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.     

Normal and stenotic human aortic valve opening: in vitro assessment of orifice area changes with flow

The ability to measure aortic valve area clinically has emphasizedthe need to understand the changes in aortic valve orifice areaduring flow. To compare the performance of normal and stenotichuman aortic valves we used a pulsatile flow model that simulatedin vivo flow conditions. Five normal autopsy specimens and 15stenotic valves removed at operation were mounted into the model.Valve function was assessed by analysis of video recordingsof valve leaflet motion during flow. Over the flow rates testednormal valves demonstrated a linear increase in orifice area.There was no resistance to leaflet opening and valve closurewas rapid. The majority of stenotic valves demonstrated an increasein orifice area at low flow rates. No valve showed any increasein maximal area beyond flow rates of 31 min^–1. Increasedleaflet resistance of these abnormal valves resulted in notablyslower opening and closing rates. In patients with a high cardiacoutput and severe stenosis, overesti-mation of the anatomicorifice area derived by the Gorlin equation can result. Thisis not related to variability in maximal orifice area.     

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.     

Aortic valve morphology influences regurgitant volume in aortic regurgitation: in vitro evaluation

STUDY OBJECTIVE--According to the Gorlin hydraulic orifice equation, aortic regurgitation volume can be determined by the regurgitant orifice cross sectional area, diastolic filling period, mean pressure gradient between the aorta and left ventricle, and a constant relating the coefficients of contraction (Cc) and velocity (Cv). This study was performed to determine whether variation in aortic valve morphology affects regurgitant flow volume, Cc and Cv. DESIGN--Four aortic valve templates, modelled after circular, rheumatic, degenerative, and bicuspid lesions, were constructed with equal orifice cross sectional areas in two sizes, 0.2 and 0.7 cm2. These valves were studied in vitro in a flow model of aortic regurgitation, wherein aortic pressure was regulated by varying the height of a column of fluid. Flow, pressure, and velocity were measured, and the coefficient Cc and Cv were calculated from standard equations. MEASUREMENTS AND MAIN RESULTS--Regurgitant volume was assessed at diastolic filling periods of 0.5 and 1.0 s and averaged 15% greater for bicuspid and degenerative as compared to circular or rheumatic valve shapes (p = 0.0001). This difference was accentuated at the shorter diastolic filling time and higher pressure gradient, such that bicuspid lesions allowed 29% more regurgitant flow across the 0.2 cm2 orifice at fluid height of 120 cm over 0.5 s. This difference in regurgitant volume between valve shapes was due to an increased Cc for the bicuspid and degenerative valve shapes, suggesting that they are more efficient orifices than rheumatic or circular valve shapes. CONCLUSIONS--Aortic valve morphology influences regurgitant volume in aortic regurgitation. Specifically, degenerative and bicuspid orifice shapes have a higher contraction coefficient and allow more regurgitant flow than rheumatic or circular orifices at a given driving pressure and diastolic filling time.     

Physiological basis of flow dependence of Gorlin formula valve area in aortic stenosis: analysis using an hydraulic model of pulsatile flow

BACKGROUND AND AIM OF THE STUDY: The study aim was to clarify the basis of the cardiac output dependence of aortic valve area calculated with the Gorlin formula which has been reported in patients with aortic stenosis. Clinical and experimental studies which have attempted to differentiate between a change in physical orifice area, versus a defect in the Gorlin formula as the cause of cardiac output related variations in Gorlin valve area in aortic stenosis have yielded conflicting results. METHODS: We employed a numerical model of pulsatile flow in which the total instantaneous transvalvular gradient was the sum of the convective and viscous pressure losses and pressure recovery beyond the stenosis. By analogy with other hydraulic devices, viscous losses due to stenosis were modeled by the term KfV(EXP), where V is flow velocity. Kf and EXP were determined for various orifices by adjusting these two parameters to obtain excellent fit between curves of the orifice discharge coefficient based upon the expression KfV(EXP), and empirically measured orifice discharge coefficient curves which have been published in the engineering literature. Mean systolic transvalvular gradient was calculated from the total instantaneous transvalvular gradient values for an assumed jet area, and an assumed systolic time-velocity flow profile. This mean gradient was substituted into the Gorlin equation to find the apparent Gorlin valve area at cardiac outputs varying from 0 to 10 l/min for a range of where V is assumed true areas between 0.5 and 2.0 cm2. RESULTS: For functional valve areas <1.5 cm2, viscous losses resulted in at most a 10-12% fall in apparent Gorlin valve area when cardiac output was decreased from 5 to 2.5 l/min. In addition, maximum viscous losses did not result in a pressure-flow relationship which was closer to linear than to quadratic. which the CONCLUSION: Clinically significant changes in valve area with flow are due to orifice area changes rather than Gorlin formula flow variability. Moreover beyond the Gorlin valve area is preferred over valve 'resistance' for assessing stenosis severity. In low cardiac output states, output should be increased to the normal range before Gorlin valve area is measured.     

Doppler echocardiography determination of the orifice area in aortic valve stenosis using a continuity equation

The continuity equation, derived from the study of fluid mechanics, may serve as the basis for calculation of orifice area of stenosed cardiac valves. As applied to aortic stenosis, the continuity equation states that the flow across the narrowed valve is equal to the flow in the left ventricular (LV) outflow tract such that A1 X v1 = A2 X v2, where A1 = LV outflow tract area, v1 = prestenotic velocity, A2 = stenotic orifice area and v2 = poststenotic velocity. Accordingly, at each point in time during pulsatile flow, the respective valve orifice area can be calculated. Hence, from the sum of all areas throughout the ejection time, the mean valve orifice area can be constructed as integral of A2/ET = A1 X integral of (v1/v2)/ET, assuming A1 to be constant, where integral of denotes the integral over the ejection time ET. To assess the usefulness of this method with respect to its clinical relevance, in 36 patients with aortic stenosis, the Doppler echocardiographically-determined orifice areas were compared with those calculated by the Gorlin formula based on invasively-obtained data. LV outflow tract area A1 was measured by echocardiography from a parasternal long-axis view. Prestenotic velocity v1 was recorded in the LV outflow tract by pulsed Doppler from an apical transducer position, whereby care was taken in positioning the sample volume not too close to the stenotic valve to avoid the prestenotic area of increased velocity. Continuous-wave Doppler was used, usually from an apical or right parasternal transducer position, to record the stenotic jet velocity v2.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Doppler echocardiographic assessment of the valve area in patients with atrioventricular valve stenosis by application of the continuity equation

The orifice area was non-invasively assessed in 19 patients with mitral or mitral and tricuspid stenosis by combined cross-sectional and Doppler echocardiography. Stroke volume was calculated as the product of aortic or pulmonic cross-sectional area and the time velocity integral of the flow across that valve, and the stenotic valve area was obtained as the stroke volume divided by the time velocity integral of the stenotic valve. In addition, the mitral valve area was estimated by the pressure half-time method of Hatle et al. The non-invasive determinations were compared with those calculated by the Gorlin formula at cardiac catheterization. The valve area obtained by combined cross-sectional and Doppler echocardiography showed a close correlation with the Gorlin area, r = 0.90, SEE = 0.13 cm2, n = 20. In contrast, the valve area estimated by the pressure half-time method showed only a moderate correlation with the Gorlin area, r = 0.68, SEE = 0.38 cm2, n = 18, and estimates by this method tended to significantly overestimate the Gorlin area. In conclusion, non-invasive valve area determinations based on combined cross-sectional and Doppler echocardiography can be used to accurately quantify the severity of the lesion in patients with atrioventricular valve stenosis, while determinations by the pressure half-time method may show errors of a magnitude that limits its clinical applicability.     

Ventricular stroke work loss: validation of a method of quantifying the severity of aortic stenosis and derivation of an orifice formula

Because aortic stenosis results in the loss of left ventricular stroke work (due to resistance to flow through the valve and turbulence in the aorta), the percentage of stroke work that is lost may reflect the severity of stenosis. This index can be calculated from pressure data alone. The relation between percent stroke work loss and anatomic aortic valve orifice area (measured by planimetry from videotape) was investigated in a pulsatile flow model. Thirteen valves were studied (nine human aortic valves obtained at necropsy and four bioprosthetic valves) at stroke volumes of 40 to 100 ml, giving 57 data points. Valve area ranged from 0.3 to 2.8 cm2 and mean systolic pressure gradient from 3 to 84 mm Hg. Percent stroke work loss, calculated as mean systolic pressure gradient divided by mean ventricular systolic pressure x 100%, ranged from 7 to 68%. It was closely related to anatomic orifice area with an inverse exponential relation and was not significantly related to flow (r = -0.15). An orifice formula was derived that predicted anatomic orifice area with a 95% confidence interval of +/- 0.5 cm2 (orifice area [cm2] = 4.82 [2.39 x log percent stroke work loss], r = -0.94, SEE = 0.029). These results support the clinical use of percent stroke work loss as an easily obtained index of the severity of aortic stenosis.     

Theoretical and practical differences between the Gorlin formula and the continuity equation for calculating aortic and mitral valve areas

Although the Gorlin formula and the continuity equation are both used to calculate valvular areas in the clinical situation, there have been few comparisons of the 2 methods. Mathematically, it can be shown that both formulas are derived from similar hydrodynamic principles which basically give a measure of the physiologic or effective area occupied by flow. However, the Gorlin formula contains errors in formulation and incorporates a constant that purports to give a measure of the anatomic rather than of the effective area of the valve. If both formulas are applied to the same hemodynamic data from aortic and mitral bioprostheses studied in a pulse duplicator system, the Gorlin formula constantly yields results 1 to 2% higher than the continuity equation for aortic valves and 12 to 13% higher for mitral valves. For any given type and size of prosthesis, the areas calculated by either formula increase linearly in relation to increasing pressure and flow (up to 20% for aortic valves and up to 35% for mitral valves). It is concluded that the Gorlin formula and the continuity equation are both pressure- and flow-dependent and are primarily related to the effective area occupied by flow rather than to the anatomic area of the valve. The 2 methods yield consistently different results due to differences in mathematical formulation. Such factors are important to consider when interpreting valve area calculations clinically.     

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.     

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.     

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.     

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.     

Hydraulic estimation of stenotic orifice area: a correction of the Gorlin formula

To determine the source of errors in the Gorlin formula for estimating stenotic valvular orifice area, we used a pulsatile flow model that emulated left ventricular and aortic pressures and flow and allowed control of ventricular outflow orifice area. After comparing orifice areas calculated by the Gorlin formula with actual orifice areas, the Gorlin formula constant (k) was found to be highly correlated with the square root of the mean transvalvular gradient (r = .95). A new formula was derived empirically and predicted areas more accurately and with smaller standard errors than the Gorlin formula in the model (r = .98, SEE = 0.11 and r = .87, SEE = 0.28, respectively) in a series of 19 patients with Hancock porcine xenograft valves (r = .89, SEE = 0.07 and r = .60, SEE = 0.12, respectively) and in the original series of patients reported by Gorlin and Gorlin in proposing the Gorlin formula (r = .93, SEE = 0.11 and r = .91, SEE = 0.12, respectively).     

Modified gorlin equation for the diagnosis of mixed aortic valve pathology

BACKGROUND AND AIM OF THE STUDY: The accuracy of the Gorlin equation when applied to mixed valve pathology has not been investigated. An in-vitro study was performed to determine how a range of valve regurgitations and stenoses affects the Gorlin aortic valve area. METHODS: Various combinations of stenosis and regurgitation were simulated by placement of constricting orifices and minimal blockage reflux tubes within a 29-mm prosthetic pericardial valve. The orifice areas ranged from 0.7 cm2 to 1.75 cm2, and regurgitant fraction (RF) ranged from 0 to 0.35. Twenty-eight tests were performed at 70 beats/min, cardiac output of 5 l/min and systole 33-36% of the cycle. The mean pressure drops across the valve were adjusted to a value appropriate to blood density. Peripheral resistance was set to give a mean value of 1,537 dyn.s.cm(-5). RESULTS: The Gorlin area varied up to 0.55 cm2 from the geometric orifice area over the range of regurgitant fractions and stenoses. To improve the Gorlin equation, an amended mean volumetric forward flow rate was obtained by multiplying the cardiac output in the equation by the factor (1 - RF)(-1), to reconcile the equation for valvular regurgitation. The area predicted by the modified equation differed by <0.15 cm2 from the non-regurgitant valve geometric orifice area over the range of regurgitation and stenoses simulated. CONCLUSION: The study supports the validity of the Gorlin equation predicting pure aortic valve stenosis (areas <1.3 cm2); however, the equation overestimates the severity of stenoses when regurgitation is present. A modified equation is proposed, which includes regurgitant fraction. The new equation improves the calculation of valve geometric area in the presence of regurgitation and may be useful in cardiac catheterization laboratories where mixed aortic valve pathology is being evaluated.     

Prediction of pressure recovery location in aortic valve stenosis: an in-vitro validation study

BACKGROUND AND AIM OF THE STUDY: Pressure recovery is a source of discrepancy between Doppler-derived and catheter aortic valve pressure drops. Pressure recovery occurs where the stenotic jet reattaches to the aortic wall. An equation to predict the jet reattachment location has been developed based on the density and viscosity of blood, the velocity in the stenotic jet, and the aortic root and valve areas. The study aim was to define the conditions where this equation is valid and could be accurately applied to Doppler echocardiographic data. METHODS: In a pulse duplicator, mean flow rates were varied between 2 and 5 l/min, and anatomic orifice areas between 0.32 and 2.85 cm2, to produce values of the ratio of anatomic valve area to the aortic root area (E) of 0.04 to 0.36. For each hemodynamic state, continuous-wave, pulsed-wave Doppler and color Doppler flow maps were recorded. Instantaneous flow rates and pressures proximal and distal to the valve were recorded. Calculated reattachment lengths were compared to measurements from color Doppler echocardiography. RESULTS: Except for the smallest E value, there was a correlation between the predicted and measured jet reattachment lengths. The equation was good for predicted attachment lengths of less than 5 cm. Overestimation was seen for the smallest E value, representing a critically stenotic valve. CONCLUSION: Except for the most severe stenoses, pressure drops for aortic valves are best measured with the aortic sensor placed approximately 5 cm above the aortic valve. For moderate stenoses, where pressure recovery is relevant, the site of fully recovered pressure can be predicted.     

Valve orifice area alone is an insufficient index of aortic stenosis severity: effects of the proximal and distal geometry on transaortic energy loss.

BACKGROUND AND AIMS OF THE STUDY: Standard measures of hemodynamic severity of aortic valve stenosis vary widely among patients with and without clinical symptoms. Our hypothesis is that valve orifice area alone is not the sole determinant of adverse clinical outcome. Stenotic orifice area ratio is ratio of the cross-sectional stenotic orifice area to the down-stream, ascending aorta cross-sectional area. Determination of workload together with aortic valve orifice area ratio might improve risk stratification among asymptomatic patients with critical aortic stenosis. Accordingly, application of both parameters together might be useful in guiding management decisions in this condition. METHODS: In this study the dependency of transaortic fluid mechanical energy transfer (one component of left ventricular workload) on aortic valve orifice area is shown using modeling and experimental techniques. RESULTS: For a stroke volume of 62 ml at a heart rate of 60 beats/min, the piston work (analogous to left ventricular work) increased by 17% as the stenotic orifice area ratio decreased from 0.60 to 0.25, by 35% as the ratio fell from 0.25 to 0.20, and by 73% as the ratio fell from 0.20 to 0.10. CONCLUSIONS: As predicted by the fundamental fluid mechanical theory, simulated left ventricular work and energy loss in aortic stenosis are influenced not only by the effective stenotic valve orifice area, but also by the geometry of the inflow and outflow conduits, proximal and distal to the valve. These findings might explain clinically observed discrepancies between valve orifice area and the onset of the classical symptoms of severe aortic stenosis that reflect the left ventricular workload. Consideration of the left ventricular work in addition to the effective valve orifice area should enhance clinical evaluation, prognostication and risk stratification among patients with severe aortic stenosis.     

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.     

What do you mean by aortic valve area: geometric orifice area, effective orifice area, or gorlin area?

Aortic valve area can be measured by cardiac catheterization, Doppler echocardiography, or imaging planimetry to assess aortic stenosis severity. These diagnostic techniques provide the Gorlin area, the effective orifice area (EOA) and the geometric orifice area (GOA), respectively. The differences between these three parameters depend mainly on the valve inflow shape and cross-sectional area of the ascending aorta. Because the values obtained may differ noticeably in the same patient, they may lead to different estimations of stenosis severity depending on the measurement method used. It is therefore essential to be aware of the underlying fundamentals on which these parameters are based. The aim of this state-of-the-art report was to clarify these hemodynamic concepts and to underline their clinical implications. Because planimetry only provides GOA and does not characterize the flow property, this method should preferably not be used to assess stenosis severity. The most appropriate parameters for this purpose are the Gorlin area and the energy loss coefficient (E(L)Co), which corresponds to the EOA adjusted for aortic cross-sectional area. From a hemodynamic viewpoint, Doppler E(L)Co and Gorlin area both reflect the fluid energy loss induced by aortic stenosis, and describe better the increased overload imposed on the left ventricle. Although the Gorlin area and Doppler E(L)Co are equivalent, the latter parameter has the advantage of being measurable non-invasively using Doppler echocardiography.