Importance of Pressure Recovery for the Assessment of Aortic Stenosis by Doppler Ultrasound
Role of Aortic Size, Aortic Valve Area, and Direction of the Stenotic Jet In Vitro
Background Pressure recovery has been shown to occur distal to aortic stenoses in experimental and clinical studies. However, its clinical relevance in this setting has not yet been evaluated.
Methods and Results To address the hypothesis that pressure recovery can cause significant differences between Doppler and catheter gradients in aortic stenosis and to examine the effects of aortic size, aortic valve area, and direction of the stenotic jet on these differences, stenoses with valve areas from 0.5 to 1.25 cm2 and aortic diameters from 1.8 to 5.0 cm were studied in a pulsatile flow model. Jets entered the aorta centrally or eccentrically with angles of 15°, 30°, or 45°. Overall, good correlation was found between Doppler and catheter gradients. However, when the various combinations of orifices and aortas were analyzed separately, slopes varied from 1.0 to 1.86, and the Doppler-catheter gradient differences ranged from −2 (small valve area with a large aorta) to 66 mm Hg (80% overestimation by Doppler echocardiography) when the stenosis was moderate and the aorta was small. Mild eccentricity of the jet did not significantly alter the results. However, overestimation by Doppler decreased with increasing jet eccentricity. Finally, differences between Doppler and catheter gradients could be predicted by estimating pressure recovery from Doppler measurements.
Conclusions Significant pressure recovery can occur in aortic stenosis and can cause differences between Doppler and catheter gradients. These differences may reach clinical relevance, particularly when the stenosis is moderate and the aorta is small and can be predicted from Doppler measurements.
Continuous-wave Doppler echocardiography has been used widely to estimate pressure gradients across stenosed aortic valves. Good agreement between Doppler and catheter gradients has previously been reported in this setting.1 2 3 Well-recognized sources of discrepancy between Doppler and catheter gradients include underestimation because of poor alignment of the ultrasound beam with the stenotic jet4 and overestimation because of neglection of elevated subvalvular velocities by the modified Bernoulli equation.5 However, most studies included at least some patients with marked overestimation of catheter gradients by Doppler echocardiography that can hardly be explained by the latter phenomenon alone.2 6 Recent reports revealed that pressure recovery—the increase of pressure downstream from the stenosis caused by reconversion of kinetic energy to potential energy—can explain apparent “overestimation” by Doppler in certain settings such as bileaflet prosthetic valves,7 8 coarctation of the aorta,9 hypertrophic obstructive cardiomyopathy,10 11 and fixed tunnel obstructions.12 Because continuous-wave Doppler measures the highest velocity in the vena contracta close to the stenosis whereas catheters are usually placed to measure a more or less recovered pressure at some distance from the stenosis, Doppler gradients can markedly exceed catheter gradients when significant pressure recovery occurs.7 13 Although pressure recovery also has been demonstrated in experimental14 15 and clinical16 studies of native aortic stenosis, this phenomenon has not yet been recognized as a source of discrepancy between Doppler and catheter gradients. The magnitude of pressure recovery critically depends on the geometry of a stenosis.13 17 In aortic stenosis, the small stenotic orifice is abruptly followed by a much larger ascending aorta. This morphology represents a rather unfavorable geometry for the occurrence of pressure recovery, which may therefore be too small to cause clinically relevant differences between Doppler and catheter gradients. However, the pressure loss in aortic stenosis is caused by the dissipation of kinetic energy resulting from flow separation and vortex formation. As predicted by fluid dynamic principles, the extent of these phenomena will depend on the size relationship between stenotic orifice and aorta.14 15 17 For example, with decreasing size of the aorta, the pressure loss for a given orifice should decrease owing to increasing pressure recovery. Thus, a certain combination of stenotic orifice area, aortic size, and other variables may still be the reason for unexpectedly high differences between Doppler and catheter gradients in some patients.
Therefore, the purposes of this study were to address the hypothesis that pressure recovery can cause significant differences between Doppler and catheter gradients in a model of aortic stenosis and to study the effects of aortic size, aortic valve area, and direction of the stenotic jet on these differences. Finally, we sought to evaluate whether pressure recovery can be predicted from noninvasively derived morphological and hemodynamic variables and whether such variables can be used to correct for differences between Doppler and catheter estimates caused by pressure recovery.
The pneumatically driven pump (Vienna elliptic heart, type 100 mL; University of Vienna) allows variation of stroke volume from 0 to 100 mL, ejection pressure from 0 to 300 mm Hg, pulse rate from 40 to 120 bpm, and ejection time from 100 to 700 milliseconds. The test section was designed to allow optimal alignment of Doppler beam and flow across the stenosis for both central and eccentric jets. Stenosis and aorta are easily exchangeable. Pressure taps proximal and distal to the stenosis either can be connected to fluid-filled catheters or can be used to insert tubing for measurement of pullback pressures. Physiological pressures can be maintained by adjustments in pump characteristics, distal compliance, and resistance.
A water glycerol solution (70% water, 30% glycerol) containing 10 g/L cornstarch served as the test fluid, approximating the viscosity of blood at a temperature of 21°C (3.5 cp).
Flow was measured with an electromagnetic flowmeter (Cliniflow, Carolina Medical Electronics, Inc) calibrated by a geared pump. The flow probe was placed between the ventricle and the stenosis.
Fluid-filled catheters were connected to electronic pressure transducers (Peter van Berg) for pressure recording.
A Vingmed CFM 800 (Vingmed Sound A/S) with a Duplex probe (2.5-MHz continuous-wave Doppler) was used for continuous-wave Doppler measurements. The ultrasound probe was coupled with gel to the model, and its position was carefully adjusted to obtain the highest Doppler velocities across the stenosis.
Pressure transducers and the flowmeter were connected to a four-channel physiological recorder system (Hellige GmbH). Doppler velocities were recorded on videotape; flow and pressure tracings also were recorded on paper. For further analysis, the analog signals from a differential pressure amplifier and the electromagnetic flowmeter were fed into an analog-to-digital converter and transferred, together with the digitized Doppler signals, to a computer system (Macintosh IIci, Apple Computer GmbH). Fig 2⇓ shows a typical example of the digitized pressure, flow, and Doppler recordings. Peak and mean catheter gradients, peak and mean Doppler gradients, and cardiac output were calculated with commercially available software (Echodisp, Vingmed Sound A/S). Peak catheter gradient was defined as the maximal instantaneous difference between proximal and distal pressures. Peak Doppler gradients (ΔP) were calculated from the maximal instantaneous Doppler velocity across the stenosis (v2) with the simplified Bernoulli equation (ΔP=4v22). Because velocities proximal to the stenosis (v1) did not exceed 1 m/s, they were neglected. The mean systolic catheter gradient was obtained by integrating the differential pressure wave over the systolic time period. Mean Doppler gradients were calculated by averaging the instantaneous Doppler gradients throughout the ejection period with the on-board quantification package. Hand tracing of the spectral display velocity curve was used. Interobserver and intraobserver variabilities for these measurements were reported previously.19 For each set of measurements, results were obtained by averaging the calculations of three beats.
Stenosis and Aorta
Lucite plates (2 mm thick) with central circular orifices of 0.5, 0.75, 1.0, and 1.25 cm2 served as stenosis models. A mechanical valve (Carbomedics; 25 mm) between the ventricle and test section and noncompliant tubing helped to avoid “regurgitation” during diastole. This setup resulted in Doppler, flow, and pressure tracings very similar to those obtained in native aortic valve stenosis (Fig 2⇑).
Aortas with diameters of 1.8, 2.4, 3.0, 4.0, and 5.0 cm and with a length of 10 cm were studied. To create eccentric jets, angled aortas 1.8 cm in diameter were machined to allow angles between the jet and aortic wall of 15°, 30°, and 45° (Fig 3⇓). The smallest aorta was chosen because the greatest extent of pressure recovery was expected for this size and differences caused by jet eccentricity should be best detected.
Each of the four stenoses with orifice areas from 0.5 to 1.25 cm2 were studied with the five straight aortas with diameters from 1.8 to 5.0 cm. The three angled aortas (15°, 30°, and 45°) were studied with the 1.0- and 1.25 cm2-orifice. Driving pressure and filling characteristics of the ventricle, outflow compliance, and outflow resistance were varied to obtain eight different flow states while maintaining physiological downstream pressures. Cardiac output ranged from 2.0 to 6.0 L/min. This maximal cardiac output could be obtained for the large orifices but not for the small valve areas. Pulse rate was maintained at 60 bpm, with ejection time ranging from 260 to 360 milliseconds. Peak and mean pressure gradients were measured simultaneously with the continuous-wave Doppler and catheter technique at each flow rate while the fluid-filled catheters were connected to the pressure tap 10 mm proximal and 50 mm distal to the stenosis. The latter distance was chosen for two reasons. First, previous studies and experiments within this project demonstrated that most pressure recovery occurs within several centimeters distal to the stenosis, and wall pressures at 50 mm are close to central pressures at 100 and 200 mm, respectively, and reflect the recovered distal pressure with acceptable accuracy for clinical purposes.7 13 Second, this setup emulates the clinical setting when aortic pressure is measured with a pigtail catheter in the ascending aorta. For the angled aorta, the pressure tap was located carefully to avoid flow toward the tap.
Prediction of Pressure Recovery
On the basis of fluid mechanics theory, the magnitude of pressure recovery—the difference (P3−P2) between lowest pressure in the stenosis or in the vena contracta (P2) and the distal recovered pressure (P3)—can be calculated in aortic stenosis from the dynamic pressure (1/2ρv22, where ρ is the fluid density and v2 is the orifice velocity), the effective aortic valve area (AVAe), and the cross-sectional area of the ascending aorta (AoA) by applying Equation 115 :P_|<|3|>||<|-|>|P_|<|2|>||<|=|>|\frac|<|1|>||<|2|>||<|\rho|>|v_|<|2|>|^|<|2|>|2\frac|<|AVA_|<|e|>||>||<|AoA|>| \left(1|<|-|>|\frac|<|AVA_|<|e|>||>||<|AoA|>|\right)
Dynamic pressure can be obtained from the maximal continuous-wave Doppler velocity across the orifice (vcw), and the effective valve area can be calculated with the continuity equation (AVAc) by dividing peak flow by peak Doppler velocity.20 Thus, one should be able to predict pressure recovery on the basis of Doppler echocardiographic data by applying Equation 2:P_|<|3|>||<|-|>|P_|<|2|>||<|=|>|4v_|<|cw|>|^|<|2|>|2 \frac|<|AVA_|<|c|>||>||<|AoA|>| \left(1|<|-|>|\frac|<|AVA_|<|c|>||>||<|AoA|>|\right)
Finally, Doppler gradients should reflect the maximal pressure drop across the stenosis (P1−P2) that is the difference between the proximal pressure (P1) and the lowest pressure in the stenosis or the vena contracta (P2); the catheter technique measures the recovered distal pressure (P3) and yields the net pressure drop (P1−P3). The difference between Doppler and catheter gradient should therefore approximate the recovered pressure (P3−P2).
In addition, subtraction of this predicted recovered pressure from the Doppler gradient should yield the catheter gradient, provided that the distal pressure is measured at a distance that allows full pressure recovery. At least in the model used in the present study, orifice area and aortic cross-sectional area remain constant throughout the cardiac cycle. Therefore, Equation 2 can be used to calculate peak and mean recovered pressure to correct both peak and mean Doppler gradients.
For each experimental setup, continuity equation valve areas were calculated at each flow rate by dividing the measured peak flow by the peak Doppler velocity. These values, together with the Doppler gradients and the known cross-sectional area of the aorta, were used to calculate the “predicted recovered pressure” for each measurement. These pressures were compared with the observed Doppler-catheter gradient differences. By subtracting these pressures from the Doppler gradients, Doppler-predicted catheter gradients were calculated and compared with the observed catheter gradients.
The relationship between Doppler and catheter gradients was assessed by linear regression analysis. Pearson correlation coefficients were calculated. A two-tailed t test was performed to test the hypothesis about two regression lines.
Relationship Between Doppler and Catheter Gradients
When all experimental setups were analyzed together, good correlation, both between peak Doppler and peak catheter gradients (r=.95) and between mean Doppler and mean catheter gradients (r=.95), was found (Fig 4⇓). However, for an in vitro study, the scatter was remarkable (2 SEE=26 and 18 mm Hg), and some overestimation of catheter gradients by Doppler was observed, on average, with slopes of 1.09 and 1.12 and intercepts of 11 and 10 mm Hg for peak and mean gradients, respectively.
However, when the various combinations of orifices and aortas were analyzed separately, there was indeed better correlation (r=.98 to .99) and less scatter, but slopes differed considerably (1.0 to 1.86). All three variables—aortic size, aortic valve area, and the direction of the stenotic jet—significantly affected the relationship between Doppler and catheter gradients.
Fig 5⇓ shows the results for a single orifice area combined with the various aortas. For the larger aortas with 3-, 4-, and 5-cm diameters, acceptable agreement or slight overestimation by Doppler was found with a variation of slopes from 1.1 to 1.27. However, for the two smaller aortas with 2.4- and 1.8-cm diameters, marked overestimation of catheter gradients by Doppler were observed, and slopes varied from 1.44 to 1.86. The greatest differences between Doppler and catheter gradients were found for the smallest aorta with slopes of 1.7 and 1.86 for peak and mean gradients, respectively, and differences up to 66 mm Hg.
Aortic Valve Area
Aortic valve area also significantly affected the results. The Doppler and catheter gradient differences increased with orifice area. Fig 6⇓ shows the four orifices in combination with the smallest aorta. Slopes varied from 1.28 (peak gradient) and 1.4 (mean gradient) for the smallest orifice to 1.72 (peak gradient) and 1.86 (mean gradient) for the largest orifice.
Fig 7⇓ demonstrates the effect of the jet direction on the Doppler-catheter gradient relationship for the 1.8-cm aorta combined with the 1.0-cm2 orifice. For the slightly eccentric jet (15°), results were similar to those for the corresponding central stenotic jet with slopes of 1.3 and 1.5 for peak and mean gradients, respectively. However, Doppler-catheter gradient differences decreased by ≈50% (30°) and ≈80% (45°) with increasing jet eccentricity, and slopes decreased to 1.23 and 1.33 for moderate jet eccentricity (30°) and 1.14 and 1.11 for the highly eccentric jet (45°).
Prediction of Pressure Recovery and Correction of Doppler Gradients
There was a wide range (Fig 8⇓) of predicted recovered pressures for the different settings from 2 to 69 mm Hg (15±13 mm Hg; peak pressure) and 1 to 47 mm Hg (10±8 mm Hg; mean pressure). For central jets, these predicted pressures compared well with the observed differences between Doppler and catheter peak gradients (range, −2 to 66 mm Hg; mean±SD, 16±13 mm Hg) and between mean gradients (range, 0 to 49 mm Hg; mean±SD, 12±9 mm Hg). Predicted and observed differences correlated well (r=.88, y=0.86x+1, and SEE=6 mm Hg; and r=.92, y=0.85x−1, and SEE=3 mm Hg). When Doppler gradients were corrected by the predicted recovered pressure to obtain the Doppler-predicted catheter gradients, these gradients showed excellent agreement with the observed catheter gradients (r=.97, SEE=6 mm Hg, and y=1.02x+1.0 for peak gradients; r=.99, SEE=3 mm Hg, and y=1.04x+0.2 for mean gradients; Fig 9⇓). However, this was no longer true when the stenotic jet was eccentric, when slopes dropped to 0.73 and 0.76 for peak and mean gradients, respectively (Fig 10⇓). Differences were still insignificant for the slightly eccentric jet (15°) but increased considerably with more marked jet eccentricity.
The present study demonstrates that pressure recovery can cause highly significant differences between Doppler and catheter gradients as long as there is a favorable combination of orifice size, aortic size, and flow rate and as long as the stenotic jet is not highly eccentric. It also could be demonstrated that these differences are very close to the magnitude of pressure recovery predicted from fluid mechanics theory and that they can, at least in vitro, be predicted from variables provided by Doppler echocardiography. Thus, it may be possible to correct for pressure recovery and calculate noninvasively the net pressure drop across the stenosis. This gradient may be clinically more relevant than the maximal gradient because it determines the proximal pressure required to maintain a given distal pressure.
Pressure recovery has been well recognized as a source of clinically relevant discrepancies between Doppler and catheter gradients in certain settings such as prosthetic valves, coarctation of the aorta, and hypertrophic cardiomyopathy. However, the potential role of this phenomenon for the Doppler sonographic assessment of aortic stenosis is not yet fully appreciated because acceptable agreement between Doppler and catheter estimates has frequently been observed despite neglection of pressure recovery. This can be explained by the differences in fluid mechanics. The most important determinant for the magnitude of pressure recovery that can occur downstream from a flow obstruction is the geometry of the stenosis and the receiving compartment.13 17 Although significant pressure recovery can occur in rather streamlined stenoses that avoid turbulences to some degree, this is not the case when a small stenotic orifice widens abruptly to a large receiving compartment. In this case, most of the kinetic energy is lost as heat and cannot be reconverted to potential energy (ie, lateral pressure).13 17 This is typically the case in patients with severe aortic stenosis and dilated ascending aorta, a frequent finding in adults with aortic stenosis. However, it has been suggested that the extent of pressure recovery in aortic stenosis depends critically on the ratio of orifice area and cross-sectional area of the aorta because it determines the extent of flow separation and vortex formation.14 15 From a clinical viewpoint, aortic size appears to be the more important variable. In the present study, we were able to demonstrate that relevant pressure recovery can hardly occur with an aorta diameter of ≥30 mm. In this case, the orifice area would have to be so large to guarantee a favorable ratio for the occurrence of relevant pressure recovery that a significant transvalvular pressure gradient is no longer realistic, considering the possible range of cardiac output in a human being. Therefore, the size of the ascending aorta has to be in the lower normal range or smaller before clinically relevant pressure recovery can be expected. In this situation, the extent of pressure recovery will then increase with the orifice area and, in absolute terms, with the orifice velocity owing to their linear relationship (see Equations 1 and 214 15 ). The latter, again, is related to the orifice size and flow rate.
The pressure recovery–related differences between Doppler and catheter gradients in the present study also depended on the direction of the stenotic jet. This is not surprising, considering that reconvertable energy is lost when an eccentric jet hits the aortic wall. It has to be emphasized that this is not a matter of the absolute angle but rather of the combination of jet angle and aortic size. For a hypoplastic aorta with a 1.8-cm diameter, for example, that allows highly significant pressure recovery, the phenomenon almost disappears with 45° jet eccentricity.
Comparison With Previous Doppler Studies of Aortic Stenosis
Although pressure recovery has generally not been recognized as a source of discrepancy between Doppler and catheter gradients in clinical studies of aortic stenosis,1 2 3 most reports included at least some patients with marked overestimation of catheter gradients by Doppler echocardiography.6 21 Ohlsson and Wranne,21 for example, studied 32 patients and reported that Doppler mean gradients were, on average, slightly but significantly higher than catheter mean gradients, and differences as great as 30 mm Hg were observed. Although the neglection of elevated proximal velocities in the simplified Bernoulli equation was not excluded as a source of error in their report and although information on aortic size was not provided, it is remarkable that the 10–mm Hg mean difference between Doppler and catheter gradients was virtually identical to that found for the whole group of experimental settings in the present study. Better agreement between Doppler and catheter gradients in other reports could be the result of a different patient population and an underrepresentation of patients with small aortas. Furthermore, some differences between Doppler and catheter gradients may actually be corrected by underestimation of the true maximal pressure gradient by Doppler owing to other reasons such as suboptimal alignment of Doppler beam and stenotic jet.
Comparison With Previous Studies of Pressure Recovery in Aortic Stenosis
So far, the occurrence of pressure recovery in aortic stenosis has been studied mostly in experimental settings. Clark14 15 studied the fluid mechanics of aortic stenosis in steady and unsteady flow experiments almost 20 years ago. Although these experiments indicated the occurrence of pressure recovery in aortic stenosis, the clinical relevance of this finding remained unclear, and the report has not influenced the thinking of cardiologists. More recently, Vo¨lker et al22 studied pressure recovery in various models of aortic valve stenosis and found the stenotic orifice area to be an important predictor of pressure recovery. Although pressure recovery in absolute terms increased with stenosis severity and flow rate, the ratio between pressure recovery and maximal gradient that may better express the clinical relevance of this phenomenon was independent of flow rate and decreased with increasing severity of the stenosis. This phenomenon also was confirmed in the present study. From these results, the authors concluded that pressure recovery would be of no clinical relevance in patients with aortic stenosis. However, they did not study other variables such as aortic size and stenotic jet direction, and their study did not include Doppler measurements.
One of the few clinical attempts to study pressure recovery in aortic stenosis was reported by Laskey and Kussmaul.16 They tried to evaluate this phenomenon in 11 patients, all with significant aortic stenosis. With high-fidelity pressure and velocity recordings, they found an increase in pressure downstream from the stenosis of 4 to 18 mm Hg, which represented 6% to 33% of the maximal pressure gradient in this cohort. That study, however, did not include patients with mild or moderate stenoses, and lacked information on the dimensions of the ascending aorta. Again, Doppler measurements were not included.
In vitro models cannot precisely duplicate the complex flow dynamics in patients with aortic stenosis. In vivo, aortic geometry is more complex and is not rigid, and some of the flow enters the coronary arteries. However, preliminary data indicate that the compliance of the aorta may be of minor importance in this regard23 and that the conclusions of the present study may to some degree be applicable to the clinical setting.21 24
The rigid orifices used in this study do not behave like stenosed native valves. The orifice area may show some variation over the systolic period, and less flow contraction may occur, especially in doming valves. Highly significant flow contraction with an effective orifice area much smaller than the anatomic orifice is also the reason for the relatively high gradients observed in the present study. Furthermore, only circular orifices were studied. However, results from previous studies suggest that irregular orifices may yield similar results.22 25
The constant distance for the distal pressure measurement is a simplification. Theoretically, the distance required for maximal pressure recovery may be longer and depends on the orifice size and aortic diameter.14 15 However, previous studies7 13 and experiments within this project showed that for the range of setups studied, most of the pressure recovery occurs within several centimeters, particularly when the combination of orifice and aorta is favorable for the occurrence of significant pressure recovery. The differences between wall measurements at 50 mm and central measurements at 100 to 200 mm downstream from the stenosis are small and clinically not relevant. The experimental setting used in this study also approximates the clinical scenario in which measurements in the descending aorta or peripheral vessels do not make sense because of phenomena such as pressure wave reflection. Normally, distal pressures are measured with a pigtail catheter in the ascending aorta. This catheter with several holes reflects the highest pressure present at one hole. This should therefore be the hole with the greatest distance to the stenosis, and this hole realistically is not located in the center but rather close to the aortic wall. Finally, a clinical study16 suggests that all measurable increase of pressure occurs within the ascending aorta.
Furthermore, pressure recovery was not directly measured by manometry in this study. Although the good agreement between predicted pressure recovery and observed pressure recovery (ie, the difference between Doppler and catheter gradients) supports the hypothesis that Doppler echocardiography measured the highest gradient based on the lowest pressure in the vena contracta and that catheter measurements involved the fully recovered distal pressure, this could be caused by the cancellation of several errors. However, we have previously shown in this flow model that Doppler echocardiography measures the maximal gradient and that the performed catheter measurements allow the detection of pressure recovery accurately enough for clinical purposes.7 13
Although the results of the present study need to be validated in vivo, they strongly indicate that pressure recovery of a clinically relevant magnitude can occur in aortic stenosis and may cause significant discrepancies between Doppler and catheter gradients. The occurrence of this degree of pressure recovery, however, requires a size of the ascending aorta in the low-normal range or smaller. This situation probably occurs in only a few adult patients with aortic stenoses and explains why acceptable agreement between Doppler and catheter gradients can usually be found despite neglection of pressure recovery. Therefore, in most cases, the recovered pressure in absolute terms may simply be too small to cause clinically relevant discrepancies or may actually be corrected by underestimation of the true maximal pressure gradient by Doppler for other reasons such as suboptimal alignment of Doppler beam and stenotic jet.
Because aortic size, the most important predictor of pressure recovery in aortic stenosis, can easily be measured by two-dimensional echocardiography, it is easy to determine whether this phenomenon requires consideration in a given case. Furthermore, one may ultimately be able to predict the extent of pressure recovery and therefore the net pressure drop reflected by catheter measurements from the continuity equation aortic valve area, continuous-wave Doppler velocity, and cross-sectional area of the aorta as long as the stenotic jet is not highly eccentric.
These considerations may be clinically most relevant in patients with moderate aortic stenoses, small aortas, and high flow rates. Under such circumstances, interpretation of the hemodynamic significance of a stenosis may differ markedly when the maximal pressure drop in the vena contracta is considered (ie, Doppler gradient) rather than the net pressure drop across the stenosis (ie, catheter gradient) and may therefore affect the clinical management of some patients with aortic stenosis.
This study was conducted in the frame of INVADYN, Biomed I, a European research program.
- Received January 31, 1996.
- Revision received April 19, 1996.
- Accepted April 23, 1996.
- Copyright © 1996 by American Heart Association
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