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1 Department of Bioengineering University of California, San Diego, La Jolla, California 92093; and 2 Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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A recent whole organ study in cat skeletal muscle showed that
the increase in venous resistance seen at reduced arterial pressures is
nearly abolished when the muscle is perfused with a nonaggregating red
blood cell suspension. To explore a possible underlying mechanism, we
tested the hypothesis that red blood cell aggregation alters flow
patterns in vivo and leads to blunted red blood cell velocity profiles
at reduced shear rates. With the use of fluorescently labeled red blood
cells in tracer quantities and a video system equipped with a gated
image intensifier, we obtained velocity profiles in venous microvessels
(45-75 µm) of rat spinotrapezius muscle at centerline velocities
between 0.3 and 14 mm/s (pseudoshear rates 3-120
s
1) under normal (nonaggregating) conditions and after
induction of red blood cell aggregation with Dextran 500. Profiles are
nearly parabolic (Poiseuille flow) over this flow rate range in the
absence of aggregation. When aggregation is present, profiles are
parabolic at high shear rates and become significantly blunted at
pseudoshear rates of 40 s1 and below. These results
indicate a possible mechanism for increased venous resistance at
reduced flows.
venous resistance; blood constitutive equation; in vivo blood viscosity; in vivo fluorescence microscopy; wall shear stress
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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VENOUS VASCULAR RESISTANCE in skeletal muscle is highly dependent on blood flow, with resistance increasing as flow decreases (12, 25, 26, 29, 41). Previous rotational viscometric studies showed that the apparent viscosity of blood increases at low shear rates (9, 13, 14, 30) and that this increase is due primarily to red blood cell aggregation (13, 14). Because this effect occurs in the physiological range of shear rates in venous vessels, we hypothesized that red blood cell aggregation is an important determinant of venous resistance. Recent studies in our laboratory (12) on the lateral gastrocnemius muscle preparation of the cat have shown that the increased venous resistance at low flow rates is dependent on the presence of formed elements of the blood and is greatly reduced when a nonaggregating suspension of red blood cells is used as the perfusate. As a possible mechanism to explain this increased resistance, we hypothesized that red blood cell aggregates cause velocity profiles in venules to become more blunt than the parabolic shape expected for Poiseuille flow and, as a result, cause increased energy loss. There is evidence from in vitro studies in glass tubes (21, 35) that aggregation causes blunting of velocity profiles, but in vivo data are limited (36).
To test this hypothesis, we determined velocity profiles in skeletal muscle venules (45-75 µm in diameter) of the rat spinotrapezius muscle with the use of fluorescently labeled red blood cells. The rat provides an excellent model because rat red blood cells normally show negligible aggregation in rat plasma (4) but can be induced to aggregate using macromolecules such as high-molecular-weight dextran. This provided us with the ability to run our experimental protocol both with and without aggregation and compare the results. With the use of an intravital microscope equipped with a charge-coupled device camera and an externally gated image intensifier and videocassette recorder, we were able to record the position of labeled red blood cells during the gate open period of the image intensifier. With the use of image analysis, we then determined velocity profiles for normal (nonaggregating) and dextran-treated (aggregating) blood at control (up to 14 mm/s) and reduced flow rates.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Animal preparation. Fourteen male Sprague-Dawley rats weighing between 250 and 400 g (mean 327.4 ± 41.5 g) were used for these investigations. Animal handling and care were provided following the procedures outlined in the Guide for the Care and Use of Laboratory Animals (NIH, National Research Council, 1996). The study was approved by the local animal subjects committee. Rats were anesthetized with an intraperitoneal injection of 50 mg/kg pentobarbital sodium (Abbott). Additional anesthetic was administered throughout the experiment as needed. The animal was placed on a heating pad to maintain body temperature during surgery. A trachea tube was inserted to assist breathing, the carotid artery was catheterized for blood withdrawals and pressure measurements, and the jugular vein was catheterized for administration of anesthetic, Dextran 500, FITC-dextran, or DiI-labeled red blood cells. All catheters were filled with a solution of heparinized saline (30 IU/ml) to prevent clotting.
An exteriorized rat spinotrapezius muscle preparation similar to that described previously (38) was used for these studies. The skin was opened to expose the spinotrapezius muscle. A drip of warm Plasma-Lyte A, adjusted to pH 7.4 (Baxter), was maintained throughout surgery to keep the muscle moist. Connective tissue was cleared from the surface of the muscle, and the muscle was separated from the surrounding tissue with the blood supply left intact. The animal was then placed on a Plexiglas platform with a raised area that enabled viewing of the muscle while maintaining normal blood flow. Size 4.0 sutures were attached to the outer edges of the muscle and used to secure the muscle to the platform. Moist gauze was placed around the edges of the muscle and covered with petroleum jelly, after which the muscle was suffused with Plasma-Lyte A and covered with a thin polyvinyl film (Saran Wrap, Dow Corning) while air bubbles were removed from the muscle surface. A temperature probe was placed beside the muscle, and temperature was maintained throughout the experiment by regulation of a heating element attached to the animal platform.Microscope system.
A schematic diagram of the experimental setup used for these
investigations is shown in Fig. 1. An
intravital microscope (Ortholux II, Leitz) equipped for both epi- and
transillumination was used with Leitz ×25 (numerical aperture 0.6) and
Olympus ×40 (numerical aperture 0.7) water immersion objectives and a
Leitz UM20 (0.33) condenser lens. The image was projected onto an
externally controlled gated image intensifier (GenIISys, Dage MTI) with
a black and white video camera (CCD-72, Dage MTI) connected to a
videocassette recorder (SVO-9500MD, Sony) and viewed on a monitor
(SSM-121, Sony). This arrangement provided full-screen magnifications
of the video image of ×750 (340 µm horizontal) and ×870 (300 µm
horizontal) for the ×25 and ×40 objectives, respectively.
Preliminary reports of this method have been given in abstract form
(6, 7), and a similar setup has also been reported by
Parthasarathi et al. (31). The muscle preparation was
illuminated with a 100-W mercury arc lamp (model 1149, Walker
Instruments, Scottsdale, AZ). A rotatable turret contained filters for
viewing both DiI (XF101 VIVID, exciter: 525RDF45; dichroic: 557DRLP;
emitter: 565EFLP; Omega Optical) and FITC (I2, exciter: BP
450-490; dichroic: RKP 510; emitter: LP515; Leitz) fluorescence
emission under epi-illumination as well as an open position for viewing
images under transillumination.
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Hematocrit, aggregation, and pressure measurements. The hematocrit and degree of red blood cell aggregation were measured during the control period and after infusion of Dextran 500. Hematocrit was determined after centrifugation with a microhematocrit centrifuge (Readacrit, Clay Adams). The degree of red blood cell aggregation was assessed from triplicate measurements on a 0.35-ml blood sample with a photometric rheoscope (Myrenne Aggregometer, Myrenne, Roetgen, Germany). The use of this technique as well as comparisons of this index of aggregation (M) with other methods and with different animal species has been described previously by Baskurt et al. (4, 5). The aggregation index (M) on the 10-s setting was used for these investigations. Erythrocyte sedimentation rate (ESR) of the same blood sample was also measured in triplicate in microhematocrit tubes allowed to stand for 1 h. The carotid artery catheter was attached to a pressure transducer (TNF-R, Viggo Spectramed) connected to a strip chart recorder (Brush 2600, Gould) for determination of arterial pressure. Pressure was recorded continuously throughout the experimental protocol and manually transferred into a microcomputer (300-MHz Pentium II, Micron) from the strip chart recordings for later analysis.
To compare our data with those of other investigators, we also measured the index of aggregation for samples of hamster blood provided to us by Dr. Amy Tsai of our laboratory.Fluorescent labeling. Red blood cells to be used as tracers were fluorescently labeled with the carbocyanine dye 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (DiIC12 (3); Molecular Probes) according to the method described by Unthank et al. (42). As discussed in that paper, this dye has been used to label a number of different cell types, and no alteration in any physical property of the cell, such as flexibility, due to this labeling procedure has been noted. We examined labeled cells under transillumination both in vivo and on a microscope slide and observed apparently normal cell shape and presence in red blood cell aggregates. Briefly, ~1.0 ml of blood was collected into a heparinized centrifuge tube (polypropylene, Fisher) from the carotid artery catheter. The red blood cells were separated from the whole blood by centrifugation (for 10 min) and aspiration of the plasma and buffy coat and then washed twice in a physiological saline solution (Hanks' balanced salt solution 1×; Cellgro). In four heparinized tubes, 0.15 ml of DiI was dissolved in 10 ml of Hanks' balanced salt solution solution, and one-fourth (~0.1 ml) of the packed red blood cells was added to the dye solution in each of the tubes. The cells were then incubated at room temperature in the dye solution for 30 min accompanied by mild mixing by hand rotation every 10 min. After the incubation period, we washed the red blood cells three times in the saline solution to remove unbound dye.
Experimental protocol. Initially, a 0.35-ml arterial blood sample was taken to determine control values of hematocrit and aggregation index. DiI-labeled cells were infused into the animal so as to obtain an in vivo concentration of ~1%. Next, a 1.0% solution of FITC ("Isomer 1," Molecular Probes) was infused into the bloodstream to achieve a concentration of 6 mg/kg body wt at the beginning of the experiment. This fluorescent label binds to albumin in the blood plasma and enables clear determination of the venular internal diameter.
A 45- to 75-µm diameter skeletal muscle venule with at least one side branch in the field of view was selected for study on the basis of the criteria of stable flow as well as clear focus and contrast of the image. The microscope was focused on the equatorial plane of the venule, and the video camera was oriented with the venule longitudinal axis diagonally on the video screen to maximize the distance available to follow red blood cell movement. A video image of the vessel was recorded under control conditions for successive 2-min periods with transillumination, excitation of the FITC dye, and excitation of DiI. Blood was then removed from the rat via the carotid artery into a heparinized syringe until arterial pressure was ~50 mmHg, and blood flow was allowed to stabilize. An average of 5.9 ± 1.8 ml of blood were withdrawn at a rate of ~2.5 ml/min to achieve this condition. The video image was again recorded at this reduced flow state under each of the three illumination conditions for ~2 min each, after which blood was reinfused into the animal over the course of 60-90 s. The arterial pressure was monitored until it returned to a steady-state value, and, in each case, these values were not significantly different from control values. This protocol was then repeated ~20 min after addition of Dextran 500 (average molecular mass 460 kDa; Sigma) to induce red blood cell aggregation. Treatment groups before and after dextran infusion are hereafter denoted as normal and dextran groups. The dextran (200 mg/kg body wt) was dissolved in saline (6%) and infused in 50 mg/kg increments over the course of 2-3 min. Occasionally, a minor (<25 mmHg) drop in arterial pressure occurred during infusion, which typically recovered to the control value in <2 min. On the basis of a total blood volume of 5.5% (2), an average hematocrit of 40%, and an average body weight of 325 g, this represents a plasma dextran concentration of ~0.6%. Hematocrit and aggregation index values were determined 15 min after dextran infusion. Although dextran is reported to cause anaphylactic reaction in this species, there was no discernable adverse reaction (e.g., visible swelling of the limbs) to the dextran infusion in any of the rats used for these investigations. With the use of fluorescently labeled red blood cells in tracer quantities, we were able to distinguish and follow single red blood cells flowing in the venules during conditions of normal and reduced arterial pressure. To obtain velocities at normal flow rates (1-14 mm/s for venules of this diameter), the repetition rate of the gated image intensifier was set to frequencies of 30-180 s1. This procedure produces multiple images of single red
blood cells on one video frame when the frequency is greater than the video framing rate (30 s1).
Determination of red blood cell luminal position and velocity. Video tape recordings of images containing labeled red blood cells and labeled plasma were transferred to digital format for computer image analysis after completion of the experimental protocol. For this purpose, the videocassette recorder was connected to a video capture board (DC30 Plus, miroVIDEO) installed in a microcomputer (300-MHz Pentium II, Micron), as shown in Fig. 1. The video frames were then digitized with Abobe Premier 4.0 (Adobe), and the image files were transferred to a compact disk (CD-Writer Plus 7200e, Hewlett-Packard) for analysis and storage. Image magnification was determined from the recorded image of a stage micrometer under transillumination.
Figure 2, A-C, shows videomicrographs of a typical vessel studied under transillumination, DiI epi-illumination, and FITC epi-illumination, respectively. In Fig. 2B, a gate open period of 5 ms was used, creating the six images of each red blood cell seen on this video frame. From the digitized images, we used an image analysis software package (SigmaScan Pro 4.0, SPSS) to obtain x- and y-axis coordinate data at 5-ms intervals for individual red blood cells. All cells with distinct images were followed during a short time period (up to 30 s) to obtain information at all radial positions in the venule lumen. These coordinate data were imported into a spreadsheet (EXCEL, Microsoft) where the radial and longitudinal positions for each red blood cell during each gate open period were determined and recorded. With the use of the same image analysis and spreadsheet software programs, venular wall position was determined from the transillumination and FITC fluorescence images, and these data were combined to obtain a composite diagram, such as that shown in Fig. 3. For clarity, only a fraction of the total number of cells analyzed in this vessel are shown. Approximately 75 cells distributed across a 50-µm-diameter vessel were needed to obtain a statistically valid profile fit.
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Statistical analysis. Both the t-test and the nonparametric Mann-Whitney rank sum test were used to determine differences in experimental and physiological parameters between normal and dextran-treated animals. Individual cell velocities and radial positions in each longitudinal section were averaged and plotted as means ± SE. Regression fits of individual profiles to the experimental data points were minimized using a linear least-squares algorithm designed for a standard software package (EXCEL, Microsoft). Regression lines for relationships between experimental parameters and red blood cell velocity or pseudoshear rate were determined by this same software package. On the basis of superior fit, curvilinear regression was used to describe the relationships between profile parameter data and pseudoshear rate or velocity for dextran-treated blood, whereas linear regression provided satisfactory fit for these relationships when describing normal blood. Correlation coefficients, 95% confidence intervals, and probability values for profile fits and regression lines were calculated with standard procedures described by Glantz (22). Differences in profile parameters between normal and dextran-treated rats were determined using both the paired t-test and the nonparametric Wilcoxon signed rank test performed by a statistical software package (SigmaStat, Jandel). For all tests and regression fits, P < 0.05 was considered statistically significant.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Hematocrit, degree of aggregation, and arterial pressure. For normal rats, the hematocrit was 45.7 ± 5.4%, the index of aggregation (M) was 0.02 ± 0.1, the ESR was 0.5 ± 0.2 mm/h, and the arterial pressures were 123 ± 11 and 50 ± 14 mmHg during control and reduced flow situations, respectively. In dextran-treated rats, the hematocrit was 39.1 ± 6.7%, the index of aggregation was 11.7 ± 5.5, the ESR was 8.0 ± 0.4, and the arterial pressures were 132 ± 17 and 48 ± 14 mmHg for control and reduced flow situations, respectively. The mean hematocrit of the dextran-treated rats was significantly (P < 0.001) less than those of normal animals. There were no significant differences (P > 0.05) between arterial pressures of normal and dextran-treated animals during either the control or reduced flow situations.
For hamster blood samples (n = 7), the hematocrit was 49 ± 2%, and the index of aggregation was 0 ± 0.0.Velocity profile determination.
Velocity data were obtained on ~75 cells in each of the five vessels
under control and reduced flow situations before and after induction of
red blood cell aggregation. The gate frequency of the image intensifier
was set so that ~25 images of each cell were obtained during transit
of the cell across the video screen, totaling ~100,000 measurements
of cell position for 4,000 cells. Figure
4 is an example of a velocity profile of
normal (nonaggregating) blood at control arterial pressure obtained by
plotting the position and velocity for all cells visible in
section 2 of the vessel shown in Fig. 3 while focused on the
equatorial plane. While the parabolic nature of the leading edge of the
profile can be observed, a number of velocity points fall substantially
below this leading edge. Because the videomicrograph is a
two-dimensional projection of a three-dimensional vessel, it was
hypothesized that those velocity points falling well below the leading
edge of the profile may have been from cells located above or below the
equatorial plane and, therefore, would be out of focus to varying
degrees.
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Location of cells in equatorial plane of vessel.
To test this assumption, a microscope slide prepared with labeled red
blood cells was placed on the microscope stage, and videomicrographs
were recorded as the sample was raised and lowered through the object
plane of the microscope. After these images were digitized, a line
intensity scan through a cell image was done to determine the cell
intensity profile. Figure 5 shows the video images and corresponding line intensity plots for a single cell
at 4-µm vertical intervals. This figure demonstrates that labeled
cells in an 8-µm section encompassing the object plane present a
narrow intense image (Fig. 5, C-E) that can be
distinguished from the wide image (Fig. 5, A and
B and F-H) for cells outside of this region.
With the use of this method, it is possible to differentiate between
cells in or out of a selected optical section on the basis of an
objective criterion. This technique extends a previous study by
Tangelder et al. (39), where the ability to localize
fluorescent microspheres and blood cells within a thin optical section
during flow was demonstrated.
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Curve fitting of velocity profiles.
After data were removed for cells out of the equatorial plane, a linear
least-squares minimization algorithm developed for and solved by a
standard software package (Excel, Microsoft) was used to fit profiles,
like the one shown in Fig. 6B, to the equation
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(1) |
Effect of aggregation on velocity profiles.
Figure 7 shows the centerline velocity
profiles obtained from section 2 of the vessel described
above (Fig. 3) under conditions of control and reduced flow for normal
(nonaggregating) and dextran-treated (aggregating) blood. As expected,
the nonaggregating profiles for both control and reduced flow rates are
nearly parabolic (K 
2) in nature. When dextran was
added to the circulating blood, red blood cell aggregation caused a
slight blunting of the velocity profiles under control flow conditions
and marked blunting at reduced flow.
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= Vmean/D, in
s1, where D is diameter) was
determined for each section. Figure 10
shows the relationship between the parameter K from
Eq. 1 and the pseudoshear rate. This plot is substantially
similar to the relationship between K and
Vmax (Fig. 8), but it emphasizes the fact that
significant differences in profile shape between normal and
dextran-treated blood can be detected at pseudoshear rates up to
40 s1 and may be present at pseudoshear rates approaching
90 s1, where the intersection of the two regression lines
occurs. A summary of the measured and analytically determined
parameters for the profiles from each section is shown in Table
1. In this table, profiles have been
grouped according to aggregation condition (normal or dextran-treated)
and flow condition (control or reduced arterial pressure). A complete
listing of the parameters for each individual profile is on file in the
journal repository as Table A.1
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Effect of aggregation on shear rate radial gradient.
The radial variation of the local shear rate (
) can be
calculated by differentiating the velocity distribution (Eq. 1) with respect to the radius, yielding the equation
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(2) |
= 2 s1) and
Vmax = 4.0 mm/s ( = 40 s1) with the use of K values from Fig. 8.
Because the profile with normal blood is parabolic, the shear rate
increases linearly with the radius r and reaches a value
eight times the pseudoshear rate at the vessel wall. In contrast, with
dextran-treated blood, the shear rate in the central 60% of the vessel
is below that for normal blood, whereas near the vessel wall it is much
higher.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Principal finding.
The purpose of this study was to test the hypothesis that red blood
cell aggregates cause velocity profiles in venules to become more blunt
than the parabolic shape expected for Poiseuille flow. Such an effect
may lead to increased energy loss, as discussed in a later section. To
this end, we made a detailed comparison of the shape of velocity
profiles obtained in venous microvessels with both nonaggregating and
aggregating blood. As shown in Figs. 8 and 10, profiles for
nonaggregating blood are uniform and nearly parabolic over a large
range of velocities and pseudoshear rates. In contrast, the shape of
profiles for aggregating blood is shear rate dependent. At high flow
rates, the parameter of profile shape (K) is similar for
aggregating and nonaggregating bloods. The regression lines for the
profile shape parameters of the two bloods diverge as pseudoshear rates
are reduced below ~90 s1, and the blunting parameters
become significantly different at 40 s1 and below. These
findings are consistent with the hypothesis that the flow properties of
aggregating blood contribute to a rise in venous resistance of skeletal
muscle at low flow rates. To our knowledge, this study is the first to
examine the effect of changing velocity and red blood cell
aggregability on velocity profiles in vivo.
Limitations of measurement. There are several sources of uncertainty in the method we used to determine red blood cell velocity. These errors are principally related to determining the center of each red blood cell image and the position of the venular wall. The errors involved in marking red blood cell positions (~1%), as discussed in MATERIALS AND METHODS, are independent and random. The error in determining the position of the vessel wall (~1.5%) was minimized (23) by combining information from both the transillumination and FITC epi-illumination images. Accounting for these sources of error, the estimated error of the profile bluntness parameter K is ±0.3. This error is less than the interexperimental scatter and does not significantly alter the present conclusions.
Comparison with velocity profiles from previous studies.
A number of previous studies (1, 10, 11, 16, 19, 21, 31, 32, 35,
37, 39) have obtained velocity profiles in vivo or in vitro. In
comparing profiles from different studies, careful attention must be
paid to the technique of velocity measurement, the tube or vessel
diameter, and erythrocyte aggregability. Velocity profiles have been
determined by visualizing individual cells in the flow stream and
storing the images with high-speed recording techniques or by
monitoring photometric signals at two points and determining the time
required for passage. The imaging technique has the advantage that the
measurement can be limited to a narrow plane at the centerline
(39, 40), whereas the photometric technique reports a
weighted average throughout the flow stream (3, 32). As a
result, imaging techniques can, in principle, determine the actual
velocity profile, whereas photometric techniques would underestimate
velocity except at the edge of the flowstream. Another consideration is
the diameter of the tube or vessel because velocity profiles become
more blunt as the tube or vessel diameter decreases (9, 10,
37) due to the increasing ratio of particle size to tube
diameter. Additionally, because red blood cell aggregability varies
widely by species (4, 33, 43), the degree of blunting seen
in the velocity profiles would also be species dependent. Table
2 shows how the normal and
dextran-treated blood of the present study compares in aggregability
(as measured by ESR or index of aggregation values) to blood from
species used in previous studies.
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1) and became more parabolic with increased flow rate or
greater tube diameter, although a quantitative description of this
relationship was not given. Reinke et al. (35) found that
velocity profiles of fluorescently labeled human red blood cells became
increasingly blunted as pseudoshear rates in a 66-µm tube were
decreased from 26.4 to 0.69 s1. Gaehtgens et al.
(21) determined velocity profiles of human blood in 30- to
130-µm glass tubes for pseudoshear rates of 1-300 s1 with the use of the dual-sensor method
(44). Their profile bluntness parameter decreased as shear
rate increased but was not parabolic even at the highest shear
rates. The inverse trend between profile bluntness and shear
rate seen in these studies agrees with the present findings for
dextran-treated blood.
Previous in vivo studies of velocity profiles have used species
(hamsters and rabbits) whose red blood cells have little or no
aggregability (Table 2) and have not specifically investigated the
effect of varying flow rate. Pittman and Ellsworth
(32) reported that profiles in arterioles and venules
(30-140 µm) of the hamster retractor muscle under both control
and reduced flow rates were significantly more blunt [degree of
bluntness (B) values (Eq. 3) between 0.18 and 0.97]
compared with a parabolic profile, possibly due to the averaging effect
of the dual-sensor method.
With the use of a high-speed movie camera, Schmid-Schönbein and
Zweifach (37) found that velocity profiles in arterioles and venules (16-54 µm) of the rabbit omentum became more blunt (as determined by the ratio of two-dimensional
Vmean to Vmax) only at
centerline velocities slower than 1.2 mm/s (pseudoshear rate ~20
s1). Because the aggregability of rabbit blood is less
than that of dextran-treated rat blood (Table 2), this result is not surprising.
Velocity profiles in arterioles and venules of the rabbit mesentery
using fluorescently labeled platelets as markers (39) were
more blunt than those of the present study (K values between 2.3 and 4.0 at higher shear rates) and showed no correlation to the
pseudoshear rate over a range of 39-326 s1. The
lack of correlation to shear rate is perhaps due to the small sample
size and relatively large scatter of the profile parameters due to
interanimal differences. The large blunting parameters reported are
unexpected given the low aggregability of rabbit blood but may reflect
the smaller diameter of vessels (17-32 µm) in that study.
Methods for characterizing profile shape. Gaehtgens and co-workers (1, 21) devised two dimensionless parameters to quantify the bluntness of velocity profiles. The first of these, R, was defined as the ratio of the volumetric flow rate for the experimentally determined profile versus that for a parabolic profile. The second parameter, F, was defined as the ratio of the area under the experimental profile versus that under a parabolic profile in the region between the tube axis and r/R = 0.5. These two parameters were shown to correlate strongly.
We determined the parameter F for each of our experimental profiles, as shown in Fig. 12A. Whereas the F values in the study of Gaehtgens et al. ranged from 1.1 to 2.9 for human blood with the use of the dual-slit measurement of velocity, the F values in our study ranged between 0.6 and 1.4 for dextran-treated animals, which have a similar aggregation tendency to that of human blood. The statistical power of the regression fits of our experimental data to the parameter F was not as high (i.e., correlation coefficient not as large) as to Eq. 1 due to loss of a considerable number of data points. However, the same conclusions may be drawn from Fig. 12A regarding the characteristics of profiles for both normal and dextran-treated animals as from the previous graphs. The intersection of the regression lines occurs at a value of ~8.7 mm/s, which is not significantly different from the value of 9.2 mm/s shown in Fig. 8.
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(4) |
![<FR><NU>V<SUB>max</SUB></NU><DE><IT>V</IT><SUB>mean</SUB></DE></FR><IT>=</IT><FR><NU>(<IT>K+2</IT>)</NU><DE>[<IT>K+2−2</IT>(<IT>a</IT>)<SUP><IT>K</IT></SUP>]</DE></FR>](/content/vol280/issue1/fulltext/H222/img005.gif)
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(5) |
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Asymmetry of velocity profiles.
In vitro velocity profiles determined in tubes where length is several
orders of magnitude greater than diameter are usually axisymmetric
(1, 10, 21). However, venular network geometry is
characterized by frequent bifurcations, which combine blood streams
that may be of different velocities and hematocrit into the same flow
stream. It has been shown in theoretical studies by Popel and
co-workers (17, 18) that asymmetric velocity profiles may
result when streams of different hematocrit converge. The degree of
asymmetry in velocity profiles can be expressed in a quantitative form
using parameter b from Eq. 4. In our profiles, the parameter b had an average value of 
0.008 ± 0.053, which is not significantly different from zero
(P > 0.05), and is equivalent to shifting the center
of the profile 0.13 µm toward the wall in a 50-µm vessel. The
asymmetry indexes are not significantly different for profiles from
sections upstream or downstream from bifurcations (P > 0.05) for both dextran-treated and normal blood (P > 0.05). It is possible that by averaging cell velocities over a 100-µm
section length, asymmetry at localized sites is also averaged. In the
studies of Tangelder et al. (39), the b value was also not significantly different from zero at a measurement site
six vessel diameters downstream from a bifurcation. In those studies,
profiles were obtained from a large number of velocity readings at each
radial position over a longitudinal distance of 35-45 µm,
effectively averaging out the random fluctuations as in our study. On
the basis of the theoretical models, it would appear that the
converging streams studied in the present experiments were of similar hematocrit.
Effect of shear rate on red blood cell aggregation in vivo.
Our study shows that venular velocity profiles are significantly
affected by red blood cell aggregation at pseudoshear rates (Vmean/diameter) up to 40 s1 (Fig.
8). The qualitative similarity of the present results to previous
rotational viscometric data (13, 14) suggests that the
exponent K is a suitable index that can be used to describe the effect of aggregation on blood flow in vivo. The rotational viscometric studies show that red blood cell aggregation increases the
apparent viscosity of human blood at shear rates below 5 s1. With the use of this value as a benchmark for
determining whether or not aggregates might be present at a given
radial position at the lowest flow rates studied, it can be seen that
aggregation extends this region by 15% of the radius on average (Fig.
11A) and up to 45% in the most extreme case. At faster flow
rates, the center of the vessel may contain red blood cell aggregates even when the pseudoshear rate is so high that aggregate formation would not occur if the shear rate had remained a linear function of
radial position.
Implications of profile blunting for vascular resistance.
Previous studies in the dog intestine (26), dog
hindlimb (41), cat sartorius muscle (25), and
cat lateral gastrocnemius muscle (12) preparations have
reported increases in venous vascular resistance of up to 300% on
reduction of arterial pressure from 100 to 40 mmHg. In a cat muscle
preparation (12), it was shown that most, if not all, of
this increase could be explained by the presence of red blood cell
aggregation. Previous studies also showed that nearly 70% of the
pressure drop in the venous network of cat sartorius muscle occurs
across the venules in the diameter range of 25-185 µm
(25) and that the diameter of these vessels changes very
little during large changes in arterial pressure (24). The
latter finding has been confirmed by us (8) in rat
spinotrapezius muscle for both horizontally and vertically oriented
venules. The pseudoshear rate in venules of cat sartorius muscle
(24) at normal arterial pressure approaches the range (<10 s1) where red blood cell aggregation has been shown
to increase blood viscosity in vitro (9, 13, 14, 30, 34).
W) was determined by differentiation of Eq. 1, yielding the equation
|
(6) |
Extent of red blood cell aggregation in circulation.
It has long been considered that for those species (such as cats, dogs,
and humans) in which it is a naturally occurring phenomenon, red blood
cell aggregation may have a significant effect on vascular resistance
in segments of the circulation other than the venular network, but
these considerations have been limited to circulatory shock and other
low flow states (12, 28). Our data provide a quantitative
basis for evaluating this suggestion. On the basis of average values
for flow and diameter, pseudoshear rates in humans have been estimated
to be less than 40 s1 in most segments of the arterial
network and in all segments of the venous network at normal flow rates
(45). Therefore, it is likely that red blood cell
aggregation is normally present to some degree in most areas of the
circulation (excluding the capillaries and other small vessels). In
support of this possibility, a number of investigators have reported an
ultrasonic backscattering effect of red blood cell aggregates in the
large arteries and veins (15). Those observations, coupled
with the present results, raise the possibility that red blood cell
aggregation may have significant effects on effective blood viscosity
in other segments of the circulation. Such effects would be more
prominent in low flow states, such as shock, where cardiac output may
fall to 25% of normal values and shear rate in individual vessels may
also fall to a similar extent (27), depending on
local changes in vascular diameter. Our data suggest that the effect of
aggregation on vascular resistance outside the venular network would be
significant, but its magnitude cannot be estimated from the data
presently available.
| |
ACKNOWLEDGEMENTS |
|---|
The authors thank Dr. Amy Tsai for many valuable discussions and for providing samples of hamster blood for ESR and aggregation measurements. We also thank Dr. Heng-Chuan Kan for helpful discussions and Masoud Paknejad, Caroline Flarity, Andilily Lai, Nhat Nguyen, and Rami Apelian for technical assistance in data acquisition.
| |
FOOTNOTES |
|---|
This work was supported by National Heart, Lung, and Blood Institute Grant HL-52684.
1 For Table A (Experimental Profile Data), order NAPS Document 05581 from NAPS % Microfiche Publications, PO Box 3513, Grand Central Station, New York, NY 10017.
2 For Table B (Comparisons of Profile Parameters from Various Analysis Methods), order NAPS Document 05581 from NAPS % Microfiche Publications, PO Box 3513, Grand Central Station, New York, NY 10017.
Address for reprint requests and other correspondence: P. C. Johnson, Dept. of Bioengineering, Univ. of California, San Diego, La Jolla, CA 92093-0412. (E-mail: pjohnson{at}bioeng.ucsd.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 1 May 2000; accepted in final form 13 July 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
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