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1Department of Mechanical Engineering, University of Los Andes, Bogota, Colombia; and 2Department of Bioengineering, University of California-San Diego, La Jolla, California 92093-0412
Submitted 11 August 2003 ; accepted in final form 6 November 2003
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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arterioles; red blood cell trajectories; shear-induced particle diffusion; intraluminal oxygen profiles
In vitro studies have shown that the formation of a cell-free or depleted plasma layer is formed when blood shear rates are below 5 s–1, a flow regime that is usually two orders of magnitude below that found in arterioles. Thus, whereas an actual RBC-free plasma layer may not be present in arterioles, geometrical considerations indicate that at the vessel wall the hematocrit (Hct) must be at most one-half of the central blood core, because for Hct to be uniform throughout the arteriole the RBC center would have occupy the blood vessel wall interface.
Because the presence of a plasma layer and/or a RBC-depleted layer next to the arteriolar vessel wall introduces a barrier to oxygen diffusion, it is of interest to determine whether this region may present features that could diminish or eliminate this diffusional barrier. A mechanism that could account for the lack of a diffusion barrier next to the vessel wall is related to the observation that RBCs do not follow linear trajectories in blood but present a random radial drift in part determined by relative motion and collisions with surrounding cells in the bloodstream. Previous studies on the radial dispersion of flowing RBCs in 45- to 70-µm-diameter venules of the rat spinotrapezius muscle (1) have shown that for cell velocities in the range of 0.3–14 mm/s the root mean square (RMS) deviation of radial position (RMSDev) of RBCs was 2.54 ± 1.47 µm, the SD of radial position was 1.98 ± 0.98 µm, and the mean coefficient of variation of velocity (CVVel) was 16.9 ± 10.5% for a distance of 100 µm. It was also found that there was no dependence of RMSDev on radial position. A conclusion of this study was that the shear-induced random cell movements observed may greatly enhance the transport of particles and solutes within the bloodstream.
In view of the findings in venules, we studied the dispersion of RBCs in arterioles of a hamster skin fold model in normal conditions and during acute isovolemic hemodilution with dextran to determine whether shear-induced particle dispersion of RBCs enhances intravascular oxygen diffusion from blood to tissue in arterioles, as evidenced by an intravascular PO2 profile that is more uniform (flatter) than that predicted by theoretical considerations (7). Furthermore, because the shape of intraluminal PO2 is also dependent on Hct, we investigated whether this phenomenon may be influenced by the Hct. Because our long-term interest in these studies is to determine the factors that may influence oxygen gradients in the proximity of the vessel wall, we carried out the study in the hamster window chamber preparation, which allowed us to study oxygen distribution in the microcirculation in a normal tissue environment.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Hamster skin fold window chamber and catheterization. Animals were anesthetized for chamber implantation with a 50 mg/kg ip injection of pentobarbital sodium (Nembutal; Abbott, IL). First, the hair on the back was shaved and epilated with a hair-removing solution. The skin was then folded on the midline. One of two identical titanium frames with 12-mm circular openings was positioned on one side of the skin fold. The skin, retractor muscle of the first skin layer, and subcutaneous connective tissue were removed after the outline of the window leaving only a thin layer of retractor muscle, connective tissue, and the intact skin of the opposite side. The exposed tissue was sealed with a glass coverslip incorporated into the second frame of the chamber. Two days after chamber implantation, the animal was reanesthetized, and the carotid artery and jugular vein were catheterized. The catheters were exteriorized at the dorsal side of the neck at the cranial end of the chamber frame where they were attached with tape away from the grasp of the animal. Catheters are filled with heparinized saline (30 IU/ml) to ensure patency at the time of the experiment.
Inclusion criteria. Experiments were performed between 24 and 48 h of catheter implantation if baseline parameters were 1) heart rate (HR) > 320 beats/min; 2) mean systemic arterial blood pressure (MAP) > 80 mmHg; 3) systemic Hct > 45%; and 4) systemic arterial PO2 > 50 mmHg. Animals were excluded from the study when signs of inflammation and bleeding were observed. Studies were performed as previously described (9).
Systemic parameters. MAP was measured periodically during the experiment via the arterial catheter and the HR was determined from the pressure trace (Gould TA400; Cleveland, OH). Systemic Hct was measured from centrifuged arterial blood samples taken in heparinized capillary tubes (Readacrit Centrifuge, Clay Adams, Division of Becton-Dickinson; Parsippany, NJ).
Blood chemistry. Arterial blood was sampled from the carotid artery catheter into a heparinized capillary tube and immediately analyzed for PO2, PCO2, and pH at 37°C (Blood Chemistry Analyzer 248, Chiron Diagnostics). The hemoglobin content of blood was determined using spectrophotometric techniques (B-Hemoglobin Photometer, Hemocue) from a drop of blood.
RBC position and velocity protocol. Samples of hamster blood of 1.0 ml were collected as previously described (1), and RBCs were fluorescently labeled with the carbocyanine dye Dil (Molecular Probes) and reinfused through the venous catheter to obtain an in vivo concentration of 
1%. Infusion was performed briefly before the isovolemic exchange protocol. Once the animal was mounted on the microscope stage (Leitz Ortholux II), arterioles of 40–95 µm internal diameter were selected for study provided they had adequate flow, image focus, and contrast. The microscope was focused on the equatorial plane of the arteriole, and a video image of the vessel was recorded using a charge-coupled device camera (COHU 4815–2000) and a gated image intensifier. The video images were recorded using a videocassette recorder (AG-7355, Panasonic) and viewed on a monitor (PVM-1271Q, Sony). The repetition rate of the intensifier was set to obtain one to six images of a cell on one video frame for determination of velocities up to 14 mm/s. The video images were digitalized with a personal computer using Adobe Premier 4.0 software, and x-y coordinate data for each cell image were obtained using SigmaScan Pro 4.0 software (SPSS). The arteriole wall position was determined from the transillumination image, and all coordinate data were imported into a spreadsheet (Excel, Microsoft) where the radial and longitudinal positions for each RBC during each gate period were determined. Cell positions were determined manually rather than by image analysis, given that the eye of a trained observer was shown to give a good estimation of the location of the center of a cell, which in general corresponds to the location of maximal fluorescence observed for most cell orientations. Individual RBCs were followed for a longitudinal distance of up to 400 µm, and the gate image intensifier was set to obtain 10 images of each cell over a 100-µm distance. Multiple determinations of position and velocity could thus be made for each cell (1). Because refraction might occur near the equatorial plane of the inner surface of the edge of the blood vessels, there is some error associated with the determination of cell position.
Intraluminal PO2 distribution. High-resolution microvascular PO2 measurements were made in the unanesthetized animal using phosphorescence quenching microscopy, a method based on the oxygendependent quenching of phosphorescence emitted by the albuminbound metalloporphyrin complex after pulsed light excitation. This technique has been used in this animal preparation for both intravascular and extravascular oxygen tension measurements (5). Animals receive a slow intravenous injection of 15 mg/kg body wt at a concentration of 10.1 mg/ml of palladium-meso-tetra(4-carboxyphenyl)porphyrin (Porphyrin Products; Logan, UT). The dye was allowed to circulate for 20 min before PO2 measurements.
Measurements were made by transmitting the emission from the location of the measurement through a rectangular diaphragm, which is back illuminated, showing with high optical resolution the exact location of the area of measurement. This allows positioning of the window at specific locations within the vessel of interest. The phosphorescence decay curves were analyzed off-line using a standard single-exponential least-squares numerical fitting technique, and the resultant time constants were applied to the Stern-Volmer equation to calculate PO2 (11).
The intraluminal oxygen profile in the arterioles was obtained by measuring PO2 in 15 windows across the vessel diameter. Each window covered an area of 5 x 30 µm. Two additional windows were used to measure PO2 in the tissue just outside the vessel wall.
Measuring PO2 in moving fluids by means of phosphorescence decay must take into account the duration of the excitation flash and the motion of the fluid during this period. The half-life of the excitation flash was of the order of 
= 5 µs and the velocity of the flow, as a maximum, was 1 cm/s in arterioles. Therefore, in terms of the moving region of fluid where fluorescence has been activated, in extreme conditions, there will be a displacement of 104 µm/s x 2 = 0.1 µm.
The window measuring phosphorescence emission was 5 x 30 µm, placed lengthwise in the lumen of the blood vessel. Consequently, in large arterioles, the excited fluid moved 0.1/30 = 0.3% of the window area. However, the phosphorescence emission from this region may take as long as 200 µs to decay for PO2 values of 20 mmHg, with a fluid displacement of 104 µm/s x 2 x 10–4 s = 2 µm, causing 7% of the signal not to be captured by the measuring window. This effect is lessened at the higher PO2 values, where phosphorescence decays more rapidly, and may require a longer window axis in the analysis of low PO2 venules.
Acute isovolemic exchange transfusion protocol. An acute anemic state was induced by lowering the systemic Hct to 40% of baseline with a two-step progressive isovolemic hemodilution using 6% Dextran 70, a colloid solution. A stepwise protocol was used because it has been found to maintain stable systemic parameters in small animals. Briefly, the volume of each exchange transfusion step was calculated as a percentage of the animal blood volume, estimated as 7% of the body weight. Level 1 exchange (L1) was 40% of the blood volume, and level 2 exchange (L2) was 35% of the blood volume. The transfusion solutions were passed through an in-line 13-mm-diameter 0.2-µm syringe filter (Corning; Corning, NY) and then into the animal via the jugular vein catheter at a rate of 100 µ1/min using a microinfusion syringe pump (CMA100 Microinjection Pump, CMA). Blood was simultaneously withdrawn by hand from the carotid artery using the indwelled catheter at the same rate, a method found to be more accurate than an automated syringe pump where the delay detection of catheter malfunction, usually due to blood clotting at the catheter tip, would result in a nonisovolemic exchange. The slow rate of exchange matched to the small animal size was chosen to ensure a stable blood pressure during the exchange period. The animal was given a 5-min recovery period after the second exchange before data acquisition was started.
Experimental setup. Anesthesia was induced by a 30 mg/kg iv injection of pentobarbital sodium (Nembutal) and maintained by continuous infusion at a rate of 2 mg·kg–1·min–1. Anesthesia depth was assessed by the judgement of consciousness, motor activity, muscle tone, and responses to nonaversive and noxious stimulation. The animal was placed in a restraining tube that was stabilized by fixing the tube and the chamber to a Plexiglas plate. The animal was allowed a 30-min adjustment period to the tube environment before the control systemic parameters (MAP, HR, arteriolar blood gases, and Hct) and cell position and velocity were measured. All variables were measured again after L1 and after L2.
Statistical analysis. Fluctuations in radial position for each cell can be described in terms of the SD and RMSDev according to the method of Bishop et al. (1). RMSDev was determined from the following equation
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 | (2) |
Fluctuations in the instantaneous velocity (calculated as the vectorial addition of the radial and axial velocity components) of individual RBCs were described in terms of the SD of the individual measurements over the recorded length. Depending on the setting of the image intensifier and the velocity of the particular RBC being traced, the number of individual measurements varied between 4 and 20. With the use of the SD calculated from these measurements, CVVel was calculated for each cell as CVVel = SD/mean velocity.
RBC shear-induced diffusion coefficient. The shear-induced selfdiffusion or dispersion coefficient of the cells (DRBC) is given by
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R is equal to RMSDev and t is the time interval between individual measurements of radial position (1). The calculation of DRBC was made for every experimental group. Statistical analysis was performed using Excel (Microsoft) and InStat (GraphPad) software. For the RBC position, velocity and diffusion coefficient parameters, basic statistics, and regression analysis were calculated for the control, L1, and L2 measurements. Differences in parameters among experimental groups were assessed using the Kruskal-Wallis test and Dunn's multiple-comparisons test. Regression and correlation coefficients and tests of slopes different from zero were performed using linear regression analysis. For the intraluminal PO2 distribution parameters, means ± SD were calculated for every measurement window and for every experimental group, and a t-test for difference between the control and L2 means was performed for every window. Changes were considered statistically significant if P < 0.05.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Systemic parameters, Hct, blood chemistry, and gasometry. The results for these system parameters, Hct, blood chemistry, and gasometry are presented in Table 1. All systemic, blood chemistry, and gasometry parameters varied as expected in these experiments (9).
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RBC movement. Individual RBCs presented random changes in position as they transited through the studied arterioles. Shown in Fig. 1 are the typical radial positions of four different cells at 7-ms intervals during transit through a 60-µm-diameter arteriole.
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RMS deviation of radial position. RMSDev was calculated with Eq. 1 for each of the cells. A plot of the values of RMSDev versus cell mean velocity for each cell during control, after L1, and after L2 is shown in Fig. 2, A–C, respectively. The distribution of the individual values of RMSDev during the control period after the L1 and L2 periods is presented in Fig. 2D. The values for each experimental group are presented in Table 2. RMSDev was significantly lower in L2 compared with both control and L1 (P < 0.001). At control and L2, RMSDev showed a small but significant increase with cell velocity.
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SD of radial position. SD was calculated for every experimental group as shown in Table 2. SD was significantly lower in L2 compared with both control (P < 0.001) and L1 (P < 0.05). At L1, SD showed a small but significant decrease with cell velocity.
Mean cell velocity. Mean cell velocity was calculated for each experimental group. The velocity was 3.28 ± 0.95 mm/s during control (n = 1,000), 3.67 ± 1.17 mm/s after L1 (n = 869), and 3.27 ± 1.61 mm/s after L2 (n = 924). Differences among experimental groups were statistically significant: control versus L1 (P < 0.001), control versus L2 (P < 0.01), and L1 versus L2 (P < 0.001).
SD of velocity. SD of velocity was calculated for every experimental group as presented in Table 2. SD of velocity was significantly lower in L2 compared with both control and L1 (P < 0.001). At control, L1, and L2, SD of velocity presented a small but significant increase with cell velocity.
CVVel. CVVel was calculated for all experimental groups as shown in Table 2. CVVel was significantly higher in control compared with L1 (P < 0.05). In all groups, CVVel showed a small but significant decrease with cell velocity.
RBC shear-induced diffusion coefficient. DRBC was calculated for all experimental groups as illustrated in Table 2. DRBC was significantly lower in L2 compared with both control and L1 (P < 0.001).
Intraluminal PO2 distribution. The intraluminal oxygen profile was determined in another group of eight animals under the same experimental conditions. Oxygen profiles from 25 vessels were obtained during control, 16 vessels after L1, and 8 vessels after L2. The mean diameter of the observed vessels was 76 ± 12 µm. The results are presented in Fig. 3. The intraluminal PO2 profiles assumed an increasingly parabolic configuration with increasing levels of hemodilution. Mean PO2 was significantly different in control compared with L2 in 14 of 17 windows measured, including the 2 tissue windows.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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1.5 µm as measured by both the RMSDev and SD. The magnitude of radial dispersion was dependent on Hct. These results are similar, although 35% lower, than those found in a previous study in venules (1). CVVel had a mean value of 19% (15% was the value found for venules), and, similarly to venules, it was inversely related to cellular velocity and, as a result, varied across the radius of the vessel. The measured PO2 distribution within the arterioles exhibited a profile whose curvature was a function of the Hct, with a greater curvature near the vessels wall (from the centerline) as hemodilution progressed. Comparison of our experimentally determined PO2 profile with theoretical predictions by Kobayashi et al. (7) based on the analysis oxygen transfer in blood in laminar flow showed very similar values and profile shape. Figure 4 shows a plot of the theoretical PO2 profile for arterioles at a mean velocity of 5.0 mm/s, 1.0-mm axial distance, and centerline PO2 of 60 mmHg compared with our experimental results normalized to the same centerline PO2.
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In these experiments, RMSDev did not change after L1 but was significantly reduced after L2, a reduction that may be explained by the tendency of RMSDev to increase with cellular velocity and with Hct (2). The fact that RMSDev remained constant from control to L1 indicates that positive effect of increased velocity is counteracted by the negative effect of reduced Hct. The reduction of RMSDev after L2 indicates that the hydrodynamic interaction between cells decreases as Hct decreases, a finding that was paralleled by the significant decrease of SD (representing the variability on radial position for each cell) after L2 compared with the control and L1 values.
SD has the tendency to correlate positively with Hct and negatively with cell velocity (1). Therefore, in view of the increased velocity and reduced Hct after L1, the reduction in SD is not statistically significant compared with the control values. Given the similarity in mean velocity at control and L2, the reduction in SD found after L2 should be due to the reduced Hct, indicating that Hct has a stronger effect than velocity. The effect of the magnitude of the velocity on the variations in cell velocity is further demonstrated by the observed changes in CVVel, which decreased slightly after L1 but not after L2.
Comparing our results with those found in venules (1), the values of SDVel and CVVel for arterioles are 40% higher and the values of SD of radial position are 15% lower. This latter result, given that the velocity and geometrical parameters are similar for venules and arterioles, indicates that the estimates of DRBC are comparable.
RBC diffusion and oxygen diffusion. As indicated by Eq. 3, DRBC increases with the square of RMSDev. Accordingly, DRBC was significantly reduced after L2 compared with control and L1. Several investigators (1) have proposed that the shear-induced particle diffusion has an important effect in the effective diffusion coefficient of oxygen, an effect demonstrated experimentally by Diller et al. (3). This work was carried out in a 300-µm-diameter oxygen-permeable tube at various shear rates and entrance levels of oxygen blood saturation. The enhancement of oxygen diffusion is primarily due to the motion of RBCs, which hold a large amount of hemoglobinbound oxygen (compared with plasma). When this motion is in the direction of the oxygen gradient, there is a concomitant increase in oxygen transfer.
The value of oxygen diffusion measured by Diller et al. (3) under optimal conditions of shear rate enhancement and partial RBC desaturation at shear rates commensurate with those prevailing in the microvasculature (220 s–1) was 3.6 ± 1.4 x 10–5 cm2/s, which is a factor of two greater than the accepted value for oxygen diffusion in blood (1.4 – 1.6 x 10–5 cm2/s) (8). Given this result, it is apparent that although RBCs present specific diffusional properties, even in the conditions of high shear rate and blood flow velocity characteristic of arterioles, the effect of this phenomenon is not as significant in facilitating oxygen exit from the column of blood as the effect due to diffusion across the laminar layers of flowing blood.
The two-step isovolemic exchange with Dextran 70 to a final Hct of 16–18% reduces the radial displacement and variation in velocity of RBCs in arterioles, reduces the particle diffusion coefficient of RBCs, and may also reduce to same extent the effective diffusion coefficient of oxygen and other solutes in plasma, because augmentation of oxygen diffusion by shear-induced diffusion of RBCs is maximal at the control Hct. Thus, at reduced Hct levels, the oxygen delivery capacity of blood may also be reduced by the decreased particle-induced diffusion augmentation in the plasma layer, as evidenced by the tendency of the intraluminal PO2 profile to become more peaked at the centerline and the plasma layer to become wider. The implications of these results for the rate of oxygen transfer from the blood column into the vessel wall cannot be fully assessed by these techniques because this is specifically dependant on the oxygen content of blood in the plasma layer and therefore on the Hct in this region.
The vessel wall gradient (i.e., difference in PO2 across the arteriolar wall) found in the present study averaged 12.0 ± 5.2 mmHg for control as well as hemodiluted arterioles. This is a comparatively large difference in PO2, which in principle could explain the large rate of oxygen exit if it were representative of the gradient within the arteriolar wall tissue, a conjecture that is plausible because it implies a large rate of oxygen consumption within the arteriolar wall, which is compatible with the aforementioned large rates of oxygen exit from the arterioles. The converse, in which this gradient develops primarily within the plasma layer adjacent to the endothelium, is less likely because in this case the large gradient is representative of a significant resistance to oxygen diffusion thus negating the measured rates of oxygen exit. These conclusions may in part be affected by the nature of the phosphorescence emission measurement, which to some extent integrates light along the optical path. This integration would equally affect intra- and extraluminal measurement carried at the wall tissue interface, where both PO2 values may be somewhat higher if the effect of the low PO2 in the overlying and underlying tissue is eliminated. Thus although this effect would significantly affect the measured PO2 difference across the arteriolar wall, it may cause an underestimation of PO2 near the blood tissue interface, evidencing a departure from the profile computed by Kobayashi et al. (7) and a more pronounced effect due to the effect of shear-enhanced diffusion.
The present study was carried out under pentobarbital anesthesia, a condition that was analyzed in the study of Kerger et al. (6), which showed a slight reduction in microhemodynamic parameters (capillary RBC velocity was 75% of baseline levels) and microvascular oxygen tension distribution 30 min after a light anesthetic plane was achieved. Presumably, if the study was done in the awake state, the blood flow velocity in the arterioles might be 25% greater; however, the RBC dispersion should not change because we did not find a relationship between RBC dispersion and flow velocity. It should be noted that if there were anesthesia-related effects, these would be common to baseline, L1, and L2 determinations.
Pentobarbital is known to inhibit mitochondrial complex I activity, which might influence vessel wall oxygen consumption. Therefore, the vessel wall gradient measured in the present study may underestimate the value of this parameter in awake conditions, as shown in the study of Intaglietta et al. (4), who found that the wall gradient, and presumably oxygen consumption by the vessel wall, was on the order 18 mmHg, which is 50% higher than that found in the present study, i.e., 12 mmHg.
In conclusion, analysis of the dispersion of RBC positions as the flow in arterioles in conditions of normal Hct and hemodilution shows a variability in the trajectory over its path length on the order of ±1.5 µm. This variability may enhance to some extent the diffusion of oxygen in blood. However, this effect is not evidenced by changes in the intraluminal oxygen concentration profile as shown by the intra-/extraluminal distribution of PO2 compared with that calculated from theoretical considerations for normal Hct. This study indicates that the comparatively large rates of oxygen exit found in arterioles do correspond to large oxygen gradients at the blood tissue interface that develop primarily within the vessel wall, where oxygen consumption is possible, rather than in the plasma layer, where the large gradients would be indicative of a large resistance to the diffusional exit of oxygen.
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ACKNOWLEDGMENTS |
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GRANTS
This study was supported by National Heart, Lung, and Blood Institute Partnership Grant R24-HL-64395 and Grants R01-HL-62318 and R01-HL-62354 (to M. Intaglietta as Principal Investigator).
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FOOTNOTES |
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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.
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REFERENCES |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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This article has been cited by other articles:
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  P. Cabrales, A. G. Tsai, P. C. Johnson, and M. Intaglietta Oxygen release from arterioles with normal flow and no-flow conditions J Appl Physiol, May 1, 2006; 100(5): 1569 - 1576. [Abstract] [Full Text] [PDF]
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