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(Circulation. 1995;92:3464-3472.)
© 1995 American Heart Association, Inc.

Articles

Pressure Recovery in Bileaflet Heart Valve Prostheses

Localized High Velocities and Gradients in Central and Side Orifices With Implications for Doppler-Catheter Gradient Relation in Aortic and Mitral Position

Pieter M. Vandervoort, MD; Neil L. Greenberg, MSE; Min Pu, MD; Kimerly A. Powell, PhD; Delos M. Cosgrove, MD; James D. Thomas, MD

From the Cardiovascular Imaging Center, Departments of Cardiology (P.M.V., M.P., J.D.T.), Biomedical Engineering (N.L.G., K.A.P.), and Thoracic and Cardiovascular Surgery (D.M.C.), Cleveland Clinic Foundation, Cleveland, Ohio.

Correspondence to Pieter M. Vandervoort, MD, Department of Cardiology, Desk F15, Cleveland Clinic Foundation, 9500 Euclid Ave, Cleveland, OH.

	Abstract

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
Background We investigate pressure recovery in central and side orifices of St Jude valves and the effect of mitral versus aortic position on the relation between Doppler- and catheter-derived pressure gradients.

Methods and Results Maximum, transvalvular, and net pressure gradients are calculated and compared with Doppler-derived gradients in an in vitro model. Pressure recovery and pressure loss coefficients are calculated. Simultaneous Doppler and catheter gradients are obtained intraoperatively in five patients undergoing mitral valve replacement. Centerline Doppler gradients correspond closely with maximum catheter gradients but are higher than transvalvular and net pressure gradients. Thirty-six percent of the initial pressure drop is recovered between the valve leaflets and is independent of valve size or configuration. A variable amount of postvalvular pressure recovery is observed depending on aortic or mitral configuration. Side orifice velocities are 85±4% of the centerline velocities. Incorporation of the pressure loss coefficient in the simplified Bernoulli equation shows close agreement between centerline Doppler gradients and transvalvular gradients (r=.99, y=1.11x-0.19).

Conclusions Gradients across the St Jude valve measured by Doppler ultrasound are higher than transvalvular or net catheter gradients due to downstream pressure recovery. This is more marked for Doppler gradients based on centerline velocities than side orifice velocities and is more pronounced for valves in an aortic than a mitral configuration. Therefore, to be comparable with invasive transvalvular catheter gradients, either Doppler gradients should be calculated based on side orifice velocity measurements or the Doppler gradient calculation should include the pressure loss coefficient when based on central orifice velocities.

Key Words: prothesis • valves • pressure

	Introduction

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
Doppler velocity measurements across stenotic lesions are widely used in clinical cardiology practice to determine pressure gradients noninvasively with the use of the simplified Bernoulli equation. The accuracy of this method has been validated in numerous clinical studies for native valvular stenosis.^{1 2 3} However, controversy remains about the accuracy of this technique to measure pressure drop across prosthetic heart valves. Although several investigators have reported good agreement between Doppler-derived and catheter gradients for a variety of different valve prostheses,^{4 5 6} others have found significant overestimation of pressure gradients by Doppler in mechanical valves.^{7 8} Although this discrepancy between Doppler and catheter gradients has been reported for several types of mechanical prostheses, it appears to be most striking for the St Jude valve.

Recently, the presence of pressure recovery downstream from the prosthesis has been proposed as a potential cause for the apparent discrepancies between the Doppler and catheter gradients.^{8 9 10 11} This has been evaluated in vitro only for valves mounted in the aortic position. Because pressure recovery depends critically on the outflow geometry,¹² we hypothesized that pressure recovery would be different in central and side orifices and for valves in a mitral and aortic configuration. In the present study, we investigated the velocity and pressure distribution in St Jude heart valves using computational fluid dynamics and in vitro flow modeling. The aim of the study was to assess pressure recovery in central and side orifices of bileaflet prosthetic valves, determine the relative discrepancy between Doppler and catheter gradients for valves in the aortic versus mitral position, and explore ways to adjust for these differences, by either altering the Doppler examination of the valve or modifying the observed data.

	Theoretical Background

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
The Bernoulli equation relates potential and kinetic energy in a closed hydrodynamic system. The Bernoulli equation contains a convective term, an inertial term, and a viscous term. To calculate pressure gradients across restrictive orifices in the clinical setting, however, the Bernoulli equation can be simplified to the following¹³ :

where p is given in Pascals, v is given in m/s, and blood density is 1050 kg/m³. This simplification is possible because (1) the effect of blood viscosity can be neglected as boundary layer formation is suppressed except in the immediate vicinity of the walls; (2) the inertial term is negligible for flow through a restrictive orifice (such as a prosthetic heart valve) since the mass of blood being accelerated across the valve at any instant is small; and (3) proximal to the orifice, most energy is present as potential energy and the proximal velocity can be omitted. This simplified Bernoulli equation is used in daily echocardiographic practice to calculate pressure gradients across stenotic valves or estimate intraventricular pressures from mitral or tricuspid regurgitant velocity spectra.¹⁴

The use of this simplified equation is based on an additional assumption: that all potential energy converted into kinetic energy at the level of the stenosis is completely lost downstream in turbulent friction, vortex formation, and heat. Although this is true for the abrupt stenoses found in most native and prosthetic valves, it is not a physical necessity. If, for example, a stenosis gradually flairs from its narrowest point, then streamlines of flow may remain attached to the walls, allowing smooth deceleration and partial conversion of kinetic energy back into potential energy or pressure.¹⁵ The slight outward flair of the two leaflets of the St Jude valve operates in a similar fashion, allowing gradual deceleration of flow with partial reattachment of streamlines and pressure recovery downstream.

The actual recovery of pressure for flow through a diffuser (or the St Jude valve) can be specified by the experimentally determined static pressure recovery coefficient C_p¹⁵ :

where p_min and p_downstr are the static pressures (in Pascals) at the orifice and downstream from the orifice, respectively; is the constant fluid density, and v is the flow velocity at the orifice. For uniform entrance and exit flows and no frictional losses, the ideal pressure recovery coefficient is the following¹⁵ :

where A_i and A_o are the entrance and exit flow areas, respectively. The second substitution is only possible for a two-dimensional diffuser (as is the case for the central orifice of the St Jude valve) where areas can be replaced by width of the inlet (W_i) and outlet (W_o) since the height of inlet and outlet are the same. The "effectiveness" of a diffuser can be defined by comparing the actual pressure recovery coefficient with the theoretical ideal¹⁵ :

In general, C_p will fall below the theoretical ideal and will be less than 1 since viscous dissipation and velocity peaking in the outlet stream will reduce pressure recovery.

The net pressure loss across a diffuser (which is more clinically relevant for prosthetic heart valves) is specified by the pressure loss coefficient K, defined by the change in total pressure through the diffuser¹⁵ :

For a diffuser discharging into a large reservoir (relative to the diffuser exhaust), the pressure loss coefficient K and the pressure recovery coefficient C_p are related by¹⁵ :

For a perfect diffuser with complete pressure recovery, C_p=1 and K=0; in the absence of any pressure recovery downstream from the flow obstruction, C_p=0 and K=1.

	Methods

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
Numerical Simulation
To illustrate in more detail the spatial pressure and velocity distribution and their relation to the structures of the St Jude bileaflet heart valve, a numerical simulation was performed. Commercially available finite difference software for computational fluid dynamics (Fluent Inc) was used to model a two-dimensional cross section of a No. 25 St Jude valve with the leaflets in a fully open position mounted in an aortic position. The Navier-Stokes flow equations were solved on a 1x1-mm grid. A noncompressible fluid was assumed with the density and viscosity of blood. The equations were solved iteratively until acceptable convergence criteria were reached (relative residual error <3 · 10^-4 after 500 iterations). This numerical simulation provided pressure information, velocity magnitude, and the axial and radial components of velocity at each point of the flow field. Velocity and pressure profiles through central and side orifices were reconstructed for comparison with the experimental data.

In Vitro Experiment
Prosthetic bileaflet heart valves (sizes No. 19 through 29, St Jude Medical Inc) were mounted in an in vitro flow model producing steady flow between 215 and 405 mL/s. The model consisted of two plexiglas chambers: a proximal chamber (8x18x30 cm) that is sealed and can be pressurized and a distal larger discharge chamber (100x18x30 cm) at atmospheric pressure. Flow entered the proximal chamber by gravity from an upper reservoir under controlled pressure and left the distal chamber via an overflow outlet, which ensured a steady pressure difference between both chambers. The fluid (1% aqueous solution of cornstarch, which provides acoustic reflectors) was pumped into the upper reservoir to maintain its level, and flow rate was varied by altering the pressure difference between proximal and distal chambers. The prosthetic heart valves were mounted with the leaflets in a vertical position in the partition between the two chambers. To simulate a prosthetic valve in a mitral position (distal chamber large compared with the valve), flow discharged directly into the distal chamber. For valves Nos. 19 through 25, an aortic position was also simulated. Circular tubings (8 cm in length) with diameters of 26 and 31 mm were fixed distal to the valve to simulate an artificial ascending aorta.

Micrometer measurements of the height and width of central orifice inlet and outlet were obtained for valve sizes Nos. 19 through 29.

Data acquisition. Pressure measurements were obtained using high-fidelity pressure transducers (Millar Inc). The catheter was connected to a microprocessor controlled infusion pump (Harvard Apparatus) and slowly (0.8 mm/s) pulled back through the central and side orifices of the St Jude heart valves. The pressure catheter (7F) was stabilized with an 8F introducer sheath to ensure stable and straight pullbacks. The pressure transducer located at the side of the catheter tip was rotated upward to avoid interference with the leaflets when the catheter was pulled back through the valve. The pressure waveforms were digitized at 1000 Hz over 100 seconds (8 cm distance) and stored to disc (Macintosh Quadra) using LABVIEW (National Instruments).¹⁶ Pressure measurements started 1.5 cm proximal to the valve and were acquired continuously until 6.5 cm downstream from the valve. Simultaneous Doppler velocity measurements were obtained using a Sonos 1500 echocardiograph (Hewlett-Packard) equipped with digital storage and retrieval capabilities. A 2.5-MHz ultrasound transducer was positioned proximal to the orifice along the centerline of the flow. By directing the continuous wave ultrasound beam, velocities in the central and side orifices could be interrogated separately. Pulsed Doppler velocities were measured 1.5 cm proximal to the valve. These proximal velocities ranged between 38 and 59 cm/s and are neglected in the simplified Bernoulli equation for gradient calculations.

Data analysis. The proximal pressure (P_prox, measured approximately 1.5 cm proximal to the valve), the minimal pressure (P_min), and the distal pressure (P_dist, measured approximately 6.5 cm downstream from the valve) were read out from both pressure tracings through central and side orifices. For the central pressure tracing only, an additional pressure measurement (P_sh) was read out at the "shoulder" of the pressure curve occurring at the distal edge of the leaflets (Fig 1).

View larger version (22K): [in this window] [in a new window]   Figure 1. Schematic representation of a centerline pressure profile showing the locations where pressures were read out for comparison; this also illustrates the calculations of maximum, net, and transvalvular pressure gradients as well as the two phases of downstream pressure recovery.

From these pressure measurements, the maximum and net pressure gradients across central and side orifices were calculated. Also, for the central orifice, a transvalvular gradient was calculated (Fig 1). The maximum catheter pressure gradient was calculated as the difference between the proximal and the minimum pressure measurements (P_prox-P_min). The net pressure drop was given by the difference between the proximal and the distal pressure measurements (P_prox-P_dist). The transvalvular pressure gradient across the central orifice was calculated as P_prox-P_sh. The percentage of maximal pressure drop in central and side orifices recovered downstream was calculated as 100 · (P_dist-P_min)/(P_prox-P_min). For flow through the central orifices, the pressure recovery consistently showed two phases. Phase 1 was the initial more rapid pressure recovery from P_min to P_sh, occurring between the valve leaflets (early or valvular recovery); the percent pressure recovery is calculated as 100 · (P_sh-P_min)/(P_prox-P_min). Phase 2 represented the pressure recovery occurring distal from the valve (late or postvalvular recovery) and was calculated as 100 · (P_dist-P_sh)/(P_prox-P_min) (Fig 1). For each valve, the pressure recovery coefficient C_p and the total pressure loss coefficient K were calculated.

From the continuous wave Doppler velocity measurements through central and side orifices, pressure gradients were calculated with the simplified Bernoulli equation.

Clinical Study
We studied five patients undergoing mitral valve replacement with a St Jude prosthetic valve intraoperatively after coming off cardiopulmonary bypass. All patients were in a regular sinus rhythm or atrioventricular paced rhythm and hemodynamically stable during the data acquisition. A transesophageal echoprobe was inserted as part of the routine diagnostic and monitoring procedure in patients undergoing valve surgery. The Omniplane transducer was rotated to clearly visualize the two valve leaflets with separation of central and side orifices of the prosthetic valve (Fig 2). It was possible to position the continuous wave Doppler cursor selectively across the central and the side orifices of the valve in all patients. Doppler velocity spectra were obtained with the use of a Sonos 1500 echocardiograph (Hewlett-Packard) and recorded on -in videotape. A left atrial fluid-filled pressure catheter was inserted through the left atrial appendage, and the left ventricular pressure was measured with a fluid-filled line through a direct needle stick of the left ventricle near the left ventricular apex. Pressure measurements of the left atrium and the left ventricle were acquired simultaneously. The pressure waveforms were amplified (module 300, Marquette Tram) and subsequently digitized at 1000 Hz with a National Instruments data acquisition board (AT-MIO-16) and stored to disc (Gateway 2000 486 Dx 2/50) using custom software written in LABVIEW III (National Instruments). Simultaneously with left atrial and left ventricular pressures, we measured Doppler velocities through the central and subsequently through the side orifices. Only cardiac cycles with high quality simultaneous left atrial and left ventricular pressure and Doppler velocity data were used for analysis. Ectopic ventricular or supraventricular beats were excluded. The peak instantaneous pressure gradient during early filling (E wave) was measured with a customized analysis package written in LABVIEW. Peak transvalvular Doppler gradients were calculated off-line with the calculation package incorporated in the echocardiograph.

View larger version (0K): [in this window] [in a new window]   Figure 2. Illustration of a transesophageal imaging view of a St Jude mitral valve prosthesis showing the position of the Doppler beam to selectively sample central and side orifice velocity profiles.

Statistical Analysis
Pressure profiles obtained from numerical simulations were compared with the experimental data, and a correlation coefficient was calculated. Pressure measurements for mitral and aortic configurations were compared with paired Student's t tests.

Doppler pressure gradients were compared with catheter gradients using linear regression analysis, and a correlation coefficient was calculated. The difference between Doppler and catheter gradients (Doppler minus catheter) were calculated and expressed as mean±SD.

The impact of valve size and outlet configuration were compared with ANOVA.

	Results

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
Numerical Simulation
Fig 3 shows the results of a numerical simulation of the St Jude valve No. 25 in the aortic position. There is a steep increase in velocity with a discrete region of highest velocity at the entrance of the central orifice of the valve. The maximum velocities in the side orifices are lower and located approximately 4 to 5 mm farther downstream than in the central orifice. The corresponding pressure distribution demonstrates a localized low pressure zone proximal between the two valve leaflets. There is a localized low pressure zone in the side orifices, but it is less pronounced and occurs more downstream. Fig 4 shows the reconstructed pressure profiles through the central and the side orifices. The pressure profile through the central orifice shows the deep pressure well proximal between the leaflets with gradual pressure recovery downstream. As much as 41% of the initial pressure drop is recovered before the end of the leaflets with an additional 19% recovered 5 cm downstream in the aorta. The pressure drop in the side orifices occurs further downstream and is less pronounced. As a result, pressure recovery in the side orifices is less with recovery of only 32%.

View larger version (0K): [in this window] [in a new window]   Figure 3. Color-coded display of the pressure (top) and velocity magnitude (bottom) distribution obtained from the numerical simulations. Red represents the highest velocity and pressure values; blue represents the lowest values. The low-pressure area at the entry of the central orifice is clearly illustrated as are the separate jets through central and side orifices.

View larger version (17K): [in this window] [in a new window]   Figure 4. Pressure profiles through central (solid) and side (dashed) orifices obtained from the numerical simulations, illustrating the marked pressure drop in the central orifice located slightly more proximal than the side orifices.

In Vitro Experiments
Pressure Measurements
Central versus side orifices. The pressure profile through the central orifice shows a deep pressure well with gradual pressure recovery downstream. This distal pressure recovery through the central orifice occurs in two phases: a first rapid increase in pressure following the minimal pressure and a second phase of further but slower increase in downstream pressure (Fig 5). This first phase corresponds to the pressure recovery occurring between the two leaflets before flow leaves the valve; the second phase reflects the additional pressure recovery downstream from the level of the valve.

View larger version (17K): [in this window] [in a new window]   Figure 5. Graph illustrating the differences in pressure profiles obtained in the in vitro experiment through central (solid) and side (dashed) orifices of a St Jude valve No. 23 in a mitral configuration. The pressure drop in the central orifice is more pronounced and occurs more proximal than in the side orifices. The amount of pressure recovered downstream is higher in the central orifice than in the side orifices.

In the side orifices, the localized low pressure zone is less pronounced and occurs more distally. The maximum pressure gradients measured in the side orifices are 24±10% (mean±SD, P<.001) lower than the maximum pressure gradients measured across the central orifices. The pressure recovery through the side orifice does not systematically show the biphasic pattern seen in the central orifice. The percent of maximum pressure drop recovered in the side orifices is significantly lower than that in the central orifices for all valves (Table 1).

View this table: [in this window] [in a new window]   Table 1. Maximum Catheter Gradient Across Central and Side Orifices Recovered Downstream From Valve Prosthesis for Three Configurations Studied

Aortic versus mitral configuration. In aortic valves with the smallest aorta (26 mm), as much as 58.1±5.0% of the initial pressure drop in the central orifice is recovered downstream; 36.7±3.9% of this total pressure is recovered during deceleration of flow within the first phase (valvular), and an additional 21.3±6.0% is recovered in the second phase (postvalvular). Increasing the size of the aorta decreases the total pressure recovered in the central orifice significantly to 49.8±4.7%, P<.001. This decrease is entirely due to less pressure recovery during phase 2 as 37.2±4.7% is recovered between the leaflets (phase 1) and only 12.6±0.7% of pressure recovery occurs downstream from the valve in the aorta (phase 2). For valves in the mitral configuration, total pressure recovery through the central orifice is only 37.3±6.4%, P<.001, occurring almost entirely at the level of the valve (phase 1, 35.6±4.2%) with virtually no further pressure recovery downstream (phase 2, 1.7±3.3%). Fig 6 shows the difference in centerline velocity profile for a valve in the mitral and aortic (26-mm aorta) positions.

View larger version (16K): [in this window] [in a new window]   Figure 6. Graph illustrating the differences in pressure profiles obtained through the central orifice of a St Jude valve No. 23 in a mitral (solid) and aortic (26-mm aorta; dotted) configuration in vitro. Pressure recovery within the central orifice is similar for mitral and aortic positions. In the aortic configuration, additional pressure recovery occurs further downstream in the aorta.

Overall, maximum pressure drop and percent pressure recovery are significantly lower (P<.001) in the side orifices than in the central orifices. The percent pressure recovery in the side orifice of the aortic valves with the smallest (26 mm) aorta is 43.9±9.9%. The percent pressure recovery decreases to 33.9±7.9% (P<.001) for the aortic valves with the bigger aorta (31 mm) and is only 17.9±4.7% for the side orifices of the mitral position.

Doppler Velocity Measurements
Continuous wave Doppler velocities through the central orifice range from 175 to 430 cm/s, and velocities through the side orifices range from 149 to 350 cm/s and are 85±4% (mean±SD, P<.001) of the central orifices. The ratio between maximum velocities in central and side orifices is independent of valve size and configuration.

Maximum versus net pressure gradients. The pressure gradients (y) calculated from the continuous wave Doppler velocity measurements in central and side orifices with the simplified Bernoulli equation correlate closely with the maximum catheter gradients (x) measured in central and side orifices, respectively, with r=.99, y=1.04x+0.22, and p (catheter minus Doppler)=1.0±1.8 mm Hg. As expected, these maximal Doppler gradients at the level of the valve are significantly higher than the net catheter gradients. This pressure difference is significantly higher for gradients based on centerline velocity measurements (114.8±52.2%, p=13.4±12.1 mm Hg) than for gradients calculated from side orifice velocities (54.2±36.4%, p=5.7±4.4 mm Hg) (P<.001) (Table 2). The discrepancies between Doppler gradients across the central orifice and the net pressure drop in aortic valves with the 26-mm aorta (167.1±51.8%) are significantly larger than in aortic valves with the 31-mm aorta (123.3±41.0%, P<.001) and larger than in the mitral valves (74.2±15.4%, P<.001). The difference between Doppler gradients across the side orifices and the net invasive pressure drop is significantly less, in particular, for the mitral configuration (Table 2).

View this table: [in this window] [in a new window]   Table 2. Difference (Doppler Minus Catheter) and Actual Difference Between Net Invasive Pressure Drop Across Valves and Doppler-Derived Pressure Gradients

Transvalvular gradients. Maximum Doppler gradients (y) obtained through the central orifices correlate closely (r=.99) but are significantly higher than the transvalvular pressure gradients (x) with y=1.73x-0.29 and p=9.9±9.6 mm Hg (73.6±18.6%).

Pressure Recovery Coefficient (C_p) and Pressure Loss Coefficient (K)
Micrometer measurements of inlet (W_i) and outlet width (W_o) of the central orifice show a fixed relation of W_i/W_o=0.65±0.02 (range, 0.63 to 0.68) for all valve sizes studied (Nos. 19 to 29). Based on these measurements, a theoretical pressure recovery coefficient for ideal uniform flow through the St Jude valve is calculated as C_p(ideal)=1-0.65²=0.58.

The actual pressure recovery coefficient C_p for the central orifice of all valves is 0.36±0.04 (mean±SD), and the total pressure loss coefficient K calculated for all valves was 0.64±0.04. ANOVA shows no effect of valve size or configuration. The diffuser effectiveness () is calculated by comparing the actual with the theoretical pressure recovery coefficient: =0.36/0.58=0.62.

When Doppler-derived gradients across the central orifice are multiplied by the pressure loss coefficient K=0.64, the transvalvular gradients (x) are closely approximated with r=.99, y=1.11x-0.19, and p=1.4±2.1 mm Hg (11.1±11.9%) as illustrated in Fig 7. Introduction of this pressure loss coefficient also reduces the difference between Doppler and net pressure gradients (including pressure recovery downstream from the valve) by almost 80% with p=3.9±4.6 mm Hg (Table 3). Residual discrepancy was present only for valves in the aortic position; for St Jude valves in a mitral configuration, Doppler velocity measurements through the central orifices showed close agreement with the net transvalvular gradient (p=0.8±0.8 mm Hg).

View larger version (26K): [in this window] [in a new window]   Figure 7. Correlation between catheter transvalvular pressure gradients and Doppler-derived pressure gradients without and with incorporating the pressure loss coefficient K=0.64 in the simplified Bernoulli equation.

View this table: [in this window] [in a new window]   Table 3. Difference (Doppler Minus Catheter) and Actual Difference Between Net Pressure Drop Across Central Orifice and Doppler-Derived Pressure Gradients Adjusted by Pressure Loss Coefficient K=0.64

Clinical Study
Fig 2 shows a transesophageal ultrasound image of a St Jude valve prosthesis in the mitral position illustrating the two valve leaflets with the central and side orifices. Fig 8 shows a Doppler velocity tracing (top) with the simultaneously acquired left atrial, left ventricular, and aortic pressures (bottom) for three consecutive cardiac cycles. The first Doppler tracing on the left was obtained through the central orifice showing the highest velocities. With slight rotation of the echoprobe, the Doppler velocity profile through the side orifice was obtained (third tracing on the right) showing a markedly lower peak velocity. On the middle tracing, a double-velocity contour can be seen when the echotransducer is in an intermediate position, sampling velocities from both the central and the side orifices. Although there is a marked difference in the calculated Doppler gradients between the first and the third cardiac cycles, the hemodynamic conditions are unchanged, as illustrated by the simultaneously acquired invasive pressure measurements.

View larger version (0K): [in this window] [in a new window]   Figure 8. Clinical example of a continuous wave Doppler velocity spectrum obtained through central (left) and side (right) orifice in a patient with a newly implanted St Jude valve No. 29 in the mitral position. The simultaneously obtained left atrial, left ventricular, and aortic pressures are displayed at the bottom.

A total of 42 cardiac cycles with high-quality simultaneous Doppler and pressure data were analyzed. The invasive peak pressure gradients during early filling range from 4 to 9 mm Hg (6.2±1.2 mm Hg). The corresponding Doppler gradients measured across the central orifice range from 7 to 11 mm Hg (9.1±1.1 mm Hg) and are significantly higher than the invasive pressure gradients with a difference (Doppler minus catheter gradient) of 47±20% (2.9±0.9 mm Hg) (Fig 9a). When the pressure loss coefficient (K=0.64) is incorporated in the simplified Bernoulli equation, the Doppler gradients calculated across the central orifice range from 5.2 to 7 mm Hg (5.9±0.7 mm Hg) and show very good agreement with invasive measurements with a difference (Doppler minus catheter gradient) of -6±13% (-0.4±0.8 mm Hg) (Fig 9b). Doppler gradients measured across the side orifices range from 5.4 to 9.1 mm Hg (6.9±1.1 mm Hg) and also agree very well with the invasive pressure gradients with a difference (Doppler minus catheter gradient) of 15±12% (0.8±0.5 mm Hg) (Fig 9a).

View larger version (20K): [in this window] [in a new window]   Figure 9. Left, Graph illustrates the difference (Doppler minus catheter) between catheter and Doppler gradients measured across the central () and side () orifices on the y axis and the invasive pressure gradients on the x axis. Right, Graph illustrates the difference (Doppler minus catheter) between catheter and Doppler gradients measured across the central orifice without () and with () the pressure loss coefficient K incorporated into the simplified Bernoulli equation on the y axis and the invasively obtained pressure gradient on the x axis.

	Discussion

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
Doppler echocardiography has evolved over recent years to become the method of choice for follow-up evaluation of patients with prosthetic heart valves.^{17 18} This technique allows visualization and evaluation of structural integrity, valvular and paravalvular regurgitation, and transvalvular gradients. From the Doppler velocity measurements, transvalvular pressure drop can be predicted by applying the simplified Bernoulli equation, which relates the conversion of pressure energy proximal to the valve into kinetic energy as blood accelerates through the valve.¹⁸ These measurements are validated for abrupt obstructions in vitro¹⁹ and for native valvular stenosis.^{1 2 3} For mechanical prostheses, however, some investigators have reported good agreement between Doppler and catheter gradients,^{4 5} whereas others have reported significant differences between Doppler and catheter gradients.^{7 8} These differences appear to be most prominent in the St Jude valve.^{8 20} In the present study, we investigated this apparent discrepancy for St Jude valves in the aortic and mitral position and evaluated whether it is possible to reconcile these differences, by either adjusting the observed data or altering the Doppler examination.

Results of Present Study
The numerical simulation shows that a localized low-pressure zone is present at the entrance of the central orifice. The pressure profile through the central orifice illustrates this deep-pressure well with gradual increase in pressure further downstream. A similar low-pressure well occurs in the side orifices but is less pronounced and is located more downstream at the distal margins of the valve leaflets. These low-pressure zones correspond to local areas of high velocities as illustrated by the numerical simulations.

Our observations in the in vitro experiments are very similar to the numerical predictions. In the vitro experiments, we find very close agreement between Doppler gradients and maximum catheter pressure gradients measured in the low-pressure well occurring between the prosthetic valve leaflets. In the clinical setting, this maximum pressure gradient cannot be measured invasively because it is not possible to position a catheter across or between mechanical prosthetic valve leaflets in patients. Doppler gradients across the central orifices are significantly higher than the transvalvular and net catheter pressure gradients measured across the valve. These differences are due to downstream pressure recovery. This downstream pressure recovery through the central orifices shows a biphasic pattern. The first part has a rapid increase in pressure and occurs predominantly between the leaflets of the valve. This phase of the pressure recovery critically depends on the gradual deceleration of flow with reattachment of streamlines between the slightly outward-directed valve leaflets. Because this phase of pressure recovery occurs between the valve leaflets, it would not be detected in the clinical situation by catheter measurements. We find that a fixed percentage of 35% of the maximum pressure drop is recovered between the two leaflets of the valve. This percentage is independent of valve size or valve configuration. A second phase of pressure recovery occurs further downstream beyond the level of the valve. The in vitro experiments showed that during the second phase, a smaller portion of the initial pressure drop is recovered and is highly dependent on the distal geometry. This second phase of pressure recovery is most pronounced in the aortic configuration with the smallest aorta, where an additional 21.3±6.0% of the initial pressure drop is recovered. In the mitral configuration, virtually no further pressure recovery occurs beyond the level of the valve. Because pressure recovery critically depends on downstream geometry and catheter position, direct comparison with previous studies is difficult when in vitro setup and testing conditions are not exactly similar. Baumgartner et al have studied pressure recovery in St Jude valves in the aortic position (32-mm aorta) under pulsatile flow conditions in vitro. They reported 41.8±9.1% pressure recovery at 3 cm downstream from the valve with the distal pressure measured at the wall of the aorta. In the present study, we found 49.8±4.7% pressure recovery for a St Jude valve with a 31-mm aorta and the distal pressure measured in the center of the aorta at 6.5 cm from the valve. These findings are very similar; however, in the study by Baumgartner et al, valvular and postvalvular pressure recoveries were not analyzed separately, and the authors did not evaluate pressure recovery with a different-size aorta or mitral configurations.

Distal pressure recovery is significantly less through the side orifices and does not show consistently the biphasic pattern observed in the central orifice. Because overall pressure recovery through the side orifices is less pronounced, Doppler gradients across the side orifices approximate the transvalvular and net pressure drop closer than Doppler gradients across the central orifice. In the central orifice, flow decelerates with reattachment of streamlines on both leaflets, allowing for less flow separation and more pressure recovery. For flow through the side orifices, reattachment of streamlines is only possible on one side and therefore less pressure recovery occurs. However, in the presence of an aorta, streamlines can also reattach downstream to the aortic wall, resulting in increased pressure recovery through the side orifices for valves in the aortic position compared with valves in the mitral configuration.

The observation of fixed percentage of pressure recovery through the central orifice is also reflected by the calculated pressure recovery coefficient C_p of 0.36±0.04. The clinically more relevant transvalvular pressure drop is reflected by the pressure loss coefficient K=0.64±0.04. For all St Jude prosthetic valves tested (Nos. 19 to 29), the total pressure loss coefficient K is constant and independent of valve size or downstream geometry. This constant K reflects the proportion of the total kinetic energy present at the orifice that is lost downstream in friction, vortex formation, and heat and therefore reflects the true net static pressure drop across a stenosis.

Implications for Measurements of Doppler Gradients
Application of the simplified Bernoulli equation to Doppler velocity measurements across the central orifices of St Jude valves will yield significantly higher calculated pressure gradients across the valve than the pressure gradient measured during cardiac catheterization. However, a thorough understanding of the hydrodynamic profile of this valve allows us to interpret this discrepancy. The results of this study have important implications for the noninvasive assessment of St Jude prosthetic valve function using Doppler ultrasound. Incorporation of the experimentally determined pressure loss coefficient K for the St Jude valve in the simplified Bernoulli equation is necessary for a comparison of noninvasive Doppler gradients with the invasive gradients measured during cardiac catheterization. We find that this pressure loss coefficient K is similar for all valve sizes, allowing us to closely approximate the invasively measured transvalvular gradient for all St Jude valves independent of valve size or position. When the Doppler gradient (v²) across the central orifice was multiplied by the pressure loss coefficient K=0.64, an excellent agreement was observed between the noninvasive and invasive transvalvular pressure gradients.

The findings of the present study also show that pressure recovery through the side orifices is less pronounced, and Doppler gradients through the side orifices closely approximate the transvalvular and net pressure gradients, especially for mitral valves. This suggests that alteration of the Doppler examination of the St Jude valve and measurement of transvalvular velocities selectively through the side orifices provide more accurate Doppler-derived pressure gradients. Although selective sampling of central and side orifices may be difficult for St Jude valves in the aortic position, it should be possible for valves in the mitral position. In particular, the transesophageal imaging window enables us to image the mitral prosthesis in the near field and selectively sample velocities through central and side orifices.

We studied five patients undergoing mitral valve replacement with a St Jude heart valve and found close agreement between Doppler gradients measured across the side orifices of the valve and the invasive pressure gradients, with the Doppler gradients being only slightly higher. Similar to the numerical and in vitro observations, Doppler gradients measured across the central orifice are significantly higher than the invasive measurements. Incorporation of the pressure loss coefficient K into the simplified Bernoulli equation across the central orifice also provides excellent agreement between noninvasive and invasive pressure gradient measurements.

Study Limitations
The purpose of the numerical simulation was to illustrate the spatial velocity and pressure distribution within the central and side orifices of a St Jude valve. The results of any numerical simulation are limited by its inherent assumptions. Our model is a simplified two-dimensional cross section of the prosthetic valve and therefore is limited in reflecting what is happening in a complex three-dimensional structure such as the St Jude valve. Although it was not the purpose of the present study to validate the results of the numerical model, the pressure profiles predicted by the numerical simulation closely match our in vitro findings, lending credibility to results of the computer simulation.

The phenomenon of pressure recovery has been well described under steady^{10 15} and pulsatile^{8 11} flow conditions. We selected a steady flow model because this setup allows for continuous pressure pull-back measurements within the valve orifices. This is necessary to locate precisely the minimal pressure, measure the amount of pressure recovery occurring within the valve orifices, and calculate pressure loss and pressure recovery coefficients within the central orifice of the St Jude valve. In the presence of pulsatile flow, the acceleration phase tends to stabilize streamlines and may reenforce pressure recovery, whereas deceleration tends to destabilize flow and become more turbulent, therefore reducing pressure recovery. The effect of acceleration and deceleration on the instantaneous pressure recovery was beyond the aim of the study; however, this question merits further study in the future.

The apparent differences between invasive and noninvasive transvalvular pressure gradients is due not only to pressure recovery at the level of the St Jude valve. As the present study illustrates, pressure recovery can also occur beyond the level of the valve, depends critically on the downstream geometry, and could be more than 20% of the maximum pressure drop in the presence of a small ascending aorta. Depending on whether the valve discharges into the aorta or into an open chamber as is the left ventricle, the exact position of the catheter downstream, and whether downstream flow is uniform throughout the cross section of the distal chamber, a variable discrepancy may remain. In our in vitro study, for the mitral position the distal chamber is large compared with the size of the left ventricle. In the clinical setting, in particular in the presence of left ventricular hypertrophy with a small left ventricular cavity, it is possible that downstream pressure recovery occurs within the ventricle, and therefore differences between mitral and aortic position may be less than those found in our in vitro study. The use of fluid-filled catheters²¹ as well as differences in sampling location in left atrium and left ventricle²² may introduce some inaccuracies into the pressure measurements obtained in our clinical study; however, overall the clinical observations closely match the numerical and in vitro findings.

Pressure recovery critically depends on the gradual deceleration of flow with reattachment of streamlines. In the present study, we evaluated normal functioning valve prostheses. In the presence of thrombus or pannus overgrowth interfering with normal leaflet excursion, the hydrodynamic profile of the valve may be significantly altered, and the amount of pressure recovery in the central orifice may be reduced or completely dissappear, as was suggested by the results of an in vitro study.²³ If prosthetic valve dysfunction is suspected, careful examination of leaflet excursion by transthoracic or transesophageal imaging is necessary. When abnormal leaflet excursion is present (or suspected), (1) the Doppler gradients across the central orifice should be calculated without incorporating the pressure loss coefficient into the simplified Bernoulli equation and/or (2) the Doppler gradients should be measured across the side orifices, where pressure recovery is minimal and the simplified Bernoulli equation is adequate.

Other possible reasons for gradient overestimation by Doppler under physiological conditions is the known difference between instantaneous peak gradients (measured by Doppler) and the peak-to-peak gradients typically measured by catheter. Doppler gradients may be erraneous under conditions where the simplified Bernoulli equation is no longer valid, eg, when the proximal velocity is not negligible or for flow through nonrestrictive orifices where the inertial term in the Bernoulli equation cannot be neglected. Doppler gradients can underestimate true gradients if the peak velocity could not be resolved or if the direction of the flow is oblique to the ultrasound beam and therefore only its component parallel to the Doppler beam is recorded.

Although maximum, transvalvular, and net pressure gradients are all different gradients that physically exist, it is currently not known which of these gradients is most relevant to reflect the work load imposed on the heart.

Conclusions
We explored and explained the previously reported differences between Doppler and catheter gradients across the St Jude valve. We demonstrated that the discrepancies between Doppler and catheter gradients are not due to errors in either Doppler or catheter techniques of measuring transvalvular gradients but; rather that Doppler ultrasound and catheters measure different gradients that both exist physically. To be able to compare catheter and Doppler gradients obtained across a St Jude valve prosthesis, we suggest either multiplying the Doppler gradient (obtained across the central orifice) by the experimentally defined pressure loss constant K=0.64 or, in particular for valves in the mitral position, calculating transvalvular gradients from Doppler velocity measurements obtained by selectively interrogating the side orifices of the prosthetic heart valve.

Received March 15, 1995; revision received August 7, 1995; accepted August 8, 1995.

	References

Top Abstract Introduction Theoretical Background Methods Results Discussion References

 
1. Hatle L, Angelsen BA, Tomsdal A. Non-invasive assessment of aortic stenosis by Doppler ultrasound. Br Heart J. 1980;43:284-292. [Abstract/Free Full Text]

2. Hegrenaes L, Hatle L. Aortic stenosis in adults: noninvasive estimation of pressure differences by continuous wave Doppler echocardiography. Br Heart J. 1985;54:396-404. [Abstract/Free Full Text]

3. Currie P, Seward JB, Reeder GS, Vliestra RE, Bresnahan DR, Bresnahan JF, Smith HC, Hagler GJ, Tajik AJ. Continuous wave Doppler echocardiographic assessment of severity of calcific aortic stenosis: a simultaneous Doppler-catheter correlative study in 100 adult patients. Circulation. 1985;71:1162-1169. [Abstract/Free Full Text]

4. Williams GA, Labovitz AJ. Doppler hemodynamic evaluation of prosthetic (Starr-Edwards and Bjork-Shiley) and bioprosthetic (Hancock and Carpentier-Edwards) cardiac valves. Am J Cardiol. 1985;56:325-332. [Medline] [Order article via Infotrieve]

5. Wilkins GT, Gillam LD, 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;74:786-795. [Abstract/Free Full Text]

6. Burstow DJ, Nishimura RA, Bailey KR, Reeder GS, Holmes DR, Seward JB, Tajik AJ. Continuous wave Doppler echocardiographic measurements of prosthetic valve gradients: a simultaneous Doppler-catheter correlative study. Circulation. 1989;80:504-514. [Abstract/Free Full Text]

7. Rothbart RM, Smucker ML, Gibson RS. Overestimation by Doppler echocardiography of pressure gradients across Starr-Edwards prosthetic valves in the aortic position. Am J Cardiol. 1988;61:475-476. [Medline] [Order article via Infotrieve]

8. Baumgartner H, Khan S, DeRobertis M, Czer L, Maurer G. Discrepancies between Doppler and catheter gradients in aortic prosthetic valves in vitro: a manifestation of localized pressure gradients and pressure recovery. Circulation. 1990;82:1467-1475. [Abstract/Free Full Text]

9. Levine RA, Jimoh A, Cape EG, McMillan S, Yoganathan AP, Weyman AE. Pressure recovery distal to a stenosis: potential cause of gradient `overestimation' by Doppler echocardiography. J Am Coll Cardiol. 1989;13:706-713. [Abstract]

10. Clark C. The fluid mechanics of aortic stenosis, I: theory and steady flow experiments. J Biomechan. 1976;9:521-528. [Medline] [Order article via Infotrieve]

11. Voelker W, Ruel H, Stelzer T, Schmidt A, Karsch KR. Pressure recovery in aortic stenosis: an in vitro study in a pulsatile flow model. J Am Coll Cardiol. 1992;20:1585-1593. [Abstract]

12. Baumgartner H, Schima H, Tulzer G, Kuhn P. Effect of stenosis geometry on the Doppler-catheter gradient relation in vitro: a manifestation of pressure recovery. J Am Coll Cardiol. 1993;21:1018-1025. [Abstract]

13. Yoganathan AP, Cape EG, Sung H, Williams FP, Timoh A. Review of hydrodynamic principles for the cardiologist: applications to the study of blood flow and jets by imaging techniques. J Am Coll Cardiol. 1988;12:1344-1353. [Abstract]

14. Hatle L, Angelsen B. Doppler Ultrasound in Cardiology: Physical Principles and Clinical Applications. 2nd Ed. Philadelphia, Pa: Lea & Febiger; 1986:24.

15. Blevins RB. Applied Fluid Dynamics Handbook. New York, NY: Van Nostrand Reinhold Company Inc; 1984:144-158.

16. Greenberg NL, Vandervoort PM, Stewart WJ, Savage RM, McCarthy PM, Thomas JD. An integrated system for simultaneous acquisition and processing of physiologic and ultrasound data. Comp Cardiolo. 1994:615-618.

17. Veyrat C, Witchitz S, Lessana A, Ameur A, Abitbol G, Kalmanson D. Valvar prosthetic dysfunction: localisation and evaluation of dysfunction using the Doppler technique. Br Heart J. 1985;54:273-284. [Abstract/Free Full Text]

18. Pandis IP, Ross J, Mintz GS. Normal and abnormal prosthetic valve function as assessed by Doppler echocardiography. J Am Coll Cardiol. 1987;8:317-326.

19. Teirstein PS, Yock PG, Popp RL. The accuracy of Doppler ultrasound measurements of pressure gradients across irregular, dual, and tunnellike obstructions to blood flow. Circulation. 1985;72:577-584. [Abstract/Free Full Text]

20. Baumgartner H, Khan S, DeRobertis M, Czer L, Maurer G. Effect of prosthetic aortic valve design on the Doppler-catheter gradient correlation: an in vitro study of normal St Jude, Medtronic-Hall, Starr-Edwards and Hancock valves. J Am Coll Cardiol. 1992;19:324-332. [Abstract]

21. Grossman W. Pressure measurement. In: Grossman W, ed. Cardiac Catheterization and Angiography. 2nd Ed. 1980:103-114.

22. Courtois M, Kovacs SJ, Ludbrook PA. Transmitral pressure-flow velocity relation. Importance of regional pressure gradients in the left ventricle during diastole. Circulation. 1988;78:661-671. [Abstract/Free Full Text]

23. Silber H, Khan S, DeRobertis M, Gray R, Matloff J, Maurer G. Effect of prosthetic valve obstruction on the Doppler-catheter gradient correlation for St Jude valves: in vitro studies. Circulation. 1992;86(suppl I):I-806. Abstract.

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