pressure recovery in aortic valve stenosis -...

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116 Pressure Recovery in Aortic Valve Stenosis Warren K. Laskey, MD; William G. Kussmaul, MD Background Pressure recovery is the variable increase in lateral pressure downstream from a stenotic orifice. The magni- tude and clinical significance of pressure recovery in aortic valve stenosis are poorly defined. Methods and Results We obtained high-fidelity pressure and velocity recordings in 11 patients with isolated significant aortic valve stenosis at the time of diagnostic cardiac catheter- ization. Systematic catheter pullback from the left ventricular cavity revealed a consistent although variable subvalvular gradient. Further pullback across and distal to the region of the stenosed aortic valve revealed a consistent and progressive increase in the ascending aortic pressure. This increase in T Nransvalvular pressure differences are the hemo- dynamic hallmark of valvular obstruction. The severity of obstruction in the clinical context is represented by a derived orifice area, with the latter a function of the transvalvular pressure difference and transvalvular flow.' Hydrodynamic theory of flow through stenotic orifices indicates convergence of the flow field proximal to and within the stenosis, with subsequent flow acceleration.2-5 Considerable effort has been expended in the quantitation and evaluation of transvalvular pressure gradients in aortic valve stenosis in humans.6 More recently, theoretical predictions and empirical studies have indicated that a significant mi- nority of the pressure loss occurs proximal to the valvular stenosis.7,8 These same model-based predic- tions indicate variable degrees of expansion of the flow field distal to the stenosis with subsequent flow decel- eration and turbulence.4'9 Although these theoretical approaches and experimental observations9-"1 have co- gently suggested the existence of pressure recovery, no direct confirmation of pressure recovery has been re- ported in humans. We analyzed systematic high-fidelity catheter pull- backs during diagnostic cardiac catheterization in pa- tients with clinically significant aortic valve stenosis in order to (1) ascertain the presence of pressure recovery, (2) quantitate the extent of pressure recovery, and (3) relate the extent of pressure recovery to traditional hemodynamic indices of stenosis severity. Methods Patient Population Eleven patients (nine men, two women) with clinically significant aortic valve stenosis were referred for diagnostic Received July 20, 1993; revision accepted August 24, 1993. From the Cardiac Catheterization Laboratory, Hospital of the University of Pennsylvania, and the Department of Medicine, University of Pennsylvania School of Medicine, Philadelphia, Pa. Correspondence to Warren K. Laskey, MD, Cardiac Catheter- ization Laboratory, Hospital of the University of Pennsylvania, 3400 Spruce St, Philadelphia, PA 19104. lateral pressure occurred pari passu with a diminution in amplitude of the velocity pulse. The extent of pressure recov- ery was directly related to systemic blood flow and transval- vular flow but inversely related to the Gorlin-derived aortic valve area. Conclsions These findings have potentially important implications for the hemodynamic evaluation of mild to moderately severe aortic valve stenosis. The extent of pres- sure recovery may be of additional utility in the assessment of aortic valve stenosis under varying physiological states. (Circulation. 1994;89:116-121.) Key Words * aorta * valves * stenosis cardiac catheterization and coronary angiography before planned aortic valve surgery. All patients were in sinus rhythm and had normal left ventricular systolic function assessed by contrast ventriculography and/or two-dimensional echocardi- ography. No subject had more than trace aortic regurgitation, again assessed by contrast aortography and/or Doppler echo- cardiography. Finally, no subject had significant obstructive coronary artery disease on angiography. Study Protocol All patients underwent cardiac catheterization via the bra- chial approach. A custom-designed multisensor catheter (Millar Instruments, Inc, Houston, Tex) consisting of a distal (tip) pressure sensor, a more proximal pressure sensor (5 cm from the tip), and an electromagnetic velocity probe located at the site of the proximal pressure sensor was advanced from the right brachial artery to the left ventricle under fluoroscopic control. The outputs from the pressure transducers were amplified and displayed in real time and recorded on FM magnetic tape. The electromagnetic velocity probe was ener- gized by a 500-Hz square wave electromagnetic flowmeter (Carolina Medical Electronics, King, NC). The output of the velocity probe was amplified, filtered at the 100-Hz setting, and displayed in real time and recorded on tape. The study protocol, performed before administration of radiocontrast, consisted of the following. The catheter was advanced to the deep left ventricular body, where both pres- sure sensors recorded left ventricular pressure. Both tracings were adjusted so that the left ventricular late diastolic contour was superimposed on a simultaneous recording of the pulmo- nary capillary wedge pressure. The proper gain setting for recording the velocity waveform was obtained and not adjusted thereafter. At this point, the catheter was slowly withdrawn, with strict attention paid to the following land- marks: (1) a zone in which a subvalvular gradient was noted, (2) a zone identified by the traversal of the aortic valve by the proximal sensor, (3) a zone in which continued withdrawal resulted in maintaining the distal sensor within the left ventri- cle and the proximal sensor within the ascending aorta, and (4) withdrawal of the distal (ventricular) sensor into the proximal ascending aorta. This sequence was performed twice in each patient, and on each occasion strict attention was paid to the acquisition of steady-state data, ie, absent ventricular ectopy. After completion of the protocol the remainder of the diagnostic procedure was performed. No complications were by guest on May 22, 2018 http://circ.ahajournals.org/ Downloaded from

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Page 1: Pressure Recovery in Aortic Valve Stenosis - Circulationcirc.ahajournals.org/content/circulationaha/89/1/116.full.pdf · 116 Pressure Recoveryin AorticValve Stenosis WarrenK. Laskey,

116

Pressure Recovery in Aortic Valve Stenosis

Warren K. Laskey, MD; William G. Kussmaul, MD

Background Pressure recovery is the variable increase inlateral pressure downstream from a stenotic orifice. The magni-tude and clinical significance of pressure recovery in aortic valvestenosis are poorly defined.Methods and Results We obtained high-fidelity pressure

and velocity recordings in 11 patients with isolated significantaortic valve stenosis at the time of diagnostic cardiac catheter-ization. Systematic catheter pullback from the left ventricularcavity revealed a consistent although variable subvalvulargradient. Further pullback across and distal to the region ofthe stenosed aortic valve revealed a consistent and progressiveincrease in the ascending aortic pressure. This increase in

TNransvalvular pressure differences are the hemo-dynamic hallmark of valvular obstruction. Theseverity of obstruction in the clinical context is

represented by a derived orifice area, with the latter afunction of the transvalvular pressure difference andtransvalvular flow.' Hydrodynamic theory of flowthrough stenotic orifices indicates convergence of theflow field proximal to and within the stenosis, withsubsequent flow acceleration.2-5 Considerable effort hasbeen expended in the quantitation and evaluation oftransvalvular pressure gradients in aortic valve stenosisin humans.6 More recently, theoretical predictions andempirical studies have indicated that a significant mi-nority of the pressure loss occurs proximal to thevalvular stenosis.7,8 These same model-based predic-tions indicate variable degrees of expansion of the flowfield distal to the stenosis with subsequent flow decel-eration and turbulence.4'9 Although these theoreticalapproaches and experimental observations9-"1 have co-gently suggested the existence of pressure recovery, nodirect confirmation of pressure recovery has been re-ported in humans.We analyzed systematic high-fidelity catheter pull-

backs during diagnostic cardiac catheterization in pa-tients with clinically significant aortic valve stenosis inorder to (1) ascertain the presence of pressure recovery,(2) quantitate the extent of pressure recovery, and (3)relate the extent of pressure recovery to traditionalhemodynamic indices of stenosis severity.

MethodsPatient Population

Eleven patients (nine men, two women) with clinicallysignificant aortic valve stenosis were referred for diagnostic

Received July 20, 1993; revision accepted August 24, 1993.From the Cardiac Catheterization Laboratory, Hospital of the

University of Pennsylvania, and the Department of Medicine,University of Pennsylvania School of Medicine, Philadelphia, Pa.

Correspondence to Warren K. Laskey, MD, Cardiac Catheter-ization Laboratory, Hospital of the University of Pennsylvania,3400 Spruce St, Philadelphia, PA 19104.

lateral pressure occurred pari passu with a diminution inamplitude of the velocity pulse. The extent of pressure recov-ery was directly related to systemic blood flow and transval-vular flow but inversely related to the Gorlin-derived aorticvalve area.

Conclsions These findings have potentially importantimplications for the hemodynamic evaluation of mild tomoderately severe aortic valve stenosis. The extent of pres-sure recovery may be of additional utility in the assessmentof aortic valve stenosis under varying physiological states.(Circulation. 1994;89:116-121.)Key Words * aorta * valves * stenosis

cardiac catheterization and coronary angiography beforeplanned aortic valve surgery. All patients were in sinus rhythmand had normal left ventricular systolic function assessed bycontrast ventriculography and/or two-dimensional echocardi-ography. No subject had more than trace aortic regurgitation,again assessed by contrast aortography and/or Doppler echo-cardiography. Finally, no subject had significant obstructivecoronary artery disease on angiography.

Study ProtocolAll patients underwent cardiac catheterization via the bra-

chial approach. A custom-designed multisensor catheter(Millar Instruments, Inc, Houston, Tex) consisting of a distal(tip) pressure sensor, a more proximal pressure sensor (5 cmfrom the tip), and an electromagnetic velocity probe located atthe site of the proximal pressure sensor was advanced from theright brachial artery to the left ventricle under fluoroscopiccontrol. The outputs from the pressure transducers wereamplified and displayed in real time and recorded on FMmagnetic tape. The electromagnetic velocity probe was ener-gized by a 500-Hz square wave electromagnetic flowmeter(Carolina Medical Electronics, King, NC). The output of thevelocity probe was amplified, filtered at the 100-Hz setting,and displayed in real time and recorded on tape.The study protocol, performed before administration of

radiocontrast, consisted of the following. The catheter wasadvanced to the deep left ventricular body, where both pres-sure sensors recorded left ventricular pressure. Both tracingswere adjusted so that the left ventricular late diastolic contourwas superimposed on a simultaneous recording of the pulmo-nary capillary wedge pressure. The proper gain setting forrecording the velocity waveform was obtained and notadjusted thereafter. At this point, the catheter was slowlywithdrawn, with strict attention paid to the following land-marks: (1) a zone in which a subvalvular gradient was noted,(2) a zone identified by the traversal of the aortic valve by theproximal sensor, (3) a zone in which continued withdrawalresulted in maintaining the distal sensor within the left ventri-cle and the proximal sensor within the ascending aorta, and (4)withdrawal of the distal (ventricular) sensor into the proximalascending aorta. This sequence was performed twice in eachpatient, and on each occasion strict attention was paid to theacquisition of steady-state data, ie, absent ventricular ectopy.

After completion of the protocol the remainder of thediagnostic procedure was performed. No complications were

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Laskey and Kussmaul Pressure Recovery in Aortic Valve Stenosis 117

TABLE 1. Hemodynamic Profile of Patient Population

Patient LVSP Grad AVA CO1 138 47 0.35 2.3

2 206 40 0.80 5.3

3 245 86 0.59 6.04 234 104 0.50 5.2

5 211 49 0.97 6.6

6 233 97 0.43 5.3

7 196 48 0.69 5.5

8 203 56 0.71 5.3

9 177 50 0.93 5.8

10 214 68 0.76 6.4

11 282 112 0.33 3.5

Mean 213 69 0.64 5.2

SD 37 26 0.22 1.3

LVSP indicates peak left ventricular systolic pressure(mm Hg); Grad, mean transvalvular gradient using minimumrecorded aortic pressure (mm Hg); AVA, Gorlin-derived valvearea (cm2); and CO, thermodilution cardiac output (lJmin).

encountered as a result of the protocol. All subjects gavewritten consent in accordance with guidelines established bythe University of Pennsylvania Committee on Studies Involv-ing Human Beings.

Data AnalysisResults are expressed as mean+SD. Least squares and

multiple linear regression were used to analyze the relationbetween selected variables.

ResultsTable 1 describes the hemodynamic profile of the

study population. The Gorlin-derived aortic valve areawas obtained from recordings of the maximum transval-vular gradient, ie, the location of the proximal (aortic)pressure sensor yielding the lowest aortic systolic pres-sure during catheter withdrawal (compare with below).Fig 1 demonstrates the presence of pressure recoveryduring catheter pullback in a patient with significantaortic valve stenosis. In Fig 1A, both pressure sensorsare located in the deep left ventricular cavity and thevelocity waveform is of small amplitude. Withdrawal ofthe catheter into zone 1 (compare with "Methods")depicts the development of a subvalvular pressure gra-dient coincident with an increase in the amplitude of thevelocity waveform. In Fig 1B, further pullback results inthe passage of the proximal sensor across the aorticvalve into the proximal ascending aorta (zone 2). Notethe further increase in amplitude of the velocity wave-form at this location. In Fig 1C, further catheter with-drawal with the distal sensor remaining in the leftventricular cavity reveals a progressive increase in theascending aortic systolic pressure with destabilizationand diminution of the (now aortic) velocity waveform(zone 3). The difference in peak systolic pressure be-tween zones 2 and 3 is the extent of pressure recovery.Finally, withdrawal of the distal pressure sensor into theascending aorta reveals matched aortic pressure wave-forms and a chaotic, destabilized aortic velocity trace

Table 2 summarizes the extent of pressure recovery

and the effect of pressure recovery on the transvalvulargradient. The results represent the average of the twocatheter pullback sequences. The correlation betweenthe two pullback sequences was excellent (r=.99,SEE= 1.3 mm Hg). It should be noted that in eachpatient, the zone in which the gradient was highest(zone 2) was characterized by a high-amplitude, orga-nized velocity waveform and that further catheter with-drawal consistently resulted in the recording of a higheraortic systolic pressure and a lower-amplitude, disorga-nized velocity waveform (zone 3). Fig 2 illustrates theeffect of pressure recovery on the assessment of themean systolic transvalvular gradient. It can be seen thatthe mean gradient in zone 3 is consistently and signifi-cantly lower than the mean gradient in zone 2. Theimplications of this disparate assessment of the transval-vular gradient are demonstrated in Fig 3. The Gorlin-derived valve area is consistently and significantly higher ifthe recovered aortic pressure is used in the transvalvulargradient. Furthermore, this disparity appears greaterwhen the aortic valve area exceeds 0.7 cm2.

There was no significant relation between pressurerecovery and the maximum transvalvular gradient(r2=.125, P=NS). Fig 4 illustrates the dependence ofpressure recovery on mean flow (cardiac output) andstroke (transvalvular) flow. Although statistically signif-icant, these relations are not precise and thereforeindicate the importance of additional unquantified vari-ables. One such variable is the aortic valve area itself.Fig 5 indicates that pressure recovery is inversely re-lated to the severity of the valvular stenosis, althoughthe latter can only explain 70% of the variation in thepressure recovery. Multiple linear regression indicatedthat the combination of stroke flow, aortic valve area,and aortic valve gradient accounted for 80% of thevariability in pressure recovery.

DiscussionIn this report, we provide direct evidence for the

presence of pressure recovery in humans with aorticvalve stenosis. The observations are in accord withtheoretical predictions and validate models of flowthrough stenotic orifices under physiological conditions.The extent of pressure recovery, in absolute terms,varies directly with the transvalvular flow and indirectlywith the severity of the stenosis.Hydrodynamic theory and experimental observations

indicate that the flow field tapers proximal to a stenoticorifice, further converges within the stenosis itself, andreaches its smallest dimension just beyond the physicalobstruction (vena contracta). We reproducibly demon-strated in each subject the presence of a subvalvulargradient upon catheter withdrawal from the deep leftventricular cavity. Such observations have been previ-ously reported7,8 and verify the theoretical predictionsof an intracavitary tapering flow field in subjects withaortic valve stenosis.12 Simultaneous recordings of lat-eral pressure and fluid velocity immediately upon entryinto the proximal ascending aorta reveal a zone ofminimum aortic pressure beyond which the pressureincreases, or recovers, along with a region of maximumvelocity. That this latter region corresponds to the venacontracta is supported by the demonstration of the

(Fig 1D). simultaneous occurrence of minimum aortic pressure

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118 Circulation Vol 89, No 1 January 1994

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FIG 1. Tracings. A shows the two laterally mounted pressure sensors located within the deep left ventricular cavity, revealingsuperimposed intracavitary pressures. Middle tracing is the intracavitary velocity signal. Note the development of a small intracavitarypressure gradient along with an increase in the amplitude of the velocity signal as the catheter is withdrawn. B shows continued slowcatheter withdrawal, which results in the passage of the proximal transducer across the left ventricular outflow tract (left side) and intothe region of the stenotic aortic valve. Note the progressive increase in amplitude of the velocity signal along with the decrease in peakpressure recorded from the proximal transducer. C shows further catheter withdrawal, which results in the recording of a distinctiveascending aortic pressure pulse. Continued slow withdrawal reveals a progressive decrease in amplitude of the velocity signal alongwith an increase in the systolic aortic pressure. D shows withdrawal of both pressure sensors into the ascending aorta; this revealssuperimposed aortic pressures and a destabilized velocity waveform.

and maximum velocity in each subject studied. It shouldbe emphasized that the vena contracta was consistentlydemonstrated distal to the aortic valve, as it was onlywith further catheter withdrawal, after the immediatetransition from left ventricular outflow tract to proximalascending aorta, that the vena contracta was identified.Distal to the vena contracta, the zone of pressurerecovery was consistently demonstrated by the simulta-neous increase in (lateral) aortic pressure and decreasein amplitude of the velocity pulse.The true extent of pressure recovery may have been

underestimated by the noncalibrated withdrawal se-quence. We think this unlikely because (1) pressurerecovery reached its maximum value whenever thevelocity waveform was no longer recognizable (indicat-ing either transducer location within turbulent eddies or

in immediate proximity to the inner curve of the aorticwall), and (2) withdrawal of both sensors into theproximal ascending aorta and beyond failed to revealany further recovery of pressure. We could not, how-ever, be certain of the linear extent of the zone ofpressure recovery because the withdrawal sequence wasnot calibrated. An upper limit of 5 cm is reasonablegiven the distance between distal and proximal sensorsand the failure to record further increments in proximaltransducer pressure when both sensors were locatedwithin the aorta.The clinical utility of the quantitation of the extent of

pressure recovery in aortic valve stenosis is as yetuntested. A number of investigators have invoked pres-sure recovery as an explanation for the discrepancybetween Doppler-derived transvalvular gradients and

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Laskey and Kussmaul Pressure Recovery in Aortic Valve Stenosis

TABLE 2. Extent of Pressure Recovery and Effect onMeasured Gradient

Patient AoP,1~ AoP,,,, P Grad,,, Gradm.1 86 90 4 52 48

2 163 173 10 43 33

3 145 153 10 100 92

4 111 121 10 123 113

5 157 175 18 54 36

6 123 130 7 110 103

7 148 161 13 48 35

8 131 138 8 72 65

9 127 141 14 50 36

10 141 152 11 73 62

11 144 153 8 138 130

Mean 134 144 10 78 68

SD 22 24 4 34 35

AoPmin indicates smallest valve of ascending aortic systolicpressure (mm Hg); AoP,,,a highest value of ascending aorticsystolic pressure (mm Hg); POec, extent of pressure recovery(mm Hg); Grad,,, difference between peak left ventricular sys-tolic pressure and AoPmjn (mm Hg); and Gradnjn, differencebetween peak left ventricular systolic pressure and AoPma,(mm Hg).

invasively determined gradients at catheterization.9"10'13It must be recalled, however, that these techniques,while assessing the severity of the valvular stenosis, doso in different ways. Doppler-derived measures rely onthe identification of the maximum velocity in the regionof the vena contracta and thus reflect the physiologicalimportance of the stenosis, whereas the Gorlin-derivedaortic valve area yields an estimate of the anatomicseverity of the stenosis. Furthermore, the implication ofpressure recovery for accurate gradient and, therefore,valve area assessment, is potentially important. Al-though the magnitude of pressure recovery is a smallfraction of the peak (maximal) gradient, Gorlin-derivedvalve areas are consistently underestimated in the pres-ence of pressure recovery. These considerations areparticularly important in the setting of moderate sever-

120

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00 20 40 60 80 100 120

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FIG 2. Graph shows that consistent underestimation of theaverage (avg.) transvalvular gradient (GRAD) will result if pres-sure recovery (REC) is not recognized. Line of identity is shownfor ease of comparison.

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AVA NO RECFIG 3. Graph shows that consistent overestimation of the Gor-lin-derived aortic valve area (AVA, cm2) will resuft H pressurerecovery (REC) is not recognized. At intermediate levels ofstenosis severity (AVA >0.7 cm2), the disparity increases.

ity, eg, >0.7 cm2, when clinical decision making oftenrests on these calculations.We extend the clinical implications of pressure recov-

ery with the empiric correlations between the extent ofpressure recovery and transvalvular flow and the Gor-lin-derived aortic valve area. Unfortunately, the smallstudy population precludes analysis of the low-flow,

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100 125 150 175 200 225 250 275 300 325FLOW

FIG 4. Graphs show dependence of pressure recovery (Prec,mm Hg) on cardiac output (upper panel) and transvalvular flow(lower panel).

119

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120 Circulation Vol 89, No 1 January 1994

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14o

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FIG 5. Graph shows that pressure recovery (Prec, mm Hg) issignificantly and inversely related to the severity of valvularstenosis (AVA, cm2).

small-valve-area subgroup of patients. However, thepotential for an additional means of assessment of valvearea in this difficult clinical situation is clear. Underphysiological conditions at the other end of the hemo-dynamic spectrum- high flow- the importance and rel-evance of pressure recovery is also demonstrated. Highflows across a relatively unchanged stenotic orifice, suchas might occur with exercise, result in higher peaktransvalvular gradients but also a greater extent ofpressure recovery (Fig 6). The maintenance of aneffective input pressure to the systemic arterial circula-tion is clear. Finally, pharmacologically mediated alter-ations in transvalvular flow would be expected fromthese data to influence the extent of pressure recovery.Although none of our patients were receiving inotropicmedications or afterload-reducing agents, the expectedeffect of these medications can be surmised from Figs 4and 5. The extent of pressure recovery for any givenvalve area is greater at higher transvalvular flows.Similarly, at equivalent levels of transvalvular flow,pressure recovery is less when the stenosis is moresevere.

Study LimitationsSeveral limitations in this study merit discussion. We

did not routinely perform aortic root angiography,which would have allowed for quantitative assessmentof aortic dimension. Theoretical predictions hold thatnot only the dimension of the stenotic orifice (or moreproperly, the vena contracta) but also the dimension ofthe aorta in the zone of pressure recovery contributeimportantly to the extent of pressure recovery.4"4 Theabsence of these data may explain the variance in thecorrelations between pressure recovery and transvalvu-lar flow and valve area. In this regard, ascending aorticdistensibility as well as geometry may impact impor-tantly on the extent of pressure recovery. Age-relatedchanges in aortic compliance may very likely contributeto this process. Although there was no significant rela-tion between age and the extent of pressure recovery inour small series, the narrow range of patient age (48 to69 years) precludes drawing any conclusions. Thus,age-related influences on pressure recovery remain adistinct possibility. The lack of quantitative velocitydata precluded us from validating a model of pressurerecovery in aortic valve stenosis. At the outset, we wereunsure of the quality and stability of the velocity signalwith the velocity transducer within and distal to thevena contracta. These concerns were formidable, giventhe variable degree of destabilization and diminution ofthe velocity signal in this region. Thus, the qualitativeobservations are emphasized. Last, it must be acknowl-edged that these considerations are overlooked in rou-tine clinical practice wherein transvalvular gradients areassessed with fluid-filled catheter systems and multipleside-hole or end-hole catheters. It is unlikely thatpressure recovery would be detected under such cir-cumstances. Nevertheless, clinicians must be aware ofthe potential for gradient underestimation using theselatter techniques. Given the importance of accurateassessment of the gradient in the setting of moderatelysevere aortic valvular stenosis, the operator should

FIG 6. Tracings. Left, Pressure re-covery in the resting state in a sub-ject with aortic valve stenosis. Themagnitude of recovery is 16mm Hg. Right, With supine bicycleexercise, all pressures increase ap-propriately. The magnitude of pres-sure recovery increases to 33mm Hg.

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Laskey and Kussmaul Pressure Recovery in Aortic Valve Stenosis 121

strive for placement of the catheter measuring ascend-ing aortic pressure at the most proximal location.

SummaryIn this article, we report the presence and extent of

pressure recovery in aortic valve stenosis in humans.Although quantitatively small in comparison to thetransvalvular gradient, the recovery of pressure is afunction of stenosis severity and transvalvular flow.These observations have important clinical implicationsfor the assessment of the severity of valvular stenosesunder varying physiological conditions encounteredduring clinical evaluation.

AcknowledgmentsThe authors gratefully acknowledge the expert assistance of

the technical staff of the catheterization laboratories, withoutwhose help this work could not have been accomplished. Wealso thank Nedra Ellis for her expert secretarial assistance.

References1. Gorlin R, Gorlin G. Hydraulic formula for calculation of area of

stenotic mitral valve, other cardiac values and central circulatoryshunts.Am HeartJ. 1951;41:1-45.

2. Bellhouse B, Bellhouse F. Fluid mechanics of model normal andstenosed aortic valves. Circ Res. 1969;25:693-704.

3. Young DF, Tsai FY. Flow characteristics in models of arterialstenosis, II: unsteady flow. J Biomech. 1973;6:547-559.

4. Clark C. The fluid mechanics of aortic stenosis, I: theory andsteady flow experiments. J Biomech. 1976;9:521-528.

5. Clark C, Schultz DL. Velocity distribution in aortic flow. Car-diovasc Res. 1973;7:601-613.

6. Carabello B, Grossman W. Calculation of stenotic valve orificearea. In: Grossman W, ed. Cardiac Catheterization and Angi-ography. 3rd ed. Philadelphia, Pa: Lea & Febiger; 1986:143-154.

7. Bird JJ, Murgo JP, Pasipoularides A. Fluid dynamics of aorticstenosis: subvalvular gradients without subvalvular obstruction.Circulation. 1982;66:835-840.

8. Pasipoularides A, Murgo JP, Bird JJ, Craig WE. Fluid dynamics ofaortic stenosis: mechanisms for the presence of subvalvularpressure gradients. Am J Physiol. 1984;246:H542-H550.

9. Levine RA, Jimoh A, Cape EG, McMillan S, Yoganathan AP,Wayman AE. Pressure recovery distal to a stenosis: potential causeof gradient overestimation by Doppler echocardiography. J AmColl Cardiol. 1989;13:706-715.

10. Baumgartner H, Schima H, Tulzer G, Kuhn P. Effect of stenosisgeometry on the Doppler-catheter gradient relation in vitro: amanifestation of pressure recovery. J Am Coll Cardiol. 1993;21:1018-1025.

11. Voelker W, Reul H, Stelzer T, Schmidt A, Karsch KR. Pressurerecovery in aortic stenosis: an in vitro study in a pulsatile flowmodel. JAm Coil Cardiol. 1992;20:1585-1593.

12. Pasipoularides A. Clinical assessment of ventricular ejectiondynamics with and without outflow obstruction. JAm Coll Cardiol.1990;15:859-882.

13. Ohlsson J, Wranne B. Non-invasive assessment of valve area inpatients with aortic stenosis. JAm Coil CardioL 1986;7:501-508.

14. Clark C. The fluid mechanics of aortic stenosis, II: unsteady flowexperiments. J Biomech. 1976;9:567-573.

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W K Laskey and W G KussmaulPressure recovery in aortic valve stenosis.

Print ISSN: 0009-7322. Online ISSN: 1524-4539 Copyright © 1994 American Heart Association, Inc. All rights reserved.

is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation doi: 10.1161/01.CIR.89.1.116

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