Heart (Supplement 2) 1996;75:36-42

Stenotic lesions

Bengt Wranne, Helmut Baumgartner, Frank Flachskampf, Michael Hasenkam,Fausto Pinto

Departments ofClinical Physiology,Linkoping HeartCentre, UniversityHospital, Linkoping,SwedenB WranneDepartment ofCardiology, ViennaGeneral Hospital,University ofVienna,Vienna, AustriaH BaumgartnerDeparment ofCardiology, RWTHAachen, GermanyF FlachskampfDepartment ofThoracic andCardiovascularSurgery, SkeibySygehus, AarhusUniversity Hospital,Aarhus, DenmarkM HasenkamUniversity HospitalSta Maria, ClinicaMedica, Lisboa,PortugalF PintoAll authors are member ofthe INVADYN group, aconcerted action in theEuropean Biomed Researchprogramme.Correspondence to:Dr Bengt Wranne, LinkopingHeart Centre, UniversityHospital, Linkoping,Sweden.

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A stenotic lesion becomes clinically significantwhen the vascular bed downstream from thestenosis is insufficiently supplied or theupstream vascular bed is subjected to intolera-ble stasis. The severity of the stenosis can beassessed by the extent of the symptoms of stasisor insufficient blood supply. From the point ofview of fluid mechanics or haemodynamics,stenosis can be clinically assessed by thestenotic orifice area, the flow passing throughthe stenosis, and the driving pressure neededto expel the blood through the stenosis.Regardless of the increasingly sophisticatedmethods available for clinical assessment ofstenotic lesions it is still important to be awareof these fundamental haemodynamic relations.From the patient's point of view, accurate

non-invasive methods for obtaining imagingand haemodynamic data are the most attrac-tive. Therefore, Doppler echocardiographyhas had a considerable clinical impact duringthe past decade. Its use to assess stenoticlesions has expanded to the entire cardiovas-cular system and to the acquisition of manyvariables.

This paper deals with aortic and mitralstenoses and focuses on the clinical impact ofDoppler echocardiography. The principles offluid dynamics that apply to the aortic andmitral valves also apply to the tricuspid andpulmonary valves but these valves are not dealtwith in this paper.

Fluid dynamicsOne of the fundamental parameters describingthe severity of a stenosis with turbulent flow isthe haemodynamic resistance (R)

R= Ap Q' (1)

where Ap is the transvalvar pressure drop and Qis the transvalvar flow. In this paper theexpression "pressure gradient" is intentionallyavoided and pressure loss, pressure drop, orpressure difference are instead used.The pres-sure gradient is dp/dx (change in pressure as afunction of change in distance). This is notmeasured either in clinical practice or in theexperimental laboratory. What we measure isthe pressure difference across a stenosis-inthe cardiovascular system this will always be apressure loss.There is an exponential increasein the transvalvar pressure drop as transvalvarflow increases (fig 1).

In many papers resistance is calculated byassuming a linear relation between pressureloss and flow (Ap/Q).2A From a fluid dynamicpoint of view this is incorrect because inimportant stenotic lesions flow is always tur-bulent. Despite this limitation the valvar resis-tance parameter calculated in this way givesinformation about the severity of a stenosiswhen invasive techniques have been used. In astrictly controlled in vitro experiment, how-ever, Voelker et al2 recently showed that valveresistance and stroke work loss, another pro-posed measure of stenosis severity, both varyconsiderably with flow. These measuresshould therefore be used with caution.

Ideally one catheter should be placed oneach side of the valve to obtain simultaneouspressure recordings. When the pull-back tech-nique is used beat-to-beat fluctuations in pres-sure will influence the pressure differencemaking measurements less reliable. Improperdampening caused by the fluid in the cathetersand the poststenotic pressure recovery phe-nomenon 5-6 are additional potential sources oferrors.As suggested by Hatle et al,7 the simplified

Bernoulli equation can be used to assess thepressure difference non-invasively by Dopplerultrasound:

Ap = 4 x v2 (2)

Figure 1 Relation Iflow model. Four meflow loop: BSC = EHall-Kaster (Medtrmexponentially with insystolic conditions. (,

5 10 15 20 25 30 where v is the peak systolic blood velocity inI/min the stenotic jet. The pressure difference esti-

between transvalvar pressure drop and transvalvar flow in a stenotic mated in this way is an instantaneous pressurechanical heart valves (all 27 mm aortic valves) were mounted in a drop, unlike the catheter derived pressure dif-3jork-Shiley convexlconcave; BSS = Bjork-Shiley standard; HK = ference which usually is reported as a "peak toonic-Hall); SJM = St Jude Medical. The pressure drop increasedwcreasingflow. Flow values in the steady state model reflect peak peak" pressure difference. The mean pressureAdapted with permission from the J Biomech 1987;20:353-64.') difference is a more meaningful measure for

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Stenotic lesions

comparing pressure drops estimated by thecatheter and Doppler techniques since one canbe calculated from the other. The Dopplerderived mean pressure loss cannot be calcu-lated directly from the mean velocity. It has tobe calculated as the time average of the instan-taneous pressure differences obtained from theBernoulli relation. This is quite cumbersometo do manually, whereas with modem equip-ment this value is calculated at the same time asthe velocity integral.

Cardiologists are conservative and most stilluse pressure differences calculated fromDoppler data by the simplified Bernoulli equa-tion. None the less it is more straightforwardto calculate the time velocity integral, whichconveys the same information as the meanpressure difference. Has the time come toreport measured velocity data instead ofderived pressure data? The advantage of usingvelocity data is obvious when the differencebetween Doppler-derived and catheter-mea-sured pressure differences seen in somemechanical valve prosthesis is considered.6

Because the blood velocity in stenotic jets isusually high, continuous wave Doppler has tobe used. This implies that velocity recordingsare made in the entire cross field of the emit-ted and received ultrasound wavefronts. Thereliability of this technique depends on its abil-ity to detect the highest blood velocity area inthe entire flow field and often a stand alonepencil probe has to be used. Furthermore, itrequires the insonated ultrasound beam andthe jet to be aligned. It is unwise to apply anglecorrection because the stenotic valve maydirect the jet in any direction into the receivingchamber,8 increasing the problem of aligningthe ultrasound wave and the jet.

Cardiac output, Q can be assessed non-invasively from the simple equation:

Q=vx A (3)

where vi is the spatial mean blood velocity inthe cross sectional area (A). Cardiac outputcan then theoretically be measured by multi-plying area obtained from the cross sectionalechocardiographic image and Doppler derivedmean blood velocity. This technique has beensuggested for use in the pulmonary artery, themitral annulus, and the left ventricular outflowtract. All these techniques assume a flat bloodvelocity profile but this is not true of the pul-monary artery9 or the mitral annulus.'O 11 Thetechnique, however, seems to work in the out-flow tract of the left ventricle in patients withaortic stenosis.'2 Rebreathing techniques have

A AU1 _______2U2

V,

Figure 2 Illustration of the continuity equation. Volumeflows on each side of a stenosis are identical. The reducedarea in the stenosis necessitates a higher mean velocity toexpel the same volume offluid through the stenosis per timeunit.

also been applied for non-invasive determina-tions of cardiac output.'3 Clearly both ultra-sound and catheter based methods havesources of errors which the user must be awareof.The functional area of the valve orifice can

be estimated by the continuity equation,which states that volume flow at each cross-section is constant (fig 2). This is an expres-sion of the conservation of mass principle.Using equation 3:

Al x v1 = A2 x v2 (4)

where Al and A2 are prestenotic and stenoticcross sectional areas, respectively, and v, andv2 are the spatial and temporal mean velocitiesin the same locations. By planimetry of Al andmeasuring vI and v2 the stenosis area can becalculated by rearranging equation (4):

VI Al xTVI~Al = Al X orxA. (5)

V2 TVI2where TVI1 and TVI2 are the time velocityintegrals of the prestenotic and stenotic areas,respectively.The Gorlin formula'4 is a special version of

the continuity equation where the Bernoulliequation has been used to recalculate pressureas velocity. Accordingly, the Gorlin formula isused to estimate stenosis orifice area (A) fromthe transstenotic flow and the resulting trans-stenotic pressure drop. The original Gorlinformula has been challenged often-by in vitrostudies,2 by animal experimental studies,'5 andin humans.'6 For example in the modificationof the Gorlin formula used to assess aorticstenosis:

QsmA= (6)

where Qsm = mean systolic flow and Apsm =the mean systolic transstenotic pressure drop;the factor "k" was originally reported as 44-3but values from 50 to 20 have been sug-gested.24When "Gorlin areas" are compared with

"continuity areas" it is important to rememberthat the Gorlin equation gives the anatomicalarea whereas the continuity equation calcu-lates the flow area (which is smaller).

Stenoses always cause stenotic jets whichinclude blood velocities above the criticalvalue for causing turbulence. Turbulence canbe heard with a stethoscope or recorded byan accelerometer. Turbulence can also bemeasured by pulsed and colour Dopplertechniques. These require specialised equip-ment'17 18 that is not used routinely.

Aortic stenosisAortic valve stenosis is often diagnosed beforethe patient is investigated with Dopplerechocardiography. The cross sectional imagewill confirm this, but for a more exact assess-ment of the severity of disease Doppler record-ings have to be made. The technique is welldescribed elsewhere.'9 We only want toemphasise that the aortic valve must be

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Wranne, Baumgartner, Flachskampf, Hasenkam, Pinto

Figure 3 Example ofaortic stenosis of differentseverity. (A) A case of mildstenosis with low velocityand an early maximum.(B) A recordingfrom aprosthetic St jude valve(size 19 mm) in the aorticposition. Note the earlymaximum despite the highvelocity. This valve has noabnormal obstruction. (C)A case with severe stenosisand a symmetrical curve.The patient has atrialfibrillation. Note thesimilarity in configurationdespite the variations in

velocity caused bydifferences in volumeflowbetween the beats.

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explored from several different positions todetect the highest velocities. None the less,velocities are flow dependent and may be highwith fairly mild aortic stenosis or low withsevere stenosis. Calculation of the stenoticarea using the continuity equation, as

described above, is then often of great help.This is achieved by measuring the velocity inthe stenosis and in the outflow tract of the leftventricle and multiplying it by the subvalvararea obtained from the cross sectional image.In most cases the subvalvar flow profile isflat.12 However, since the subvalvar diameter issometimes difficult to measure this approachis not always feasible. Visual analysis of thespectral curve is always important. With mildstenosis and high flow, the peak velocityoccurs early in systole, whereas with severe

stenosis the maximum is reached in midsys-tole-that is, the curve is symmetrical (fig 3).

Analysis of the spectral curve is also of spe-

cial importance when subvalvar obstructionsare assessed. Dynamic subvalvar obstruction,such as that seen in hypertrophic obstructivecardiomyopathy, typically produces a spectralcurve with late maximum (fig 4) in addition towell known signs such as septal hypertrophy,systolic anterior motion of the mitral valve,and premature closure of the aortic valves. If apatient with dynamic subvalvar obstructionalso has mitral regurgitation this can start lateand peak late and may be mixed with the sub-

valvar component.Patients with aortic valve stenosis some-

times also have dynamic subvalvar obstruc-tions. This is of special importance becausesurgical resection of the hypertrophic septummay be necessary as part of the surgical proce-dure. The information is also relevant to thetreatment of the patient in the immediate post-operative period when inotropic drugs, whichmay provoke dynamic outflow obstruction,must be used with care.

Patients with aortic stenosis who are in car-

diac failure are often difficult to assess becausethey have a low cardiac output and thereforelow blood velocities and accordingly a lowtransvalvar pressure loss. In addition to visualanalysis of the spectral curve, measurement ofejection time is of value here. A normal ejec-tion time in a patient with cardiac failure ishighly indicative of severe aortic stenosis or

regurgitation.2021

Use of the continuity equation in low flowstates may yield falsely low valve areas. Dobu-tamine22-24 or exercise echocardiography25 havebeen suggested as being helpful in these cir-cumstances. The rationale behind this is that ifthe valve area increases with increasing flow,then the stenosis can not be severe. It is notobvious from these reports that this is the finalanswer to this question.

Transoesophageal echocardiography withits higher resolution and overall image quality

Figure4 SpectralDoppler recordings fromleft ventricular outflow in apatient with obstructivecardiomyopathy. Note how -

difficult it can be to recordthe highest velocities, thelate peak when these high __ __ ___ _velocities are recorded, andhow the appearance of thespectral curve changes -when these high velocitiesare missed.

.ii...t..I...I.,.i...3..l.....I . 1..I.,.I.,.i...I..I.. I .1 . . 1

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Stenotic lesions

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Figure 5 Shaded boxes show haemodynamic conditionsknown to occur with increasing severity of mitral stenosis-that is, increasing pressure difference (Ap) across the valveand decreasing stroke volume (SV). The influence onpressure half time (TO.) is shown to the right. Thus thedirect and net effect ofdecreasing area is a prolongedpressure halftime, but the extent ofchange depends onchanges in ApO and SV. The expected changes in both tendto shorten To.,. Reproduced with permission from the J AmSoc Echocardiogr 1988;1:313-21.33

allows direct visualisation of the aortic orificearea. Planimetry of aortic valve area usingmultiplane transoesophageal transducers hasbeen described. The level of the smallest ori-fice in the long axis view (130-1500) is locatedand the transducer plane is then rotated to a

short axis view at 40-600. Planimetry is per-

formed in this view. Sometimes colourDoppler can be helpful to delineate the orifice.Sometimes planimetry is not feasible whenthere is heavy calcification, and misalignmentwith the valve plane may also induce errors.Good correlations with Gorlin areas have,however, been reported.26 This techniqueshould be reserved for the few patients inwhom conventional Doppler echocardiogra-phy does not give adequate information.

Doppler echocardiography, used in the waydescribed above, generally provides an accu-

rate assessment of the severity of stenosis.However, it is important that the assessmentincludes other information obtained in theechocardiographic investigation-for example,left ventricular cavity size and wall thickness.

Mitral stenosisDiagnosis of mitral stenosis was the first clinicalapplication of echocardiography.27 The Mmode two dimensional patterns are character-istic but do not provide exact information on

the degree of stenosis. Doppler too was firstused clinically to acquire data on mitral steno-

Si.28sis.2

Planimetry of the mitral valve area from thecross sectional image is a well established tech-nique29but is subject to certain limitations: thestenotic orifice is seldom circular or even sym-metrical, it may vary during the cardiac cycle. Itmay also vary with changing blood flowthrough the valve and be influenced bymachine settings. Furthermore the techniquerequires that a directly orthogonal imagingplane can be achieved and recognition thatexcessive reflecting material, such as calcifiedtissue, may cause blooming-especially whenolder equipment is used. Those who see onlyoccasional patients with mitral stenosis shoulduse the technique with caution.The pressure gradient half time method for

assessing mitral stenosis was introduced foruse at catheterisation30 and later adapted toechocardiography.3' It was initially appliedwith great enthusiasm and a number of reportssupported its value. However, theory andmodel experiments predicted that the gradienthalf time should be influenced by atrial andventricular compliance as well as the imped-ance exerted by the mitral orifice.32 Fluiddynamics predict that the gradient half timewill be influenced by the diastolic transmitralflow and peak early transmitral pressure differ-ence as well as the orifice area33 (fig 5).When the half time concept was introduced

and initially evaluated cardiologists wereunaware of the importance of diastolic relax-ation to mitral flow. We all now know that theflow velocity pattern of impaired diastolicrelaxation can be characterised by a prolongeddeceleration time (equivalent to a prolongedgradient half time). Therefore the combina-tion of delayed ventricular relaxation and mildmitral stenosis may give a long gradient halftime and simulate severe stenosis.34 It is alsowell known that gradient half time is incorrectafter balloon dilatation of the mitral valve35and shortened in patients with coexisting aorticregurgitation.36 For these reasons gradient halftime shall not be used in isolation to assessmitral stenosis.How then should we assess the severity of

mitral stenosis? The qualitative diagnosis isgenerally obtained directly from the cross sec-tional image or M mode recording. Thedegree of calcification and involvement of thesubvalvar apparatus are also obtained from thecross sectional image. The mean pressure lossor the diastolic velocity integral can easily becalculated from the spectral curve. Themotion of the interventricular septum will pro-vide further information; the more severe thestenosis the later the filling of the left ventriclein relation to the right and consequently themore severe the abnormality of the septalmotion. Assessment of right ventricular sys-tolic pressure from a tricuspid regurgitationprovides further evidence. The valve area canbe calculated by planimetry of the cross sec-tional image and also by using the continuityequation, where flow can be calculated fromthe left ventricular outflow (if there is no aorticregurgitation). The proximal accelerationtechnique has also been used for this pur-pose.'537 Use of a combination of these tech-niques should generally give the correctdiagnosis.

Prosthetic valvesNormal prosthetic valves cause some degree offlow obstruction, sometimes resulting in a sig-nificant pressure loss. It is important to recog-nise that Doppler-derived flow velocities andpressure differences vary with valve type andsize because of the variation in effective orificeareas. Therefore, valve type and size must bespecified when Doppler data are interpreted.Even when these variables have been defined,the reported range of normal velocities andgradients for prosthetic valves varies widely,

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Wranne, Baumgartner, Flachskampf, Hasenkam, Pinto

A StJude30-

20 - 19mm

10 j= 23 mmHE-.-.~~~~:.~~ 25 mm

27 mm

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--/,~=~ 21 mm

=. 1 t _- 25 mm

Coo C Hancock' 40 19mm

530_/~~~~~~~19 mm

0 10 20 30Distance from valve (mm)

particularly for small valve sizes.38 The reason

for this variation is the marked flow depen-dence of Doppler velocities across prostheticvalves.39 Therefore, particularly for small valvesizes, accurate evaluation of prosthetic valvefunction from Doppler velocities requiressome information on the flow rate at whichthey were measured.To provide a flow independent variable the

continuity equation has been proposed as a

method of calculating aortic prosthetic valveareas. However, at least for bileaflet valves,these calculations are not correct (see below).For mitral prosthetic valves, the pressure halftime can be used. Normal values have beencollected for most of the commonly usedvalves.'8 Despite some variation, this variablehas proved to be useful for the detection ofprosthetic valve obstruction. As for the othervariables, it is important to obtain baselinedata early after surgery for comparison duringlater follow up.40 There are no data to justifythe calculation of prosthetic valve areas frompressure half time.

The good agreement between Doppler andcatheter data for native aortic valve stenosishas not always been found in heart valve pros-

theses.39 Particularly for mechanical valveprostheses, conflicting results have beenreported. In vitro studies have helped toexplain this phenomenon, demonstrating thedependence of the Doppler-catheter gradientrelation on the geometric design of the valveprostheses. While acceptable agreement was

found for normal Medtronic-Hall tilting discand Hancock bioprosthetic valves, Dopplergradients significantly exceeded catheter gradi-ents in normal bileaflet valves and caged ballvalves.639 For bileaflet valves, it has also beenshown that these discrepancies betweenDoppler and catheter gradients are not due toerroneous measurements by either techniquebut to spatial variation in pressure within anddistal to the valve. Catheter pullback measure-

ments (figs 6 and 7) showed that the Dopplercalculated pressure loss accurately reflectedthe highest obtainable values obtained by thecatheter technique. The maximal pressure losswas localised between the two leaflets of thevalve and not in the side orifices. However,when distal pressures were measured 30 mmdownstream from the valve, catheter gradientsdecreased and were significantly smaller thanDoppler gradients (fig 7). The differencebetween Doppler and catheter measurementswas, therefore, due to localised high gradientsand pressure recovery and to the fact that thetwo techniques measured gradients in differ-ent locations; Doppler gradients reflect thehighest gradient along the interrogation lineand across the orifice (that is, the localisedhigh gradient between the two leaflets)whereas catheterisation measures a recoveredpressure further downstream from the valve.6The discrepancies between Doppler and

catheter pressure differences become particu-larly clinically relevant in small valves and athigh flow rates, where differences as great as

44 mmHg have been observed,39 but are of lessimportance in large valves with very low pres-

sure differences. The relation betweenDoppler and catheter measurements is sig-nificantly altered by malfunction of the valve

Figure 7 Peak (leftpanel) and mean (rightpanel) Doppler derivedgradients in relation tocorresponding cathetergradients. Open circlesrefer to highest cathetergradient and closed circlesto gradients 30 mm distalto the valve.Measurements wereobtained in St Jude valves(19-27 mm). Reproducedwith the permission ofCirculation.6

Catheter gradiento Highest* At30mm

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Figure 6 Plots ofmeancatheter gradient anddistance fromvalve. (A) Gradientobtained when the catheterwas pulled back throughthe central orifice of the StJude valve. (B) Gradientsobtainedfor two sizes ofStJude valves when thecatheter was pulled backthrough either the centralor the side orifice. (C)Gradients as a function ofdistance from the valveringfor Hancock tissuevalves. Reproduced withthe permission ofCirculation.6

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Stenotic lesions

Figure 8 Correlationbetween mean Doppler andmean catheter gradients ina 19mm CarboMedicsbileaflet valve studiedduring normalfunctionand in various stages ofmalfunction ranging fromslightly restricted openingto total occlusion of oneleaflet. The differentsymbols indicate thefunctional status at whichthe gradients weremeasured. Reproducedwith the permission ofCirculation.4'

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Mean catheter gradient (mm Hg)

(fig 8). With increasing restriction of openingof one leaflet, the differences between Dopplerand catheter gradients decrease and eventuallyalmost disappear when one leaflet is totallyoccluded. This is due to the changing flowcharacteristics of this valve type4' that occur

with malfunction. The pressure recovery seen

in the "central tunnel" of normal bileafletvalves is not present with restricted leafletmotion where hydraulic conditions are similarto those seen in native stenotic valves.

These observations have several importantimplications. First, the dependence of theDoppler-catheter gradient relation on thefunctional status of the valve precludes theapplication of correcting factors. Second, one

should not assess the function of bileaflet aorticvalve prostheses by calculating the valve orificearea with the continuity equation. Becausethese calculations are based on localised highvelocities between the two leaflets rather thanon the average velocity across the orifice, theDoppler valve area underestimates the true

effective orifice area of bileaflet valves.42 Sincedifferences between localised high velocitiesand average velocities across the orificedecrease with increasing restriction of leafletmotion the decrease of Doppler valve area

caused by restricted leaflet opening will alsounderestimate the true change in effective ori-fice area. Therefore, bileaflet valves with highDoppler gradients should be studied carefullywith additional non-invasive techniques suchas cinefluoroscopic evaluation of leafletmotion to avoid erroneous diagnoses of pros-

thetic valve stenosis. Transoesophageal echo-cardiography can often image leaflet motion inthe mitral position very well.

In this review we have concentrated on aor-

tic and mitral valve stenosis. The general prin-ciples described here for these valve lesionsalso apply to pulmonary and tricuspid steno-sis. We believe that Doppler echocardiographyis currently the best technique for evaluatingvalve lesions. However, a good knowledge offluid dynamics, the machine, and clinical car-

diology is needed to get optimal informationfrom the investigation and to avoid mistakes ininterpretation of data. Every echocardiogramhas to be interpreted taking into account theclinical condition of the patient.

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ization of axial velocity profiles downstream of six differentmechanical aortic valve prostheses, measured with a hot-film anemometer in a steady state flow model. Y Biomech1987;20:353-64.

2 Voelker W, Reul H, Nienhaus G, Stelzer T, Schmitz B,Steegers A, et al. Comparison of valvular resistance,stroke work loss and Gorlin valve area for quantification ofaortic stenosis. An in vitro study in a pulsatile aortic flowmodel. Circulation 1995;91:1196-204.

3 Ford LE, Feldman T, Chiu YC, Carroll JD. Hemodynamicresistance as a measure of fimctional impairment in aorticvalvular stenosis. Circ Res 1990;66: 1-7.

4 Cannon SR, Richards KL, Crawford M. Hydraulic estima-tion of stenotic orifice area: a correction of the Gorlin for-mula. Circulation 1985;71:1170-8.

5 Levine RA, Jimoh A, Cape EG, Mcmillan S, YoganathanAP, Weyman A. Pressure recovery distal to a stenosis:potential cause of gradient "overestimation" by Dopplerechocardiography. JAm Coll Cardiol 1989;13:706-13.

6 Baumgartner H, Khan S, DeRobertis M, Czer L, MaurerG. Discrepancies between doppler and catheter gradientsin aortic prosthetic valves in vitro. A manifestation oflocalized gradients and pressure recovery. Circulation1990;82: 1467-75.

7 Hatle L, Angelsen BA, Tromsdal A. Non-invasive assess-ment of aortic stenosis by Doppler ultrasound. Br Hearty1980;43:284-92.

8 Grimes RY, Burleson A, Levine RA, Yoganathan AP.Quantification of cardiac jets: Theory and limitations.Echocardiography 1994;11:267-80.

9 Sloth E, Pedersen EM, Nygaard H, Hasenkam JM, Juhl B.Multiplane transesophageal Doppler-echocardiographymeasurements of the velocity profile in the human pul-monary artery. J Am Soc Echocardiogr 1994;7:132-40.

10 Kim WY, Bisgaard T, Nielsen SL, Poulsen JK, PedersenEM, Hasenkam JM, et al. Two-dimensional mitral flowvelocity profiles in pig models using epicardial echo-Doppler-cardiography. J Am Coll Cardiol 1994;24:532-45.

11 Kupari M, Jarvinen V, Poutanen V-P, Hekali P. Skewness ofinstantaneous mitral transannular flow-velocity profilesin normal humans. AmJPhysiol 1995;268:H1232-38.

12 Janerot Sjoberg B, Loyd D, Ask P, Wranne B. Subaorticflow profiles in aortic valve disease. JAm Soc Echocardiogr1994;7:276-85.

13 Ohlsson J, Wranne B. Noninvasive assessment of valve areain patients with aortic stenosis. J Am Coil Cardiol 1986;7:501-8.

14 Gorlin R, Gorlin SG. Hydraulic formula for calculation ofarea of the stenotic mitral valve, other cardiac valves andcentral circulatory shunts. Am HeartJ 1951;41:1-29.

15 Shiota T, Jones M, Valdes-Cruz LM, Shandas R, Yamada I,Sahn DJ. Color flow Doppler determination of transmi-tral flow and orifice area in mitral stenosis: Experimentalevaluation of the proximal flow-convergence method. AmHeartJ 1995;129:114-23.

16 Fischer JL, Haberer T, Dickson D, Henseimann L.Comparison of Doppler echocardiographic methods withheart catheterization in assessing aortic valve area in 100patients with aortic stenosis. Br HeartJ 1995;73:293-98.

17 Nygaard H, Paulsen PK, Hasenkam JM, Kromann-Hansen0, Pedersen EM, Rovsing PE. Quantitation of the turbu-lent stress distribution downstream of normal, diseasedand artificial aortic valves in humans. EurJ CardiothoracSurg 1992;6:609-17.

18 Nygaard H, Hasenkam JM, Pedersen EM, Kim WY,Paulsen PK. A new perivascular multielement pulsedDoppler ultrasound system for in vivo studies of velocityfields and turbulent stresses in large vessels. Med Biol EngComput 1994;32:55-62.

19 Skjaerpe T, Hegrenaes L, Hatle L. Noninvasive estimationof valve area in patients with aortic stenosis by Dopplerultrasound and two-dimensional echocardiography.Circulation 1985;72:810-8.

20 Lewis RP, Rittgers SE, Forester WF, Boudoulas H. A criti-cal review of the systolic time intervals. Circulation 1977;56:146-58.

21 Nylander E, Ekman I, Marklund T, Sinnerstad B, karlssonE, Wranne B. Severe aortic stenosis in elderly patients.Br HeartJ 1986;55:480-7.

22 Burwash IG, Thomas DD, Sadahiro M, Pearlman AS,Verrier ED, Thomas R, et al. Dependence of Gorlin for-mula and continuity equation valve areas on transvalvularvolume flow rate in valvular aortic stenosis. Circulation1994;89:827-35.

23 Tardif J-C, Miller DS, Pandian NG, Schwartz SL, GordonG, Tiemey R, et al. Effects of variation in flow on aorticvalve area in aortic stenosis based on in vivo planimetryof aortic valve area by multiplane transoesophagealechocardiography. Am J Cardiol 1995;76: 193-8

24 deFilippi CR, Willet DL, Brickner E, Appleton CP, YancyCW, Eichhom EJ, et al. Usefulness of Dobutamineechocardiography in distinguishing severe from nonse-vere valvular aortic stenosis in patients with depressed leftventricular function and low transvalvular gradients.AmJCardiol 1995;75:191-4.

25 Burwash IG, Pearlman AS, Kraft CD, Miyake-Hull C,Healy NL, Otto CM. Flow dependence of measures ofaortic stenosis severity during exercise. JAm Coll Cardiol1994;24: 1342-50.

26 Hoffman R, Flachskampf FA, Hanrath P. Planimetry oforifice area in aortic stenosis using multiplane trans-esophageal ephocardiography.JAm Coll Cardiol 1993;22:529-34.

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