Application of Color Doppler Flow Mapping to Calculate Orifice Area of St Jude Mitral Valve
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Abstract
Background—The effective orifice area (EOA) of a prosthetic valve is superior to transvalvular gradients as a measure of valve function, but measurement of mitral prosthesis EOA has not been reliable.
Methods and Results—In vitro flow across St Jude valves was calculated by hemispheric proximal isovelocity surface area (PISA) and segmentofspheroid (SOS) methods. For steady and pulsatile conditions, PISA and SOS flows correlated with true flow, but SOS and not PISA underestimated flow. These principles were then used intraoperatively to calculate cardiac output and EOA of newly implanted St Jude mitral valves in 36 patients. Cardiac output by PISA agreed closely with thermodilution (r=0.91, Δ=−0.05±0.55 L/min), but SOS underestimated it (r=0.82, Δ=−1.33±0.73 L/min). Doppler EOAs correlated with Gorlin equation estimates (r=0.75 for PISA and r=0.68 for SOS, P<0.001) but were smaller than corresponding in vitro EOA estimates.
Conclusions—Proximal flow convergence methods can calculate forward flow and estimate EOA of St Jude mitral valves, which may improve noninvasive assessment of prosthetic mitral valve obstruction.
Assessment of prosthetic heart valve function with current techniques is imprecise. Transvalvular gradients obtained by catheterization or Doppler echocardiography are indicative of prosthetic valve obstruction^{1} but are highly flowdependent. Furthermore, pressure recovery occurs in some prosthetic designs, resulting in discrepancies between catheter and Doppler pressure gradients.^{2} ^{3} ^{4} ^{5} ^{6}
Analogous to native valve area, prosthetic orifice area is a more flowindependent measure of obstruction. Unfortunately, the Gorlin formula may be unreliable in this setting,^{7} and the pressure halftime method,^{8} widely used in native mitral stenosis, has not been validated for prosthetic valves. Pulsedwave Doppler has been used to calculate prosthetic aortic valve area^{9} but is more problematic for prosthetic mitral valves.
Analysis of the proximal flow convergence region on color flow mapping can quantify mitral regurgitant severity^{10} ^{11} ^{12} ^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{19} as well as lowvelocity flow across relatively large orifices such as stenosed native mitral valves^{20} and atrial septal defects.^{21} However, the utility of the proximal flow convergence to measure prosthetic forward flow and effective orifice area (EOA) is unclear.
The aim of this study was to investigate, in flow models and in the operating room, the feasibility and accuracy of measuring flow across St Jude valves and calculating their EOAs by analyzing the flow convergence region proximal to the prosthesis by use of color Doppler mapping.
Methods
Theoretical Background
The theory of the proximal flow convergence method is well described.^{10} ^{12} ^{13} ^{17} ^{18} Briefly, flow converges on a small orifice as concentric hemispheric shells of decreasing surface area and increasing velocity. For a specific contour of velocity v_{a} and radius r from the orifice (highlighted as the bluered aliasing boundary on color Doppler), the instantaneous flow rate Q is given by Q=2πr^{2}v_{a}. However, relatively lowvelocity flow across large orifices such as prosthetic valves causes flattening of the isotachs and underestimation of flow,^{22} but this can be countered by multiplying Q by v/(v−v_{a}), where v is the peak transorifice velocity. The isovelocity surface area can also be calculated by the segmentofspheroid (SOS) method^{23} ^{24} using the chord (p) from the zenith of the contour to its outer edge (Figure 1⇓): EOA then is given by Q/v, where v is the transorifice velocity. Although localized high velocities and pressure recovery have been shown in the central orifice of the St Jude valve, we recently demonstrated that pressure recovery across the lateral orifices of mitral prostheses is limited.^{25} Because most flow passes through the side orifices, these were subsequently used in the EOA and stroke volume calculations.
In Vitro Models
SteadyFlow Model
This in vitro flow model was described in detail previously^{10} : a Plexiglas model with 2 chambers (proximal, 28×20×8.5 cm [H×W×L]; distal, 90 cm long) divided by a septum with a mount for prosthetic heart valves. St Jude heart valves (3 each of 23, 25, 27, 29, and 31 mm) were mounted with the leaflets oriented vertically to eliminate gravity effect. Flow, a 1% to 2% aqueous suspension of cornstarch, entered the proximal chamber from an upper reservoir whose height could be adjusted to vary transorifice pressure and flow rate and then passed through the mounted prosthetic valve under constant hydrostatic pressure causing steady flow. Flow rate was measured by the average of 3 to 5 timed collections. At least 3 different flow rates were examined for each valve size. Measurement variability was expressed as mean percent error for all flow rates studied, given by the SD of a set of timed collection measurements divided by their mean. Flow rates were chosen to simulate normal mitral transprosthetic velocities.
PulsatileFlow Model
To examine the effects of flow pulsatility on our method, St Jude heart valves (23, 25, 27, 29, and 31 mm) were studied in triplicate in the mitral position of a left heart pneumatic pump model. Cardiac output was measured by timed collections, with variability expressed as mean percent error. Four cardiac outputs were examined for each prosthesis, with heart rate constant at 70 bpm.
Echocardiographic Study
A HewlettPackard Sonos 1500 system was used with 2.5 or 3.5MHz phasedarray transducers held by an adjustableclamp system to yield an imaging plane perpendicular to the leaflets to show 3 distinct orifices. Flow velocities across the center and side orifices were interrogated separately with continuouswave (CW) Doppler. Color flow images of the proximal convergence zone were obtained with 3 different aliasing velocities between 17 and 41 cm/s and stored digitally on 650MB optical disks and recorded onto 2in VHS videotape.
Clinical Study
Patients
Patients in regular rhythm without significant tricuspid regurgitation who were undergoing St Jude mitral valve replacement were considered for the study. Cardiac output was measured in triplicate by thermodilution. The size of the implanted prosthetic heart valve was recorded.
Echocardiographic Examination
Intraoperative transesophageal echocardiography was performed with HP Sonos 1500 or Acuson 128XP with 5MHz probes when patients were stable after weaning from cardiopulmonary bypass. Images of the prosthesis showing 3 distinct orifices were obtained at a depth of 6 to 10 cm. Velocities across the center and side orifices were obtained by CW Doppler during suspended respiration, and the pressure halftime (t_{1/2}) of the E wave was measured.^{8} Images of the proximal convergence zone were obtained with a color aliasing velocity between 17 and 26 cm/s,^{11} reducing sector size to maximize frame rate (generally 18 to 22 frames per second), and stored on optical disks and/or VHS videotape. Thermodilution cardiac output was obtained simultaneously.
Data Analysis and Calculations
SteadyFlow Model
We selected 5 frames with a clear bluered aliasing boundary to measure r and p, assuming the valve orifice to be at the prosthetic annular level. Prosthetic EOA was given by Q_{c}/v for the hemispheric proximal isovelocity surface area (PISA) method and by Q_{p}/v for the SOS method.
PulsatileFlow Model
Stroke volume was calculated by multiplying Q_{c} or Q_{p} by the timevelocity integral normalized by the peak transorifice velocity, v. Cardiac output was given by the stroke volume×70 bpm. Prosthetic EOA was given by (1) Q_{c}/v for the PISA method, (2) Q_{p}/v for the SOS method, and (3) the modified Gorlin equation: where Δp is the mean gradient across the St Jude side orifice by CW Doppler.
Clinical Study
Forward stroke volume across the prosthetic orifice was calculated by multiplying Q_{p} or Q_{c} by the timevelocity integral normalized by v. The product of stroke volume and heart rate yielded cardiac output. Prosthetic EOA was calculated by (1) Q_{c}/v (PISA), (2) Q_{p}/v (SOS), (3) 220/t_{1/2} (pressure halftime),^{8} and (4) the modified Gorlin equation above. In both the clinical and in vitro studies, the localized high velocities in the small central orifice were disregarded and the side orifice velocities used in the calculations.^{25}
Statistical Analysis
In Vitro Models
Flow rates and cardiac outputs calculated by (1) PISA and (2) SOS were each compared with timed collections by linear regression, with the difference between calculated and measured flow (ΔQ) expressed as mean±SD. These 3 measurements of flow were also compared by repeatedmeasures ANOVA. Calculated in vitro EOAs were reported as mean±SD for each size, and the triplicate prostheses were compared by ANOVA. Center and side orifice velocities were compared by paired Student’s t test. To evaluate the impact of aliasing velocities on flow estimation in the pulsatile model, ΔQ for 3 ranges of v_{a} (≤20, 21 to 29, and ≥30 cm/s) were compared by ANOVA, with ΔQ for PISA and SOS in each range compared by paired Student’s t test. ΔQ by PISA and SOS were also correlated with v_{a} by linear regression.
Clinical Study
Cardiac outputs calculated by (1) PISA and (2) SOS were each compared with thermodilution by linear regression, with the difference between Doppler and thermodilution cardiac output expressed as mean±SD. These 3 cardiac output measurements were also compared by repeatedmeasures ANOVA. In vivo EOA (reported for each valve size as mean±SD) calculated by (1) PISA, (2) SOS, and (3) pressure halftime method were each compared with Gorlin calculations and the geometric orifice area. Center and side orifice velocities were compared by paired Student’s t test, with the difference expressed as mean±SD. Statistical significance was defined as a 2tailed P<0.05.
Interobserver and Intraobserver Variability
Ten randomly selected color Doppler images and continuous Doppler recordings from the in vitro and clinical studies were used to assess interobserver and intraobserver variability in measurement of the radius r and chord p of the proximal convergence. Variability was expressed as the ratio of the difference between the 2 measurements to their mean.^{26}
Results
In Vitro Models
SteadyFlow Model
Flow rates ranged from 218 to 406 cm^{3}/s, with mean error in the timed collections of 1.7±1%. The peak velocities through the center orifices (153.9±39.6 cm/s; range, 82.9 to 245 cm/s) were significantly higher than that through the side orifices (133.1±32.4 cm/s; range, 73.5 to 190 cm/s, Δv=20.9±10.9 cm/s, P<0.001). The ratio of the side to center velocities was 0.87±0.04. PISA and SOS flow rates correlated well with the timed collections (Figures 2⇓ and 3⇓), but compared with PISA, SOS underestimated true flow rate (ΔQ=−29.8±42.3 versus 0.7±28.2 cm^{3}/s, P<0.001), also significant by repeatedmeasures ANOVA (P<0.0001). PISA and SOS EOAs (y) correlated with but underestimated the geometric orifice area (x) significantly (PISA: y=0.52x+0.43, r=0.87, P<0.001, Δ=−1.47±0.50 cm^{2}; SOS: y=0.61x−0.09, r=0.87, P<0.001, Δ=−1.6±0.45 cm^{2}, Table 1⇓). There was no significant variation in EOAs for the 3 sets of prostheses by ANOVA.
PulsatileFlow Model
Cardiac output ranged from 1.6 to 8.6 L/min, with a mean of 5.9 L/min and variation in the timed collections of 2.2±1.3%. The ratio of side to center orifice velocity was 0.83±0.11. The cardiac output calculated by PISA agreed closely with timed cardiac output (y=0.997x−0.09, r=0.95, P<0.001, ΔQ=−0.11±0.59 L/min, P=NS), but SOS showed poorer correlation (y=0.81x+0.52, r=0.88, P<0.001) and significant underestimation of flow (ΔQ=−0.55±0.82 L/min, P<0.001), significantly worse (P<0.0001) than the PISA calculations. PISA and SOS EOAs correlated with but underestimated geometric orifice areas (r=0.79 and 0.78, respectively, Table 2⇓), without significant variation among the 3 sets of prostheses by ANOVA.
By SOS, ΔQ was −0.88±0.7 L/min for aliasing velocities ≤20 cm/s, −0.49±0.9 L/min for 21 to 29 cm/s, and −0.28±0.8 L/min for ≥30 cm/s (P=0.07 by ANOVA). SOS ΔQ was significantly worse than PISA ΔQ for ≤20 cm/s (−0.05±0.4 L/min, P<0.001) and 21 to 29 cm/s (0.12±0.3 L/min, P=0.007) but not for ≥30 cm/s (−0.38±0.8 L/min, P=NS). There were opposite but nonsignificant linear trends between aliasing velocity and ΔQ for PISA (r=−0.24, P=NS) and SOS (r=0.24, P=NS).
Clinical Study
The study population comprised 36 patients (26 women, 58±11 years old). At the time of study, 24 were AV paced, with the remainder in sinus rhythm. Heart rate was 92±10 bpm.
The peak and mean velocities through the center orifice (161±29 and 97±16 cm/s, respectively) were significantly higher than through the side orifices (137±23 and 86±14 cm/s, respectively, Δ_{peak}=23.6±11 cm/s, P<0.001 and Δ_{mean}=11±6.5 cm/s, P<0.001), with a sidetocentral velocity ratio of 0.86±0.05 (Figure 4⇓).
Cardiac output by thermodilution (x) was 5.2±1.2 L/min (3.3 to 8.1 L/min), with close agreement by PISA (y=1.018x−0.21, r=0.91, ΔCO=−0.05±0.55 L/min, Figure 5⇓) but underestimation by SOS (y=0.79x−0.21, r=0.82, ΔCO=−1.33±0.73 L/min, Figure 6⇓), P<0.001 for the significance of this difference by repeatedmeasures ANOVA (P<0.001).
Table 3⇓ and Figure 7⇓ summarize EOA calculated by the different methods. EOA by the modified Gorlin equation was significantly smaller than the geometric orifice area provided by the manufacturer (y=0.37x+0.24, r=0.64, P<0.001, Δ= −2.5±0.5 cm^{2}, P<0.001). PISA EOA agreed closely with Gorlin valve area (y=0.78x+0.7, r=0.75, P<0.001, Δ=0.3±0.28 cm^{2}, P<0.001) and also underestimated the geometric area (y=0.48x+0.05, r=0.8, P<0.001, Δ= −2.15±0.43 cm^{2}, P=0.001). Similarly, SOS EOA agreed with Gorlin area (y=0.64+0.41, r=0.68, P<0.001, Δ= −0.23±0.3 cm^{2}, P<0.001) and underestimated the geometric area (y=0.42x−0.23, r=0.76, P<0.001, Δ=−2.7±0.46 cm^{2}). Orifice area calculated by pressure halftime showed very poor (inverse) agreement with both Gorlin (y=4.9−1.01x, r=−0.44) and geometric valve area (y= −0.44x, r=−0.33).
Interobserver and Intraobserver Variabilities
In vitro interobserver variabilities in the measurement of proximal convergence radius and chord were 3.3±3.8% and 3.9±2.9%, respectively, with intraobserver variabilities of 3.5±1.4% and 2.1±1.1%, respectively. In the clinical study, interobserver variabilities for r and p were 3.6±3.2% and 3.2±2.4%, respectively, with intraobserver variabilities of 4.1±3.4% and 5.3±2.9%, respectively.
Discussion
The proximal convergence method, a recently developed color Doppler technique for quantification of mitral regurgitation,^{10} ^{11} ^{12} ^{13} ^{14} ^{15} ^{16} ^{17} ^{18} ^{19} has been validated in experimental and clinical studies for calculation of regurgitant stroke volume and effective regurgitant orifice area.^{10} ^{11} ^{12} ^{13} ^{14} ^{15} ^{16} ^{17} ^{18} The same principle has been used to calculate mitral stenotic orifice area, where there is relatively lowvelocity flow across a finite orifice.^{20} Extending this concept to mitral valve prostheses is reasonable, because the planar nature of the ring obviates much of the need to correct for proximal flow constraint, which is often necessary for mitral stenosis^{20} and regurgitation.^{27} Moreover, the difficulties commonly encountered in locating the convergent focus^{28} are eliminated, because the level of the orifice is defined by the prosthetic annulus. However, the finite size and relatively low transorifice velocity of a mitral prosthesis are associated with isotach flattening near the orifice.^{22} Fortunately, the resultant flow underestimation can largely be corrected by a correction factor, v/(v−v_{a}), where v is the transorifice velocity and v_{a} the aliasing velocity.^{22}
The SOS method has been advocated as an alternative to the conventional hemispheric modeling of the proximal convergence flow field. This method has the advantage that only 1 measurement, p, is required, compared with the more accurate hemielliptical model.^{23} ^{24} However, total forward flow by SOS, although well correlated to actual flow in our models and clinical study, showed systematic underestimation, which will merit further study.
Effective Prosthetic Orifice Area
All prosthetic valves are inherently mildly stenotic. Analogous to stenotic native valve area, prosthetic orifice area, incorporating flow and pressure gradient, gives a more flowindependent measure of prosthetic resistance. Although the continuity equation and pressure halftime methods^{8} ^{29} are accepted Doppler techniques for native mitral and aortic stenosis, effective prosthetic orifice area has been more elusive.^{30} Although Doppler has been used in flow models to calculate effective prosthetic valve areas^{31} and the continuity equation has been used clinically for prosthetic aortic valves,^{9} ^{32} a reliable noninvasive method to estimate prosthetic mitral orifice area clinically is still lacking.
The present study demonstrated that the pressure halftime method has little value in measuring effective prosthetic orifice areas, actually showing an inverse relation to valve size. We have previously shown that the pressure halftime method is unreliable immediately after balloon valvuloplasty^{33} because of abrupt changes in transvalvular gradient and chamber compliance. In the present study, the pressure halftime was measured immediately after mitral valve replacement, when sudden changes in net chamber compliance and transvalvular gradient might have contributed to the inaccuracy of the pressure halftime method for effective prosthetic valve area.
The effective prosthetic valve areas in our clinical study are consistent with some published studies^{31} but smaller than others.^{34} ^{35} ^{36} Baumgartner et al^{31} calculated EOA in a pulsatileflow model with the Gorlin formula and Doppler gradients and obtained values similar to our in vivo EOA. However, in the same study, EOAs were significantly larger when catheter gradients were used with the Gorlin formula. Similarly, Yoganathan and his group obtained significantly larger EOAs with the catheterbased Gorlin formula both in vitro^{35} and in vivo,^{36} related to the overestimation of catheter gradients by Doppler^{34} due to the phenomenon of pressure recovery.^{25} Interestingly, Baumgartner et al observed larger EOAs in their steady in vitro model than in the pulsatile one. This is supported by a preliminary study by Trujillo et al,^{37} who showed that for rigid circular orifices, Doppler continuity EOAs during steady flow are consistently larger than in pulsatileflow conditions. Further preliminary data show flow dependency of EOA in pulsatile conditions.^{37} ^{38} In our clinical study, the relatively fast heart rate and therefore lower stroke volume observed just after cardiopulmonary bypass may contribute to smaller calculated EOAs. In addition, the geometry surrounding the prosthesis in vivo and the presence or absence of the mitral subvalvular apparatus may also have important effects on the calculated EOA.
Limitations
The major limitation in all studies examining effective prosthetic orifice area is the lack of a proper, universally accepted “gold standard.” Various references have been used, including geometric, Gorlin, continuity, and halftime EOAs. However, true in vivo EOA may vary for a given prosthesis depending on physiological conditions, shown by the range in reported EOA in our and prior studies. In vitro results suggest that flow pulsatility affects EOA. Our data showed consistent results across 3 valves of each size, suggesting relatively little actual interprosthesis variance.
Clinical Application
Although we would not recommend this technique for routine assessment of mitral prostheses (because of the need for transesophageal echocardiography), we have found it quite useful in relatively subtle or questionable situations of prosthetic obstruction. When a leaflet is completely stuck by thrombus or pannus, this is usually evident by direct 2dimensional imaging and a high transprosthetic gradient in the presence of a lowoutput state. In contrast, the PISA EOA is helpful for assessing nonobvious obstruction or, conversely, ruling it out when a high gradient occurs in a highoutput state.
Conclusions
This is the first study to demonstrate that mitral prosthetic EOA can be measured noninvasively by proximal flow convergence methods. We examined the St Jude prosthesis because it is the mostly commonly implanted prosthetic valve; because its hydrodynamic profile is among the most complex, this technique is likely to be applicable to other types of prostheses. This may improve the management of patients with mitral prostheses by allowing accurate detection and assessment of prosthetic valve obstruction independent of transvalvular flow.
Acknowledgments
This study was supported in part by grant NCC960 from the National Aeronautics and Space Administration, Houston, Tex, with valve prostheses provided by St Jude Medical, Inc, Minneapolis, Minn.
Footnotes

Presented in part at the 44th Annual Scientific Session of the American College of Cardiology, March 19–22, 1995, New Orleans, La, and at the 6th Scientific Sessions of the American Society of Echocardiography, June 14–16, 1995, Toronto, Canada.
 Received December 19, 1997.
 Revision received May 14, 1998.
 Accepted May 20, 1998.
 Copyright © 1998 by American Heart Association
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 Application of Color Doppler Flow Mapping to Calculate Orifice Area of St Jude Mitral ValveDominic Y. Leung, James Wong, Leonardo Rodriguez, Min Pu, Pieter M. Vandervoort and James D. ThomasCirculation. 1998;98:12051211, originally published September 22, 1998http://dx.doi.org/10.1161/01.CIR.98.12.1205
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 Application of Color Doppler Flow Mapping to Calculate Orifice Area of St Jude Mitral ValveDominic Y. Leung, James Wong, Leonardo Rodriguez, Min Pu, Pieter M. Vandervoort and James D. ThomasCirculation. 1998;98:12051211, originally published September 22, 1998http://dx.doi.org/10.1161/01.CIR.98.12.1205
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