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Circulation. 1995;91:192-200

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(Circulation. 1995;91:192-200.)
© 1995 American Heart Association, Inc.

Articles

Noninvasive Assessment of Left Ventricular Relaxation Using Continuous-Wave Doppler Aortic Regurgitant Velocity Curve

Its Comparative Value to the Mitral Regurgitation Method

Kazuhiro Yamamoto, MD; Tohru Masuyama, MD; Yasuji Doi, MD; Johji Naito, MD; Toshiaki Mano, MD; Hiroya Kondo, MD; Reiko Nagano, MD; Jun Tanouchi, MD; Masatsugu Hori, MD; Takenobu Kamada, MD

From the First Department of Medicine, Osaka University School of Medicine, Suita, Japan.

Correspondence to Tohru Masuyama, MD, The First Department of Medicine, Osaka University School of Medicine, 2-2, Yamadaoka, Suita 565, Japan.


*    Abstract
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 *Abstract
down arrowIntroduction
 down arrowMethods
down arrowResults
down arrowDiscussion
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Background The most established parameters of left ventricular (LV) relaxation are peak negative value of the first derivative of LV pressure (-dP/dtmax) and the time constant of isovolumic LV pressure fall. The instantaneous pressure gradient between the aorta and the LV during diastole can be calculated from the continuous-wave Doppler aortic regurgitant velocity spectrum. Because the fluctuation of aortic pressure during LV isovolumic relaxation is negligibly minor and because LV minimal pressure is negligibly low, LV pressure during the isovolumic relaxation period may be derived from the continuous-wave Doppler aortic regurgitant velocity spectrum. This study was designed to clarify whether analysis of continuous-wave Doppler aortic regurgitation recording provides accurate measures of LV relaxation over a wide range of LV function and to determine comparative values of aortic and mitral regurgitation methods in the assessment of LV relaxation.

Methods and Results In eight mongrel dogs with acute ischemic LV dysfunction, the continuous-wave Doppler aortic regurgitant velocity spectrum was recorded simultaneously with high-fidelity LV and aortic pressures, while the continuous-wave Doppler mitral regurgitant velocity spectrum was recorded simultaneously with high-fidelity left atrial and LV pressures. The aortic regurgitant velocity spectrum was provided for the determination of Doppler-derived mean rate of LV pressure fall in 20 ms after the onset of aortic regurgitation ({Delta}P/{Delta}t-AR) and the time interval from the onset of aortic regurgitation to the point at (1-1/e)1/2 of the maximal aortic regurgitant velocity as an estimate of the time constant. The mitral regurgitant velocity spectrum was provided for Doppler-derived mean rate of LV pressure fall in 20 ms after the point of -dP/dtmax ({Delta}P/{Delta}t-MR) and the time interval from the point of -dP/dtmax to the point with mitral regurgitant velocity of (1/e)1/2 of the mitral regurgitant velocity at the point of -dP/dtmax as an estimate of the time constant. {Delta}P/{Delta}t-AR and {Delta}P/{Delta}t-MR correlated well with catheter-derived -dP/dtmax (r=.92, r=.98, P<.01, respectively). The time constant derived from aortic and mitral regurgitant velocity spectra (tau-AR and tau-MR) also correlated well with catheter-derived time constant (r=.84, r=.76, P<.01, respectively). However, a mean difference of the catheter-derived time constant minus tau-MR was larger than tau-AR (29±30 versus 4±17 ms, P<.01, presented as mean±2 SD).

Conclusions LV relaxation can be assessed from the continuous-wave Doppler aortic regurgitant velocity spectrum. The aortic regurgitation method provides an even more accurate estimate of the time constant compared with the mitral regurgitation method, particularly in the presence of LV dysfunction.


Key Words: regurgitation • echocardiography • diastole


*    Introduction
up arrowTop
 up arrowAbstract
 *Introduction
down arrowMethods
down arrowResults
down arrowDiscussion
down arrowReferences
 
The assessment of left ventricular (LV) diastolic function is valuable in patients with diseased hearts,1 2 3 4 and a noninvasive assessment of LV diastolic function is desirable. Pulsed Doppler transmitral flow velocity pattern has been widely used in the noninvasive assessment of LV diastolic function5 6 7 8 9 10 11 12 ; however, it has many limitations.13 14 15 16 17 18 19 20 21 Recently, the time constant of LV isovolumic pressure fall and peak negative value of the first derivative of LV pressure (-dP/dtmax), the most established parameters of LV relaxation obtained from invasive LV pressure measurements,22 23 were shown to be reliably determined from the continuous-wave Doppler mitral regurgitant velocity spectrum.24 25 26 However, a well-delineated Doppler spectral envelope of mitral regurgitation, particularly its deceleration limb, cannot always be obtained in patients with trace or mild mitral regurgitation; thus, other measures should widen Doppler application to noninvasive assessment of LV relaxation. Nishimura and Tajik27 showed that a velocity of aortic regurgitation reflects instantaneous pressure gradient between the aorta and the LV. Because the fluctuation of aortic pressure is relatively minor during the isovolumic relaxation period, changes in the pressure gradient may reflect those in LV pressure.

We attempted to estimate the time constant and -dP/dtmax from continuous-wave Doppler aortic regurgitation recording in dogs with various degrees of LV dysfunction. We also studied comparative values of aortic and mitral regurgitant flow velocity analysis in the estimation of LV relaxation.


*    Methods
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 up arrowAbstract
 up arrowIntroduction
 *Methods
down arrowResults
down arrowDiscussion
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Animal Preparation and Data Collection
This study conforms to the guiding principles of Osaka University School of Medicine with regard to animal care and to the "Position of the American Heart Association on Research Animal Use." Eight mongrel dogs (16 to 35 kg) were sedated with morphine sulfate (3 mg/kg SC) 30 minutes before induction of general anesthesia with {alpha}-chloralose (50 mg/kg IV). After the induction of general anesthesia, intravenous infusion of {alpha}-chloralose (30 mg · kg-1 · h-1) was continued until the end of the experiment. Each dog, in the supine position, was intubated and artificially ventilated with a Harvard-type respirator (R-60, Aika). A central thoracotomy was performed, and the pericardium was incised. The heart was stabilized in a pericardial cradle. An 8F high-fidelity manometer-tipped catheter (Sentron) was introduced retrograde across the aortic valve into the LV through the left carotid artery, and this introduction contributed to the creation of aortic regurgitation. Another 8F high-fidelity manometer-tipped catheter was introduced into the ascending aorta through the right carotid artery. A 6F high-fidelity manometer-tipped catheter (Millar Instruments) was introduced into the left atrium (LA) through the left pulmonary vein. The manometers were calibrated relative to atmospheric pressure before introduction of the catheters into the cardiac chambers. Continuous lead II ECG tracing, LV pressure, dP/dt, and LA or aortic pressure were displayed on the eight-channel recorder (Nihon Kohden), and all recordings were made at a paper speed of 100 mm/s.

A commercially available echocardiograph (SSH-65A, Toshiba) was used to record continuous-wave Doppler aortic or mitral regurgitant signals. First, the presence of aortic and/or mitral regurgitation was examined by color Doppler echocardiography, and the Doppler recordings were obtained from the apical approach with a small, nonimaging, 2.5-MHz transducer. The nonimaging transducer was positioned to obtain the maximal and most clearly delineated velocity envelope. The Doppler echocardiographic recordings were made at a paper speed of 100 mm/s on a strip chart recorder (LSR-20B, Toshiba) (Fig 1Down).



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  		Figure 1. A, Example of simultaneously recorded pressure tracings (top) and continuous-wave Doppler aortic regurgitant velocity spectrum (bottom). B, Example of simultaneously recorded pressure tracings (top) and continuous-wave Doppler mitral regurgitant velocity spectrum (bottom). AoP indicates aortic pressure; dP/dt, first derivative of left ventricular pressure; LAP, left atrial pressure; and LVP, left ventricular pressure.

Before each recording, the manometric LV and aortic pressures were aligned with the pressure measured by their fluid-filled lumens connected to a fluid-filled pressure transducer (model TP-400T, Nihon Kohden) positioned at the midthoracic level, and the difference between manometric LA and LV pressures during middiastole of long diastolic cycles was recorded. All measurements were made during the end-expiratory portion of the respiratory cycle.

Experimental Protocol
LV dysfunction was produced before the Doppler examination according to a method previously described.13 14 19 28 A 5F Judkins left coronary catheter (Schneider Inc) was introduced through the right femoral artery and advanced into the left coronary ostium under echocardiographic guidance. Then plastic microspheres (50±2 µm in diameter; 3M) were injected into the left coronary artery to induce acute ischemic LV dysfunction. A sequence of injections was made to elevate LV end-diastolic pressure by at least 5 mm Hg. After the production of ischemic LV dysfunction, dobutamine or propranolol was infused to alter LV function. Aortic regurgitant signals were obtained at a total of 32 hemodynamic stages, and mitral regurgitant signals were obtained at a total of 31 hemodynamic stages in the eight dogs. In each experimental stage, the Doppler velocity curve, LV pressure tracing, LA or aortic pressure tracing, and ECG were simultaneously recorded.

Data Analysis
The pressure tracings and continuous-wave Doppler tracings were digitized with a digitizing pad (KD 4300, Graphtec) interfaced with a personal computer system (NEC) at a rate of 60 samples per second. To get reliable results, we digitized the recordings very slowly and carefully.

The tracings of high-fidelity LV pressure were digitized from the time of -dP/dtmax until 5 mm Hg above LV end-diastolic pressure at 5-ms intervals for measurements of the time constant of LV isovolumic pressure fall, assuming a zero-pressure asymptote22 :


where P(0) is the pressure at the time of -dP/dtmax, P(t) is the LV pressure, t is time, and tau is the catheter-derived time constant. To calculate tau, the natural logarithm of P(t) was fitted to the line A+Bt, and tau was defined as -1/B. The same tracings of LV pressure were also used to calculate the non–zero-pressure asymptote time constant by a nonlinear least-squares technique.29 The time constant calculated assuming a zero-pressure asymptote has been shown to be directionally equal to other mathematical approaches.30 31 In addition, it has been shown that assuming zero-pressure asymptote introduces only a small, insignificant underestimation of the time constant calculated by use of the "true" pressure asymptote (determined from nonfilling beats).32 In tracing LA pressure, the difference between manometric LA and LV pressures during middiastole of long diastolic cycles was subtracted from the recorded LA pressure to adjust LA and LV pressures to a common baseline.13 14 15

Aortic regurgitant velocity reaches a peak velocity (Vmax-AR) at the point of LV minimal pressure (Fig 2ADown). Assuming that the fluctuation of aortic pressure between the onset of aortic regurgitation and the point at LV minimal pressure was minor and that LV minimal pressure is negligible, LV pressure at the onset of aortic regurgitation is equal to 4(Vmax-AR)2. Therefore, LV pressure during isovolumic diastole was calculated from the following equation:



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  		Figure 2. Schematic drawings showing measurements of Doppler indexes of left ventricular relaxation. A, Schema of aortic and left ventricular pressure tracings and continuous-wave Doppler aortic regurgitant velocity spectrum. B, Schema of left atrial and left ventricular pressure tracings and continuous-wave Doppler mitral regurgitant velocity spectrum. LV minP indicates left ventricular minimal pressure; {Delta}P, pressure gradient; VAR, velocity of aortic regurgitation; VMR, velocity of mitral regurgitation; and PCG, phonocardiogram. Tau-AR, tau-MR, VAR1, Vmax-AR, VMR1, VMR2, Vtau-AR, and Vtau-MR are defined in the text. Other abbreviations as in Fig 1Up.


where VAR is an instantaneous aortic regurgitant velocity.

The onset of aortic regurgitation is at the aortic valve closure, and this point is close to the point of -dP/dtmax. Thus, the aortic regurgitant velocity at 20 ms after the onset of aortic regurgitation (VAR1) was measured, and a rate of LV pressure fall derived from continuous-wave Doppler aortic regurgitant recording ({Delta}P/{Delta}t-AR) was calculated as


To derive the time constant, assuming a zero-pressure asymptote, from the aortic regurgitant velocity curve, the following equation was solved:



and the time interval between the point at the onset of aortic regurgitation and the point with aortic regurgitant velocity of Vtau-AR was defined as the time constant derived from the aortic regurgitant velocity curve (tau-AR). In addition to this simplified method, the Doppler tracings of aortic regurgitation were digitized at 5-ms intervals from the onset of aortic regurgitation to the R wave on the ECG to derive the LV pressure contour and then to calculate the zero-pressure asymptote time constant (tau-AR-trace) and the non–zero-pressure asymptote time constant in the same fashion as done in the high-fidelity LV pressure tracings. In applying this conventional manner (tracing method) to the aortic regurgitant data, the Doppler-derived LV pressure tracings were used from the onset of the aortic regurgitation until 5 mm Hg above the Doppler-derived LV pressure at the R wave on the ECG.

Assuming that the fluctuation of LA pressure is minor and that a value of LA pressure is negligible, LV pressure is equal to 4(VMR)2, where VMR equals an instantaneous mitral regurgitant velocity (Fig 2BUp). In this study, we measured a mitral regurgitant velocity at the point of -dP/dtmax (VMR1) and a velocity at the point 20 ms after -dP/dtmax (VMR2) and calculated a rate of LV pressure fall derived from the mitral regurgitant velocity spectrum ({Delta}P/{Delta}t-MR) using the following equation:


The mitral regurgitant velocity curve and dP/dt were recorded simultaneously on different sheets of paper. Thus, the time interval between the R wave on the ECG and the point at -dP/dtmax was measured, and mitral regurgitant velocity at the point of the same time interval from the R wave was defined as VMR1.

To derive the time constant, assuming a zero-pressure asymptote, from the mitral regurgitant velocity spectrum, the following equation was solved:



and the time interval between the point with a mitral regurgitant velocity of VMR1 and the point with a mitral regurgitant velocity of Vtau-MR was defined as the time constant derived from the mitral regurgitant velocity curve (tau-MR). In addition to this simplified method, the Doppler tracings of mitral regurgitation were digitized at 5-ms intervals to derive LV pressure contour and then to calculate the zero-pressure asymptote time constant (tau-MR-trace) and the non–zero-pressure asymptote time constant in the same fashion as done in the high-fidelity LV pressure tracings. In the application of this conventional manner (tracing method) to the mitral regurgitant data, the Doppler-derived LV pressure tracings were used from the point at -dP/dtmax to the baseline (at the mitral valve opening).

Correction of the Time Constant Derived From the Doppler Velocity Curve
LV minimal pressure may not be negligible, particularly in the presence of heart failure. Therefore, a formula with a correction for LV minimal pressure was offered, as follows (see "Appendix"):(1) for LV minimal pressure <10 mm Hg, Vtau-AR=0.79xVmax-AR;(2) for 10 <= LV minimal pressure <20 mm Hg, Vtau-AR= 0.79x(1+1.25/Vmax-AR2)xVmax-AR; and (3) for 20 <= LV minimal pressure, Vtau-AR=0.79x(1+2.5/Vmax-AR2)xVmax-AR.

LA pressure should not be negligible, particularly in the presence of heart failure. Therefore, a formula with a correction for LA pressure was offered, as follows (see "Appendix"): (1) for LA pressure at -dP/dtmax <10 mm Hg, Vtau-MR=0.61xVMR1; (2) for 10 <= LA pressure at -dP/dtmax <20 mm Hg, Vtau-MR=0.52xVMR1; (3) for 20 <= LA pressure at -dP/dtmax <30 mm Hg, Vtau-MR=0.41xVMR1; and (4) for 30 mm Hg <= LA pressure at -dP/dtmax, Vtau-MR=0.27xVMR1.

Variability Study
Intraobserver and interobserver variabilities were calculated for Doppler- and catheter-derived indexes in 10 randomly selected tracings each for aortic and mitral regurgitation. Mean±SD of absolute values of percent difference was 4±5% (intraobserver) and 6±4% (interobserver) for {Delta}P/{Delta}t-AR, 4±3% and 6±3% for tau-AR, 16±16% and 20±13% for {Delta}P/{Delta}t-MR, 7±3% and 7±4% for tau-MR, 2±3% and 3±3% for catheter-derived -dP/dtmax, and 5±3% and 5±3% for catheter-derived time constant.

Statistical Analysis
Bivariate correlations between Doppler echocardiographic and hemodynamic parameters were performed with a simple least-squares linear regression analysis. Changes in indexes associated with alteration of LV function were defined as a value after the alteration minus a value before the alteration in each dog. The statistical significance of the difference between the data derived from different formulas was tested with an ANOVA and Scheffé's F test. Results were considered significant at a probability value of P<.05. All calculations were performed with the STATVIEW II statistical program (Abacus Inc).


*    Results
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 up arrowIntroduction
 up arrowMethods
*Results
down arrowDiscussion
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Catheter-derived -dP/dtmax ranged from 336 to 2191 mm Hg/s; the catheter-derived time constant, assuming a zero-pressure asymptote, ranged from 33 to 113 ms; aortic pressure drop from the point at -dP/dtmax to the point at LV minimal pressure ranged from 5 to 16 mm Hg (mean, 11 mm Hg); the difference between LV pressure at the point of -dP/dtmax and LV pressure at the onset of aortic regurgitation ranged from 0 to 13 mm Hg (mean, 5 mm Hg); and LV minimal pressure ranged from 4 to 29 mm Hg (mean, 12 mm Hg) in the data collected during the recording of aortic regurgitant velocity. Catheter-derived -dP/dtmax ranged from 356 to 1686 mm Hg/s, and the catheter-derived time constant, assuming a zero-pressure asymptote, ranged from 34 to 120 ms in the data collected during the recording of mitral regurgitant velocity.

Indexes Derived From Aortic Regurgitant Velocity
{Delta}P/{Delta}t-AR correlated with catheter-derived -dP/dtmax (r=.92, P<.01), and a mean difference of catheter-derived -dP/dtmax minus {Delta}P/{Delta}t-AR was -27±419 mm Hg/s (mean±2 SD, Fig 3Down). Changes in {Delta}P/{Delta}t-AR also correlated with those in catheter-derived -dP/dtmax (r=.78, P<.01). Tau-AR correlated with the catheter-derived time constant (r=.84, P<.01), and a mean difference of the catheter-derived time constant minus tau-AR was 4±17 ms (mean±2 SD, Fig 4Down). Tau-AR-trace also correlated with the catheter-derived time constant (r=.86, P<.01), and a mean difference of the catheter-derived time constant minus tau-AR-trace was 5±16 ms (mean±2 SD, Figs 5 and 6). After the correction of tau-AR with LV minimal pressure, the correlation coefficient increased, although not significantly, from 0.84 to 0.91, and the mean difference decreased, slightly but significantly, from 4±17 to -4±14 ms (mean±2 SD, P<.01). Changes in tau-AR correlated with those in the catheter-derived time constant both before and after the correction (r=.71, r=.86, and P<.01, respectively). The Doppler-derived non–zero-pressure asymptote time constant correlated only poorly with the catheter-derived non–zero-pressure asymptote time constant (r=.47, P<.05), and a mean difference was 13±51 ms (mean±2 SD).



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  		Figure 3. A, Plot showing relation between catheter-derived -dP/dtmax and Doppler-derived {Delta}P/{Delta}t-AR. Dashed line is a line of identity, and solid line is a regression line. B, Mean vs the difference of catheter-derived -dP/dtmax minus Doppler-derived {Delta}P/{Delta}t-AR. Solid line indicates mean difference, and dashed lines are 2 SD of mean difference.



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  		Figure 4. A, Plot showing relation between the catheter-derived time constant (tau) and the time constant derived from continuous-wave Doppler aortic regurgitant velocity spectrum in the simplified method (tau-AR). B, Mean vs the difference of the catheter-derived time constant (tau) minus the time constant derived from continuous-wave Doppler aortic regurgitant velocity spectrum (tau-AR). C, Relation between the catheter-derived time constant (tau) and the Doppler-derived time constant corrected for left ventricular minimal pressure (corrected tau-AR). D, Mean vs the difference of the catheter-derived time constant (tau) minus the Doppler-derived time constant corrected for left ventricular minimal pressure (corrected tau-AR). In A and C, dashed lines are lines of identity, and solid lines are regression lines. In B and D, solid lines indicate mean difference, and dashed lines are 2 SD of mean difference.

Indexes Derived From Mitral Regurgitant Velocity
{Delta}P/{Delta}t-MR correlated with catheter-derived -dP/dtmax (r=.98, P<.01), and a mean difference of catheter-derived -dP/dtmax minus {Delta}P/{Delta}t-MR was -8±159 mm Hg/s (mean±2 SD, Fig 7Down). Changes in {Delta}P/{Delta}t-MR also correlated with those in catheter-derived -dP/dtmax (r=.97, P<.01). Tau-MR correlated with the catheter-derived time constant (r=.76, P<.01); however, a mean difference of the catheter-derived time constant minus tau-MR was 29±30 ms (mean±2 SD, Fig 8Down). Tau-MR-trace also correlated with the catheter-derived time constant (r=.79, P<.01), and a mean difference of the catheter-derived time constant minus tau-MR-trace was 24±28 ms (mean±2 SD, Fig 9Down). After the correction of tau-MR with LA pressure, the correlation coefficient increased, although not significantly, from 0.76 to 0.86, and the mean difference decreased significantly, from 29±30 to 8±21 ms (mean±2 SD, P<.01). Changes in tau-MR correlated with those in the catheter-derived time constant both before and after the correction (r=.74, r=.58, and P<.01, respectively). The Doppler-derived non–zero-pressure asymptote time constant correlated only poorly with the catheter-derived non–zero-pressure asymptote time constant (r=.48, P<.01), and the mean difference was 9±55 ms (mean±2 SD).



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  		Figure 7. A, Plot showing relation between catheter-derived -dP/dtmax and Doppler-derived {Delta}P/{Delta}t-MR. Dashed line is a line of identity, and solid line is a regression line. B, Mean vs the difference of catheter-derived -dP/dtmax minus Doppler-derived {Delta}P/{Delta}t-MR. Doppler-derived {Delta}P/{Delta}t-MR is defined in the text. Solid line indicates mean difference, and dashed lines are 2 SD of mean difference.



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  		Figure 8. A, Plot showing relation between the catheter-derived time constant (tau) and the time constant derived from continuous-wave Doppler mitral regurgitant velocity spectrum in the simplified method (tau-MR). B, Mean vs the difference of the catheter-derived time constant (tau) minus the time constant derived from continuous-wave Doppler mitral regurgitant velocity spectrum (tau-MR). C, Relation between the catheter-derived time constant (tau) and the Doppler-derived time constant corrected for left atrial pressure (corrected tau-MR). D, Mean vs the difference of the catheter-derived time constant (tau) minus the Doppler-derived time constant corrected for left atrial pressure (corrected tau-MR). In A and C, dashed lines are lines of identity, and solid lines are regression lines. In B and D, solid lines indicate mean difference, and dashed lines are 2 SD of mean difference.



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  		Figure 9. A, Plot showing relation between the catheter-derived time constant (tau) and the time constant derived from continuous-wave Doppler mitral regurgitant velocity spectrum in the conventional manner (tau-MR-trace). B, Mean vs the difference of the catheter-derived time constant (tau) minus the time constant derived from continuous-wave Doppler mitral regurgitant velocity spectrum (tau-MR-trace). In A, dashed line is a line of identity, and solid line is regression line. In B, solid line indicates mean difference, and dashed lines are 2 SD of mean difference.


*    Discussion
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 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
up arrowResults
*Discussion
down arrowReferences
 
The present study showed that the time constant of LV relaxation and -dP/dtmax can be estimated from the continuous-wave Doppler aortic regurgitant velocity spectrum and that the accuracy of the aortic regurgitant velocity method was even better than the mitral regurgitant velocity method, particularly in the presence of LV dysfunction.

Estimation of LV Pressure From Continuous-Wave Doppler Aortic and Mitral Regurgitant Velocity Spectra
Continuous-wave Doppler echocardiography provides noninvasive and accurate estimates of pressure gradient between two cardiac chambers using the simplified Bernoulli equation.27 33 34 Mitral regurgitant velocity reflects instantaneous LV-LA pressure gradient, while aortic regurgitant velocity reflects instantaneous aortic-LV pressure gradient. The fluctuation of LA pressure during the isovolumic relaxation period is minor, and LA pressure is usually negligibly low. Thus, it has been agreed that LV pressure can be derived from the mitral regurgitant velocity spectrum, and several studies have shown that indexes of LV function derived from LV pressure tracings can be determined from the mitral regurgitant velocity spectrum.24 25 26 35 36 Similarly, the fluctuation of aortic pressure during the isovolumic relaxation period is minor, and LV minimal pressure should usually be negligible. Therefore, LV pressure and pressure-derived indexes of LV function should also be derived from the aortic regurgitant velocity spectrum. We did not compare Doppler-derived and catheter-derived LV pressure wave forms in a quantitative fashion, but these were qualitatively similar to each other.

Indexes Derived From Aortic and Mitral Regurgitant Velocity Spectra
We showed that {Delta}P/{Delta}t-AR and {Delta}P/{Delta}t-MR correlated with catheter-derived -dP/dtmax and that tau-AR and tau-MR correlated with the catheter-derived time constant. However, the Doppler method tended to underestimate the time constant, and the underestimation was particularly gross for the mitral regurgitation method. The underestimation may be most adequately explained by the fact that Doppler-derived velocity estimates pressure gradient rather than absolute pressure. In other words, when applying Doppler data to the estimation of the LV pressure curve, we have to consider the effects of LV minimal pressure and the fluctuation of aortic pressure for the aortic regurgitation method and those of an absolute value and the fluctuation of LA pressure for the mitral regurgitation method. Doppler estimate of -dP/dtmax was determined from regurgitant velocity spectra as a rate of the changes in LV pressure between two instances, and thus, the errors may well be small. In contrast, the semilogarithmic method, assuming zero-pressure asymptote, was applied to the calculation of the Doppler-derived time constant, and thus, the effects of LV minimal or LA pressure may not be neglected. The underestimation of the Doppler-derived time constant may be explained in this way. Such underestimation of the mitral regurgitation method was also observed in the previous studies.25 26

In terms of the assumption of negligible LV minimal pressure in the aortic regurgitation method, LV minimal pressure was negligibly low in the condition with mild LV dysfunction; however, it increased with the depression of LV function. Furthermore, correction with LV minimal pressure improved the correlation coefficient between Doppler and catheter estimates. Therefore, LV minimal pressure may not necessarily be negligible, particularly in the presence of severe LV dysfunction. However, our results showed that the underestimation of tau-AR was smaller than that of tau-MR under a wide range of LV minimal pressures (4 to 29 mm Hg), probably because LV minimal pressure is lower than LA pressure. Therefore, the error in the assumption may not be large enough to lessen the value of the aortic regurgitation method.

Comparison of Indexes Derived From Aortic and Mitral Regurgitant Velocity Spectra
Negative dP/dtmax derived from the aortic or mitral regurgitant velocity spectrum corresponded to that derived from the LV pressure tracing. Therefore, -dP/dtmax can be assessed with the same accuracy from aortic and mitral regurgitant velocity spectra. However, the mean difference of the catheter-derived time constant minus tau-MR was larger compared with tau-AR. In other words, the underestimation of the time constant becomes smaller if the aortic rather than mitral regurgitant velocity spectrum is used. This may be because LA pressure is much higher than LV minimal pressure. Thus, although both aortic and mitral regurgitant velocity spectra provide accurate estimates of -dP/dtmax, the aortic regurgitant velocity spectrum is likely to provide a more accurate estimate of the time constant, particularly in the presence of LV dysfunction and the elevation of LA pressure.

Calculation of the Time Constant
In this study, we used only two points to derive the time constant from the aortic or mitral regurgitant velocity spectra. An LV pressure contour can be constructed from the Doppler tracings using a modified Bernoulli equation, and thus, both the zero-pressure asymptote and the non–zero-pressure asymptote time constants can be calculated in the conventional manner (tracing method), which uses a number of points. In terms of calculating the zero-pressure asymptote time constant, the results of this study showed that our simplified method can estimate the time constant as well as such a conventional or tracing method.

The effects of LV minimal pressure or LA pressure on the derivation of the time constant might be minimized by the use of the non–zero-pressure rather than the zero-pressure asymptote method. This is because the non–zero-pressure asymptote method, in contrast to the zero-pressure asymptote method, is independent of absolute LV pressure and because absolute LV pressure cannot be directly estimated from the Doppler method. Thus, the non–zero-pressure asymptote method might be considered to be appropriate in deriving the time constant from the Doppler velocity spectra. However, the correlation between the catheter-derived and the Doppler-derived non–zero-pressure asymptote time constants was suboptimal. These data are partially consistent with the results of Nishimura et al26 because they showed that the non–zero-pressure asymptote time constant derived from the mitral regurgitant velocity curve did not correlate with the catheter-derived time constant. Their and our unexpected results may be due to significant beat-to-beat variability in the calculation of a non–zero-pressure asymptote time constant.37 Considering that the measurements of one or two points of the aortic or mitral regurgitant velocity curve provide reliable estimates of the zero-pressure asymptote time constant, our simpler method for estimating the zero-pressure asymptote time constant may be more practical than the tracing method.

Study Limitations
There are several limitations in this study. First, a complete, well-delineated spectral envelope from aortic regurgitation is necessary to determine the time constant and -dP/dtmax. This may be difficult in patients with trace or mild aortic regurgitation. However, this limitation does not lower the value of this study. The same limitation is present in the mitral regurgitation method. In clinical practice, there are patients in whom a well-delineated spectral envelope can be obtained from aortic regurgitation but not from mitral regurgitation. Further, it is noted that the acceleration limb of the aortic regurgitant velocity spectrum, where all of our indexes are measured, is much easier to record than the subsequent portion. We recognize that the proportion of patients in whom aortic regurgitation is detectable with Doppler echocardiography is smaller than that of patients with mitral regurgitation detectable with Doppler echocardiography. However, we believe that the results of this study offer an alternative Doppler echocardiographic method of noninvasive assessment of the time constant and -dP/dtmax. Furthermore, future improvement of Doppler equipment and the development of contrast medium that passes the pulmonary bed may increase the frequency of detection of aortic regurgitation in the near future, and the importance of our results may increase.

Second, the ultrasound beam should be aligned parallel to the velocity vector of the regurgitant flow. This limitation may be minimized by careful scanning with a nonimaging transducer or the guidance of color Doppler flow imaging with an image-directed continuous-wave Doppler transducer.

Third, although LV minimal or LA pressure cannot be precisely evaluated with noninvasive methods, the correction for them improved the accuracy of the estimation of the time constant. Therefore, further investigations may be necessary to develop noninvasive methods for the estimation of LV minimal or LA pressure and to establish more accurate assessment of LV relaxation. However, changes in tau-AR and tau-MR correlated with those in the catheter-derived time constant, and thus, tau-AR and tau-MR, even if without corrections, are useful at least in estimating changes in LV relaxation.

Fourth, in calculating {Delta}P/{Delta}t-MR and tau-MR, we measured the mitral regurgitant velocity at -dP/dtmax, which was obtained from simultaneous measurement of LV pressure. However, the phonocardiographic second heart sound may be used as a substitute for -dP/dtmax. Note that such measurements are not required if the aortic rather than mitral regurgitant velocity spectrum is used.

Finally, the point at -dP/dtmax is included in the descending limb of the mitral regurgitant velocity curve. If the mitral regurgitant velocity curve is traced and is converted to the pressure curve, -dP/dtmax can be directly calculated. However, the point at -dP/dtmax is not necessarily included in the ascending limb of the aortic regurgitant velocity curve because aortic regurgitation occurs near the point at -dP/dtmax. Thus, -dP/dtmax may not be directly calculated from the aortic regurgitant velocity curve. However, our results showed that {Delta}P/{Delta}t-AR agreed well with the catheter-derived -dP/dtmax, and there was no significant underestimation. A time lag between the point at -dP/dtmax and the point used to calculate {Delta}P/{Delta}t-AR may not significantly hamper the value of the aortic regurgitant velocity curve method in the noninvasive assessment of -dP/dtmax.

Clinical Implications
The time constant of LV isovolumic pressure fall and -dP/dtmax are widely used as indexes of LV relaxation and are obtained from high-fidelity LV pressure tracings. Recently, these indexes have been shown to be noninvasively derived from the continuous-wave Doppler mitral regurgitant velocity spectrum. However, it is impossible to obtain a well-delineated velocity spectral envelope from mitral regurgitation in all patients. The present study showed that the time constant and -dP/dtmax can also be assessed from the aortic regurgitant velocity spectrum. The results of this study offer an alternative method of noninvasively assessing LV relaxation.



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  		Figure 5. Representative recordings of the aortic regurgitant velocity curve in dogs with different -dP/dtmax and time constant (tau). Abbreviations as in previous figures.



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  		Figure 6. A, Plot showing relation between the catheter-derived time constant (tau) and the time constant derived from continuous-wave Doppler aortic regurgitant velocity spectrum in the conventional manner (tau-AR-trace). B, Mean vs the difference of the catheter-derived time constant (tau) minus the time constant derived from continuous-wave Doppler aortic regurgitant velocity spectrum (tau-AR-trace). In A, dashed line is a line of identity, and solid line is a regression line. In B, solid line indicates mean difference, and dashed lines are 2 SD of mean difference.


*    Acknowledgments
 
This study was supported in part by research grants from the Ministry of Health and Welfare of Japan.

Correction of the Time Constant Derived From the Continuous-Wave Doppler Aortic Regurgitant Velocity Spectrum for LV Minimal Pressure
If we do not assume that LV minimal pressure (LV minP) is zero, LV pressure during isovolumic diastole is described as follows:


Therefore, in deriving the time constant from the aortic regurgitant velocity spectrum, we have to solve the following equation:





We substituted 0 for LV minP if LV minP was <10 mm Hg, 10 if LV minP was >=10 and <20 mm Hg, and 20 if LV minP was >=20 mm Hg.

Correction of the Time Constant Derived From Continuous-Wave Doppler Mitral Regurgitant Velocity Spectrum for LA Pressure
If we do not assume that LA pressure (LAP) is zero, LV pressure during isovolumic diastole is described as follows:


Therefore, in deriving the time constant from the mitral regurgitant velocity spectrum, we have to solve the following equation:


We substituted 0 for LAP if LAP at -dP/dtmax was <10 mm Hg, 10 if LAP at -dP/dtmax was >=10 and <20 mm Hg, 20 if LAP at -dP/dtmax was >=20 and <30 mm Hg, and 30 if LAP at -dP/dtmax was >=30. As a result, Vtau-MR was 0.61xVMR1 if LAP at -dP/dtmax was <10 mm Hg, 0.52xVMR1 if LAP at -dP/dtmax was >=10 and <20 mm Hg, 0.41xVMR1 if LAP at -dP/dtmax was >=20 and <30 mm Hg, and 0.27xVMR1 if LAP at -dP/dtmax was >=40 mm Hg.

Received June 7, 1994; accepted August 15, 1994.


*    References
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