Effect of three-dimensional valve shape on the hemodynamics of aortic stenosis: three-dimensional echocardiographic stereolithography and patient studies

OBJECTIVES: This study tested the hypothesis that the impact of a stenotic aortic valve depends not only on the cross-sectional area of its limiting orifice but also on three-dimensional (3D) valve geometry. BACKGROUND: Valve shape can potentially affect the hemodynamic impact of aortic stenosis by altering the ratio of effective to anatomic orifice area (the coefficient of orifice contraction [Cc]). For a given flow rate and anatomic area, a lower Cc increases velocity and pressure gradient. This effect has been recognized in mitral stenosis but assumed to be absent in aortic stenosis (constant Cc of 1 in the Gorlin equation). METHODS: In order to study this effect with actual valve shapes in patients, 3D echocardiography was used to reconstruct a typical spectrum of stenotic aortic valve geometrics from doming to flat. Three different shapes were reproduced as actual models by stereolithography (computerized laser polymerization) with orifice areas of 0.5, 0.75, and 1.0 cm(2) (total of nine valves) and studied with physiologic flows. To determine whether valve shape actually influences hemodynamics in the clinical setting, we also related Cc (= continuity/planimeter areas) to stenotic aortic valve shape in 35 patients with high-quality echocardiograms. RESULTS: In the patient-derived 3D models, Cc varied prominently with valve shape, and was largest for long, tapered domes that allow more gradual flow convergence compared with more steeply converging flat valves (0.85 to 0.90 vs. 0.71 to 0.76). These variations translated into differences of up to 40% in pressure drop for the same anatomic area and flow rate, with corresponding variations in Gorlin (effective) area relative to anatomic values. In patients, Cc was significantly lower for flat versus doming bicuspid valves (0.73 +/- 0.14 vs. 0.94 +/- 0.14, p < 0.0001) with 40 +/- 5% higher gradients (p < 0.0001). CONCLUSIONS: Three-dimensional valve shape is an important determinant of pressure loss in patients with aortic stenosis, with smaller effective areas and higher pressure gradients for flatter valves. This effect can translate into clinically important differences between planimeter and effective valve areas (continuity or Gorlin). Therefore, valve shape provides additional information beyond the planimeter orifice area in determining the impact of valvular aortic stenosis on patient hemodynamics.     

Continuity equation and Gorlin formula compared with directly observed orifice area in native and prosthetic aortic valves.

Orifice areas calculated by the continuity and Gorlin equations have been shown to correlate well in vivo. The continuity equation, however, gives underestimates compared with the Gorlin formula and it is not clear which is the more accurate. Both equations have therefore been tested against maximal orifice area measured by planimetry in eight prepared native aortic valves and four bioprostheses. A computer controlled, ventricular flow simulator (cycled at 70 beats/min) was used at five different stroke volumes that gave cardiac outputs of 2.8 to 7.0 l/min. The mean difference between measured and estimated orifice area was zero for the continuity equation, but -0.14 cm2 for the conventional Gorlin formula. Thus the Gorlin formula tended to give overestimates compared with both measured area and area estimated by the continuity equation, probably because of the effect of pressure recovery. When predictive equations derived from these data were tested, residual standard deviations were around 0.3 cm2 at all stroke volumes for the continuity equation, around 0.2 cm2 for the invasive Gorlin formula, and between 0.2 and 0.4 cm2 for the modified Gorlin formula. These results suggest that estimates of orifice area in an individual valve as judged by any of the equations tested should be seen as a guide to rather than as a precise measure of actual orific area.     

Continuity equation and Gorlin formula compared with directly observed orifice area in native and prosthetic aortic valves.

Orifice areas calculated by the continuity and Gorlin equations have been shown to correlate well in vivo. The continuity equation, however, gives underestimates compared with the Gorlin formula and it is not clear which is the more accurate. Both equations have therefore been tested against maximal orifice area measured by planimetry in eight prepared native aortic valves and four bioprostheses. A computer controlled, ventricular flow simulator (cycled at 70 beats/min) was used at five different stroke volumes that gave cardiac outputs of 2.8 to 7.0 l/min. The mean difference between measured and estimated orifice area was zero for the continuity equation, but -0.14 cm2 for the conventional Gorlin formula. Thus the Gorlin formula tended to give overestimates compared with both measured area and area estimated by the continuity equation, probably because of the effect of pressure recovery. When predictive equations derived from these data were tested, residual standard deviations were around 0.3 cm2 at all stroke volumes for the continuity equation, around 0.2 cm2 for the invasive Gorlin formula, and between 0.2 and 0.4 cm2 for the modified Gorlin formula. These results suggest that estimates of orifice area in an individual valve as judged by any of the equations tested should be seen as a guide to rather than as a precise measure of actual orific area.     

Effects of increasing flow rate on aortic stenotic indices: evidence from percutaneous transvenous balloon dilatation of the mitral valve in patients with combined aortic and mitral stenosis.

OBJECTIVES: To investigate the effects of transvalvar flow rate on aortic valve resistance and valve area after percutaneous transvenous balloon dilatation of the mitral valve in a homogeneous group of patients with rheumatic heart disease. DESIGN: Retrospective analysis of 12 patients with combined aortic and mitral stenosis who had undergone balloon dilatation of the mitral valve over a period of 9 years. SETTING: Tertiary referral centre. PATIENTS: Twelve (8 women, 4 men; mean (SD) age 37 (9) of 227 consecutive patients with critical mitral stenosis undergoing transvenous balloon dilation of the mitral valve in the centre also had aortic stenosis, defined as a transaortic pressure gradient of more than 25 mm Hg measured at a catheterisation study before valvuloplasty. INTERVENTIONS: Echocardiographic variables (mitral valve area measured by the pressure half-time method and planimetry, and the aortic valve area derived from the continuity equation) and haemodynamic measurements (cardiac output, left ventricular mean systolic pressure, aortic mean pressure, transaortic valve pressure gradient, mitral valve and aortic valve areas derived from the Gorlin formula, and aortic valve resistance) were assessed before and after transvenous balloon dilatation of the mitral valve. Follow up catheterisation to measure haemodynamic variables was performed one week after mitral valvuloplasty. RESULTS: Mean transaortic flow rate increased 33% after mitral valvuloplasty (from 198 (68) to 254 (41) ml/s, P = 0.002). Aortic valve areas derived from the Gorlin formula were significantly increased from 0.57 (0.12) to 0.73 (0.14) cm2 (P = 0.006) after mitral valvuloplasty. However, aortic valve area and valve resistance derived from the continuity equation were independent of the increase in flow rate after mitral valvuloplasty (from 1.29 (0.35) to 1.30 (0.29) cm2 and from 317 (65) to 259 (75) dyn.s.cm-5, both P = NS). CONCLUSION: The Gorlin-derived aortic valve area tends to be flow-dependent, and continuity equation-derived aortic valve area and catheterisation-derived valve resistance seem to be less flow-dependent. In patients with combined mitral and aortic stenosis, these flow-independent indices are important for decision-making.     

Doppler assessment of prosthetic valve orifice area. An in vitro study.

BACKGROUND. Although Doppler echocardiography has been shown to be accurate in assessing stenotic orifice areas in native valves, its accuracy in evaluating the prosthetic valve orifice area remains undetermined. METHODS AND RESULTS. Doppler-estimated valve areas were studied for their agreement with catheter-derived Gorlin effective orifice areas and their flow dependence in five sizes (19/20-27 mm) of St. Jude, Medtronic-Hall, and Hancock aortic valves using a pulsatile flow model. Doppler areas were calculated three ways: using the standard continuity equation; using its simplified modification (peak flow/peak velocity); and using the Gorlin equation with Doppler pressure gradients. The results were compared with Gorlin effective orifice areas derived from direct flow and catheter pressure measurements. Excellent correlation between Gorlin effective orifice areas and the three Doppler approaches was found in all three valve types (r = 0.93-0.99, SEE = 0.07-0.11 cm2). In Medtronic-Hall and Hancock valves, there was only slight underestimation by Doppler (mean difference, 0.003-0.25 cm2). In St. Jude valves, however, all three Doppler methods significantly underestimated effective orifice areas derived from direct flow and pressure measurements (mean difference, 0.40-0.57 cm2) with differences as great as 1.6 cm2. In general, the modified continuity equation calculated the largest Doppler areas. When orifice areas were calculated from the valve geometry using the area determined from the inner valve diameter reduced by the projected area of the opened leaflets, Gorlin effective orifice areas were much closer to the geometric orifice areas than Doppler areas (mean difference, 0.40 +/- 0.31 versus 1.04 +/- 0.20 cm2). In St. Jude and Medtronic-Hall valves, areas calculated by either technique did not show a consistent or clinically significant flow dependence. In Hancock valves, however, areas calculated by both the continuity equation and the Gorlin equation decreased significantly (p less than 0.001) with low flow rates. CONCLUSIONS. Doppler echocardiography using either the continuity equation or Gorlin formula allows in vitro calculation of Medtronic-Hall and Hancock effective valve orifice areas but underestimates valve areas in St. Jude valves. This phenomenon is due to localized high velocities in St. Jude valves, which do not reflect the mean velocity distribution across the orifice. Valve areas are flow independent in St. Jude and Medtronic-Hall prostheses but decrease significantly with low flow in Hancock valves, suggesting that bioprosthetic leaflets may not open fully at low flow rates.     

Calculation of aortic valve area by Doppler echocardiography: a direct application of the continuity equation

The continuity equation suggests that a ratio of velocities at two different cardiac valves is inversely proportional to the ratio of cross-sectional areas of the valves. To determine whether a ratio of mitral/aortic valve orifice velocities is useful in determining aortic valve area in patients with aortic stenosis, 10 control subjects and 22 patients with predominant aortic stenosis were examined by Doppler echocardiography. The ratio of (mean diastolic mitral velocity)/(mean systolic aortic velocity), (Vm)/(Va), and the ratio of (mitral diastolic velocity-time integral)/(aortic systolic velocity-time integral), (VTm)/(VTa), were determined from Doppler spectral recordings. Aortic valve area determined at catheterization by the Gorlin equation was the standard of reference. High-quality Doppler recordings were obtained in 30 of 32 subjects (94%). Catheterization documented valve areas of 0.5 to 2.6 (mean 1.1) cm2. There was good correlation between Doppler-determined (Vm)/(Va) and Gorlin valve area (r = .90, SEE = 0.23 cm2); a better correlation was noted between (VTm)/(VTa) and Gorlin valve area (r = .93, SEE = 0.18 cm2). The data demonstrate the usefulness of Doppler alone in the determination of aortic valve area in adults with absent or mild aortic or mitral regurgitation and no mitral stenosis. Although the use of mean velocity and velocity-time integral ratios requires accurate measurement of mitral and aortic velocities, it does not require squaring of these velocities or measurement of the cross-sectional area of flow.     

Effects of dobutamine on Gorlin and continuity equation valve areas and valve resistance in valvular aortic stenosis.

Previous studies demonstrated changes in aortic valve area calculated by the Gorlin equation under conditions of varying transvalvular flow in patients with valvular aortic stenosis (AS). To distinguish between flow-dependence of the Gorlin formula and changes in actual orifice area, the Gorlin valve area and 2 other measures of severity of AS, continuity equation valve area and valve resistance, were calculated under 2 flow conditions in 12 patients with AS. Transvalvular flow rate was varied by administration of dobutamine. During dobutamine infusion, right atrial and left ventricular end-diastolic pressures decreased, left ventricular peak systolic pressure and stroke volume increased, and systolic arterial pressure did not change. Heart rate increased by 19%, cardiac output by 38% and mean aortic valve gradient by 25%. The Gorlin valve area increased in all 12 patients by 0.03 to 0.30 cm2. The average Gorlin valve area increased from 0.67 +/- 0.05 to 0.79 +/- 0.06 cm2 (p < 0.001). In contrast, the continuity equation valve area (calculated in a subset of 6 patients) and valve resistance did not change with dobutamine. The data support the conclusion that flow-dependence of the Gorlin aortic valve area, rather than an increase in actual orifice area, is responsible for the finding that greater valve areas are calculated at greater transvalvular flow rates. Valve resistance is a less flow-dependent means of assessing severity of AS.     

Non-invasive assessment of mitral stenosis before and after percutaneous balloon mitral valvotomy by Doppler continuity equation.

The continuity equation was used to estimate non-invasively the stenotic mitral valve area by comparison with two other echocardiographic methods (planimetry and pressure half-time) and with Gorlin's formula as the gold standard. The accuracy of the equation of continuity was determined before and 24 h after valvuloplasty in a study group of 21 patients with severe mitral stenosis. According to the equation of continuity, mitral valve area was calculated by the product of the cross-sectional area and the aortic or pulmonary annulus and the ratio of the time velocity integral of the aortic or pulmonary flow to that of the mitral stenotic jet. In pre-valvotomy basal conditions, the Doppler continuity equation demonstrated significant correlations with 2D planimetry (r = 0.72, P less than 0.01), with the pressure half-time method (r = 0.62, P less than 0.01) and with the Gorlin formula (r = 0.66, P less than 0.01). There was no significant difference between the haemodynamic data and the echocardiographic measurements. Twenty-four hours after valvotomy, the Doppler continuity equation also demonstrated significant correlations with 2D planimetry (r = 0.83, P less than 0.01), with pressure half-time (r = 0.82, P less than 0.01) and with the Gorlin formula (r = 0.69, P less than 0.01). However, the haemodynamic measurements significantly overestimated (P less than 0.01) the echographic measurements. Thus, we conclude that the continuity equation provides an accurate estimation of mitral valve area in mitral stenosis before and after balloon valvotomy.     

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

Two Doppler methods, the pressure half-time method proposed by Hatle and the method based on the equation of continuity, were used to estimate stenotic mitral valve area noninvasively, and the accuracy of these methods was examined in patients with and without associated aortic regurgitation. Mitral valve area determined at catheterization by the Gorlin formula was used as a standard of reference. The study population consisted of 41 patients with mitral stenosis, and 20 of the 41 patients had associated aortic regurgitation. According to the equation of continuity, mitral valve area was determined as a product of aortic or pulmonic annular cross-sectional area and the ratio of time velocity integral of aortic or pulmonic flow to that of the mitral stenotic jet. Mitral valve area was determined by the pressure half-time method as 220/pressure half-time, the time from the peak transmitral velocity to one-half the square root of the peak velocity on the continuous-wave Doppler-determined transmitral flow velocity pattern. The pressure half-time method tended to overestimate catheterization measurements, and the correlation coefficient for this relation was .69 (SEE = 0.44 cm2). The correlation coefficient improved to .90 when the patients with associated aortic regurgitation were excluded. Mitral valve areas determined by the continuity equation method correlated well with catheterization measurements at a correlation coefficient of .91 (SEE = 0.24 cm2), irrespective of the presence of aortic regurgitation. The ratio of the time-velocity integral or aortic or pulmonic flow to the time-velocity integral of mitral stenotic jet also correlated well with mitral valve area determined by catheterization at a correlation coefficient of .84 (SEE = 0.10).(ABSTRACT TRUNCATED AT 250 WORDS)     

Evaluation of the valve area underestimation by the continuity equation.

During the last years, noninvasive determination of the aortic valve area by Doppler echocardiography using the continuity equation became popular. However, a systematic valve area underestimation of about 15% compared to invasive measurements using the Gorlin formula has been reported. The cause therefore is unknown. The purpose of this study was to evaluate whether the valve area underestimation by the Doppler method might be due to differences in the hydrodynamic background of both methods. This comparison is facilitated by the fact that the Gorlin formula is based on the continuity equation. Compared to the continuity equation, there are four changes within the Gorlin formula: (1) the additional use of a discharge coefficient, which leads to valve area overestimation by the factor 1.17; (2) neglect of the pre-stenotic velocity, causing further overestimation by the factor 1.036 (in mild stenosis this factor may be 1.18 and more); (3) the wrong calculation of the mean pressure drop, which leads to a mean change by the factor 0.95, and (4) the incorrect substitution of the height by the pressure drop in the derivation of the Gorlin formula causes underestimation by the factor 0.97. Combining these four factors results in valve area overestimation of the Gorlin formula compared to the continuity equation by the factor 1.12. This explains to a large extent the valve area underestimation by the continuity equation.     

Cardiac valve orifice equation independent of valvular flow intervals: application to mitral valve area computation in mitral stenosis and comparison with the Gorlin formula and direct anatomical measurements

An orifice equation is developed which relates the effective mitral valve area (A), the average mitral valve pressure gradient (dP), the cardiac output (Q) and the heart frequency (f) through considerations of momentum conservation across the mitral valve. The form of the new equation is A = (4.75 X 10(-5)Qf/dP, where A, Q, and dP are expressed in cm2, ml X min-1 and mmHg respectively. Mitral valve areas computed with the new orifice formula are found to correlate with those computed by the Gorlin formula in conditions of equilibrium associated with the resting state at a level of r = 0.95, SE = 0.15 cm2, with autopsy measurements at a level of r = 0.85, SE = 0.18 cm2 and with direct anatomical measurements of excised valves at a level of r = 0.78, SE = 0.41 cm2. The results suggest that the new formula may be considered as an independent orifice equation enjoying a similar domain of validity as the Gorlin formula. The new equation offers the possibility of deriving additional useful haemodynamic relationships when used in combination with established cardiological formulas.     

Using Cardiac Magnetic Resonance Tomography for Assessment of Aortic Valve Area in Aortic Valve Stenosis

Calcified aortic valve stenosis (AS) is the most common valvular disease in the elderly population and constitutes a significant health and socioeconomic problem. Doppler echocardiography is the recommended diagnostic tool for the initial evaluation of AS. Transvalvular pressure gradients and aortic valve area have been used as quantitative parameters for grading the severity of AS, but the latter one is less susceptible to changes in flow dynamics and therefore considered the more independent and reliable parameter. The aortic valve area can be assessed directly by transesophageal echocardiography (TEE), which reflects the anatomic or geometric orifice area, or it can be calculated noninvasively by transthoracic echocardiography (TTE) using the continuity equation, or, invasively, by cardiac catheterization (CC) using the Gorlin formula, both reflecting the effective orifice area.Assessment of aortic valve area by TTE can be limited in some patients due to inadequate acoustic window. Similarly, TEE as a semi-invasive technique is not well tolerated by some patients and the planimetry is limited in patients with heavily calcified aortic valve leaflets. CC is an invasive procedure associated with a substantial risk of cerebral embolism and the Gorlin formula has been shown to be susceptible to changes in flow dynamics.Cardiac magnetic resonance tomography (CMR) is a new imaging technique capable of imaging the aortic valve with high resolution and has recently been used for assessment of the aortic valve area in AS. This review focuses on the feasibility of CMR for the assessment of aortic valve area in AS compared to current standard techniques and discusses some of the typical pitfalls and the sources for the discrepant results observed between the different techniques for assessment of the aortic valve area.     

Inadequacy of the Gorlin formula for predicting prosthetic valve area

A total of 135 patients with normally functioning prosthetic aortic valves who were catheterized 6 months after placement of Hancock, modified Hancock or Bjork-Shiley prostheses were studied to determine the magnitude of error in Gorlin formula estimates of prosthetic aortic valve area. All patients were male, selected from 13 participating hospitals and routinely followed after valve replacement for 5 years. Hemodynamically determined Gorlin valve areas were compared with independently verified actual valve areas. Actual Hancock areas were measured from videotapes of valves exercised in a pulse duplicator flow model. Actual Bjork-Shiley areas were calculated directly from the valves' inner ring radius. Gorlin valve areas correlated poorly with actual valve areas (r = 0.39). The mean Gorlin formula error was 0.36 cm2 (standard deviation = 0.32). Gorlin areas overestimated actual areas by greater than 0.25 cm2 in 43 patients (32%) and underestimated actual areas by greater than 0.25 cm2 in 29 (21%). It was concluded that the Gorlin formula inaccurately predicts prosthetic valve area in the aortic position. Overreliance on this formula in assessing aortic stenosis could lead to errant clinical decisions.     

Valve orifice area in aortic stenosis evaluated by planimetry, Gorlin and continuity equations: a prospective study.

In evaluation of the severity of aortic valve stenosis, multiple parameters can be determined. All of them, except valve orifice area, are influenced by other factors such as cardiac output, heart rate or aortic insufficiency. OBJECTIVES: This is a prospective study which proposes, in the determination of the valve orifice area in aortic stenosis, to evaluate the accuracy of and correlation between three methods--planimetry by multiplane transesophageal echocardiography, the continuity equation by transthoracic echocardiography, and invasive measurement using the Gorlin formula. METHODS: Forty-five patients with known calcified valvular aortic stenosis 27 men, mean age 70 +/- 10 years, (range 27-82), were studied. In all patients the area was determined by planimetry and by the continuity equation. In 25 (56%) patients invasive measurements were obtained using the Gorlin formula. RESULTS: Evaluation of the valve orifice area by planimetry was easily performed and did not prolong the duration of the exam, except in five patients (11%). The area determined by the continuity equation had a mean value of 0.74 +/- 0.25 cm2, by planimetry 0.74 +/- 0.24 cm2 and by the Gorlin formula 0.65 +/- 0.17 cm2. Correlations between areas obtained by the three methods used were: continuity equation and planimetry 0.82; continuity equation and Gorlin formula 0.51; and planimetry and Gorlin formula 0.80. Concordance analysis (Bland and Altman's method) gave mean (Mn) values for the differences in the areas determined by the Gorlin formula and the continuity equation of 0.01 +/- 0.15 cm2 (Mn - 2SD = -0.29, Mn + 2SD = 0.30). The estimated value by the Gorlin formula and planimetry was 0.02 +/- 0.10 (Mn - 2SD = -0.19, Mn + 2SD = 0.23). CONCLUSIONS: 1) Planimetry of the valve orifice area by transesophageal echocardiography is feasible and does not prolong the duration of the exam in the majority of patients. 2) The strong correlation and the results of concordance analysis, in the determination of valve orifice area, between traditional invasive methods and planimetry, support the use of this noninvasive method in clinical practice.     

Contribution of the continuity equation for the assessment of mitral valve area in mitral stenosis]

The aim of this study was to evaluate the continuity equation in the quantification of mitral valve area in mitral stenosis, the area being considered as the product of the area of the left ventricular outflow tract multiplied by the ratio of the velocity time integrals of the aortic or pulmonary flow to that mitral flow. The continuity equation was compared to two other echocardiographic methods, planimetry and Hatle's method, and to the results obtained at catheterization using the Gorlin formula in a population of 44 patients with mitral stenosis. All were in sinus rhythm; twelve had Grade I mitral regurgitation and 9 patients had Grade I aortic regurgitation. Excellent correlation were observed between the values obtained by the continuity equation and planimetry (r = 0.91; SEE = 0.19 cm2; p less than 0.001) and Hatle's method (r = 0.87; SEE = 0.20 cm2, p less than 0.001). The correlation with the catheter values were also excellent (r = 0.83; SD = 0.22 cm2, p less than 0.001), better than those observed with Hatle's method (r = 0.73; SEE = 0.27 cm2, p less than 0.001) and very similar to those obtained with planimetry (r = 0.87; SEE = 0.23 cm2, p less than 0.001). The sensibility and specificity of the continuity equation for the diagnosis of severe mitral stenosis (surface less than 1.5 cm2) were 90% and 100% respectively, when those of Hatle's method were 88% and 91% respectively. The continuity equation in the evaluation of mitral valve area in mitral stenosis seems to be reliable and accurate compared with catheter data, and superior to Hatle's method.     

When should Doppler-determined valve area be better than the Gorlin formula?: Variation in hydraulic constants in low flow states

In low flow states, underestimation errors occur when the Gorlin formula is used to calculate valve area. A model of valvular stenosis designed to examine changes in the hydraulic discharge coefficient (Cd) and coefficient of orifice contraction (Cc) may explain these errors. Unsteady flow was examined in a pulsatile pump model and in a dog model. Valve areas were calculated from pressure and flow data using: a modified form of the Gorlin formula (assuming constant values for Cd and Cc) and a corrected formula (with values of Cd and Cc obtained from steady state data). Valve area was also calculated using the continuity equation with velocity and flow data (constant Cc). Flow velocities were measured using a newly designed ultrasound Doppler catheter capable of resolving flow velocities of up to 5.5 m/s. Both the corrected formula and continuity equation were highly predictive of actual valve area (r = 0.99, slope or M = 0.96 and r = 0.99, M = 1.06, respectively). The modified Gorlin equation was less accurate and tended to underestimate valve areas (r = 0.87, M = 0.83). This underestimation was most notable at low rates of flow (Gorlin: r = 0.94, M = 0.53; continuity: r = 0.93, M = 0.81 and r = 0.94, M = 0.89, respectively) more accurately than the modified Gorlin formula (r = 0.69, M = 0.49). In patients with low cardiac output, hemodynamic formulas, such as the Gorlin formula, which assume a constant value for the hydraulic discharge coefficient (Cd), may be less accurate than formulas using either a corrected value of Cd or Doppler-determined flow velocity and mean systolic flow.     

Prediction of stenotic valve orifice area: an in vitro study on a bioprosthesis

The Gorlin equation for the hemodynamic assessment of valve area is commonly used in cardiac catheterization laboratories. A study was performed to test the prediction capabilities of the Gorlin formula, as well as those of the Aaslid and Gabbay formulas for the effective orifice area of a porcine valve of varying degrees of stenosis. Pressure gradient, flow, and valve opening area measurements were performed on Carpentier-Edwards porcine valve prostheses (made stenotic by suturing at the commissures) mounted in the aortic position of an in vitro pulse duplicator. With the known valve orifice area, a discharge coefficient was computed for each of the three orifice area formulas. After some theoretical considerations, it was proposed that the discharge coefficient would be a function of the flow rate through the valve. The discharge coefficient was observed to increase with increasing systolic flow rate. An empirical relationship of the discharge coefficient as a linear function of the systolic flow rate was determined through a regression analysis, with a different relationship for each orifice area formula. Using this relationship in the orifice area formulas improved the accuracy of the prediction of the effective orifice area with all three formulas performing equally well.     

Comparison between the Gorlin formula and a simplified formula to measure the severity of pulmonic stenosis

In a previous study we showed that the Gorlin formula for measuring the valve areas in patients with stenotic mitral or aortic valves can be simplified without loss of accuracy. The simplified formula states that the valve area is equal to cardiac output (liters/min) divided by the square root of the pressure gradient across the valve. In this study we compare the Gorlin formula and the simplified formula in measuring the valve areas in 12 patients with congenital pulmonic stenosis. There was an excellent correlation between the two methods (r = 0.98 y = 0.07 + 1.16 X, P less than 0.001). Therefore the simplified formula can be used in measuring the severity of pulmonic stenosis. This method is simpler and easier to memorize than the Gorlin formula.     

Comparison of two-dimensional and Doppler echocardiography and intracardiac hemodynamics for quantification of mitral stenosis

Forty-three patients with mitral stenosis (MS) were studied to assess the relation of catheter-derived pressure gradient half-time (P 1/2), mitral valve areas (calculated by the Gorlin formula and 2-dimensional echocardiography [2-D echo]) to mitral valve areas derived from Doppler pressure half-time (T 1/2) in order to establish an accurate line-drawing method in nonlinear velocity tracings and to revalidate the use of the empiric constant of 220 ms as the T 1/2 that predicts a 1.0-cm2 mitral valve area. Mitral valve area could be quantified by 2-D echo in 39 of 43 patients and by Doppler in 31 of 34 patients, for a success rate of 91%. A reliable technique for measuring Doppler T 1/2 in nonlinear Doppler velocity tracings was a "mid-diastolic" line-drawing method, validated with the "anatomic" mitral valve area by 2-D echo (r = 0.89) and with the "hemodynamic" mitral valve area by the Gorlin formula (in pure MS without regurgitation) (r = 0.95). By both Doppler T 1/2 and hemodynamic P 1/2, the use of 220 ms to predict a mitral valve area of 1.0 cm2 was validated. Each T 1/2 and P 1/2 had an exponential inverse relation to the mitral valve area by the Gorlin formula in pure MS. Doppler and 2-D echocardiographic quantification of MS are complementary. Reliable measurement of T 1/2 in nonlinear velocity tracings is achieved by a mid-diastolic line-drawing method and use of the equation 220 ms/T 1/2 = mitral valve area accurately quantifies MS.     

A new formula for the measurement of diastolic mitral valve orifice area

This study evaluated the accuracy of a new formula for the calculation of mitral valve area. Fifty-two patients with mitral stenosis who underwent cardiac catheterization were evaluated by the standard Gorlin and the new formulas. The correlation between the two formulas was excellent (r = 0.89) for valve areas of 0–1.5 cm². When the new valve area formula yielded an area greater than 1.5 cm², there was no correlation with the Gorlin formula. However, the likelihood of the Gorlin mitral valve area being less than 1.0 cm² was low (10%). The results of the new formula do not appear to be affected by atrial fibrillation and are probably subject to the same limitations when used in the presence of a regurgitant lesion. Therefore, with moderate to severe mitral stenosis, this new formula shows a good correlation. However, with mild stenosis, further work is needed to determine the accuracy and limitations of the new formula.