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Experimental Studies |
1 From the Department of Radiology, TC 2910K, University of Michigan Medical Center, 1500 E Medical Center Dr, Ann Arbor, MI 48109. Received April 23, 1998; revision requested June 10; revision received August 21; accepted November 25. Address reprint requests to R.O.B.
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Abstract |
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 TOP Abstract IntroductionMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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MATERIALS AND METHODS: An in vitro model that made use of a pulsatile pump, blood-mimicking fluid, and variable compliance and resistance was used to investigate the relationship between the RI and both vascular compliance and resistance.
RESULTS: In the absence of vascular compliance, the RI was independent of vascular resistance. With vascular compliance, the RI was dependent on vascular resistance and increased with increasing resistance. The higher the compliance, the more the RI was affected by resistance.
CONCLUSION: The RI is misnamed and should actually be called the "impedance index" because resistance and compliance interact to alter the Doppler arterial waveform. A greater understanding of this relationship may enable future studies that take both resistance and compliance into account to better detect pathologic conditions.
Index terms: Blood, flow dynamics, 961.12984 • Phantoms • Renal arteries, flow dynamics, 961.12984 • Ultrasound (US), Doppler studies, 961.12984 • Ultrasound (US), experimental • Ultrasound (US), physics
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Introduction |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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We hypothesized that vascular compliance (defined as the change in volume of a vessel with a change in pressure) is also a critical factor affecting the RI. Because vascular compliance varies from individual to individual (7–107–10;11, pp 77–124;12;13), if our hypothesis is true this variability may affect the relationship between the RI and vascular resistance. An in vitro model was constructed and experiments were performed to evaluate the dependence of the RI on both vascular compliance and vascular resistance.
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MATERIALS AND METHODS |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Flow Phantom
Pump and pump output tubing.—A pump (model 1421; Harvard Apparatus, Millis, Mass) supplied pulsatile flow through 
-inch (1.0-cm) inside diameter, 9/16-inch (1.4-cm) outside diameter vinyl tubing at fixed settings throughout the experiment: 60 strokes per minute, 10 mL per stroke, and a duty cycle (systolic fraction of the "cardiac" cycle) of 0.3. Because the pump output was very pulsatile without diastolic flow, the fluid-flow analogue of a resistive-capacitive circuit (18) was installed immediately downstream to the pump to alter the pump output waveform so that a baseline renal arterial RI of 0.60 could be obtained. The resistive-capacitive network was created by varying the position and degree of stenosis of variable clamps on two parallel lengths of gum rubber tubing (5/16-inch [0.8-cm] inside diameter, 7/16-inch [1.1-cm] outside diameter), 24 and 45 cm long (Fig 1).
Aortic, body, and renal branches.—After installation of the resistive-capacitive network, the descending aorta was simulated with 
-inch (0.6-cm) inside diameter, -inch (1.0-cm) outside diameter vinyl tubing. This tubing branched into the body branch, which was entirely composed of the same tubing as the aortic and renal branches. Needle valves (catalog number 6393-60; Cole-Parmer Instrument, Vernon Hills, Ill) near the ends of the branches simulated the total vascular resistances of the body and kidney. Initially, these valves were set so that the mean pressure was physiologic, with approximately 10% of pump output directed through the renal branch (the normal kidney receives approximately 10% of cardiac output [19]) and the remainder directed to the body. Once set at the beginning, the valve of the body branch was not readjusted throughout the remainder of the experiment. Mean renal arterial pressure increased only slightly as renal vascular resistance increased, varying from 71 to 98 mm Hg for all three runs together.
The proximal renal branch, from the aorta to the compliance segment, was composed of the same tubing as the aorta, through which Doppler US could be performed. Renal arterial pressure upstream to the compliance segment was measured with a pressure transducer (TRANSPAC IV; Abbott Laboratories, North Chicago, Ill) connected to a pressure monitor (model 78354A; Hewlett-Packard, Bad Homburg, Germany) (Fig 1). The remainder of the renal branch was composed of stiff polypropylene tubing (-inch [0.6-cm] inside diameter, -inch [1.0-cm] outside diameter) to simulate zero compliance as closely as possible. US could not be performed through this tubing, except for the following exceptions: (a) the region of interchangeable compliance (Fig 1) and (b) a 27-cm-long segment of vinyl tubing immediately proximal to the resistance valve that provided an insonation port when necessary (not shown in Fig 1). The polypropylene tubing was so stiff that it could not be perceptibly compressed by hand. It was bent to fit the model by softening it in near-boiling water and allowing it to cool and set in place. Flow through the body and renal branches returned to a common reservoir on top of a mechanical stirrer (Magnestir; Aloe, St Louis, Mo).
Interchangeable renal arterial compliances.—Arteries and rubber tubing have similar viscoelastic properties (20). The use of rubber tubes to simulate arterial compliance in hydrodynamic physiologic studies has been established (20–22). Two finite renal arterial compliances were simulated by using 61.6-cm and 7.0-cm lengths of -inch (0.6-cm) inside diameter, -inch (1.0-cm) outside diameter gum rubber tubing, with total compliance assumed to be proportional to length. The 7.0-cm-long segment thus had 11.4% (7.0/61.6) of the compliance of the 61.6-cm-long segment. The 61.6-cm length was selected by means of trial and error at baseline conditions (10.2% of pump output directed to the kidney) to provide just enough compliance, without use of excess tubing, to completely damp the input renal arterial RI to zero distal to the compliance (as occurs in vivo). Zero renal arterial compliance was simulated by using no rubber tubing.
Inlet lengths of tubing.—A flow perturbation (bifurcation, stenosis, tight turn, etc) transiently alters the flow profile for a variable distance, up to a maximal length known as the inlet length (11, pp 38–43). Because the inlet length for nonpulsatile, laminar flow is longer than the inlet lengths for other types of flow, this inlet length was used to ensure that our Doppler US measurements were performed in areas of stable flow. The inlet length for nonpulsatile, laminar flow is defined as L = 2kVr2/
, where L is the inlet length in centimeters, k is an experimentally derived constant with a value of 0.08, V is the mean velocity in centimeters per second, r is the tube radius in centimeters, and is the kinematic viscosity in stokes (square centimeters/second) (11, pp 38–43). The calculated inlet lengths were 1.7 cm for the renal artery and 17.1 cm for the aorta; the actual lengths used were 25 cm for the renal artery and 70 cm for the aorta.
Blood-mimicking fluid.—The model was filled with 1,500 mL of a solution with the mean viscosity of blood (2.5 cp [23]). The solution was composed of 35 mL of glycerol and 0.67 g of microparticles (Sephadex G-50; Sigma Chemical, St Louis, Mo) as ultrasound scatterers for every 100 mL of water (24). Green food coloring was used to tint the fluid so that air bubbles could be seen and eliminated from the nearly opaque, white tubing; air bubbles cyclically changed volume with the cardiac cycle and thus caused undesirable and unmeasurable compliance.
Method of Measuring Renal Vascular Resistance
The fluid-flow analogue of Ohm's law (P = QR, where P is the transstenotic pressure drop, Q is the volume flow rate, and R is the resistance) was not used to calculate vascular resistance. The reason was our data at 0% of pump output (Figs 2a, 2b, 3 [bottom waveform]), at which point flow pulsed into the renal artery during systole and flowed back into the aorta during diastole. If Ohm's law had been used, R = P/Q, and when Q = 0 (absence of bulk flow through the kidney), division by zero is impossible and the resistance is undefined. Therefore, we would have been unable to plot these data. To avoid this problem, we used the method of Norris and Barnes (5), who investigated the relationship between the RI and vascular resistance in an in vivo canine study. Once the compliance was set for each run, the only variable altered was the degree of stenosis of the renal resistance valve. Relative renal resistance was calculated as the ratio of the flow rate at increased resistance to the flow rate at baseline. This ratio decreased with increasing renal resistance because the amount of flow through the kidney decreased with increasing renal resistance. This ratio was zero and therefore able to be plotted (as opposed to the undefined resistance if Ohm's law had been used) when there was no bulk flow through the kidney.
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RIs were calculated by hand with calipers (Absolute Digimatic; Mitutoyo, Tokyo, Japan) according to the formula RI = (S - D)/S, where S is the height of the systolic peak and D is the height of the end-diastolic trough. All RIs were reported as the means of four consecutive waveform RIs. The largest possible Doppler scale was used to decrease measurement error. In several instances when the renal vascular resistance was very high (Fig 2b, 2c), renal arterial RIs could not be measured because the diastolic velocities were lost in the wall filter. (Adamson et al [25] also encountered this difficulty in sheep placentas.)
Validation That the Model without Gum Rubber Tubing Had Very Little Compliance
Vascular compliance is defined as dV/dP, where V is the volume and P is the pressure. Compliance is a dynamic phenomenon and could not be measured directly. Therefore, we used the following indirect method to determine if the model had appreciable compliance in the zero compliance mode. Vascular compliance, in conjunction with vascular resistance, causes the progressive damping of pulsatility as flow progresses from the highly pulsatile central arteries to the essentially nonpulsatile capillaries (14, pp 3, 295–296;15;16). Therefore, our model in the zero compliance mode (absence of a compliant segment of rubber tubing) can be assumed to have zero compliance if the RI in the proximal renal artery equals the RI in the distal renal artery just proximal to the resistance valve during maximal flow. Under these conditions, the upstream RI was 0.59 ± 0.02 (mean ± SD) and the downstream RI was 0.57 ± 0.01. Because the upstream measurements were not independent of each other (the downstream ones were not either), it was not possible to statistically prove that the upstream and downstream RIs were not significantly different; however, the RIs are so nearly the same that they indicate that the compliance of the model in the zero compliance mode was minimal and essentially zero.
Experimental Runs
Three experimental runs were performed: one with normal renal arterial compliance (61.6 cm of rubber tubing), one with low compliance (7.0 cm of rubber tubing), and one with zero compliance (no rubber tubing). With normal compliance, the initial renal flow rate was set by adjusting the renal resistance valve so that approximately 10% of pump output flowed to the kidney, with the same initial renal flow rate subsequently used at the beginnings of the other two compliance runs. (The renal flow rate was 0.774 mL/sec, and the body flow rate was 6.83 mL/sec; therefore, the percentage of renal flow was 0.774/[0.774 + 6.83] x 100% or 10.2%.) For all three runs, the initial renal arterial RI was set at 0.6 as measured on the display screen with the calipers of the machine. Subsequent measurement with manual calipers from hard-copy film images showed the initial RIs to be 0.61 ± 0.02 (mean ± SD), 0.58 ± 0.01, and 0.62 ± 0.02 for the normal, low, and zero compliance runs, respectively. For the normal compliance run, the renal resistance valve was then incrementally tightened, with the valve settings noted so that they could be used for the other runs, until the renal limb was completely occluded. Doppler waveforms were obtained from the aorta upstream to the renal artery and from the renal artery upstream to the compliance segment for each valve setting. The same procedure was followed for the low and zero compliance runs. Reynolds numbers indicated laminar flow throughout the cardiac cycle at all waveform measurement sites.
Statistics and Data Analysis
Aortic and renal RIs were obtained for each value of end-organ resistance for all compliance runs. The input aortic RI varied slightly during each run: from 0.15 to 0.20 for normal compliance, from 0.29 to 0.35 for low compliance, and from 0.61 to 0.68 for zero compliance. This variation in turn affected the renal RI independently of changes in renal vascular resistance. Therefore, it was necessary to correct for this effect. Such correction was performed in each run by multiplying each renal RI obtained at an elevated renal vascular resistance by the ratio of the aortic RI at that level of vascular resistance to the aortic RI at baseline. The following example illustrates the method: In the run with zero compliance, the aortic RI at baseline was 0.68. At the highest level of renal vascular resistance for which a renal arterial RI could be measured (the data point nearest the vertical axis in Fig 2c), the aortic RI was 0.61 and the nonnormalized renal arterial RI was 0.63. The normalized renal arterial RI was therefore 0.57 (0.63 x 0.61/0.68).
Normalized renal arterial RIs were plotted versus the percentage of pump output flowing through the kidney for each value of renal arterial compliance. Linear regression was performed to determine the slopes of the lines, and regression coefficients were compared with one-way analysis of variance to determine if the linear regression fits were significantly different from each other; a P value of less than .05 was used to indicate a statistically significant difference. For the zero compliance model, the 95% confidence limits of the data were calculated for the slope of the linear regression fit of the data to determine if the 95% confidence limits included zero. Percentages of pump output flowing through the kidney for the intersections of each regression line with an RI of 1.0 were determined to identify the threshold pump outputs (and hence the relative renal vascular resistances) for the appearance of reversed end-diastolic flow (Fig 2).
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RESULTS |
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DISCUSSION |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Adamson et al (25) and Morrow et al (26) progressively embolized the placental vasculature in sheep. The umbilical cord RI progressively increased as placental resistance increased. Reversed diastolic flow appeared at high placental resistance. These authors concluded that their findings were due to increased vascular resistance. Vascular compliance was not considered.
Reversed diastolic flow has been reported in cases of renal vein thrombosis in both transplants (27–31) and native kidneys (32). Increased vascular resistance was presumed to be the cause of the reversed diastolic flow. Vascular compliance was not considered.
The studies mentioned in the preceding three paragraphs are related in that RI changes were described and attributed to increased vascular resistance without consideration of vascular compliance. Recently, Saunders et al (33) performed a study in sheep and concluded that it is impedance (a combination of resistance and capacitance [compliance]), not resistance alone, that alters the Doppler waveform and the RI. We agree with their results; however, their study was not designed to allow compliance to be altered independently of resistance in a measurable way. Our study was performed with the compliance, as well as the resistance, varied in measurable ways to show the interrelationship between vascular resistance and compliance and the RI.
With zero vascular compliance, the renal arterial RI was independent of vascular resistance to the highest level of resistance that could be studied with our model. This level of resistance was high enough to reduce inflow into the renal artery to only 1.41% of pump output. (The renal flow rate was 0.110 mL/sec, and the body flow rate was 7.71 mL/sec; therefore, the percentage of renal flow was 0.110/[0.110 + 7.71] x 100% or 1.41%.) This result corresponded to a flow rate of only 14% of baseline (1.41%/10.2% [initial pump output into the kidney] x 100% = 14%) (Fig 2c). (The inability to measure RIs at higher resistances is explained later in this section.) Therefore, vascular resistance alone does not affect the RI.
Our results at normal and low compliance show that vascular compliance is necessary for vascular resistance to affect the RI. They also show that the lower the compliance, the lower the RI for the same degree of vascular resistance. This point is important because vascular compliance is not constant but varies in vivo with blood pressure, age, and medications (7–107–10;11, pp 77–124;12;13). For example, aortic compliance decreases by a factor of approximately three between the ages of 10 and 60 years in healthy individuals as part of the aging process (7) and by a factor of approximately five between normotensive individuals 20–24 years old and hypertensive individuals 71–78 years old (8). These compliance changes are within the compliance range of the normal and low compliance models in our experiment and therefore have the potential to produce substantial RI variability. If an individual has a substantially lower compliance than normal (such as a hypertensive elderly individual), this individual will have lower RIs for the same levels of vascular resistance than an individual with normal compliance and may have clinically important disease with increased vascular resistance but still have a "normal" RI. Our data illustrate this point: At a vascular resistance high enough to reduce volume flow (amount of pump output) into the kidney to 80% of baseline, the renal arterial RI was 0.72 with normal compliance but only 0.63 with low compliance; 0.72 exceeds a commonly advocated RI threshold of 0.70 for detection of renal disease (34,35), whereas 0.63 is in the normal range.
Our results at normal and low compliance also show, however, that for fixed compliance, the RI does increase with increasing vascular resistance. This result corroborates the results of prior studies, which showed the RI to increase with increasing vascular resistance. However, this result also shows that these studies were incomplete because they did not show that there is a different relationship to the RI for each degree of vascular compliance.
Our data also help explain the less than stellar results that have been reported with use of reversed diastolic flow to detect renal vein thrombosis. In native kidneys, the presence of reversed diastolic flow allowed prediction of renal vein thrombosis with a sensitivity and specificity of only 40% and 47%, respectively (32). Our results show that a greater degree of increased vascular resistance (flow to the kidney reduced to only 22% of baseline) is needed to produce reversed diastolic flow if the compliance is low than if the compliance is normal (flow to the kidney reduced to 56% of baseline) (Fig 2a, 2b). Therefore, a degree of partial thrombosis sufficient to produce reversed diastolic flow in an individual with normal compliance may not produce it in an individual with lower compliance. Our results also show that once main renal vein thrombosis occurs, reversed diastolic flow disappears after less venous collateral flow has developed at low compliance than at normal compliance. The reason is because a higher resistance is needed to produce reversed diastolic flow at low compliance than at normal compliance. Thus, as collateral veins develop, a resistance level is reached at low compliance at which reversed diastolic flow disappears but the resistance would still be high enough at normal compliance for reversed diastolic flow to be present. Finally, our results also help explain why the presence of reversed diastolic flow is so poorly predictive of renal vein thrombosis in renal transplants. In one study (29), only four of 25 renal transplants with reversed diastolic flow demonstrated renal vein thrombosis; almost all of the remaining transplants demonstrated acute tubular necrosis or rejection. As long as acute tubular necrosis or rejection produces a high enough resistance to sufficiently interact with the compliance that is present, the increased resistance that is caused can also produce reversed diastolic flow.
One limitation of our model is that it only mimics in vivo conditions. For instance, it does not simulate the autoregulatory ability of the kidney. However, autoregulation changes renal arterial resistance, and even if a kidney is autoregulating, the relationship we have shown between resistance and compliance still applies. Another limitation is that RIs could not be measured in the zero compliance model at the two highest resistances used in the low and normal compliance models. These resistances were the resistance required to reduce pump output flowing into the kidney to approximately one-eighth of the initial value and the resistance required to completely occlude flow. The former resistance was that high enough to reduce the renal flow from a baseline of 10.2% of pump output to 1.19%. (The renal flow rate was 0.094 mL/sec, and the body flow rate was 7.78 mL/sec; therefore, the percentage of renal flow was 0.094/[0.094 + 7.78] x 100% or 1.19%.) For this resistance, the diastolic velocity was so low at zero compliance that it was lost in the low wall filter and could not be measured. When the renal limb was completely occluded at zero compliance, there was no appreciable flow into the renal artery; thus, it was impossible to measure the RI. We believe that the latter observation does not actually constitute a limitation but reflects what should be expected. In a parallel-vessel network, if one of the vessels is noncompliant (completely stiff) and the distal end is occluded, flow cannot enter that vessel because the fluid is incompressible and the vessel is not free to expand; thus, the flow must be diverted to the other limb of the network. (This situation is in contrast to that of a kidney with a compliant artery and a completely occluded venous system. Flow can enter the artery during systole because the artery expands, and flow passes retrogradely back into the aorta during diastole as the artery contracts or relaxes.) Although the effects of the two highest levels of resistance on the renal arterial RI in the zero compliance model could not be studied, we believe it is extremely unlikely that the trend of the data altered appreciably at resistances higher than we could study.
In summary, our results are important for several reasons. First, they show that the RI is altered not by vascular resistance alone but by the combination of vascular resistance and vascular compliance. This result agrees with the conclusions of Saunders et al (33). The RI is therefore inappropriately named and should be called the "impedance index" instead. Second, because vascular compliance varies from individual to individual, the RI may therefore vary from individual to individual even if the vascular resistances in these individuals are the same. Hence, our results may also help explain the variable results reported in the literature when a mean RI threshold determined from a population was used to predict disease in an individual.
Practical application: A greater understanding of the combined role of vascular compliance and resistance in altering the Doppler arterial waveform may enable future studies that take both factors into account to better detect pathologic conditions.
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Acknowledgments |
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Footnotes |
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Author contributions: Guarantor of integrity of entire study, R.O.B.; study concepts and design, R.O.B.; definition of intellectual content, R.O.B., J.M.R.; literature research, R.O.B.; experimental studies, R.O.B.; data acquisition, R.O.B.; data analysis, R.O.B., J.M.R.; statistical analysis, J.M.R.; manuscript preparation, R.O.B.; manuscript editing and review, R.O.B., J.M.R.
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