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Comparison of hemodynamic pressure half-time method and Gorlin formula with Doppler and echocardiographic determinations of mitral valve area in patients with combined mitral stenosis and regurgitation
Comparison of hemodynamic pressure half-time method and Gorlin formula with Doppler and echocardiographic determinations of mitral valve area in patients with combined mitral stenosis and regurgitation Mitral valve area d e t e r m i n e d by the Gorlin formula in patients with c o m b i n e d mitral stenosis and r e g u r g i t a t i o n u n d e r e s t i m a t e s the true orifice size. Recent data suggest Doppler ultrasound and t w o - d i m e n s i o n a l e c h o c a r d i o g r a p h y more a c c u r a t e l y estimate the mitral valve area in patients with mixed mitral valvular disease. This study assessed the accuracy of an a l t e r n a t e method, the h e m o d y n a m i c pressure half-time method, for mitral valve area d e t e r m i n a t i o n in such patients. In 22 patients, 28 separate mitral valve areas w e r e calculated by the h e m o d y n a m i c pressure half-time method, the Gorlin formula, and the Gorlin formula c o r r e c t e d for mitral regurgitation, and w e r e c o m p a r e d with results calculated by the Doppler pressure half-time method. Six patients w e r e studied both b e f o r e and after balloon mitral valvuloplasty. In addition, mitral valve areas calculated by all four m e t h o d s w e r e c o m p a r e d with results o b t a i n e d by p l a n i m e t r y in 15 patients with t e c h n i c a l l y optimal e c h o c a r d i o g r a m s . The mitral valve areas d e t e r m i n e d by h e m o d y n a m i c pressure half-time c o r r e t a t e d closely with the valve areas d e t e r m i n e d by Doppler (r = 0.90), w h e r e a s mitral valve areas d e t e r m i n e d by the Gorlin formula (both w i t h o u t and with c o r r e c t i o n for mitral regurgitation) did not c o r r e l a t e as well with the Doppler-estimated valve areas (r = 0.47 and 9 = 0.56, respectively). Correlation b e t w e e n the Doppler-derived mitral valve areas and the p l a n i m e t e r e d valve areas was also g o o d (r = 0.84), as was that b e t w e e n the mitral valve areas calculated by h e m o d y n a m i c pressure half-time and those calculated by p l a n i m e t r y (r = 0.78). The mitral valve areas calculated by the Gorlin formula, e v e n with correction for mitral regurgitation, did not c o r r e l a t e well with the p l a n i m e t e r e d valve areas (r = 0.30 and 9 = 0 . 3 5 , respectively). These comparisons indicate that in patients with c o m b i n e d mitral stenosis and regurgitation, the h e m o d y n a m i c pressure half-time m e t h o d is more accurate than the Gorlin formula and should be considered for h e m o d y n a m i c assessment of mitral valve orifice area in patients with mixed mitral valvular disease. (AM HEART J 1 9 9 0 ; 1 1 9 : 1 2 1 . )
Carey S. Fredman, MD, Anthony C. Pearson, MD, Arthur J. Labovitz, MD, and Morton J. Kern, MD. St. Louis, Mo. In 1951 Gorlin and Gorlin 1 introduced the hydraulic calculation of the mitral valve area, noting t h a t the formula was very accurate in the presence of pure mitral stenosis; however, in the presence of coexistent mitral regurgitation, the formula would underestimate the true valve a r e a ) More recently, calculation of the mitral valve area using the Dopplerderived pressure half-time method has been shown to
From the Divisionof Cardiology,Department of Internal Medicine,St. LouisUniversitySchoolof Medicine. Receivedfor publicationJuly 21, 1989;acceptedSept:5, 1989. Reprint requests: CareyS. Fredman,MD, CardiologyDivision,St. Louis UniversityMedicalSchool,3635VistaAve.at GrandBlvd.,P.O.Box15250, St. Louis,MO63110-0250. 4/1/16737
estimate reliably the area of the mitral orifice, both in patients with pure mitral stenosis 2, 3 as well as in those with combined mitral stenosis and regurgitation. 4 Two-dimensional echocardiography also affords a method of accurately measuring the mitral valve area in patients with mitral stenosis and is uninfluenced by accompanying mitral regurgitation. 5, 6 The echocardiographic method, however, requires technically optimal studies, proper gain settings, location of t h e true orifice in the short-axis view, and may be inaccurate in patients with a previous surgical commissurotomy. 7, s Over two decades ago, Libanoff and Rodbard 9,10 introduced the hemodynamically derived pressure half-time method as an alternative hemodynamic means for accurately determining the mitral valve 121
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a r e a in p a t i e n t s with mitral stenosis. Because the Gorlin f o r m u l a for the calculation of m i t r a l valve a r e a in p a t i e n t s with c o m b i n e d m i t r a l stenosis and regurgitation is s u b o p t i m a l , the p r e s e n t s t u d y was u n d e r t a k e n to c o m p a r e t h e accuracy of m i t r a l valve a r e a determined by the hemodynamic pressure half-time m e t h o d with t h a t d e t e r m i n e d b y the G o r l i n f o r m u l a in such patients. M i t r a l valve areas calculated with each h e m o d y n a m i c m e t h o d were c o m p a r e d with results o b t a i n e d b y D o p p l e r as well as those o b t a i n e d b y t w o - d i m e n s i o n a l echocardiography.
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METHODS Study population. Twenty-eight valve area determina-
tions were performed in 22 consecutive patients who underwent cardiac catheterization, two-dimensional echocardiographic, and cardiac Doppler evaluations between July 1986 and July 1988, and who were found to have combined mitral stenosis and regurgitation. Six patients were studied both before and within 24 hours after balloon mitral valvuloplasty. In 26 out of 28 valve area determinations, each patient's mitral regurgitation was visualized by both left ventricutography and by cardiac Doppler echocardiography. In one case, mild (1+) mitral regurgitation was present only on left ventriculography and in one case mild to moderate mitral regurgitation was seen only on the cardiac Doppler echocardiographic image. In the 27 studies of mitral regurgitation by ventriculography, five patients had trace, seven had mild (1+), two had mild to moderate (1+ to 2+), 10 had moderate (2+), two had moderately severe (3+), and one had severe (4+) mitral regurgitation. All patients had two-dimensional echocardiographic and cardiac Doppler studies performed within 1 day to 3 months (mean 12 days) of cardiac catheterization. There were 18 women and four men, ages 34 to 87 years (mean 64 _+ 14 years). Sixteen patients had known rheumatic heart disease and five patients had undergone a previous surgical mitral commissurotomy. Sinus rhythm was present during mitral valve area determinations in 12 patients, atrial fibrillation was present in 12, ventricular paced rhythm was seen in three, and junctional rhythm was found in one. Heart rate at the time of the cardiac catheterization ranged from 51 to 122 (mean 82 _+ 19) beats/min. All patients had mitral valve areas determined by the Gorlin equation (with and without correction for mitral regurgitation), by the hemodynamic pressure half-time method, and by the Doppler pressure half-time method. In 15 patients whose two-dimensional echocardiographic studies were of optimal quality and who did not have a prior surgical commissurotomy, mitral valve area was determined by computer-assisted planimetry as well. Hemodynamic, echocardiographic, and Doppler mitral valve area determinations were calculated independently of each other and in a blinded fashion. Cardiac catheterization and hemodynamic procedure.
Simultaneous right and left heart hemodynamic data were obtained after introducing fluid-filled catheters from the femoral approach. A 7F balloon-tipped thermodilution catheter was used to record pulmonary capillary wedge
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Fig. 2. In patients with combined mitral stenosis and regurgitation, mitral valve areas (MVA) measured by (A) the Gorlin formula, (B) by the Gorlin formula corrected for mitral regurgitation, and (C) by the hemodynamic pressure half-time (P 89 method are compared with mitral valve areas measured by the Doppler half-time method. Regression lines for each comparisorr are shown and correlation coefficients are given. pressure and to determine cardiac output. In 14 patients left atrial pressure was measured directly by the transseptal technique. Simultaneous left ventricular pressures were recorded using a 7F high-flow pig-tail catheter. Equisensitivity of the model 800 Bentley pressure transducers (Bentley Laboratories Inc., Irvine, Calif.) was checked against a common mercury pressure source before each procedure. Each transducer zero line was connected t~ a manifold positioned at the mid chest level. Simultane6us recordings of left ventricular and pulmonary wedge or left atrial pressures were obtained at 100 mm/sec paper speed on a 0 to 50 mm Hg scale. The mean diastolic gradient across the mitral valve was calculated by computer-assisted planimetry from the simultaneously recorded left ventricular and left atrial or pulmonary capillary wedge pressures after correcting the wedge pressure for time delay by shifting the peak "V wave" to coincide with the left ventricular pressure downstroke. After the hemodynamic data were obtained, biplane (30-degree right anterior oblique [RAO], 60-degree left anterior oblique [LAO]) left ventriculography was performed for qualitative assessment of the severity of mitral regurgitation. The degree of opacification of the left atrium was graded on a standard qualitative scale as trace, 1+ (mild), 2+ (moderate), 3+ (moderately severe), or 4+ (severe) regurgitation. 11 Correction of the Gorlin
formula for mitral regurgitation was based on a semiquantitative grading of the regurgitation from the ventriculograms. A scale similar to that previously reported 11 assigned a regurgitant fraction of 5 % for trace regurgitation, 15% for 1+, 25% for 1+ to 2+, 30% for 2+, 40% for 3+, and 60% for 4+ regurgitation. The cardiac output as determined by the thermodilution method was utilized in calculating the mitral valve area by the Gorlin formula (except in one case where only the Fick determination of cardiac output was made).12,13 Data from five cardiac cycles were averaged for patients in sinus rhythm and from 10 cardiac cycles for patients in atrial fibrillation. Hemodynamic pressure half-time method. T h e h e m o
dynamically derived pressure half-time was defined as the time interval in milliseconds required for the diastolic atrioventricular pressure gradient to fall from the peak value to one half the peak value and was calculated from the pressure tracings, as shown in Fig. 1, A. The method used was identical to that described by Libanoff and Rodbard,9,10 except that zero time was considered to be at the point of the greatest atrioventricular pressure difference occurring during the firSt 120 msec of the diastolic filling period, rather than at the onset of rise of the left ventricular diastolic pressure. This modification avoided
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uncertainty in identifying the exact point of rise of the left ventricular diastolic pressure and assured that the peak left atrial-left ventricular pressure gradient in early diastole was measured. The gradient across the mitral valve was measured at 20 msec intervals until the onset of an "a" wave in the left atrial or pulmonary capillary wedge pressure tracing or (if no "a" wave was visible) until the onset of ventricular systole at the upstroke of the left ventricular pressure. In order to eliminate the hemodynamic artifact of "catheter whip," the logarithm of the atrioventricular pressure difference was plotted against time. 9,14 Using a linear fit with extrapolation to the y axis, the time required for the pressure difference to decrease from the extrapolated maximal gradient to one half that value was recorded as the hemodynamic pressure half-time (Fig. 1, B). The mitral valve area was then calculated as 220 msec/pressure half-time, the half-time of 220 msec having been shown to correlate well with a valve area of 1.0 cm 2 when utilizing hemodynamically derived valves./4 Doppler and two-dimensional echocardiography. Two-dimensional echocardiographic and cardiac Doppler studies were obtained on either an Irex System IIIB (Johnson & Johnson Ultrasound Inc., Ramsey, N.J.), a Hewlett-Packard Model 77020A (Hewlett-Packard Co., Medical Products, Andover, Mass.), or a Diasonics CFM700 (Diasonics, Inc., San Francisco, Calif.) using technical methods previously described. 4 Briefly, two-dimensional echocardiograms were performed using phased array imaging systems with a 2.5 or 3 MHz transducer. The mitral valve was interrogated from the apical window using continuous and pulsed wave Doppler. Hard copy Doppler recordings of mitral flow were obtained at a paper speed of 100 mm/sec. The mitral valve area was calculated using the Doppler pressure half-time method. The Doppler pressure half-time is the time from Vrnaxto Vmax/1.4, where Vm~ is the maximal transmitral diastolic velocity, and Vmax/1.4 is the velocity at which the maximal diastolic transvalvular
gradient has fallen by one half. 15 Mitral valve area was calculated using the Doppler pressure half-time as 220 msec/ pressure half-time. &16 Mitral regurgitation, using continuous wave Doppler, was defined as a holosystolic transmitral flow reversal of more than 2 m/sec. Tricuspid and aortic insufficiency jets were flow-mapped using either pulsed wave or color flow Doppler echocardiography. Tricuspid insufficiency was graded as mild (within 2 cm of the valve), moderate (2 to 4 cm into the right atrium), or severe (greater than 4 cm into the right atrium). Aortic insufficiency was graded as mild (extending less than 2 cm from aortic valve plane into the left ventricle), moderate (between 2 cm and the papillary muscle level), or severe (extending beyond the papillary muscle level). Mitral valve areas were planimetered 5 in 15 patients directly from video recordings, utilizing images in the shortaxis view. The smallest mitral orifice obtained by computer-assisted planimetry in early diastole was recorded. Statistical analysis. Measurements of mitral valve orifice area calculated by the Gorlin formula, with and without correction for mitral regurgitation, and by the hemodynamic pressure half-time method were correlated with the mitral valve area obtained by the Doppler method using simple least squares linear regression anlaysis. In 15 patients, mitral valve areas determined by all four methods were correlated with the mitral valve area obtained by planimetry, also using simple linear regression analysis. RESULTS Gorlin, hemodynamic pressure half-time, and Dopplerderived mitral valve areas. For the 28 valve area determinations, linear regression analyses of mitra] valve
areas measured, by the Gorlin formula, by the Gorlin formula corrected for mitral regurgitation, a n d by h e m o d y n a m i c pressure half-time c o m p a r e d with the valve areas d e t e r m i n e d by the Doppler pressure half-time m e t h o d are shown in Fig. 2. T h e correlation between the Gorlin-derived mitral valve areas a n d those calculated by Doppler was poor (r = 0.47, p = 0.01, slope = 0.287, y intercept = 0.656). Correction of the Gorlin-derived valve areas for mitral regurgitation yielded a stronger correlation (r = 0.56, p = 0.002, slope = 0.402, y intercept = 0.70). T h e strongest correlation was f o u n d between the mitral valve areas calculated by the h e m o d y n a m i c pressure half-time m e t h o d and the D o p p l e r pressure halftime m e t h o d (r = 0.90, p = 0.0001, slope = 1.112, y intercept = -0.157). W h e n p a t i e n t s with ~>2+ mitral regurgitation (n = 13) were considered separately (Fig. 3), the correlation for mitral valve areas between h e m o d y n a m i c pressure half-time and Doppler pressure half-time remained strong (r = 0.90, p = 0.0001, slope = L039, y intercept = -0.007). Comparison with two-dimensional echocardiographically determined mitral valve areas. Mitral valve areas
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Fig. 4. In patients with combined mitral stenosis and regurgitation, mitral valve areas (MVA) measured by (A) the Gorlin formula, (B) the Gorlin formula corrected for mitral regurgitation, (C) the hemodynamic pressure half-time (P 89 method, and (D) the Doppler half-time method'are compared with mitral valve areas measured by two-dimensional echocardiographic planimetry. Regression lines for each comparison are shown and correlation coefficients are given. determined by each method were compared with mitral valve areas determined by planimetry in 15 patients with technically optimal two-dimensional echocardiographic studies and no history of previous mitral commissurotomy. Linear regression analyses are shown in Fig. 4. Correlations between the Gorlinderived mitral valve areas (both without and with correction for mitral regurgitation) and the planimetered valve areas were poor (r = 0.30, p = 0.27, slope=0.258, y intercept=0.88; and r = 0.35, p = 0.20, slope = 0.361, y intercept = 0.933, respectively). Correlation was strong between the mitral valve areas determined by hemodynamic pressure half-time and the planimetered areas (r = 0.78, p = 0.0006, slope = 1.385, y i n t e r c e p t = - 0 . 6 8 7 ) , while the strongest relationship was between the Doppler-derived mitral valve areas and the planimetered areas (r = 0.84, p = 0.0003, slope = 1.176, y intercept = -0.329). Fig. 5 shows the simultaneous left atrial-left ventricular pressure waveforms, the transmitral Doppler
velocity tracings, and an echocardiographic parasterhal short-axis view of the mitral valve in a single patient with 4+ mitral regurgitation. Calculation of this patient's mitral valve area by the Gorlin formula, even after correction for mitral regurgitation, yielded moderately severe mitral stenosis. However, calculation of this patient's mitral valve area by the hemodynamic pressure half-time method, Doppler halftime method, or by planimetry resulted in valve areas that were only mildly stenotic. The valve areas calculated by each method are shown in the figure. DISCUSSION
The Gorlin method of calculating the mitral valve area in patients with coexisting mitral stenosis and regurgitation underestimates the true valve area. The forward cardiac output is utilized in the numerator of the valve area formula and fails to account for the regurgitant fraction that contributes to the total transmittal diastolic flow. Qualitative estimates of regurgitant fraction have been proposed to achieve
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Fig. 5 . Hemodynamic, Doppler, and two-dimensional echocardiographic data from a single patient with mitral stenosis and 4+ mitral regurgitation. A, Simultaneous left atrial and left ventricular pressures showing diastolic transmitral pressure gradient. The mitral valve areas (MVA) calculated by the G0rlin formula, Gorlin formula corrected for mitral regurgitation, and the hemodynamic pressure half-time (P 89 method are shown. B, Doppler velocity tracings of transmitral flow. The mitral valve area (MVA) calculated by the Doppler half-time method is shown. (3, Parasternal short-axis view of the mitral valve orifice frozen during diastole. The mitral valve area (MVA) determined by planimetry is shown.
more accurate mitral valve area determinations in patients with Combined mitral stenosis and regurgitation, but qualitative angiographic assessment has significant limitations for determining the severity of mitral regurgitation, 17Accuracy of the Gorlin method may be enhanced in patients with mixed mitral valvular disease by employing the cineangiographic left
ventricular stroke volume as the numerator in the formula. 18 This requires meticulous attention to calibration of the left ventricular volume and may be inaccurate in patients with atrial fibrillation or extrasystoles during ventriculography. Two-dimensional echocardiography5, 6, 7, 19, 20 and Doppler ultrasound 4 are two noninvasive methods th a t have
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been shown to measure accurately the mitral valve area, even inpatients with combined mitral stenosis and regurgitation. This study assessed the accuracy of an alternative method to the Gorlin formula for the hemodynamic measurement of mitral valve area in the presence of combined mitral stenosis and regurgitation. The hemodynamic pressure half-time method, originally described by Libanoff and Rodbard 9, 10 and recently correlated with the Gorlin formula in patients with pure mitral stenosis, 14 has never been evaluated in a large group of patients with combined mitral stenosis and regurgitation. The present study compared mitral valve areas calculated by this method, as well as by the Gorlin formula, and the Gorlin formula corrected for mitral regurgitation, with the mitral valve areas calculated by the Doppler pressure halftime method. The mitral valve areas calculated by all four methods were compared with those calculated by planimetry. The current analysis found that the mitral valve area calculated by the hemodynamic pressure halftime method correlated well with that determined by
Doppler and planimetry. Neither the valve area determined by the Gorlin formula nor that determined by the Gorlin formula corrected for mitral regurgitation had as good a correlation with Doppler or planimetry. The patient whose valve areas are shown in Fig. 5 illustrates that in patients with mixed mitral valvular disease the Gorlin formula may significantly underestimate the true valvular orifice. In this case a mildly stenotic mitral valve as determined by planimetry (area = 1.9 cm 2) and by the Doppler half-time method (area = 1.6 cm 2) was calculated by the Gorlin formula to have severe stenosis (area = 0.7 cm2). Even after correction for mitral regurgitation, stenosis was still calculated to be moderately severe (area = 1.1 cm2). The hemodynamic pressure halftime method, however, yielded a valve area that was mildly stenotic (area = 2.3 cm 2) and that was in close agreement with the findings of both Doppler and planimetry. The relationship between transvalvular pressure gradient and velocity can be seen from Fig. 6, a tracing of the hemodynamic atrioventricular pressure gradient taken with a simultaneous Doppler tracing
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showing transmitral flow. The more prolonged the atrioventricular pressure difference, the longer the transmitral velocity remains elevated, and the longer the resultant pressure half-time whether it is calculated by Doppler or by the hemodynamic method. The rate of decay of the transmitral gradient, and hence the pressure half-time, varies inversely with the mitral valve orifice area. Thomas et al. 21, 22 have shown t h a t the pressure half-time also varies directly with the left atrial compliance and square root of the peak transmittal gradient. The present study indicates that use of the pressure half-time method for assessment of the mitral valve area remains valid even in the presence of mitral regurgitation, probably because the initial pressure gradient and chamber compliance change in opposite directions. Study limitations. The use of the Doppler half-time method as the "gold standard" for determining mitral valve areas in the entire study group may be seen as a limitation. Previous data, 4 however, have shown that in patients with combined mitral stenosis and regurgitation Doppler-derived valve areas correlate very closely with mitral valve areas determined by two-dimensional echocardiographic planimetry. The 15 patients whose mitral valve areas were determined by planimetry in the present study are consistent with the earlier data in showing a good correlation with Doppler-determined valve areas and a poor correlation with Gorlin-derived valve areas. Based on these comparisons with planimetry data, the Doppler pressure half-time method would seem to be a valid "gold standard" for determining mitral valve areas in our study group. Several additional limitations in hemodynamic studies of this type should be considered. Use of the thermodilution cardiac output method in all valve area determinations except for one (Fick method) may have led to an artifactually lower cardiac output in 14 patients who had associated moderate or greater degrees of tricuspid regurgitation. However, when the average thermodilution cardiac output (3.8 + 0.6) was compared with the average Fick cardiac output (3.1 z 0.9) in the six patients from this group who had both measurements simultaneously, the thermodilution cardiac output was found to be slightly higher than the Fick measurements. Highfidelity catheters were not used in this study. Because the use of fluid-filled catheters for obtaining hemodynamic data is common clinical practice, we believe the results of this study are widely applicable. Four of the study patients also had associated moderate aortic insufficiency. While data suggest that pressure half-time estimates of mitral valve areas are accurate even in patients with aortic
insufficiency, ~ a recent study ~4 disputes this claim, asserting that the mitral valve area is overestimated by the pressure half-time method in patients with associated moderate to severe aortic insufficiency. However, when analyzed with these few patients excluded, the results of the present study remained unchanged. Last, six patients had measurements obtained both before and after balloon mitral valvuloplasty. There are data suggesting that following valvuloplasty the pressure half-time method for determining mitral valve area is inaccurate due to alterations in chamber compliance and peak transmitral gradient.21, 22, 25, 26 If this were the case, we might expect that inclusion of these post-valvuloplasty patients would weaken the correlation between pressure halftime (Doppler or hemodynamic) and planimetry. Even with the inclusion of the four such patients with technically optimal echocardiograms, correlation remained stronger and better than that between the Gorlin formula and planimetry. Conclusions. In conclusion, while the Gorlin formula has proved to be an accurate method for calculating the mitral valve area in pure mitral stenosis, it underestimates the true size of the valve when mitral regurgitation coexists. The hemodynamic pressure waveforms necessary to calculate the mitral valve area using the Gorlin formula contain the information required to calculate the mitral valve area by an alternative method, the hemodynamically derived pressure half-time. The present study has shown that, in the presence of combined mitral stenosis and regurgitation, the mitral valve area calculated by the hemodynamic pressure half-time method is more accurate than that calculated by the Gorlin formula, even after semiquantitative correction is made for mitral regurgitation. These data support using the hemodynamically derived pressure half-time method for invasive mitral valve area determination when there is coexistent mitral stenosis and regurgitation. The authors wish to thank Jan St. Vrain and Pattie Wallace for their technical assistance and Susan Buenger Johnson for her secretarial expertise in the preparation of this report.
REFERENCES
1. Gorlin R, Gorlin SG. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. AM HEART J 1951;41:1. 2. Hatle J, Angelsen B. Doppler ultrasound in cardiology: Physical principles and clinical applications. Philadelphia: Lea & Febiger, 1982:83. 3. Stamm RB, Martin RP. Quantification of pressure gradients across stenotic valves by Doppler ultrasound. J Am Coll Cardiol 1983;2:707. 4. Bryg RJ, Williams GA, Labovitz AJ, Aker U, Kennedy HL.
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9. 10. 11. 12. 13. 14.
15.
Effect of atrial fibrillation and mitral regurgitation on calculated mitral valve area in mitral stenosis. Am J Cardiol 1986;57:634. Henry WL, Griffith JM, Michaels LL, McIntosh CL, Morrow AG, Epstein SE. Measurement of mitral orifice area in patients with mitral valve disease by real-time, two-dimensional echocardiography. Circulation 1975;51:827. Wann LS, Weyman AE, Feigenbaum H, Dillon JC, Johnston KW, Eggleton RC. Determination of mitral valve area by corss-sectional echocardiography. Ann Intern Med 1978;88: 337. Martin RP, Rakowski H, Kleiman JH, Beaver W, London E, Popp K. Reliability and reproducibility of two-dimensional echocardiographic measurement of the stenotic mitral valve orifice area. Am J Cardiol 1979;43:560. Smith MD, Handshoe R, Handshoe S, Kwan OL, DeMaria AN. Comparative accuracy of two-dimensional echocardiography and Doppler pressure half-time methods in assessing severity of mitral stenosis in patients with and without prior commissurotomy. Circulation 1986;73:1000. Libanoff AJ, Rodbard S. Evaluation of the severity of mitral stenosis and regurgitation. Circulation 1966;33:218. Libanoff AJ, Rodbard S. Atrioventricular pressure half-time: measure of mitral valve orifice area. Circulation 1968;38:144. Grossman W. Profiles in valvular heart disease. In: Grossman W, ed. Cardiac catheterization and angiography. Philadelpha: Lea & Febiger, 1986:359. Grossman W. Blood flow measurement: the cardiac output. In: Grossman W, ed. Cardiac catheterization and angiography. Philadelhia: Lea & Febiger, 1986:101. Carabello BA, Grossman W. Calculation of stenotic valve orifice area. In: Grossman W, ed. Cardiac catheterization and angiography. Philadelphia: Lea & Febiger, 1986:143. Gonzalez MA, Child JS, Krivokapich J. Comparison of twodimensional and Doppler echocardiography and intracardiac hemodynamics for quantification of mitral stenosis. Am J Cardiol 1987;60:327. Hatle L, Angelsen B, Tromsdol A. Noninvasive assessment of atrioventricular pressure half-time by Doppler ultrasound. Circulation 1979;60:1096.
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16. Hatle L, Angelsen B. Doppler ultrasound in cardiology. Physical principles and clinical applications. 2nd ed. Philadelphia: Lea & Febiger, 1985:110. 17. Croft CH, Lipscomb K, Mathis K, Firth BG, Nicod P, Tilton G, Winniford WD, Hillis LD. Limitations of qualitative angiographic grading in aortic or mitral regurgitation. Am J Cardiol 1984;53:1593. 18. Askenazi J, Carlson CJ, Alpert JS, Dexter L. Mitral valve area in combined mitral stenosis and regurgitation. Circulation 1976;54:480. 19. Henry WL, Kostl DG. Echocardiographic evaluation of patients with mitral stenosis. Am J Med 1977;62:813. 20. Nichol PM, Gilbert BW, Kisslo JA. Two-dimensional echocardiographie assessment of mitral stenosis. Circulation 1977; 55:120. 21. Thomas JD, Weyman AE. Doppler mitral pressure half-time: a clinical tool in search of theoretic justification. J Am Coll Cardiol 1987;10:923. 22. Thomas JD, Wilkins GT, Choong CYP, Abascal VM, Palacios IF, Block PC, Weyman AE. Inaccuracy of mitral pressure half-time immediately after percutaneous mitral valvotomy. Circulation 1988;78:980. 23. Grayburn PA, Smith MD, Gurley JC, Booth DC, DeMaria AN. Effect of aortic regurgitation on the assessment of mitral valve orifice area by Doppler pressure half-time in mitral stenosis. Am J Cardiol 1987;60:322. 24. Nakatani S, Masuyama T, Kodama K, Kitabatake A, Fujii K, Kamada T. Value and limitations of Doppler echocardiography in the quantification of stenotic mitral valve area: comparison of the pressure half-time and the continuity equation methods. Circulation 1988;77:78. 25. Abascal VM, Wilkins GT, Choong CY, Thomas JD, Palacios IF, Block PC, Weyman AE. Echocardiographic evaluation of mitral valve structure and function in patients followed for at least 6 months after percutaneous balloon mitral valvuloplasty. J Am Coll Cardiol 1988;12:606. 26. Chen C, Wang Y, Gui B, Lin Y. Reliability of the Doppler pressure half-time method for assessing effects of percutaneous mitral balloon valvuloplasty. J Am Coll Cardiol 1989; 13:1309.
Carey S. Fredman, MD, Anthony C. Pearson, MD, Arthur J. Labovitz, MD, and Morton J. Kern, MD. St. Louis, Mo. In 1951 Gorlin and Gorlin 1 introduced the hydraulic calculation of the mitral valve area, noting t h a t the formula was very accurate in the presence of pure mitral stenosis; however, in the presence of coexistent mitral regurgitation, the formula would underestimate the true valve a r e a ) More recently, calculation of the mitral valve area using the Dopplerderived pressure half-time method has been shown to
From the Divisionof Cardiology,Department of Internal Medicine,St. LouisUniversitySchoolof Medicine. Receivedfor publicationJuly 21, 1989;acceptedSept:5, 1989. Reprint requests: CareyS. Fredman,MD, CardiologyDivision,St. Louis UniversityMedicalSchool,3635VistaAve.at GrandBlvd.,P.O.Box15250, St. Louis,MO63110-0250. 4/1/16737
estimate reliably the area of the mitral orifice, both in patients with pure mitral stenosis 2, 3 as well as in those with combined mitral stenosis and regurgitation. 4 Two-dimensional echocardiography also affords a method of accurately measuring the mitral valve area in patients with mitral stenosis and is uninfluenced by accompanying mitral regurgitation. 5, 6 The echocardiographic method, however, requires technically optimal studies, proper gain settings, location of t h e true orifice in the short-axis view, and may be inaccurate in patients with a previous surgical commissurotomy. 7, s Over two decades ago, Libanoff and Rodbard 9,10 introduced the hemodynamically derived pressure half-time method as an alternative hemodynamic means for accurately determining the mitral valve 121
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a r e a in p a t i e n t s with mitral stenosis. Because the Gorlin f o r m u l a for the calculation of m i t r a l valve a r e a in p a t i e n t s with c o m b i n e d m i t r a l stenosis and regurgitation is s u b o p t i m a l , the p r e s e n t s t u d y was u n d e r t a k e n to c o m p a r e t h e accuracy of m i t r a l valve a r e a determined by the hemodynamic pressure half-time m e t h o d with t h a t d e t e r m i n e d b y the G o r l i n f o r m u l a in such patients. M i t r a l valve areas calculated with each h e m o d y n a m i c m e t h o d were c o m p a r e d with results o b t a i n e d b y D o p p l e r as well as those o b t a i n e d b y t w o - d i m e n s i o n a l echocardiography.
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METHODS Study population. Twenty-eight valve area determina-
tions were performed in 22 consecutive patients who underwent cardiac catheterization, two-dimensional echocardiographic, and cardiac Doppler evaluations between July 1986 and July 1988, and who were found to have combined mitral stenosis and regurgitation. Six patients were studied both before and within 24 hours after balloon mitral valvuloplasty. In 26 out of 28 valve area determinations, each patient's mitral regurgitation was visualized by both left ventricutography and by cardiac Doppler echocardiography. In one case, mild (1+) mitral regurgitation was present only on left ventriculography and in one case mild to moderate mitral regurgitation was seen only on the cardiac Doppler echocardiographic image. In the 27 studies of mitral regurgitation by ventriculography, five patients had trace, seven had mild (1+), two had mild to moderate (1+ to 2+), 10 had moderate (2+), two had moderately severe (3+), and one had severe (4+) mitral regurgitation. All patients had two-dimensional echocardiographic and cardiac Doppler studies performed within 1 day to 3 months (mean 12 days) of cardiac catheterization. There were 18 women and four men, ages 34 to 87 years (mean 64 _+ 14 years). Sixteen patients had known rheumatic heart disease and five patients had undergone a previous surgical mitral commissurotomy. Sinus rhythm was present during mitral valve area determinations in 12 patients, atrial fibrillation was present in 12, ventricular paced rhythm was seen in three, and junctional rhythm was found in one. Heart rate at the time of the cardiac catheterization ranged from 51 to 122 (mean 82 _+ 19) beats/min. All patients had mitral valve areas determined by the Gorlin equation (with and without correction for mitral regurgitation), by the hemodynamic pressure half-time method, and by the Doppler pressure half-time method. In 15 patients whose two-dimensional echocardiographic studies were of optimal quality and who did not have a prior surgical commissurotomy, mitral valve area was determined by computer-assisted planimetry as well. Hemodynamic, echocardiographic, and Doppler mitral valve area determinations were calculated independently of each other and in a blinded fashion. Cardiac catheterization and hemodynamic procedure.
Simultaneous right and left heart hemodynamic data were obtained after introducing fluid-filled catheters from the femoral approach. A 7F balloon-tipped thermodilution catheter was used to record pulmonary capillary wedge
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Fig. 2. In patients with combined mitral stenosis and regurgitation, mitral valve areas (MVA) measured by (A) the Gorlin formula, (B) by the Gorlin formula corrected for mitral regurgitation, and (C) by the hemodynamic pressure half-time (P 89 method are compared with mitral valve areas measured by the Doppler half-time method. Regression lines for each comparisorr are shown and correlation coefficients are given. pressure and to determine cardiac output. In 14 patients left atrial pressure was measured directly by the transseptal technique. Simultaneous left ventricular pressures were recorded using a 7F high-flow pig-tail catheter. Equisensitivity of the model 800 Bentley pressure transducers (Bentley Laboratories Inc., Irvine, Calif.) was checked against a common mercury pressure source before each procedure. Each transducer zero line was connected t~ a manifold positioned at the mid chest level. Simultane6us recordings of left ventricular and pulmonary wedge or left atrial pressures were obtained at 100 mm/sec paper speed on a 0 to 50 mm Hg scale. The mean diastolic gradient across the mitral valve was calculated by computer-assisted planimetry from the simultaneously recorded left ventricular and left atrial or pulmonary capillary wedge pressures after correcting the wedge pressure for time delay by shifting the peak "V wave" to coincide with the left ventricular pressure downstroke. After the hemodynamic data were obtained, biplane (30-degree right anterior oblique [RAO], 60-degree left anterior oblique [LAO]) left ventriculography was performed for qualitative assessment of the severity of mitral regurgitation. The degree of opacification of the left atrium was graded on a standard qualitative scale as trace, 1+ (mild), 2+ (moderate), 3+ (moderately severe), or 4+ (severe) regurgitation. 11 Correction of the Gorlin
formula for mitral regurgitation was based on a semiquantitative grading of the regurgitation from the ventriculograms. A scale similar to that previously reported 11 assigned a regurgitant fraction of 5 % for trace regurgitation, 15% for 1+, 25% for 1+ to 2+, 30% for 2+, 40% for 3+, and 60% for 4+ regurgitation. The cardiac output as determined by the thermodilution method was utilized in calculating the mitral valve area by the Gorlin formula (except in one case where only the Fick determination of cardiac output was made).12,13 Data from five cardiac cycles were averaged for patients in sinus rhythm and from 10 cardiac cycles for patients in atrial fibrillation. Hemodynamic pressure half-time method. T h e h e m o
dynamically derived pressure half-time was defined as the time interval in milliseconds required for the diastolic atrioventricular pressure gradient to fall from the peak value to one half the peak value and was calculated from the pressure tracings, as shown in Fig. 1, A. The method used was identical to that described by Libanoff and Rodbard,9,10 except that zero time was considered to be at the point of the greatest atrioventricular pressure difference occurring during the firSt 120 msec of the diastolic filling period, rather than at the onset of rise of the left ventricular diastolic pressure. This modification avoided
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uncertainty in identifying the exact point of rise of the left ventricular diastolic pressure and assured that the peak left atrial-left ventricular pressure gradient in early diastole was measured. The gradient across the mitral valve was measured at 20 msec intervals until the onset of an "a" wave in the left atrial or pulmonary capillary wedge pressure tracing or (if no "a" wave was visible) until the onset of ventricular systole at the upstroke of the left ventricular pressure. In order to eliminate the hemodynamic artifact of "catheter whip," the logarithm of the atrioventricular pressure difference was plotted against time. 9,14 Using a linear fit with extrapolation to the y axis, the time required for the pressure difference to decrease from the extrapolated maximal gradient to one half that value was recorded as the hemodynamic pressure half-time (Fig. 1, B). The mitral valve area was then calculated as 220 msec/pressure half-time, the half-time of 220 msec having been shown to correlate well with a valve area of 1.0 cm 2 when utilizing hemodynamically derived valves./4 Doppler and two-dimensional echocardiography. Two-dimensional echocardiographic and cardiac Doppler studies were obtained on either an Irex System IIIB (Johnson & Johnson Ultrasound Inc., Ramsey, N.J.), a Hewlett-Packard Model 77020A (Hewlett-Packard Co., Medical Products, Andover, Mass.), or a Diasonics CFM700 (Diasonics, Inc., San Francisco, Calif.) using technical methods previously described. 4 Briefly, two-dimensional echocardiograms were performed using phased array imaging systems with a 2.5 or 3 MHz transducer. The mitral valve was interrogated from the apical window using continuous and pulsed wave Doppler. Hard copy Doppler recordings of mitral flow were obtained at a paper speed of 100 mm/sec. The mitral valve area was calculated using the Doppler pressure half-time method. The Doppler pressure half-time is the time from Vrnaxto Vmax/1.4, where Vm~ is the maximal transmitral diastolic velocity, and Vmax/1.4 is the velocity at which the maximal diastolic transvalvular
gradient has fallen by one half. 15 Mitral valve area was calculated using the Doppler pressure half-time as 220 msec/ pressure half-time. &16 Mitral regurgitation, using continuous wave Doppler, was defined as a holosystolic transmitral flow reversal of more than 2 m/sec. Tricuspid and aortic insufficiency jets were flow-mapped using either pulsed wave or color flow Doppler echocardiography. Tricuspid insufficiency was graded as mild (within 2 cm of the valve), moderate (2 to 4 cm into the right atrium), or severe (greater than 4 cm into the right atrium). Aortic insufficiency was graded as mild (extending less than 2 cm from aortic valve plane into the left ventricle), moderate (between 2 cm and the papillary muscle level), or severe (extending beyond the papillary muscle level). Mitral valve areas were planimetered 5 in 15 patients directly from video recordings, utilizing images in the shortaxis view. The smallest mitral orifice obtained by computer-assisted planimetry in early diastole was recorded. Statistical analysis. Measurements of mitral valve orifice area calculated by the Gorlin formula, with and without correction for mitral regurgitation, and by the hemodynamic pressure half-time method were correlated with the mitral valve area obtained by the Doppler method using simple least squares linear regression anlaysis. In 15 patients, mitral valve areas determined by all four methods were correlated with the mitral valve area obtained by planimetry, also using simple linear regression analysis. RESULTS Gorlin, hemodynamic pressure half-time, and Dopplerderived mitral valve areas. For the 28 valve area determinations, linear regression analyses of mitra] valve
areas measured, by the Gorlin formula, by the Gorlin formula corrected for mitral regurgitation, a n d by h e m o d y n a m i c pressure half-time c o m p a r e d with the valve areas d e t e r m i n e d by the Doppler pressure half-time m e t h o d are shown in Fig. 2. T h e correlation between the Gorlin-derived mitral valve areas a n d those calculated by Doppler was poor (r = 0.47, p = 0.01, slope = 0.287, y intercept = 0.656). Correction of the Gorlin-derived valve areas for mitral regurgitation yielded a stronger correlation (r = 0.56, p = 0.002, slope = 0.402, y intercept = 0.70). T h e strongest correlation was f o u n d between the mitral valve areas calculated by the h e m o d y n a m i c pressure half-time m e t h o d and the D o p p l e r pressure halftime m e t h o d (r = 0.90, p = 0.0001, slope = 1.112, y intercept = -0.157). W h e n p a t i e n t s with ~>2+ mitral regurgitation (n = 13) were considered separately (Fig. 3), the correlation for mitral valve areas between h e m o d y n a m i c pressure half-time and Doppler pressure half-time remained strong (r = 0.90, p = 0.0001, slope = L039, y intercept = -0.007). Comparison with two-dimensional echocardiographically determined mitral valve areas. Mitral valve areas
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Fig. 4. In patients with combined mitral stenosis and regurgitation, mitral valve areas (MVA) measured by (A) the Gorlin formula, (B) the Gorlin formula corrected for mitral regurgitation, (C) the hemodynamic pressure half-time (P 89 method, and (D) the Doppler half-time method'are compared with mitral valve areas measured by two-dimensional echocardiographic planimetry. Regression lines for each comparison are shown and correlation coefficients are given. determined by each method were compared with mitral valve areas determined by planimetry in 15 patients with technically optimal two-dimensional echocardiographic studies and no history of previous mitral commissurotomy. Linear regression analyses are shown in Fig. 4. Correlations between the Gorlinderived mitral valve areas (both without and with correction for mitral regurgitation) and the planimetered valve areas were poor (r = 0.30, p = 0.27, slope=0.258, y intercept=0.88; and r = 0.35, p = 0.20, slope = 0.361, y intercept = 0.933, respectively). Correlation was strong between the mitral valve areas determined by hemodynamic pressure half-time and the planimetered areas (r = 0.78, p = 0.0006, slope = 1.385, y i n t e r c e p t = - 0 . 6 8 7 ) , while the strongest relationship was between the Doppler-derived mitral valve areas and the planimetered areas (r = 0.84, p = 0.0003, slope = 1.176, y intercept = -0.329). Fig. 5 shows the simultaneous left atrial-left ventricular pressure waveforms, the transmitral Doppler
velocity tracings, and an echocardiographic parasterhal short-axis view of the mitral valve in a single patient with 4+ mitral regurgitation. Calculation of this patient's mitral valve area by the Gorlin formula, even after correction for mitral regurgitation, yielded moderately severe mitral stenosis. However, calculation of this patient's mitral valve area by the hemodynamic pressure half-time method, Doppler halftime method, or by planimetry resulted in valve areas that were only mildly stenotic. The valve areas calculated by each method are shown in the figure. DISCUSSION
The Gorlin method of calculating the mitral valve area in patients with coexisting mitral stenosis and regurgitation underestimates the true valve area. The forward cardiac output is utilized in the numerator of the valve area formula and fails to account for the regurgitant fraction that contributes to the total transmittal diastolic flow. Qualitative estimates of regurgitant fraction have been proposed to achieve
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Fig. 5 . Hemodynamic, Doppler, and two-dimensional echocardiographic data from a single patient with mitral stenosis and 4+ mitral regurgitation. A, Simultaneous left atrial and left ventricular pressures showing diastolic transmitral pressure gradient. The mitral valve areas (MVA) calculated by the G0rlin formula, Gorlin formula corrected for mitral regurgitation, and the hemodynamic pressure half-time (P 89 method are shown. B, Doppler velocity tracings of transmitral flow. The mitral valve area (MVA) calculated by the Doppler half-time method is shown. (3, Parasternal short-axis view of the mitral valve orifice frozen during diastole. The mitral valve area (MVA) determined by planimetry is shown.
more accurate mitral valve area determinations in patients with Combined mitral stenosis and regurgitation, but qualitative angiographic assessment has significant limitations for determining the severity of mitral regurgitation, 17Accuracy of the Gorlin method may be enhanced in patients with mixed mitral valvular disease by employing the cineangiographic left
ventricular stroke volume as the numerator in the formula. 18 This requires meticulous attention to calibration of the left ventricular volume and may be inaccurate in patients with atrial fibrillation or extrasystoles during ventriculography. Two-dimensional echocardiography5, 6, 7, 19, 20 and Doppler ultrasound 4 are two noninvasive methods th a t have
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been shown to measure accurately the mitral valve area, even inpatients with combined mitral stenosis and regurgitation. This study assessed the accuracy of an alternative method to the Gorlin formula for the hemodynamic measurement of mitral valve area in the presence of combined mitral stenosis and regurgitation. The hemodynamic pressure half-time method, originally described by Libanoff and Rodbard 9, 10 and recently correlated with the Gorlin formula in patients with pure mitral stenosis, 14 has never been evaluated in a large group of patients with combined mitral stenosis and regurgitation. The present study compared mitral valve areas calculated by this method, as well as by the Gorlin formula, and the Gorlin formula corrected for mitral regurgitation, with the mitral valve areas calculated by the Doppler pressure halftime method. The mitral valve areas calculated by all four methods were compared with those calculated by planimetry. The current analysis found that the mitral valve area calculated by the hemodynamic pressure halftime method correlated well with that determined by
Doppler and planimetry. Neither the valve area determined by the Gorlin formula nor that determined by the Gorlin formula corrected for mitral regurgitation had as good a correlation with Doppler or planimetry. The patient whose valve areas are shown in Fig. 5 illustrates that in patients with mixed mitral valvular disease the Gorlin formula may significantly underestimate the true valvular orifice. In this case a mildly stenotic mitral valve as determined by planimetry (area = 1.9 cm 2) and by the Doppler half-time method (area = 1.6 cm 2) was calculated by the Gorlin formula to have severe stenosis (area = 0.7 cm2). Even after correction for mitral regurgitation, stenosis was still calculated to be moderately severe (area = 1.1 cm2). The hemodynamic pressure halftime method, however, yielded a valve area that was mildly stenotic (area = 2.3 cm 2) and that was in close agreement with the findings of both Doppler and planimetry. The relationship between transvalvular pressure gradient and velocity can be seen from Fig. 6, a tracing of the hemodynamic atrioventricular pressure gradient taken with a simultaneous Doppler tracing
128
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showing transmitral flow. The more prolonged the atrioventricular pressure difference, the longer the transmitral velocity remains elevated, and the longer the resultant pressure half-time whether it is calculated by Doppler or by the hemodynamic method. The rate of decay of the transmitral gradient, and hence the pressure half-time, varies inversely with the mitral valve orifice area. Thomas et al. 21, 22 have shown t h a t the pressure half-time also varies directly with the left atrial compliance and square root of the peak transmittal gradient. The present study indicates that use of the pressure half-time method for assessment of the mitral valve area remains valid even in the presence of mitral regurgitation, probably because the initial pressure gradient and chamber compliance change in opposite directions. Study limitations. The use of the Doppler half-time method as the "gold standard" for determining mitral valve areas in the entire study group may be seen as a limitation. Previous data, 4 however, have shown that in patients with combined mitral stenosis and regurgitation Doppler-derived valve areas correlate very closely with mitral valve areas determined by two-dimensional echocardiographic planimetry. The 15 patients whose mitral valve areas were determined by planimetry in the present study are consistent with the earlier data in showing a good correlation with Doppler-determined valve areas and a poor correlation with Gorlin-derived valve areas. Based on these comparisons with planimetry data, the Doppler pressure half-time method would seem to be a valid "gold standard" for determining mitral valve areas in our study group. Several additional limitations in hemodynamic studies of this type should be considered. Use of the thermodilution cardiac output method in all valve area determinations except for one (Fick method) may have led to an artifactually lower cardiac output in 14 patients who had associated moderate or greater degrees of tricuspid regurgitation. However, when the average thermodilution cardiac output (3.8 + 0.6) was compared with the average Fick cardiac output (3.1 z 0.9) in the six patients from this group who had both measurements simultaneously, the thermodilution cardiac output was found to be slightly higher than the Fick measurements. Highfidelity catheters were not used in this study. Because the use of fluid-filled catheters for obtaining hemodynamic data is common clinical practice, we believe the results of this study are widely applicable. Four of the study patients also had associated moderate aortic insufficiency. While data suggest that pressure half-time estimates of mitral valve areas are accurate even in patients with aortic
insufficiency, ~ a recent study ~4 disputes this claim, asserting that the mitral valve area is overestimated by the pressure half-time method in patients with associated moderate to severe aortic insufficiency. However, when analyzed with these few patients excluded, the results of the present study remained unchanged. Last, six patients had measurements obtained both before and after balloon mitral valvuloplasty. There are data suggesting that following valvuloplasty the pressure half-time method for determining mitral valve area is inaccurate due to alterations in chamber compliance and peak transmitral gradient.21, 22, 25, 26 If this were the case, we might expect that inclusion of these post-valvuloplasty patients would weaken the correlation between pressure halftime (Doppler or hemodynamic) and planimetry. Even with the inclusion of the four such patients with technically optimal echocardiograms, correlation remained stronger and better than that between the Gorlin formula and planimetry. Conclusions. In conclusion, while the Gorlin formula has proved to be an accurate method for calculating the mitral valve area in pure mitral stenosis, it underestimates the true size of the valve when mitral regurgitation coexists. The hemodynamic pressure waveforms necessary to calculate the mitral valve area using the Gorlin formula contain the information required to calculate the mitral valve area by an alternative method, the hemodynamically derived pressure half-time. The present study has shown that, in the presence of combined mitral stenosis and regurgitation, the mitral valve area calculated by the hemodynamic pressure half-time method is more accurate than that calculated by the Gorlin formula, even after semiquantitative correction is made for mitral regurgitation. These data support using the hemodynamically derived pressure half-time method for invasive mitral valve area determination when there is coexistent mitral stenosis and regurgitation. The authors wish to thank Jan St. Vrain and Pattie Wallace for their technical assistance and Susan Buenger Johnson for her secretarial expertise in the preparation of this report.
REFERENCES
1. Gorlin R, Gorlin SG. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. AM HEART J 1951;41:1. 2. Hatle J, Angelsen B. Doppler ultrasound in cardiology: Physical principles and clinical applications. Philadelphia: Lea & Febiger, 1982:83. 3. Stamm RB, Martin RP. Quantification of pressure gradients across stenotic valves by Doppler ultrasound. J Am Coll Cardiol 1983;2:707. 4. Bryg RJ, Williams GA, Labovitz AJ, Aker U, Kennedy HL.
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5.
6.
7.
8.
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