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1Biomedical Engineering Program, Arizona Health Sciences Center, Tucson 85724-5084; and 2Department of Physiology, College of Medicine, The University of Arizona, Tucson, Arizona 85724-5051
Submitted 6 November 2003 ; accepted in final form 7 January 2004
| ABSTRACT |
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endothelium; residual distension; interstitial fluid volume; hydration
Previous studies have been conducted on fluid motion through artery walls (5), usually by varying hydrostatic pressure and allowing transient viscoelastic effects to subside. Arterial hydraulic conductance (Lp), a characteristic parameter of convective fluid motion, has been measured at different steady-state pressures in arteries (5, 8). However, in vivo, pulsatile pumping of the heart causes cyclic changes in arterial transmural pressure, creating rapid shifts in arterial wall stress, possibly changing wall transport properties and vessel transmural flow permeability.
In this study, vessels were examined that were initially subjected to steady pressure and then, subsequently, a pulsatile pressure was superimposed. Although this model differs from real arteries, such a study is useful for three reasons. First, diagnosis of the mechanics of arteries, specifically, which structures are more affected by pulsatile pressures versus steady pressure. In this case, studying the transition from steady to pulsatile pressure could be of great use in determining which wall structures are changed as the artery settles into a pulsatile regime. Second, physiologically, this study may be of interest with regard to smaller arteries and arterioles operating in the region in which pulsatile pressure becomes damped into steady pressure, dependent on the degree of constriction of arterioles further upstream. It is conceivable that as the upstream vessels experience vasodilation or vasoconstriction, the vessels further downstream may also experience a transition from steady to pulsatile pressure, or vice versa, along all, or part of, their length. Multiple animal in vivo preparations in frog, cat, and rat arterioles as small as 40 µm (29) have experimentally verified the presence of pulsatile flow (20, 24, 35), likely depending on the resistance of upstream arterioles. For example, experiments in the cat omentum have demonstrated a pulsatility of ±15 mmHg in 40-µm-diameter arterioles downstream of the abdominal aorta (20). Finally, the reapplication of pulsatile pressure may give further insight into reperfusion injury in vessels that have been occluded and then reperfused. Many molecules thought to cause injury in such situations, such as oxidized low-density lipoprotein (LDL), require convective transport into artery walls because of their size. Therefore, understanding how initial filtration is affected by reestablishment of pulsatile pressure could be important.
Within the artery wall under pulsatile pressure, complex pressure gradients may occur that alter transmural fluid flux direction (23). Wall stress variations may affect both the intima and the media. Regarding the intimal response to periodic mechanical stress, Rosales and Sumpio (31) noted transient changes in inositol trisphosphate and diacylglycerol, over a period of seconds, in endothelial cells stressed cyclically. Diacylglycerol and PKC [which is activated by calcium and diacylglycerol (31)] increase endothelial permeability. With regards to the media, substances that are produced by the endothelium in response to pulsatile stretch may affect arterial tone. For example, nitric oxide, endothelial-derived hyperpolarizing factor, and prostaglandin I2 are vasodilators that are produced by the endothelium in response to cyclic stretching (13). In addition, pulsatile stretch and oscillatory flow through the artery wall stimulate endothelial cells to produce endothelin-1, a vasoconstrictor (30). Results from a previous study (3) suggest that the tone of arterial muscle cells may affect the transport properties of the artery wall. The smooth muscle cells themselves may also produce vasodilators. Three-dimensional modeling has revealed that flow through fenestral pores in the internal elastic lamina creates shear stresses on subjacent vascular smooth muscle cells on the order of 1 dyn/cm2 (36), which can increase their synthesis of nitric oxide (17, 40) and prostaglandins (1, 40). These findings indicate that arterial transmural fluid flux may be modified by the characteristics of the applied intravascular pressure.
When measuring rates of fluid filtration in the artery wall under pulsatile pressure, it is essential to simultaneously monitor arterial inner diameter; otherwise, extra fluid entering the vessel lumen, as a result of a residual distension, will be counted as filtration, and thus the volume of fluid entering the artery wall will be overestimated. Residual distension can be defined as any measurable, sustained increase in arterial diameter caused by hysteresis in the pressure and diameter relation (creep). This hysteresis may have multiple causes, such as alterations in vascular tone, or in stretching of other structural components of the wall. To make an accurate measure of residual distension, a precise noninvasive technique must be used. For example, low-coherence reflectometry has been used for geometrical measurements on retinas and ocular structures (19). Extending low-coherence reflectometry to tomographic systems produced optical coherence tomography (OCT) (19). OCT has captured detailed images of stents and layered structural details in the intima and media in porcine coronary vessels that cannot be resolved by intravenous ultrasound (38). OCT has imaged vessels in skin of small animals with micrometer accuracy, forming cross-sectional images to find average blood vessel depth and luminal diameter (10). Therefore, OCT was used in this study to monitor arterial inner diameter throughout each experiment.
| MATERIALS AND METHODS |
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Surgery. Carotid arteries were exposed and any branches were ligated. The vessels were then cannulated at both ends, without allowing arterial pressure to fall, and perfused with PBS (4.0% bovine serum albumin, pH 7.4) containing trypan blue dye to check for leaks. Next, the stopcock attached to the distal cannula was closed, and the pressure was adjusted to 40 mmHg. The proximal stopcock was then closed, and the artery was kept warm (37° C) and moist with PBS. The fluids perfusing and surrounding the artery contained the same albumin concentration (4.0%) (39). Tedgui and Lever (39) have studied albumin concentration gradients in artery walls with equal concentrations of isotopically labeled albumin at the luminal and adventitial sides. In these experiments, the eventual concentration profile, after 90 min, was fairly uniform throughout the artery wall (at
6% of the perfusate/suffusate concentration). Thus there is a net tendency for water flux to be directed outward from the center of the wall, due to the colloid osmotic pressure difference of
20 mmHg (25). Although the colloid osmotic fluid flux toward the lumen wall opposes the hydrostatic fluid flux, the former flux is considerably smaller than the latter.
The artery was excised, and the original physiological length was maintained with a stainless steel holder clipped to each cannula. The cannulae were attached to closed stopcocks to maintain artery pressure, and the artery was connected to a rig and preconditioned by repeatedly pressurizing and depressurizing between 10 and 100 mmHg, following a previously established procedure (7). An air bubble introduced into a length of tubing attached to the artery (Fig. 1A) was used to measure the artery Lp under steady pressure, following a previously established procedure (7). With the use of this technique, a step change in pressure is imposed on the arterial lumen and the bubble undergoes a rapid displacement consistent with filtration through, and distension of, the artery wall. After a few minutes, the bubble then moves with a constant velocity corresponding to the transmural fluid filtration rate, which then is used to obtain Lp (see Eq. 1 below). The steady state Lp was measured in each vessel used in this study before application of the pulsatile pressure pulsations.
Pressure pulse creation. Pulsatile pressure was created with a Harvard Apparatus pump (model 1421, Pulsatile Blood Pump). The pump acted on a recirculating loop that branched to a smaller diameter tube connected to the artery, creating a high resistance branch with oscillatory pressure without net fluid flow (Fig. 1A). A Viggo-Spectramed pressure transducer was attached to the cannula at the other end of the artery, and the outlet was closed. Baseline pressure was set via an attached pressure reservoir and sphygmomanometer bulb, and a calibration curve for the pressure transducer was created at the start of the experiment. Next, the Harvard pump was activated, and 6 sets of 5-pulse trains, followed by 6 sets of 20-pulse trains at 60- and 80-mmHg baseline pressures at a frequency of 1 pulse/s, were applied. Therefore, there was a period of steady, baseline pressure, followed by the pulse train, and then a return to steady pressure before the next pulse train (allowing the OCT files to be saved, the OCT system to be reset, and, if necessary, the camera position to be changed to capture the bubble motion). The duration of the steady pressure period between pulse trains was estimated to be 1020 s. Data on the fluid flux into the artery during these interim periods were not obtained. The reason that six 5-pulse trains were used at the beginning of each experiment was because preliminary experiments showed that 5-pulse trains optimized the number of runs available during the initial 30-s period. The experiments were continued with 20-pulse trains rather than 5-pulse trains because initial tests showed that by this time the filtration rate was not rapidly changing and so did not require such frequent monitoring.
Figure 1B shows a typical 5-pulse train. Synchronized data outputs were recorded from the transducer and imaging system throughout each pulse train. The bubble oscillated back and forth with each pressure pulse and was often shifted toward the vessel after passage of the pulse train. Each pulse train was videotaped to record the time and position at which the oscillatory bubble motion stopped when the pulse train was over, so as to determine the total time of oscillatory motion and shift from the prepulse position. This shift arose from the sum of any residual arterial distension and the fluid filtered from the artery lumen. Thus, to determine the fluid loss from the arterial lumen, it was necessary to measure the residual distension. Predicted fluid loss by filtration from the steady-state calculation was found using the following equation (27)
![]() | (1) |
is the time-averaged transmural pressure, and t is duration of oscillation.
The duration of the oscillatory motion was used in the above equation to ensure that a direct comparison is made between the predicted fluid lost and the experimental fluid lost over the same given time interval. The time-averaged pressure is equal to the sum of the baseline pressure plus the time-averaged value of the superimposed pulsatile pressure acting on the vessel over the duration of oscillation. The "cumulative volume" referenced in Figs. 3 and 4 is the summed volume, either experimental or predicted (steady-state) volume, over time. For example, experimental cumulative volume at 20 s is the sum of the experimental volume values at 5, 10, 15, and 20 s. The time scale in Figs. 3, 4, 5, 6, 7 represents the integrated duration of the pulse trains themselves; 5 pulses are one 5-pulse train, lasting
5 s. Ten pulses are the sum of two 5-pulse trains, such that the artery is under a total of 10 s of pulsatile pressure.
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Measurement of residual distension. OCT is an imaging technique using back-reflected infrared light to form depth-resolved images, analogous to the ultrasound technique. In OCT, near-infrared, short-coherence source light is combined with an aiming beam and then split into two beams; one-half of the light goes to a reference arm and one-half goes to a sample arm to image the tissue sample. Light entering the tissue back reflects when refraction index mismatches occur at tissue boundaries and internal structural interfaces (19). The light back reflected from the tissue recombines with light from the moving reference arm and, due to the difference in the path length between two beams, interferes by the Doppler effect. This interference reflects structural changes in the tissue. Interference only occurs when the optical pathlength of the light in the reference and sample arms is within a coherence length of the light source, so back reflections from a select depth in the sample can be measured, with one retroreflector period corresponding to a single A-scan or measure of back reflectance versus depth. Thus the detector of the recombined light produces a complicated output due to intensity changes in the received signal as structural interfaces are traversed. The image is then processed by the OCT computer software to reduce noise, and every point on the scan is assigned a grayscale pixel value. In this way, an image of the artery wall, at a single point on the artery length, is obtained at each sampling period (0.1 s) (10). From these scans, the arterial inner diameter can be measured at a given time point using NIH Image computer software.
A similar OCT system has been described previously (21). In the present experiment, the short-coherence length source was a superluminescent diode with a 1,290-nm center wavelength and a 49-nm bandwidth allowing for a 16-µm coherence length (and thus axial resolution) in air. Assuming a tissue index of refraction of 1.4 (11), the tissue axial resolution was
11 µm. The sample arm light was focused to a 15-µm spot on the tissue. The aiming beam was used to align the sample so that the maximum artery diameter was imaged. A-scans were taken at the same lateral location beginning
2 s before pressure pulse initiation and continued until
5 s after the pulses stopped. The two-dimensional OCT images are m-scans; i.e., functions of depth and time. The OCT image time resolution was 100 ms (10 A-scans/s).
A typical 20-pulse train image is shown in Fig. 2. Depth is plotted on the ordinate (4.2-mm optical path length full range), whereas the A-scan (time) is plotted on the abscissa. The dark bands are the upper and lower walls and the oscillations demonstrate changes in arterial wall diameter in response to the pulsatile pressure. Volume displaced by residual distension (Vres) is given by the following equation
![]() | (2) |
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The estimated residual increase in artery diameter required to create the observed shift in bubble position was calculated to be 90 µm, which is within the 11-µm resolution of the OCT, assuming an arterial inner diameter of
2.0 mm. Therefore, OCT could be used to determine whether or not an apparent increase in filtration was merely due to residual distension of the artery.
Statistics. The mean volume accounted for by residual distension, after a given number of pulses, was compared with the corresponding mean experimental volume (averaged over the 5 arteries) using a Student's t-test (P
0.05) (in cases in which the Kolmorogov-Smirnov test showed normality). When normality was not found in a population, groups were tested using Wilcoxon's rank sum test (Mann-Whitney rank-sum test). Error bars represent SEs. The experimental volume corrected for residual distension, averaged over the six 5-pulse values between 0 and 30 pulses, was compared with the corresponding steady-state value using the Student's t-test (P < 0.05) after assuring a normal distribution of the values using Kolmorogov-Smirnov test. The 0- to 30-pulse mean experimental value was also compared with the average of the experimental values obtained between 50 and 150 pulses; the latter parameter being divided by 4 to account for the fact that these were 20-pulse trials rather than 5-pulse trials.
| RESULTS |
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Figures 3 and 4 show the cumulative experimental volume (experimental volume is defined hereafter as the volume entering the artery, as measured from the bubble shift forward after a pulse train minus the volume accounted for by the residual distension) compared with the cumulative steady-state predicted volume with respect to time. Where graphs are labeled either 60 or 80 mmHg, this refers to the baseline pressure used experimentally. The volume plot for 60-mmHg baseline pressure (Fig. 3) shows an initial rapid increase in filtration volume during the first 30 s after the onset of pulsatile pressure (30 s =
30 pulses) that far exceeds that predicted for steady pressure. After 30 s, the plot becomes more linear and the slope is reduced but still exceeds that predicted for steady pressure by threefold (3.9 x 105 vs. 1.3 x 105 cm3/s). These slopes were obtained using linear regression analysis of data from 50 to 150 pulses. The change to a lesser slope after 30 s implies that there is less volume accumulating over time and hence a reduced fluid flux. The volume plot for 80 mmHg (Fig. 4) contains the results of trials performed on five separate arteries instead of six arteries due to experimental difficulties with the recording of the bubble movements during one of the experiments. Individual averages at different time points may contain <5 or 6 runs due to difficulties with either failure of the OCT system to record pressure or distension files or difficulties with achieving 6 exact sets of 5 or 20 pulses. At 80 mmHg, a similar plot is obtained as for 60 mmHg except that the reduction in slope (at later time points) appears to be more gradual and is not clearly associated with a particular number of pulses. The slope between 90 and 150 pulses, where linearity is achieved, is 7.3 x 105 cm3/s compared with the slope of 1.4 x 105 cm3/s for steady pressure (a slightly greater than the 5-fold increase).
The graphs in Figs. 5 and 6 show the individual experimental volumes, corrected for residual distension, at each pulse train as well as the individual steady-state predicted volumes for baseline pressures of 60 and 80 mmHg, respectively. Error bars have been removed for clarity and can be found in Table 1. These graphs are noncumulative, representing the respective fluid volumes at each individual 5- or 20-pulse train (i.e., a "snapshot" of the fluid volume associated with each pulse train). Both graphs show that the experimental volumes are significantly increased compared with the steady-state predicted volumes. In addition, the mean average experimental volumes between 0 and 30 s are significantly greater than those between 50 and 150 s (when the latter volumes are divided by 4 to account for the longer pulse time) at both 60 and 80 mmHg. This means that the increase in filtration observed between 0 and 30 s is a transient increase and will be referred to as the initial, transient "burst" of filtration.
Figure 7 compares the total experimental volumes of fluid measured in experiments to the volume accounted for by residual distension of the arterial wall at 80-mmHg pressure. Because the first 6 sets of 5 pulses represent the initial transient excess filtration (before 30 pulses), excluding later runs should not compromise the results. At 80-mmHg pressure after 5 pulses, the arteries mostly showed contractile behavior, although, rarely, some arteries displayed distension. After 20 pulses, nearly all of the arteries examined experienced a contraction of varying magnitude. There were significant differences between the experimental volume and residual distension volume at 80-mmHg pressure at the initial portion of the transient period (at the 5- and 10-s values) and at the end of the period (30-s value), indicating that it is possible to distinguish between the two quantities. Similar results may be demonstrated for the 60-mmHg baseline pressure (not shown).
| DISCUSSION |
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1 s. These mechanical changes in arteries observed with the transition from steady to pulsatile pressure are important because they may alter arterial wall macromolecular transport properties (15, 16). An example in which such conditions might be encountered in vivo is when arteries become occluded, or partially occluded. After relief of the occlusion, a pulsatile pressure is suddenly superimposed on a steady pressure, and our experimental findings predict that there will be a subsequent transient burst of filtered fluid. A main cause of reperfusion injury has been described as a burst of reactive oxygen species (22), which might correspond to the burst of filtration found in this study. The transient burst could serve to drive these toxic agents deeper into the artery, thereby causing more injury, and a more inflammatory-like response, as well as convectively moving larger molecules, such as oxidized LDL, which has been implicated in the pathogenesis of atherosclerosis (32).
Two to three minutes after the onset of pulsatile pressure, at 60 or 80 mmHg,
7 to 9 times the predicted steady-state filtration volume had passed through the endothelium into the artery wall. It might be expected that such a large transendothelial fluid transfer would trigger a structural change in the media, either to facilitate absorption of the fluid or to lower wall resistance to allow fluid passage through the wall. Wall filtration could be caused by altered colloidal osmotic pressure (COP). The magnitude of such filtration is limited by the concentration of the perfusate in the artery lumen. Plasma has a COP of 28 mmHg (25), well below the hydrostatic pressures of 60 and 80 mmHg. Therefore, even if pulsatile pressure maximized interstitial COP (at 28 mmHg), this would not account for the increase in fluid filtration. In these experiments, the COP was <28 mmHg because the physiological solution used was 4.0% albumin. So the burst of filtration must be true filtration and not due to simple changes in the artery wall osmotic pressure gradient.
Another possible cause of the transient burst of filtration could be alterations in fluid shear stress at the endothelial surface of the artery. The applied pulsatile transmural pressure generates pulsatile fluid flow in the vessel, which results in unsteady shear stress. Fluctuations in shear stress might alter the transport properties of endothelium. The variations in shear stress were estimated assuming Poiseuille flow in a cylindrical artery, using approximate values for rabbit carotid arteries (APPENDIX). The fluctuation in shear stress was found to be 0.35 dyn/cm2. This value is much lower than physiological levels of fluctuating wall shear stress in arteries and is therefore unlikely to result in alterations in endothelial transport properties.
To distinguish between fluid entering the artery wall and fluid causing a residual distension of the vessel, it was necessary to use OCT. This study has shown that OCT can resolve the arterial walls and measure small changes in distension (distension corresponding to fluid volume changes <0.0005 cm3) in those walls over time. OCT allows us greater resolution in the tissue than ultrasound techniques, better depth-resolved imaging (compared with video or photography), and better depth of image and longer working distance than con-focal or deconvolution microscopy (12). However, it was not possible to measure whether the excess fluid lost through the arterial intima was retained in the arterial wall or filtered through the media/adventitia to the outer surface (i.e., thickness changes in the wall of the order of those corresponding to retention of fluid in the wall could not be resolved). Using the maximum average value obtained for the volume of fluid lost (0.0035 cm3), one can calculate that the wall thickness should increase by
23 µm, which is close to the borderline of the OCT resolution (presuming incompressible fluid and cylindrical artery geometry). Most values of experimental volume were lower than 0.0035 cm3, and so OCT does not have the ability to resolve residual changes in wall thickness or to define separate layers within a pulsing artery wall.
The mechanism by which pulsatile pressure causes greater fluid influx initially and possibly accumulates fluid overall in the wall is not known. Hypothesizing, there may be a transient increase in the number or size of endothelial junctional gaps causing the response depicted in Figs. 3 and 4. Monolayers of cyclically stretched cultured endothelial cells show transiently increased permeability (31), but no such data are available for arterial endothelium in vivo. Physiologically, endothelium accounts for a considerable fraction of the total resistance to flux of water through the artery wall, at least in the aorta (39). Pressure-induced oscillating stretch of endothelial cells also affects production of factors such as endothelin-1 or autocorticoids (30), which could effect the permeability of the artery wall by causing contraction of the smooth muscle cells, thereby creating medial density changes. Although an increase in endothelial permeability may be explained by biochemical responses to the onset of pulsatile pressure, it is hard to account for the fact that the major part of this response lasts only for
2 min or less. For example, endothelial recovery from permeability changes after treatment with histamine, or other mediators such as bradykinin, requires
30 min, with the limitation being the ability of the cells to reform cell-to-cell junctions and remodel their cytoskeletons accordingly to close junctional gaps (4). Therefore, it would be difficult to attribute the behavior seen in Figs. 3 and 4 solely to endothelial recovery or remodeling. It is more likely that the attenuation of the initial burst of filtration is produced by completion of hydration of the arterial media. It should be noted, however, that many arteries in other species, including humans, contain vasa vasora and lymphatic vessels in the outer media and adventitia. The vasa vasora and lymphatic vessels could participate in the exchange of fluid between the circulating blood and the artery wall, assuming that the artery was not excised, as in the present study. If the artery were equipped with functioning vasa vasora and lymphatic vessels, there may be no need to invoke medial hydration as a mechanism for attenuating the burst of filtration produced by the onset of pulsatile pressure.
However, in the case of an excised artery, a remaining question is where in the artery the excess fluid is accommodated. One possibility would be that medial smooth muscle cells imbibe the extra fluid. However, because cells have relatively small Lps (26), this is unlikely. Another possibility could be that changes in the tone of the smooth muscle cells, induced by pulsatility, alter the configuration of the extracellular space so as to increase the available space for water. Previous experiments have shown that arteries treated with agents producing smooth muscle cell contraction or relaxation, the available space for water is not significantly altered (3). A third possibility is that there must be another wall structural component hydrating after the onset of a pulse pressure. The most likely remaining components explaining this fluid loss are the extracellular matrix and connective tissues that form the interstitium.
Guyton (18) described arterial wall "tissue" spaces as an interlacing mat of collagen fibers with the spaces between the fibers filled with a mucopolysacharide gel hydrated with trapped extracellular fluid. This mucopolysacharide gel, or "ground substance," is generally resistant to flow through interstitial spaces but does allow for small molecule diffusion. Excess fluid in these spaces can expand this ground substance and disrupt the gel reticulum, allowing for there to be two phases in the gel: a fluid-poor phase consisting of the gel reticulum with "trapped"fluid and a "free"fluid-rich phase that occurs when excess fluid or pressure breaks up the gel reticulum and forms free fluid pockets or eventually flow channels in the tissue spaces (18). Evidence for such inhomogeneities is provided by electron microscopic images showing two kinds of tissue spaces: spaces free of protein and spaces with protein "tunnels" containing interstitial fluid (8). When describing pressure effects on the volume of interstitial gel spaces, authors have expressed the results graphically with a compliance curve in terms of interstitial pressure versus interstitial fluid volume (IFV), which in all studies takes the form of a sigmoid-shaped curve (2). Whereas authors disagree over the exact values of interstitial pressures involved, they agree that a low IFV corresponds to a dehydrated tissue with low compliance. Then, there follows a high (theoretically; infinite) compliance phase representing an initial "filling" or rehydration of the tissue (18), followed by a third lesser compliance phase when the tissue has filled and is now under tension (18). Auckland (2) describes this latter state as "reduced compliance due to restriction by fascias." Figures 3 and 4 likely show a similar initial filling phase followed by a restricted phase afterward.
From these previous studies, it appears that two effects, either singly or in combination, might provide a mechanism for our results. Increased strain, produced by the pulsatile pressure, may open up free fluid pockets in the ground substance, allowing for suddenly greater filling of the media. Such a mechanism could explain the results obtained at 60 mmHg. At higher pressure, more free fluid pockets may open, or perhaps flow "channels" could open in the mucopolysacharides, or at the interfaces of the connective tissue fibers and the ground substance. These channels would allow more fluid to enter the interstitium, and so at 80-mmHg baseline pressure the artery wall would take longer to saturate, explaining the time delay in the reduction of the slope of the plot.
Figures 3 and 4 imply that with initiation of a pulsatile pressure regime, the pressure change and its changes in filtration may interact more directly with the interstitium than theoretically predicted. A working hypothesis would be the following: although not observably edemic, the transiently increased filtration, after the onset of pulsatile pressure, strains the interstitial connective tissues and the ground substance, so that free fluid regions or channels form, perhaps resulting in regions of localized edema. The transiently increased filtration may also assist passage and accumulation of lipoproteins and free radicals into the interstitial fluid pockets, creating a source of chronic inflammation and tissue damage.
| APPENDIX: ESTIMATION OF PULSATILE WALL SHEAR STRESS |
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t)] cm, assuming a ±5.0% change in radius with pulsation, and the internal volume is approximately V = 0.02
[1 + 0.1 cos(2
t)] cm3. The volume flow rate at the end of the artery at which the pressure is applied is then equal to the rate of change of volume with time, and its maximum value is Qmax = 0.004
2 cm3/s. From well-known properties of Poiseuille flow, the maximum value of the wall shear stress, in time and space, is given by
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30 min after application of the stress to the cells. This time scale is almost 12 times longer than that involved in the transient filtration burst demonstrated in the present study. Therefore, activation of the endothelium by unsteady shear stress is unlikely to affect our experimental results. | ACKNOWLEDGMENTS |
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GRANTS
This study was supported by a National Aeronautics and Space Administration/Spacegrant Graduate Fellowship, National Institutes of Health (NIH) Predoctoral Fellowship HL-697352, and The University of Arizona Small Grants Program. NIH Small Animal Imaging Resource Grant CA-83148 supported the development of the OCT system.
| 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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