aggregation
2.0
τ*
τ
1.5
1.0
0.0
0.2
0.4
0.6
0.8
Cv
Figure 5. Ratio between wall shear stress values with (s*) and without
(s) consideration of the cell-free layer width variations as a function of
Cv. A 2nd order polynomial function is utilized for the curve fit:
y = 1 ) 0.05x + 1.37x2; R2 = 0.66 for non-aggregating condition,
y = 1 ) 0.16x + 1.59x2; R2 = 0.87 for normal-aggregating condition
and y = 1 ) 0.06x + 1.80x2; R2 = 0.70 for hyper-aggregating condition.
,
, and
represent the curve fits for the non-aggregating,
normal-aggregating, and hyper-aggregating conditions, respectively.
from each magnitude of the layer width, while s was
obtained based on the mean width of the layer with no
variations. Thus, s* ⁄ s > 1 indicates an enhancement of the
wall shear stress by the layer width variations. The s* ⁄ s
were generally greater than unity in the entire range of Cv
(0.22–0.78), implying an enhancement of the wall shear
stress by the layer width variations in all aggregating conditions. A distinct augmentation in steepness (B2) of the 2nd
order polynomial curve fit (y = 1 + B1x + B2x2) was found
in the hyper-aggregating condition compared with the
other aggregating conditions. Accordingly, B2 was 1.37,
1.59, and 1.80 for the non-aggregating, normal-aggregating,
and hyper-aggregating conditions, respectively. The curve
fits for non-aggregating and normal-aggregating conditions
appeared to be very similar to each other, indicating no
significant effects of aggregation at physiological levels
on the relationship between s* ⁄ s and Cv. However, an
aggregation effect on this relationship was found as the
aggregation level was further increased as s* ⁄ s for
hyper-aggregating condition was consistently greater than
those for these two aggregating conditions. This finding
suggested that the enhancement in wall shear stress by the
layer width variations could become more pronounced at
pathological hyper-aggregation levels.
Potential Limitations
The cell-free layer width in rats could vary from that in
humans due to differences in the size of their red blood cells
and vessel radii. The size of rat cells (mean corpuscular
549
P.K. Ong et al.
volume 55 lm3) is smaller than that of human cells
(90 lm3) [32]. However, the mean magnitudes of the
cell-free layer widths obtained from the rats [25] were in
agreement with those found with the perfusion of human
red blood cells [19] for similar-sized microvessels. By taking
the cube root of the ratio of approximated volumes between
red blood cells of the human and rat, the vessel radii of the
human arterioles were estimated to be 1.18 times larger
than those of the rat arterioles [23]. Therefore, compared
with the mean rat arteriole radius (16.0 lm) obtained in
the present study, the bigger mean human arteriole radius
(18.9 lm) might result in corresponding smaller magnitudes of normalized mean cell-free layer width by 9%
under hyper-aggregating condition at reduced flow rates.
In this study, the aggregation level of rat blood was elevated to levels seen in normal and pathological human
blood, which was purely based on the M index produced
by the Myrenne aggregometer. It is of note that, as the rat
red blood cell is about 40% smaller in volume than the
human cell as mentioned above, the measured aggregation
levels in blood samples from the rat and human may not
be directly comparable based on the Myrenne indexes.
However, this approach, by using the Myrenne index to
match the aggregation tendency of rat red blood cells to the
human red blood cells, has been well established by many
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