Quantification of regurgitant flow through bileaflet heart valve prostheses: Theoretical and in vitro studies

Ultrasound rn Med Printed in the USA

& Eiol

Vol. 19, No. 6, pp. 461-468,

1993

0301-56?9/93 $6.00 + .oO D 1993 Pergamon Press Ltd.

*Original Contribution QUANTIFICATION OF REGURGITANT FLOW THROUGH BILEAFLET HEART VALVE PROSTHESES: THEORETICAL AND IN VITRO STUDIES EDWARD G. CAPE, + NAVIN C. NANDA* and AJIT P. YOGANATHAN* +Division of Pediatric Cardiology, Children’s Hospital of Pittsburgh, University of Pittsburgh School of Medicine, Pittsburgh, PA; *Division of Cardiovascular Disease, School of Medicine, University of Alabama at Birmingham, Birmingham, AL; and *Cardiovascular Fluid Mechanics Laboratory, School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA, USA (Received 27 October 1992; inJinal.form

22 January 1993)

Abstract-A theoretical treatment using turbulent jet theory has yielded a new equation for predicting regurgitant flow through bileaflet heart valve prostheses, the most commonly implanted mechanical valve design. Previously reported techniques assuming an axisymmetric jet are not applicable to the slot-like orifices presented in these valves. The equations were therefore rederived in the context of the prosthetic valve geometry. The purpose of this study was to develop such a method and demonstrate its applicability in principle by using in vitro models. The method was validated under both steady and pulsatile flow conditions. Having derived a method geometrically specific to the orifices presented in bileaflet mechanical heart valves, it should be applicable from patient to patient due to the rigid nature of the valve. These idealized in vitro studies, along with the accompanying theoretical derivation, will guide implementation in the clinical setting.

Key Words: Heart valves, Regurgitation, Artificial heart valves.

Doppler echocardiography,

INTRODUCTION

Jets, Ultrasound,

Turbulence,

Prostheses,

extent behind closed bileaflet valves due to “normal” leakage included in the design of the valve (Flachskampf et al. 199 1). An application of conservation of momentum principles in the turbulent regurgitant jet has produced a method which uses centerline velocity measurements for quantitative calculation of regurgitant volume (Cape et al. 1990). It was validated through lesions modeled in vitro (Cape et al. 1989)) and has been subsequently verified in vivo in a canine model (Rodriguez et al. 1989). The regurgitant jet lesions presented in malfunctioning mechanical prosthetic heart valves, however, are inherently eccentjc in nature and might not be adequately assessed using this theory. Specifically, bileaflet heart valves, the most commonly used mechanical valve design, can present a slot-like orifice along the central plane of the valve as the occluders do not fully close due to thrombus formation and/ or tissue overgrowth along the lateral contact points on the sewing ring. While the axisymmetric conservation of momentum approach was shown to hold for significantly noncircular orifices (Cape et al. 1989), the extreme case in which it does not hold is one in which the orifice is “infinitely” long, or the length of the orifice is much greater than

Although a large number of artificial heart valves are implanted to correct native valvular regurgitation, mechanical and tissue valves often become insufficient themselves due to thrombus formation, tissue overgrowth, calcification and structural deterioration. Traditional angiographic means of assessment of valvular regurgitation are invasive, time consuming, semiquantitative and involve the use of ionizing radiation (Sellers et al. 1964). Noninvasive Doppler ultrasound provides a potential alternative by allowing relatively quick acquisition of quantitative data (velocities) using a medium with no demonstrated patient hazard (Nanda 1985). Attempts to assess the severity of regurgitation using color Doppler measurements of regurgitant jet area have correlated well with the angiographic grade, but remain semiquantitative at best, producing no calculation of regurgitant volume (Helmcke et al. 1987; Perry et al. 1987). A recent study has even demonstrated significant color jet Addresscorrespondenceto: EdwardG. Cape, Ph.D., Division of Pediatric Cardiology, Children’s Hospital of Pittsburgh, University of Pittsburgh School of Medicine, 3705 Fifth Ave., Pittsburgh, PA 15213, USA. 461

Ultrasound in Medicine and Biology

462

the width. Such a configuration is what occurs in central regurgitant jets through malfunctioning bileaflet prostheses. While leakage may also occur through lateral orifices, it is important to first address flow in the baseline case through a central orifice to develop a basic mathematical theory which can then be extended to more complex situations. Such a study is especially important given the absence of any such theory in the current body of literature. The purpose of this study was therefore to address the hypothesis that turbulent jet theory can be applied in the context ofprosthetic valve geometry to produce a new method for quantification of regurgitation through these commonly implanted valves. THEORY Regurgitation commonly occurs in bileaflet valves due to thrombus formation and/or tissue overgrowth along the orifice and/or sewing ring. The lateral edges of the leaflets are unable to contact the internal orifice surface and instead rest on the thrombus and/or tissue overgrowth. This leaves a slot-like orifice along the central plane of the valve as shown in Fig. 1; during the time period the valve should be closed. While additional openings may be present around the lateral portions of the valve, the primary goal of this study was to develop an equation for predicting flow through the central slot-like regurgitant orifice in terms of Doppler measurable quantities. Additional flows through lateral orifices can then be superimposed on this central flow which is expected to be quite consistent due to the rigid nature of the occluders.

Volume 19, Number 6, 1993

01

Um,X

H

WLbo

x=0 Fig. 2. Structure of the slot geometry turbulent jet. Q, and U,, represent flow rate and velocity at the orifice, respectively. U,,, is the maximal velocity at a specific distance X from the orifice. His the slot height, and W = 2b, is the slot width.

The relationship between a distal maximum velocity, U,, and the orifice velocity, U,, is given as (Blevins 1984): u 3 = 3.4 U0

(1)

where b, is one half of the width of the orifice and X is the distance from the orifice at which U,,, is measured, as shown in Fig. 2. This equation assumes that U, is uniform along the orifice, a reasonable assumption for flow through an abrupt contraction (Durst and Loy 1985 ) . This equation is valid beyond the laminar core of the jet which extends between five and six slot widths distal to the orifice-solving eqn ( 1) for Xwith U, = U,, X = 5.78W. Eqn ( 1) can be written U

9 D

2=3.4

f

U*

g

where the width W = 26,. Continuity requires that

Silicone

Orlflce

Fig. 1. Simplified schematic showing the central slot-like orifice presented due to tissue overgrowth in bileaflet mechanical heart valves. Here, the placement of silicone rubber sealant is shown in place of tissue along the lateral edges of the valve in the vicinity of the sewing ring. The amount of “tissue overgrowth” was varied to produce slot widths of 0.2 to 3 mm.

Q, = U,WH

(2) at the orifice

(3)

where H is the height (long dimension) of the orifice, and Q, is the orifice flow rate. Substituting eqn (3), expressed as W = Q/ U,H, into eqn (2), U

-??I! = 3.4

UO

ti

QO 2u,Hx’

(4)

Solving eqn (4) for Q, yields Q,

U2 HX

= L

5,78U, .

(5)

Quantification of regurgitant flow 0 E. G. CAPE et al.

U, is available from continuous wave Doppler and U,,, is available from pulsed wave Doppler at a set distance X. H, which is of the order 2-3 cm, can be directly measured by 2D echocardiography. Eqn ( 5) therefore allows calculation of flow through the central orifice as a function of four quantities ( U,, U,, X, H) available from clinically used Doppler echocardiography. To extend the calculation to total regurgitant volume, a time velocity integral calculation can be made (Cape et al. 1989). The total regurgitant volume (RV) is:

R~ _ e o,Deak U,dt. Uo-peaks

(6)

is the flow rate at peak systole from eqn (5). Qo,peak

Uo,F_k is the peak orifice velocity from continuous wave Doppler. The integral term is calculated by tracing (digitizing) the continuous wave trace over the period of leakage. This new eqn ( 5) allows calculation of regurgitant flow through geometries which must be presented in the central slot of bileaflet prostheses due to the rigid nature of the valve. It is noted, however, that the equation is based fundamentally on a combination of eqn ( 1) and the continuity eqn ( 3). Eqn ( 1)) which was referenced to Blevins ( 1984), has been thoroughly validated over decades of research in the fluid mechanics literature and we chose this reference only because it is a compilation of those studies. The equation has been validated using quantitative engineering techniques and therefore is a reliable starting point for the derivation of eqn ( 5 ) .

EXPERIMENTAL

METHODS

To test the above theory in principle, two commonly implanted bileaflet prostheses (St. Jude and Carbomedics) were tested in vitro under both steady and pulsatile flow conditions using a physiologic pulse duplicator system. Size 27 mm valves were made regurgitant by simulating thrombus formation and/or tissue overgrowth around the sewing ring of the valve. Silicone rubber sealant was placed around the sewing ring in the vicinity of the lateral orifices. The leaflets were then gently brought to the surface of the material to form a molding. After drying overnight, the leaflets were easily dislodged from the sealant. With this fabrication, the leaflets would contact the sealant material during closure, leaving a central slot available for regurgitant flow, and without the

463

compounding effects of leakage through lateral orifices which will be added in a subsequent study. The smallest slot width studied was 0.2 mm and increased to produce the physiologic flow rates and velocities listed below. The valves were placed in the mitral position in a two-chamber cylindrical flow model as shown in Fig. 3. Doppler interrogation of the regurgitant jet was performed from a distal window as shown. Steady flow experiments were first performed to test the basic applicability of the technique. Using a calibrated pump and rotameter system, flow rates were generated across the closed valve to achieve orifice velocities of 2-6 m/s. Slot widths were varied to produce flow rates ranging from 50-190 mL/s. After measuring U, and U,,, (at distances of 30, 39, and 50 mm), using a 2 MHz transducer interfaced to a VingMed SD- 100 spectral Doppler unit, flow rate was calculated by eqn ( 5 ) and compared to the known value of true flow. The valves were then placed in the mitral position of a left heart pulse duplicator system described elsewhere (Cape et al. 1989). Heart rate was set at 70 beats per minute with a systolic interval of 300 ms and diastolic interval of 560 ms. Peak flow rates ranged from 90-190 mL/s. Forward and regurgitant flow rates were acquired using an electromagnetic flow probe meter (Carolina Medical Electronics) and interfaced through an analog-to-digital board to a microprocessor. From this digitized flow probe data, standard peak regurgitant flow rates could be selected and total regurgitant volume integrated using customized software. Regurgitant jet presence and direction were clearly visualized by color flow Doppler using a 3.5 MHz transducer interfaced to an ATL UM9 unit. Spectral Doppler measurements were again obtained on the VingMed unit. Maximal orifice velocity ( U,) was then obtained using continuous wave Doppler. Switching to pulsed wave mode allowed acquisition of the desired distal jet velocity ( U,) at a specified depth (X). Distal jet velocities were obtained at distances greater than 1 cm from the distal wall to avoid impingement effects. Spectral Doppler data were recorded on 4” ( 12.5 mm) videotape for subsequent off-line analysis. Peak regurgitant flow rates were calculated by inserting Doppler measurements of peak U, and U, into eqn (5). Spectral Doppler traces were digitized off-line using a Sony Cardiologic Analysis system. The time velocity integral of the continuous wave trace was calculated using available software on the Sony system and total regurgitant volume determined using eqn (6). For all studies, calculations were performed using the theory developed in this

464

Ultrasound in Medicine and Biology 75 mm

Volume 19, Number 6, 1993 75 mm

4

+

25.4 mm Prosthetic Valve Seating Area

Regurgitant

Jet

Fig. 3. In vitro flow model. Having created the central regurgitant lesion, the valve was placed in a cylindrical mitral flow model. This model was used for steady flow studies, driven by a calibrated pump and rotameter, and placed in the mitral position in the left heart pulse duplicator system described elsewhere (eqn 7).

paper, and the equation developed previously for axisymmetric lesions (Cape et al. 1989)) that is, ?rU2,X2

Qo = 158.76U,. EXPERIMENTAL

(7)

RESULTS

Steady flow Using the axisymmetric jet eqn (7), significant deviations from the true flow were obtained (Y = 0.22X + 0.53, r = 0.896, standard error of estimate [SEE] = 5.93 mL/s). Good agreement was found using the slot-jet eqn (5) applied at three different distances from the orifice as shown in Fig. 4 (Y = 0.99X + 2.01, r = 0.999, SEE = 2.82 mL/s). Pulsatile flow Distal jet velocity decay patterns agreed well with theory under the conditions tested as shown for example in Fig. 5, which illustrates high velocity “mitral” regurgitant jets of 5 and 7 m/s orifice velocity (Y = 0.99X - 0.0035, r = 0.994, SEE = .052 m/s). Use of eqn ( 5 ) was also successful in predicting peak regurgitant flow under pulsatile conditions as shown in Fig. 6 (Y= 1.14X- 14.319,r=0.978,SEE=8.11 mL/s), although slight overestimation was noted. Correction for the time-velocity integral by eqn (6) produced excellent agreement with computer-integrated electro-

magnetic flow volumes (Y = 1.02X - 1.7 1, r = 0.883, SEE = 5.07 mL). DISCUSSION Although heart valve prostheses are commonly implanted to correct native valvular regurgitation, they often become insufficient themselves as thrombus formation, tissue overgrowth, calcification and structural deterioration occur. The aim of this study was to develop a technique for noninvasively estimating the degree of regurgitant flow through the most commonly implanted mechanical valve, the bileaflet prosthesis. An application of turbulent jet principles yielded such a technique which was subsequently verified in vitro under both steady and pulsatile flow conditions using the clinical technique of Doppler ultrasound. Regurgitant orifices presented in malfunctioning mechanical prosthetic valves are inherently eccentric, owing to the eccentric geometries of the valve designs. Consider the ball-and-cage valve as an extreme case. Theories developed previously which assumed axisymmetry (Cape et al. 1990), would therefore not be expected to hold for these valves and this hypothesis was confirmed in this study. The axisymmetric theory was therefore modi!ed in terms of a slot-like orifice morefitting for the bileajlet prosthesis. Although the in vitro model is clearly simplified, the results of this study show that the slot-jet theory works well in princi-

Quantification of regurgitant flow 0 E. G. CAPEet al

180 160

,’

140

465

X5

/’/

A X=39mm

/ d

Xx= 50 mm

//’

120

30 mm

t..,,”

100 i

/A

40 6@[, 40

, 60

/,

80 100 120 140 160 ACTUAL FLOW RATE (ML/S)

180

200

Fig. 4. Steady flow results. Excellent agreement was found between Doppler predicted flow rates from eqn (5), and those set directly by calibrated pump and rotameter (Y = 0.99X + 2.01, r = 0.999, SEE = 2.82 mL/s).

ple in predicting regurgitant flow through the malfunctioning bileaflet valve geometry. This was expected as the theory relies exclusively on the slot-jet eqn ( 1) which has been derived and validated in the fluid mechanics literature using techniques far more precise than ultrasound. Contrast between axisymmetric and slot-jet theory Orifices in which the length greatly exceeds the width may be treated as “infinite” slots in fluid dy-

namics. Methods using conservation of momentum through an axisymmetric orifice have been shown to hold for significantly noncircular orifices including ellipses, triangles and rectangles. However, the extreme case of an “infinite” slot is the limiting condition in which these equations fail. Triangular or elliptical jets for example will behave according to axisymmetric jet equations as turbulence obliterates the details of orifice shape (Blevins 1984). There is of course no instant at which any jet from a triangular orifice is per-

240

1 I

2202001801601401201008060

80

100 120 Urn FROM

140 THEORY

160 180 - EQUATION

200 (1)

220

id0

Fig. 5. Correlation of distal pulsed wave velocity measurements for high velocity mitral jets. Good agreement was found (Y = 0.99X - 0.0035, r = 0.994, SEE = 0.052 m/s) with theoretical values from eqn ( 1) for the high orifice velocities (5 and 7 m/s) in this example showing data from a slot width ( W) of 0.2 mm.

466

Volume 19, Number 6, 1993

Ultrasound in Medicine and Biology

8060

90

I 100

I 110

1 120

I 130

I 140

I 150

I 170

160

I 180

190

ACTUAL PEAK FLOW (ML/S) Fig. 6. Pulsatile flow results. Using peak CJO and U,,, values from continuous

and pulsed wave Doppler respectively,

eqn (5) was accurate in predicting peak regurgitant flow rate (Y = 1.14X - 14.32, r = 0.978, SEE = 8.1 I mL/s) as compared to electromagnetic

fectly triangular due to turbulent fluctuations, and taken on average, velocity decay patterns conform to those found for a circular orifice. Intuitively, one might think of a central axis, and moving away from that axis in a lateral direction, similar velocity decays would be observed. Jets issuing from slot-like orifices will not be slotlike at any single instant either, again due to turbulent fluctuations, but the extent of the long orifice axis compared to the narrow width imparts a permanent nonsymmetry to the velocity decay functions. Intuitively, one might think of the short jet axis which is almost immediately consumed by the turbulent shear layer and the great axis which is not so rapidly consumed. The resultant velocity decay curve along the central axis of the jet is therefore different than that for the axisymmetric geometry or other shapes which conform to axisymmetric equations as noted above. Mathematically, one can compare the slot-jet flow rate eqn ( 5 ) to the axisymmetric eqn ( 7 ) . They differ basically by the fact that the square of the axial distance X appearing in the axisymmetric equation is replaced by the product of that distance and the long axis dimension of the orifice. The constant is also modified as might be expected to account for this change. (One may more directly compare the two velocity decay patterns by solving each equation for U,,, and plotting the resultant values versus X for a given flow rate and orifice area.) To avoid confusion to the clinician who may think in terms of the qualitative technique of color

flow meter values.

Doppler, we note that orthogonal views using color Doppler may show jet images which appear to be equal in size distal to the orifice. It cannot be stated strongly enough, however, that simple equivalence of jet size in orthogonal views by color Doppler does not confirm an achievement of axisymmetric flow in the fluid dynamics sense in that portion of the jet. Reconciliation with “normal” leakage patterns Recent studies have shown that these mechanical valve designs exhibit leakage through lateral hinge points before development of an abnormal lesion (Flachskampf et al. 199 1), and these small jets can produce significantly sized images on color Doppler maps. On creation of a lesion, however, this leakage becomes negligible as expected from the principles of fluid dynamics. Flow through an orifice is characterized by a resistance proportional to the fourth power of the hydraulic radius. Therefore, given a hypothetical lesion which is twice the size of the opening in the hinge point, flow through the hinge point would have a resistance sixteen times higher than that through the regurgitant lesion. Of course, a significant regurgitant lesion would be much greater than twice the diameter of the tiny opening in the hinge point and for that reason we would expect these so-called normal regurgitant flows to disappear or become negligible when true regurgitation develops. This is confirmed by the data in which such jets were not observed. In summary, it is clear from the principles of fluid dynamics that “normal” regurgitant flows through tiny aper-

Quantification of regurgitant flow 0 E. G. CAPE ef nl.

tures become insignificant with development blown lesions.

of full

Potentialfor clinical application The method derived in this study is the first step in a theoretically based approach for quantifying flow through malfunctioning mechanical bileaflet prostheses. Once a comprehensive method has been derived which accounts for symmetric central lesions, the rigid nature of the mechanical valves can be taken advantage of to superimpose additional lateral flows which may occur clinically. In other words, although the central regurgitant orifices are eccentric, similar geometries should be expected from patient to patient due to the rigid nature of the occluders. Given thrombus formation and/or tissue overgrowth around the valve orifice and/or sewing ring, slot-like orifices must be left along the central plane of the valve, assuming no deformation of the occluders. This in vitro study was idealized to demonstrate that the method works in principle. In moving to the clinical setting, difficulties will arise, but can be addressed in subsequent studies given the basic theoretical foundation provided here. For example, the jets studied here issued straight into the receiving chamber. Nonsymmetric thrombus formation and/ or tissue overgrowth in patients will produce eccentrically directed jets which can attach to and flow along the atria1 wall by the Coanda effect (Blevins 1984). Such jets will have altered entrainment properties and velocity decay patterns (Cape et al. 199 1)) potentially making the theory inapplicable. Fortunately, such cases can be detected by color Doppler flow mapping and misapplication of the theory avoided. Further studies may yield a modified theory for these cases. The theory may also be inapplicable for exceptionally small atria. In order to measure the distal velocity, U,,,, it must have fallen below the level of the Nyquist limit for pulsed wave Doppler. With driving pressures of approximately 100 mm Hg (producing regurgitant jet velocities of 5 m/s) across the mitral position, velocities may not decay into the measurable range for exceptionally small atria, such as might be encountered in pediatric cases. In adult cases, however, atria can extend to the relatively large distances analyzed here, especially in chronic mitral regurgitation (which is associated with dilated atria). Cases of tricuspid regurgitation generally produce lower orifice velocities ( 2 m/s) in the absence of pulmonary hypertension, so the distal velocities should be measurable for these cases, even within relatively small atria. Furthermore, future refinements in “antialiasing” algorithms (Fan et al. 1990) may allow application of the

467

technique even for the high velocities and small atria described above. Advantage qf the spectral Doppler technique vs. color Doppler Color Doppler flow mapping allows imaging of the regurgitant jet. While measurements of jet spatial extent have correlated with angiography, they remain semiquantitative at best (Flachskampf et al. 199 1; Perry et al. 1987 ). The current technique uses quantitative spectral Doppler measurements with color Doppler imaging as a guide. This has at least two distinct advantages. First, in practice, pulsed wave spectral Doppler is generally characterized by significantly higher Nyquist limits than color Doppler, thus being advantageous in view of the last section of this discussion. (While Nyquist limits are determined solely by the transducer frequency and pulse repetition frequency, in practice, available pulse repetition frequency settings for color Doppler are generally lower than those available for spectral Doppler.) Second, color Doppler flow mapping is almost exclusively applied clinically as a two-dimensional modality. This introduces a frame rate limitation, as sweeping of the color Doppler scan lines may not correspond to peak flow, disallowing measurement of true Q,,,,l, in eqn (6). This effect is especially apparent for adult patients with tachycardia, which often accompanies cases of acute regurgitation, and for elevated heart rates commonly found in the pediatric population (Cape et al. 1993; Rao et al. 1990; Utsunomiya et al. 1990). The current technique applies spectral Doppler which is accompanied by no such frame rate limitation. Study limitations As noted above, the lesions created through the bileaflet valves in this study are idealized in nature, consisting of a slot-like orifice produced by symmetric tissue overgrowth around the lateral edges of the valve. While additional lateral flows will be found in vivo, this study of flow along the central plane is fundamentally the baseline case due to the rigid nature of the mechanical occluders. This idealized lesion was designed in order to make the mathematical theory tractable for this initial study. Having shown the validity of this basic theory, further modifications can potentially be made to account for nonsymmetric overgrowth and paravalvular and lateral orifice leaks. Given the total absence qfa quantitative method based on fluid mechanics theory at present, the theory and results of this study are critical,first steps toward quanttjication.

468

Ultrasound in Medicine and Biology

A major limitation of this study is related to the state of imaging technology. Depending on the direction of the jet, it is difficult to fully interrogate a regurgitant jet issuing from a mechanical valve in the mitral position. Continuous wave velocities are available from an apical view, but the distal jet may be “shadowed” from the transducer, requiring a transesophageal examination. Such exams are increasingly common in echocardiography laboratories so the technique can in principle be applied now. It is important to note, however, that the theory and experimental validation here represent an analysis of the flow field which yields an accurate prediction of regurgitant flow. Further refinements in Doppler technology, or application of other imaging modalities such as magnetic resonance imaging, will enhance the usefulness of this basic theory which is independent of the measurement technique. While care has been taken to stress the accuracy of spectral Doppler over color Doppler, even the spectral technique is arguably acceptable as a standard fluid mechanical measurement technique. We performed these studies, however, to show that the clinical modality could be used to make the appropriate measurements. For true quantitative confidence in the technique, we defer to the extensive fluid mechanical studies of slot jets performed over the years which yielded the basic eqn ( 1). The only other equation used in the derivation, the continuity eqn (3), hopefully requires no explanation. CONCLUSIONS In summary, no technique currently exists in the clinical setting for the quantitative (and noninvasive) assessment of regurgitation across any type of prosthetic heart valve. The technique presented in this paper is tailored to the eccentric geometry created by the malfunction of the most commonly used mechanical valve design. It has been demonstrated that the method accurately assesses regurgitation under physiologic pulsatile flow conditions. When such lesions occur, due to the rigid nature of the valve design, similar regurgitant orifices should be expected from patient to patient, with applicability of the theory along the central plane maintained as a consequence. Additional studies are required to address lateral leaks superimposed on this basic central lesion.

Volume 19, Number 6, 1993 Acknowledgements-We thank Pete Noel and Greg Goolsby for their skill in constructing the flow model, and Carol Reder and Helen Rinehart for expert secretarial assistance. This work was supported by a grant ofthe United States Food and Drug Administration (Grant 789906 00 90 LH) and the National Institutes of Health (ROI HL 45485).

REFERENCES Blevins, R. D. Applied fluid dynamics handbook. New York: Van Nostrand Reinhold; 1984:229-278. Cape, E. G.; Skoufis, E. G.; Weyman, A. E.; Yoganathan, A. P.; Levine, R. A. A new method for noninvasive quantification of valvular regurgitation based on conservation of momentum: In vitro validation. Circulation 79: I343- 1353; 1989. Cape, E. G.; Yoganathan, A. P.; Levine, R. A. A new theoretical model for noninvasive quantification of mitral regurgitation. J. Biomech. 230:27-33; 1990. Cape, E. G.; Yoganathan, A. P.; Weyman, A. E.; Levine, R. A. Adjacent solid boundaries alter the size of regurgitant jets on Doppler color flow maps. J. Am. COIL Cardiol. 17: 1094-I 102; 1991. Cape, E. G.; Yoganathan, A. P.; Levine, R. A. Increased heart rate can cause underestimation of regurgitant jet size by Doppler color flow mapping. J. Am. Coil. Cardiol. 21: 1029-1037; 1993. Durst, F.; Loy, T. Investigations of laminar flow in a pipe with sudden contraction of cross sectional area. Comput. Fluids 13: 15-36; 1985. Fan, P.: Nanda, N. C.; Cooper, J. W.; Cape, E. G.; Yoganathan, A. P. Color Doppler assessment of high flow velocities using a new technology: In vitro and clinical studies. Echocardiography 71763-769; 1990. Flachskampf. F. A.; O’Shea, J. P.; Griffin, B. P.; Guerrero, L.; Weyman, A. E. Patterns of normal transvalvular regurgitation in mechanical valve prostheses. J. Am. Coil. Cardiol. 18:14931498: 1991. Helmcke, F.; Nanda, N. C.; Hsiung, M. C.; Sota, B.; Adey, C. K. Color Doppler assessment of mitral regurgitation with orthogonal planes..Circulation 75: 175- 183; 1987. Nanda. N. C. Doooler echocardioaraohv. New York: Iaaku-Shoin: 1985:453-475.’ Perry, G. J.; Helmcke, F.; Nanda, N. C.; Byard, C.; Soto, B. Evaluation of aortic insufficiency by Doppler color flow mapping. J. Am. Coll. Cardiol. 9:954-959; 1987. Rao, S. R.; Richardson, S. G.; Simonetti, J.; Katz, S. E.; Caldeira, M. Problems and pitfalls in the performance and interpretation of color Doppler flow imaging: Observation based on the influences of technical and physiological factors or the color Doppler examination of mitral regurgitation. Echocardiography 7:747762; 1990. Rodriguez, L.; Vlahakes. G. J.; Cape, E. G.; Yoganathan, A. P.; Guerrero, J. L. In vivo validation ofa new method for noninvasive quantification of mitral regurgitation. Circulation 80:11577; 1989. Sellers, R. D.; Levy, M. J.; Amplatz, K.; Lillihei, C. W. Left retrograde cineangiography in acquired cardiac disease. Am. J. Cardiol. 14:437-447: 1964. Utsunomiya, T.; Ogawa, T.; King, S. W.; Sunada, E.; Lobodzinski, S. M. Pitfalls in the displav ofcolor Donuler iet areas: Combined variability due to Doppler angle frame role,-and scanning direction. Echocardiography 7:739-745; 1990. I

.

_