- Email: [email protected]
Doppler puts pressure on our hemodynamic thinking
Doppler puts pressure thinking
on our hemodynamic
Hugh D. Allen, M.D., Stanley J. Goldberg,
M.D., and Gerald R. Marx, M.D.
Tucson, Ark.
Those of us schooled in clinical decision-making based upon pressure gradients measured at cardiac catheterization may be forced by Doppler echocardiography to reconsider our present approach to acquisition, evaluation, and application of hemodynamic data. Traditionally obtained peak-to-peak gradients (Fig. 1) are not true measures of the physiologic phenomenon that is occurring. When most catheterizations are performed, this “gradient” is measured as the difference in peak pressures during a catheter pullback across a stenotic area. The pullback introduces possible errors in timing and magnitude of the pressure tracings influenced by changes in the respiratory cycle and in heart rates that may have occurred during the pullback procedure. In severe pressure drop situations, the error is not important, but will be magnified in mild to moderate lesions. More accurate, but still problematic, is simultaneous measurement of pressures by fluid-filled catheters located within the two chambers or chamber and vessel on either side of an obstruction. Harmonic distortions can result in pressure overestimation and fluid-filled catheter systems may introduce a time delay in inscription of the curve. The most accurate measurements are obtained with dual intravascular or intracavitary micromanometer transducers placed into the areas of interest. Nonetheless, in all of these approaches, a necessary time delay exists between peak pressure development in the chamber or vessel proximal to the obstruction and peak pressure development in the chamber or vessel distal to the obstruction because pressure drop across an obstruction is phase-shifted in time. Thus, do peak-to-peak gradients reflect the instanProm the Department (‘enter. Received Reprint Arinma.
for publication
of Pediatrics. June
University
4, 1987; accepted
requests: Hugh D. Allen, Health Sciences Center,
of Arizona
Health
Sciences
Jan. 15, 1988.
M.D., Dept. of Pediatrics, Tucson, AZ 85724.
University
of
taneous situations that occur physiologically? No. Measurement of mean pressures is another approach that cardiologists use for clinical assessment of transobstructive pressures. These are determined by superimposing R-R matched pullback records and determining the area by planimetry or by measuring the difference between the superimposed pressure curves and dividing by the time interval. Accurate superimposition of these records is difficult, especially if scales are compressed and records are run at a slow paper speed. Another depiction of the physiologic events taking place across an obstruction is direct measurement of instantaneous pressure differences across the area of pressure drop, which is best measured by dual intravascular manometry. Similar results may or may not be obtained by dual fluid-filled catheters because of the distortion of pressure harmonics by the fluid system. The peak instantaneous pressure drop can be influenced by flow. It is thus increased in hyperthyroidism, excessive catecholamine states, aortic regurgitation, pregnancy, and anemia. Aortic elasticity may also influence the peak instantaneous gradient. Doppler velocities depict the instantaneous pressure differences across an obstruction. The proximal velocity curve (V,) can be measured by pulsed wave Doppler as the highest velocity Doppler signal obtained at a site proximal to the obstruction. The highest postobstructive velocity curve (V,) usually exceeds the sampling limits of pulsed Doppler and thus continuous wave Doppler is used for best sampling of this curve. Fig. 2 demonstrates incorporation of pulsed Doppler with continuous wave Doppler for evaluation of a patient with coarctation of the aorta.’ The continuous wave Doppler velocity curve often contains the proximal velocity envelope (V,) that contains the preobstructive events and a second envelope (V,) that reflects the postobstruction total velocities (Fig. 3). The modified Bernoulli equation can be applied to these curves as: 1145
May 1988
1146
Allen,
Goldberg,
and Marx
American
Ao
Ao
Peak-Peak
Max Instantaneous
Heart Journal
Mean
Fig. 1. Diagram depicting types of pressure measurements from cardiac catheterization. Superimposed ventricular-vascular tracings are shown. The first panel demonstrates peak-to-peak pressure measurement from the highest amplitude peak of each curve. The second panel shows the maximum instantaneous gradient as depicted by a line of greatest separation of the two curves. The last panel shows that multiple measurements are made with respect to time. A mean value can then be derived. Abbreviations: P LV = peak left ventricular pressure; P Ao = peak aortic pressure; A4IG = maximal instantaneous gradient. (From Goldberg SJ, et al. Doppler echocardiography. 2nd. ed. Philadelphia: Lea & Febiger, 1987. Reproduced by permission.)
Fig. 2. Doppler tracings from a patient with coarctation of the aorta. The upper left panel shows the ascending aortic pulsed Doppler tracing. The insert shows the Doppler sample volume location. The upper right panel shows the precoarctation velocities, V,, obtained from a site just above the coarctation (insert). The lower left panel shows pulsed Doppler signal aliasing because the sampling limits have been exceeded. Thus continuous wave Doppler is used to sample VP, as shown in the lower right panel. (From Marx GR, and Allen HD. J Am Co11 Cardiol 1986;7:1379. Reproduced by permission.)
P, - P, = (VZ,- VT), where PI is the pressure proximal to the obstruction, P, is the pressure distal to the obstruction, V, is the peak velocity distal to the obstruction, and V, is the peak velocity proximal to the obstruction. Several studies2-l6 have demonstrated close correlations of peak gradients measured at catheterization with Doppler results predicted by the Bernoulli equation. Most correlations are enhanced when gradients are clinically signifi-
cant, because little difference exists between peak velocities and instantaneous velocities, especially if V, is negligible. On the other hand, if the pressure drop is slight and V, is of sufficient magnitude to influence the gradient prediction, ignoring it in the equation, as is often done, will result in gradient overestimation. This is certainly possible in patients with aortic regurgitation, where a high V, reflects the excessive volume ejected across the aortic valve
Volume 115 Number 5
Doppler
echocard:c~qr~~phy
1147
li j
i -1 i
c
-iI
-55&n/r
Fig. 3. Tracing from a patient with residual subpulmonary stenosis after balloon dilation valvuloplasty for valvular pulmonary stenosis. The darkened inner envelope of each curve represents the infundibular component of the pressure curve and the outer envelope represents the peak total pressure drop. Not subtracting V, from the total pressure drop will overestimate the contribution of the valve to the total pressure drop. See text for details. (From Goldberg SJ, et al. Doppler echocardiography. 2nd ed. Philadephia: Lea & Febiger, 1987. Reproduced by permission.)
during systole. V, is accordingly increased, but if the valve is also stenotic, V, will be increased in proportion to the degree of stenosis as well as in proportion to the amount of increased flow. Subtracting V, from V, here will give a much better estimate of the stenotic component in a mixed lesion. Peak-to-peak pressure results are temporally shifted. An accurate result will be obtained if the instantaneous pressure difference between the inscribed Doppler velocity curves is measured, but this is not the peak gradient-it is the maximal instantaneous gradient (Fig. 1). Presently, many clinical decisions are made on the basis of peakto-peak gradients. If these criteria are applied to interpretation of the always higher maximal instantaneous gradient, exaggerated clinical decision-making could occur, especially in mid-to-moderate lesions. Mean pressure gradients across obstructions predicted by Doppler closely parallel those measured by manometry.16 These are evaluated in exactly the same manner as is done with cardiac catheterization data. The area between the two curves can be measured by planimeterizing the differences between the velocity curves at evenly divided time intervals so that a mean value can be derived (Fig. 1). Valve area is calculated by taking mean gradient, systolic time, and flow into account. This concept has more meaning for evaluation of the effects of
stenosis than gradient measurement alone. Valve areas have been calculated from cardiac catheterization data by the modified Gorlin formu1a.17 Studies have shown’h1s that similar data can be derived by Doppler measured pressure gradients, cardiac outputs, and systolic time intervals. More recently,20,21 the continuity equation, Peak V, X A, = Peak V, X AZ, where A, is the area of the left ventricular outflow tract just below the aortic valve and A, is the stenotic valve area that is solved from the equation, has allowed easier calculation of aortic valve areas that have correlated well with catheterizationderived values. Doppler technology and reevaluation of catheterization data now pressure us to rethink our clinical decision-making criteria. Many decisions have been made upon the basis of peak-to-peak gradients. Some incorporate mean gradient data, especially when valve areas are calculated. Unfortunately, to date few clinical criteria are available that state the meaning of maximal instantaneous gradients in terms of need for operation or the chronic effects of a stenotic lesion on the ventricles. In spite of the many factors that influence maximal instantaneous gradients, do they have clinical meaning? Do the other gradient measurements have greater or less meaning? Should gradient information be used primarily, abandoned, or incorporated in other data? Let us see some studies with regard to these questions.
May
1148
Allen,
Goldberg,
and Marx
REFERENCES
1. Marx GR, Allen HD. Accuracy and pitfalls of Doppler evaluation of the pressure gradient in aortic coarctation. J Am Co11 Cardiol 1986;7:1379. SJ, Allen HD, Marx GR, Donnerstein RL. Doppler 2. Goldberg echocardiography. 2nd ed. Philadelphia: Lea & Febiger, 1987. 3. Hatle L, Angelsen B. Doppler ultrasound in cardiology. Philadelphia: Lea & Febiger, 1985. LM, Goldberg SJ, Barron 4. Lima CO, Sahn DJ, Valdes-Cruz JV, Allen HD, Grenadier E. Noninvasive prediction of transvalvular pressure gradient in patients with pulmonary stenosis by quantitative two-dimensional echocardiographic Doppler studies. Circulation 1983;67:866. 5. Lima CO, Sahn DJ, Valdes-Cruz LM, Allen HD, Goldberg SJ, Grenadier E. Prediction and severity of left ventricular outflow tract obstruction by quantitative two-dimensional echocardiographic Doppler studies. Circulation 1983;68:348. 6. Hatle L. Noninvasive assessment and differentiation of left ventricular outflow obstruction by Doppler ultrasound. Circulation 1981;64:381. 7. Panidis J, Mints J, Ross J. Values and limitations of Doppler ultrasound in the evaluation of aortic stenosis: a statistical analysis of 70 consecutive patients. AM HEART J 1986;112:150. 8. Currie PJ, Hagler DJ, Seward JB, Reeder GS, Fyfe DA, Bove AA, Tajik AJ. Instantaneous pressure gradient: a simultaneous Doppler and dual catheter correlative study. J Am Co11 Cardiol 1986;7:800. 9. Berger M, Berdoff RL, Gallerstein PE, Goldberg E. Evaluation of aortic stenosis by continuous wave Doppler ultrasound. J Am Co11 Cardiol 1984;3:150. 10. Krafchek J, Robertson JH, Radford M, Adams D, Kisslo J. A reconsideration of Doppler assessed gradients in suspected aortic stenosis. AM HEART J 1984;110:765. 11. Smith MD, Dawson PL, Elion JL, Wisenbaugh T, Kwan OL, Handshoe S, DeMaria AN. Systematic correlation of continuous wave Doppler and hemodynamic measurements in patients with aortic stenosis. AM HEART J 1986;111:245.
American
198s
Heart Journal
M, Yock PG, Popp RL. Comparison of Doppler12. Yeager derived pressure gradient to that determined at cardiac catheterization in adults with aortic valve stenosis: implications for management. Am J Cardiol 1986;57:644. 13. Goldberg SJ, Vasko SD, Allen HD, Marx CR. Can the technique for Doppler estimate of pulmonary stenosis gradient be simplified? AM HEART J 1986;111:709. 14. Houston AB, Simpson IA, Sheldon CD, Doig WB, Coleman EN, Doppler ultrasound in the estimation of the severity of pulmonary infundibular stenosis in infants and children. Br Heart J 1986;55:381. 15. Johnson GL, Dwan OL, Handshoe S, Noonan JA, DeMaria AN. Accuracy of combined two-dimensional echocardiography and continuous wave Doppler recordings in the estimation of pressure gradient in right ventricular outlet obstruction. J Am Co11 Cardiol 1984;3:1013. 16. Wilkins GT, Gillam LF, Kritzer GL, Levine RA, Palacios IF, Weyman AE. Validation of continuous-wave Doppler echocardiographic measurements of mitral and tricuspid prosthetic valve gradients: a simultaneous Doppler-catheter study. Circulation 1986;74:786. SG. Hvdraulic formula for calculation of the 17. Gorlin R. Gorlin area of the stenotic mitral valve, other cardiac valves, and central circulation shunts. AM HEART J 1951;41:1. 18. Kosturakis D, Allen HD, Goldberg SJ, Sahn DJ, Valdes-Cruz LM. Noninvasive quantification of stenotic semilunar valve areas by Doppler echocardiography. J Am Co11 Cardiol 1984;3:1256. P, Yeager M, Yock PG, Popp RL. Doppler echocar19. Teirstein diographic measurement of aortic valve area in aortic stenosis: a noninvasive application of the Gorlin formula. J Am Co11 Cardiol 1986;8:1659. KL. Cannon SR. Miller FJ. Crawford MH. Calcula20. Richards tion of aortic valve area by Doppler echocardiography: a direct application of the continuity equation. Circulation 1986;73:964. 21. Zobhgi W, Farmer K, Soto J, Nelson J, Quinones M. Accurate noninvasive quantification of stenotic aortic valve area by Doppler echocardiography. Circulation 1986;73:452.
on our hemodynamic
Hugh D. Allen, M.D., Stanley J. Goldberg,
M.D., and Gerald R. Marx, M.D.
Tucson, Ark.
Those of us schooled in clinical decision-making based upon pressure gradients measured at cardiac catheterization may be forced by Doppler echocardiography to reconsider our present approach to acquisition, evaluation, and application of hemodynamic data. Traditionally obtained peak-to-peak gradients (Fig. 1) are not true measures of the physiologic phenomenon that is occurring. When most catheterizations are performed, this “gradient” is measured as the difference in peak pressures during a catheter pullback across a stenotic area. The pullback introduces possible errors in timing and magnitude of the pressure tracings influenced by changes in the respiratory cycle and in heart rates that may have occurred during the pullback procedure. In severe pressure drop situations, the error is not important, but will be magnified in mild to moderate lesions. More accurate, but still problematic, is simultaneous measurement of pressures by fluid-filled catheters located within the two chambers or chamber and vessel on either side of an obstruction. Harmonic distortions can result in pressure overestimation and fluid-filled catheter systems may introduce a time delay in inscription of the curve. The most accurate measurements are obtained with dual intravascular or intracavitary micromanometer transducers placed into the areas of interest. Nonetheless, in all of these approaches, a necessary time delay exists between peak pressure development in the chamber or vessel proximal to the obstruction and peak pressure development in the chamber or vessel distal to the obstruction because pressure drop across an obstruction is phase-shifted in time. Thus, do peak-to-peak gradients reflect the instanProm the Department (‘enter. Received Reprint Arinma.
for publication
of Pediatrics. June
University
4, 1987; accepted
requests: Hugh D. Allen, Health Sciences Center,
of Arizona
Health
Sciences
Jan. 15, 1988.
M.D., Dept. of Pediatrics, Tucson, AZ 85724.
University
of
taneous situations that occur physiologically? No. Measurement of mean pressures is another approach that cardiologists use for clinical assessment of transobstructive pressures. These are determined by superimposing R-R matched pullback records and determining the area by planimetry or by measuring the difference between the superimposed pressure curves and dividing by the time interval. Accurate superimposition of these records is difficult, especially if scales are compressed and records are run at a slow paper speed. Another depiction of the physiologic events taking place across an obstruction is direct measurement of instantaneous pressure differences across the area of pressure drop, which is best measured by dual intravascular manometry. Similar results may or may not be obtained by dual fluid-filled catheters because of the distortion of pressure harmonics by the fluid system. The peak instantaneous pressure drop can be influenced by flow. It is thus increased in hyperthyroidism, excessive catecholamine states, aortic regurgitation, pregnancy, and anemia. Aortic elasticity may also influence the peak instantaneous gradient. Doppler velocities depict the instantaneous pressure differences across an obstruction. The proximal velocity curve (V,) can be measured by pulsed wave Doppler as the highest velocity Doppler signal obtained at a site proximal to the obstruction. The highest postobstructive velocity curve (V,) usually exceeds the sampling limits of pulsed Doppler and thus continuous wave Doppler is used for best sampling of this curve. Fig. 2 demonstrates incorporation of pulsed Doppler with continuous wave Doppler for evaluation of a patient with coarctation of the aorta.’ The continuous wave Doppler velocity curve often contains the proximal velocity envelope (V,) that contains the preobstructive events and a second envelope (V,) that reflects the postobstruction total velocities (Fig. 3). The modified Bernoulli equation can be applied to these curves as: 1145
May 1988
1146
Allen,
Goldberg,
and Marx
American
Ao
Ao
Peak-Peak
Max Instantaneous
Heart Journal
Mean
Fig. 1. Diagram depicting types of pressure measurements from cardiac catheterization. Superimposed ventricular-vascular tracings are shown. The first panel demonstrates peak-to-peak pressure measurement from the highest amplitude peak of each curve. The second panel shows the maximum instantaneous gradient as depicted by a line of greatest separation of the two curves. The last panel shows that multiple measurements are made with respect to time. A mean value can then be derived. Abbreviations: P LV = peak left ventricular pressure; P Ao = peak aortic pressure; A4IG = maximal instantaneous gradient. (From Goldberg SJ, et al. Doppler echocardiography. 2nd. ed. Philadelphia: Lea & Febiger, 1987. Reproduced by permission.)
Fig. 2. Doppler tracings from a patient with coarctation of the aorta. The upper left panel shows the ascending aortic pulsed Doppler tracing. The insert shows the Doppler sample volume location. The upper right panel shows the precoarctation velocities, V,, obtained from a site just above the coarctation (insert). The lower left panel shows pulsed Doppler signal aliasing because the sampling limits have been exceeded. Thus continuous wave Doppler is used to sample VP, as shown in the lower right panel. (From Marx GR, and Allen HD. J Am Co11 Cardiol 1986;7:1379. Reproduced by permission.)
P, - P, = (VZ,- VT), where PI is the pressure proximal to the obstruction, P, is the pressure distal to the obstruction, V, is the peak velocity distal to the obstruction, and V, is the peak velocity proximal to the obstruction. Several studies2-l6 have demonstrated close correlations of peak gradients measured at catheterization with Doppler results predicted by the Bernoulli equation. Most correlations are enhanced when gradients are clinically signifi-
cant, because little difference exists between peak velocities and instantaneous velocities, especially if V, is negligible. On the other hand, if the pressure drop is slight and V, is of sufficient magnitude to influence the gradient prediction, ignoring it in the equation, as is often done, will result in gradient overestimation. This is certainly possible in patients with aortic regurgitation, where a high V, reflects the excessive volume ejected across the aortic valve
Volume 115 Number 5
Doppler
echocard:c~qr~~phy
1147
li j
i -1 i
c
-iI
-55&n/r
Fig. 3. Tracing from a patient with residual subpulmonary stenosis after balloon dilation valvuloplasty for valvular pulmonary stenosis. The darkened inner envelope of each curve represents the infundibular component of the pressure curve and the outer envelope represents the peak total pressure drop. Not subtracting V, from the total pressure drop will overestimate the contribution of the valve to the total pressure drop. See text for details. (From Goldberg SJ, et al. Doppler echocardiography. 2nd ed. Philadephia: Lea & Febiger, 1987. Reproduced by permission.)
during systole. V, is accordingly increased, but if the valve is also stenotic, V, will be increased in proportion to the degree of stenosis as well as in proportion to the amount of increased flow. Subtracting V, from V, here will give a much better estimate of the stenotic component in a mixed lesion. Peak-to-peak pressure results are temporally shifted. An accurate result will be obtained if the instantaneous pressure difference between the inscribed Doppler velocity curves is measured, but this is not the peak gradient-it is the maximal instantaneous gradient (Fig. 1). Presently, many clinical decisions are made on the basis of peakto-peak gradients. If these criteria are applied to interpretation of the always higher maximal instantaneous gradient, exaggerated clinical decision-making could occur, especially in mid-to-moderate lesions. Mean pressure gradients across obstructions predicted by Doppler closely parallel those measured by manometry.16 These are evaluated in exactly the same manner as is done with cardiac catheterization data. The area between the two curves can be measured by planimeterizing the differences between the velocity curves at evenly divided time intervals so that a mean value can be derived (Fig. 1). Valve area is calculated by taking mean gradient, systolic time, and flow into account. This concept has more meaning for evaluation of the effects of
stenosis than gradient measurement alone. Valve areas have been calculated from cardiac catheterization data by the modified Gorlin formu1a.17 Studies have shown’h1s that similar data can be derived by Doppler measured pressure gradients, cardiac outputs, and systolic time intervals. More recently,20,21 the continuity equation, Peak V, X A, = Peak V, X AZ, where A, is the area of the left ventricular outflow tract just below the aortic valve and A, is the stenotic valve area that is solved from the equation, has allowed easier calculation of aortic valve areas that have correlated well with catheterizationderived values. Doppler technology and reevaluation of catheterization data now pressure us to rethink our clinical decision-making criteria. Many decisions have been made upon the basis of peak-to-peak gradients. Some incorporate mean gradient data, especially when valve areas are calculated. Unfortunately, to date few clinical criteria are available that state the meaning of maximal instantaneous gradients in terms of need for operation or the chronic effects of a stenotic lesion on the ventricles. In spite of the many factors that influence maximal instantaneous gradients, do they have clinical meaning? Do the other gradient measurements have greater or less meaning? Should gradient information be used primarily, abandoned, or incorporated in other data? Let us see some studies with regard to these questions.
May
1148
Allen,
Goldberg,
and Marx
REFERENCES
1. Marx GR, Allen HD. Accuracy and pitfalls of Doppler evaluation of the pressure gradient in aortic coarctation. J Am Co11 Cardiol 1986;7:1379. SJ, Allen HD, Marx GR, Donnerstein RL. Doppler 2. Goldberg echocardiography. 2nd ed. Philadelphia: Lea & Febiger, 1987. 3. Hatle L, Angelsen B. Doppler ultrasound in cardiology. Philadelphia: Lea & Febiger, 1985. LM, Goldberg SJ, Barron 4. Lima CO, Sahn DJ, Valdes-Cruz JV, Allen HD, Grenadier E. Noninvasive prediction of transvalvular pressure gradient in patients with pulmonary stenosis by quantitative two-dimensional echocardiographic Doppler studies. Circulation 1983;67:866. 5. Lima CO, Sahn DJ, Valdes-Cruz LM, Allen HD, Goldberg SJ, Grenadier E. Prediction and severity of left ventricular outflow tract obstruction by quantitative two-dimensional echocardiographic Doppler studies. Circulation 1983;68:348. 6. Hatle L. Noninvasive assessment and differentiation of left ventricular outflow obstruction by Doppler ultrasound. Circulation 1981;64:381. 7. Panidis J, Mints J, Ross J. Values and limitations of Doppler ultrasound in the evaluation of aortic stenosis: a statistical analysis of 70 consecutive patients. AM HEART J 1986;112:150. 8. Currie PJ, Hagler DJ, Seward JB, Reeder GS, Fyfe DA, Bove AA, Tajik AJ. Instantaneous pressure gradient: a simultaneous Doppler and dual catheter correlative study. J Am Co11 Cardiol 1986;7:800. 9. Berger M, Berdoff RL, Gallerstein PE, Goldberg E. Evaluation of aortic stenosis by continuous wave Doppler ultrasound. J Am Co11 Cardiol 1984;3:150. 10. Krafchek J, Robertson JH, Radford M, Adams D, Kisslo J. A reconsideration of Doppler assessed gradients in suspected aortic stenosis. AM HEART J 1984;110:765. 11. Smith MD, Dawson PL, Elion JL, Wisenbaugh T, Kwan OL, Handshoe S, DeMaria AN. Systematic correlation of continuous wave Doppler and hemodynamic measurements in patients with aortic stenosis. AM HEART J 1986;111:245.
American
198s
Heart Journal
M, Yock PG, Popp RL. Comparison of Doppler12. Yeager derived pressure gradient to that determined at cardiac catheterization in adults with aortic valve stenosis: implications for management. Am J Cardiol 1986;57:644. 13. Goldberg SJ, Vasko SD, Allen HD, Marx CR. Can the technique for Doppler estimate of pulmonary stenosis gradient be simplified? AM HEART J 1986;111:709. 14. Houston AB, Simpson IA, Sheldon CD, Doig WB, Coleman EN, Doppler ultrasound in the estimation of the severity of pulmonary infundibular stenosis in infants and children. Br Heart J 1986;55:381. 15. Johnson GL, Dwan OL, Handshoe S, Noonan JA, DeMaria AN. Accuracy of combined two-dimensional echocardiography and continuous wave Doppler recordings in the estimation of pressure gradient in right ventricular outlet obstruction. J Am Co11 Cardiol 1984;3:1013. 16. Wilkins GT, Gillam LF, Kritzer GL, Levine RA, Palacios IF, Weyman AE. Validation of continuous-wave Doppler echocardiographic measurements of mitral and tricuspid prosthetic valve gradients: a simultaneous Doppler-catheter study. Circulation 1986;74:786. SG. Hvdraulic formula for calculation of the 17. Gorlin R. Gorlin area of the stenotic mitral valve, other cardiac valves, and central circulation shunts. AM HEART J 1951;41:1. 18. Kosturakis D, Allen HD, Goldberg SJ, Sahn DJ, Valdes-Cruz LM. Noninvasive quantification of stenotic semilunar valve areas by Doppler echocardiography. J Am Co11 Cardiol 1984;3:1256. P, Yeager M, Yock PG, Popp RL. Doppler echocar19. Teirstein diographic measurement of aortic valve area in aortic stenosis: a noninvasive application of the Gorlin formula. J Am Co11 Cardiol 1986;8:1659. KL. Cannon SR. Miller FJ. Crawford MH. Calcula20. Richards tion of aortic valve area by Doppler echocardiography: a direct application of the continuity equation. Circulation 1986;73:964. 21. Zobhgi W, Farmer K, Soto J, Nelson J, Quinones M. Accurate noninvasive quantification of stenotic aortic valve area by Doppler echocardiography. Circulation 1986;73:452.