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From 'Emax' to pressure-volume relations: a

broader viewDAVID A. KASS, M.D., AND W. LOWELL MAUGHAN, M.D.

THE REQUIREMENT for making accurate and de-tailed assessments of organ function has always de-pended on the scope and capabilities of available ther-apies. Over the past decade, we have witnessed an

explosion in the pharmacologic and interventionaltreatment options for coronary artery, myocardial, andvalvular heart disease, and with that has come a grow-

ing need for more precise measurements of cardiacperformance. A complete evaluation of ventricularperformance ideally includes relatively load insensi-tive measures of both systolic and diastolic pump prop-

erties, assessments of inotropic state and contractilereserve, and an evaluation of the cardiac response toaltered vascular loading conditions. However, routineclinical hemodynamic evaluation falls short of thismark, being generally limited to the determination ofsteady-state end-diastolic and peak systolic pressures,

ejection fraction, and occasionally maximum dP/dt.In his recent review, Arnold Katz' described the

utility of pressure-volume loops and relationships toassess "the effects of different forms of heart diseaseand to predict responses to the many therapeutic op-tions now available for the treatment of the patient withcardiac disease." This approach was originally studiedas a means of integrating and modeling the heart andvascular systems. Two principal observations were

made: (1) that the left upper corners of pressure-vol-ume loops ("the end-systolic pressure-volume points")obtained at various loads at a constant inotropic stateappeared to reach the same straight line, and (2) thatthis linear relation between pressure-volume pointswas in effect at all times in the cardiac cycle, givingrise to the concept that cardiac contraction could bemodeled as a "time-varying volume elastance."2"Theend of systole was defined as the time at which thiselastance reached a maximal value, termed Emax. Fora given set of systolic and diastolic properties, cardiac

Vol. 77, No. 6, June 1988

contraction was bounded by the end-diastolic and end-systolic pressure-volume relations (EDPVR andESPVR).

The pressure-volume framework has providedphysiologists with a single approach with which ven-

tricular properties,4 myocardial energetics,5, 6 andpump performance predictions through ventriculovas-cular coupling7 (recently reviewed by Sunagawa et

al.8) can all be studied. It has proven to be a fertile areaof research, and has significantly helped broaden our

understanding of cardiac mechanics and hemodynam-ics. The clinical application of this approach, howev-er, has tended to be more narrowly focused primarilyon the use of Emax as an "index of contractile state."This particular application has encountered some diffi-culties; studies of the ESPVR have revealed afterloaddependencies,9-2measurement variability,'1' 13 nonlin-earity of ESPVRs,'4 16 and dependence of ESPVR on

chamber size", ` and possibly cavity shape.'9However, these potential complicating features of

the ESPVR primarily frustrate attempts at deriving a

single number, Emax. By adopting a broader view thatuses all of the information conveyed by pressure-vol-ume relations, the approach provides a powerful toolfor understanding and quantifying the function of theheart and its interactions with the vascular system.Furthermore, with the development of new techniquessuch as the multielectrode conductance catheter pro-

viding on-line continuous left ventricular volumes,and methods of rapid, reversible load alteration such as

inferior vena caval occlusion, clinical applicationsmay finally be practical.Amid concerns regarding Emax, there has been a

growing interest in the use of pressure-volume rela-tions. Thus we believed it timely to review the currentstatus of these relations and their potential uses. Wefirst present a clinical example: that of assessing theinfluence of coronary occlusion and reperfusion on

global chamber performance. Next several currentconcerns regarding Emax and the assessment of cham-ber contractile state are discussed and put in perspec-

tive. Finally, pressure-volume relations are applied to

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From the Division of Cardiology, Department of Internal Medicine,The Johns Hopkins Medical Institutions, 600 N. Wolfe St., Baltimore.

Address for correspondence: David A. Kass, M.D., Division ofCardiology, Carnegie 565, Johns Hopkins University Hospital, 600 N.Wolfe St., Baltimore, MD 21205.

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the evaluation of pump performance of patients withcongestive heart failure, and the utility of the approachfor predicting the response to alterations in volumestatus, vasodilation, and inotropic state, is shown.A clinical example. Determining the influence of a

coronary occlusion on global left ventricular functionis important to many clinical studies of coronary heartdisease. The ultimate efficacy of reperfusion tech-niques, whether thrombolytic agents or angioplasty,often relies on a demonstration of improved pump per-formance. Yet characterization of global systolic anddiastolic dysfunction with coronary occlusion and re-perfusion in man has been limited.

Figure 1 displays a series of pressure-volume loopsand relations in a patient with a single-vessel coronaryartery stenosis (proximal left anterior descending ar-tery [LAD]), and no prior myocardial infarction. Thepatient underwent percutaneous coronary angioplastyof the LAD lesion. Continuous pressure-volume loopswere obtained before, during, and after angioplasty bythe conductance catheter technique.20 21 BaselineESPVR and EDPVR were generated by transient re-

duction of left ventricular filling volume via inferiorvena caval occlusion with a balloon catheter.

Panel A shows the baseline pressure-volume loopsand ESPVR and EDPVR. The cardiac performancewas essentially normal at rest despite the critical steno-sis. The ejection fraction was 59%, with an end-dia-stolic volume of 100 ml. The control relationships arereproduced in subsequent panels for comparison.

Panel B displays every third beat after the completeocclusion of the LAD by the angioplasty balloon. Overa 30 sec period, the pressure-volume loops shiftedmarkedly to the right and displayed a fall in systolicpressure. Panel C shows a steady-state pressure-vol-ume loop after 90 sec of coronary occlusion. Twomajor changes in pump performance are easily dis-cerned: (1) the end-systolic pressure-volume point hasshifted markedly to the right from baseline, demon-strating a substantial reduction in systolic pump prop-erties, and (2) the EDPVR is markedly elevated abovecontrol, consistent with a significant alteration inchamber compliance. The latter change was likelycritical in limiting further increases in end-diastolic

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FIGURE 1. Pressure-volume loops and relations obtained before, during, and after balloon angioplasty of a LAD stenosis inman. Left ventricular volume data were obtained with a multielectrode conductance catheter, with an intraluminal high-fidelitymicromanometer catheter for pressure recording. Pressure-volume relations were assessed by transient IVC occlusion with aballoon catheter. A, Baseline ESPVR, EDPVR, and pressure-volume loops. B, Pressure-volume loops during the first 30 sec ofcoronary occlusion. The ESPV point shifted significantly rightward while the DPVR shifted up and became steeper. C, Steady-state pressure-volume loop after 90 sec of coronary occlusion displaying both systolic and diastolic changes. D, Pressure volumeloops during the initial 15 sec of reperfusion. The ESPV point shifted back up and to the left, while the DPVR shifted back downessentially back to control. E, Steady-state loop before and after reperfusion. There is no indication of residual dysfunction.

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volume and thus stroke volume during coronary occlu-sion. Should further study reveal a relation between theextent of rightward ESPVR shift and ischemic mass,similar to that previously demonstrated in animals,22this approach could provide important clinical infor-mation regarding anatomic-functional correlates.

Panel D displays every other beat after deflation ofthe angioplasty balloon. The pressure-volume loopsreturned to normal within seconds of reperfusion, andif anything slightly exceeded the baseline condition(panel E). There was no evidence for myocardial"stunning," and the demonstration of functional recov-ery with reperfusion was as clear as the initial displayof dysfunction during coronary occlusion.We chose this example because it demonstrated the

overall use of pressure-volume relations to describe acomplex setting of altered loading and mechanical per-formance, without actually requiring mention ofchamber contractility or Emax. In the next fewsections, however, we specifically examine someof the issues and controversies regarding Emax de-termination.

Assessing Emax: definitions and issuesESPVR vs Emax. Some of the controversy surrounding

Emax has resulted from confusion over its definition.Emax [the maximal value of the time-varying elas-tance, E(t)] was originally considered to be identical tothe slope of the ESPVR. To measure Emax one had todetermine E(t) [E(t) = P(t)/(V(t) - Vo(t)] using differ-ently loaded beats synchronized in time, and obtain itsmaximal value.2 The ESPVR, on the other hand, wascomprised of the set of individual end-systolic points,one from each beat, [point of maximal P/(V - Vo)]chosen regardless of timing. The slope of this relation-ship is called the end-systolic elastance, Ees.23Why is the distinction between Ees and Emax im-

portant? In isolated hearts with isovolumetric or eject-ing beats determined over a range of preloads, Emaxand Ees are nearly identical.23 24 However, when theafterload is significantly altered among the cardiac cy-cles used for Ees or Emax determination, the two canbe very different.24 In vivo, afterload and preload areinterrelated, and Emax and Ees frequently differ (fig-ure 2). The differences likely relate to resistive andinertial influences on end-systolic pressures,25-28 aswell as changes in the time to reach end-systole (te,) asa function of load.29 These influences can often lead toan Emax that is significantly steeper, and in contrast toEes, does not fall at the corners of the pressure-volumeloops.Most experimental and clinical studies of ESPVRs

have determined Ees rather than Emax, although the

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VOLUME (ml)FIGURE 2. Disparity between Emax and Ees in situ. Data are from aclosed-chest dog, with volumes measured by conductance catheter. TheE(t) relations are shown at four time points: 10, 40, 60 (dotted lines),and 260 msec after the onset of systole (dashed line), the last being thetime of maximal E(t) or Emax. The solid line shows the ESPVR, with aslope significantly less than Emax.

latter notation is frequently used regardless. Ees is themore useful measure of systolic properties for the pur-pose of assessing pump function. While estimation ofEmax modified with internal resistances and othercomponents will continue to be a useful concept forventricular modeling, it is less likely to be of clinicalutility in characterizing systolic performance in man.ESPVR nonlinearity. Most studies performed in the

1970s revealed the ESPVR to be approximately linearover a reasonably wide range of loading conditions.This linearity was convenient as it allowed a simpledescription of the ESPVR with only two parameters: aslope (Ees) and intercept (Vo).While earlier studies often stressed the importance

of ESPVR linearity, recent evidence has shown thatthe ESPVR becomes significantly nonlinear under avariety of conditions.'4 16, 22 One example of this wasprovided by the study of Sunagawa et al.22 on theeffects of regional ischemia on ESPVR. Coronary oc-clusion produced an ESPVR convex to the volumeaxis, with a net rightward shift of the relation in thehigh-pressure range. Thus, the local slope of theESPVR varied somewhat as a function of the end-systolic pressure, making a linear model inadequatefor describing the entire relation (figure 3).Even homogeneous conditions can yield nonlinear-

ity of ESPVRs. Burkhoff et al.'4 examined ESPVRsfrom isovolumetrically contracting isolated canine leftventricles, varying contractile state over a wide rangewith the use of pharmacologic agents, lowered coro-nary perfusion, and extrasystolic premature and poten-tiated beats (figure 4, A). Within the inotropic range

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Control seemingly negative values for the volume axis inter-Distal LAD cept (Vo), which could be explained by ESPVR non-Proximal LAD linearity (figure 4, B). 15 16, 21, 31LCX Recent studies into the underlying mechanisms forLCX &LAD the myocardial force-length relation have revealed cur-

vilinear relations in a variety of preparations.33 34 Theshape and degree of curvilinearity have been found tovary depending on the Ca2+ concentration in the bath-ing solutions,34 35 and have been ascribed to lengthdependence of the affinity of myofilaments36 to Ca2+ aswell as the Ca2+ available to them.37' 38 In addition,

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FIGURE 3. Top, Isolated canine heart data showing the effects ofregional ischemia on ESPVR (from Sunagawa et al.22). With increasingextents of ischemia, the ESPVR becomes more curvilinear. Bottom,Intact canine heart data (Kass DA: unpublished data) displaying shift inESPVR with distal LAD occlusion. Over the range of data obtained, theESPVR appears shifted rightward with little change in Ees. The dashedline represents the theoretical ESPVR based on isolated heart data. LCX= left circumflex artery.

typical of isolated hearts (Ees from 3.5 to 7.0 mmHg/ml), the ESPVR was essentially linear; however, athigher contractile states, such as those accompanyingconditions in situ, ESPVRs were concave to the vol-ume axis (much lower contractile states led to convexESPVRs). Data we have recently obtained from caninehearts in situ`7 over a broad range of contractile stateshave shown results similar to those reported by Burk-hoff et al. ESPVRs were frequently concave to thevolume axis, (figure 4, B), and the degree of nonlin-earity depended on contractile state.

Experimental and clinical studies in vivo often de-termine ESPVR over a limited range of altered load-ing, with few individual pressure-volume loops (thelatter particularly true in human studies).30 32 Evenconsiderable nonlinearity may not be discerned withthese limited data. However, it is common to observe

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FIGURE 4. A, Curvilinearity ofESPVR in isolated canine hearts (datafrom Burkhoff et al. 14). Five different contractile states varied by dobut-amine or altered coronary perfusion pressure (CPP) are shown. Each setof data are fit by a quadratic equation. The shape ofESPVR nonlinearitywas dependent on contractile state. B, Curvilinearity of ESPVR in situ.Data were again obtained by conductance catheter technique. Linearapproximation was inadequate to properly describe the ESPVR and ledto a negative extrapolated Vo (dashed line), while curvilinear fit (solidline) predicted a small positive Vo.

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ESPVR nonlinearity has been predicted by models re-lating the ESPVR to myocardial stiffness-naturalstrain relations.'5 However, the ESPVR was never in-tended to directly define myocardial properties. Ratherit was thought to provide a useful measure of chambersystolic properties. Thus, in addition to reflecting thestatus of the myofilaments, the ESPVR is likely sensi-tive to the architectural arrangement of fibers, chambergeometry, left ventricular mass, and connective tissueelements. Given the complex three-dimensional geom-etry of the ventricle, it is not surprising that ESPVR isnonlinear.

It is important to recognize that linearity is a conven-ience that enables the relationship to be described insimple terms. Lack of linearity does not change thefact that the relationship defines the limits of systolicperformance for a given heart in a given state. It doesmean that investigators who wish to use the ESPVR toassess systolic properties must carefully considerwhether the model they choose to fit to the relationshipadequately describes the data in the pressure-volumerange of interest. Comparisons between ESPVRs ob-tained over very different pressure loads should becarefully interpreted, taking potential nonlinearity intoaccount.

Afterload and ESPVR. Otto Frank's experiments onpressure-volume relations of the frog ventricle, per-formed near the turn of the century, revealed a substan-tial influence of afterloading conditions on theESPVR.39 For several decades, concern about thisdependence led many investigators away from pres-sure-volume descriptions of ventricular performance.However, when pressure-volume relations were re-examined in mammalian ventricles in the 1960s and1970s, it became apparent that the degree of afterloadsensitivity was much less than that in the amphibianheart. Evidence provided from a number of differentlaboratories using a variety of experimental prepara-tions2', ` `1 demonstrated that the ESPVR was rela-tively insensitive to afterloading conditions.

Yet, it has been well appreciated that ESPVR loadinsensitivity is relative, and that substantial alterationsin afterload impedance or ejection pattern can changethe ESPVR. Suga et al.42 examined ESPVRs under awide variety of ejecting conditions, and found that ifthe end-diastolic and end-systolic volumes were keptconstant, the end-systolic pressure points clustered to-gether independent from the ejection pattern. Howev-er, if the stroke volume was widely varied, then aneffect on the end-systolic pressure-volume point wasobserved, with the end-systolic pressure being slightlylower if preceded by a large stroke volume.

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Maughan et al.'2 subsequently compared ESPVRsdetermined at multiple combinations of different arte-rial resistances, compliances, and characteristic impe-dances, each independently varied over a fourfoldrange. Each ESPVR was obtained by varying preloadat a fixed afterload impedance. These data showed thatthe slope of the ESPVR (Ees) was not significantlyaltered by changes in any of the parameters; however,the ESPVR shifted rightward by as much as 5 ml with amarked increase in resistance. Similar rightward paral-lel shifts of the ESPVR were demonstrated by Freemanet al.9 in closed-chest dogs in a study in which steady-state afterload was altered by infusion of angiotensin IIor nitroprusside, and ESPVRs were determined bytransient inferior vena caval (IVC) occlusion.

Parallel ESPVR shifts with marked changes in after-load could result in a much greater change in ESPVRslope (Ees) if the loading sequence consists of beat-to-beat changes in afterload resistance with relativelyconstant preload. With a reduction in afterload resis-tance, ejection fraction would increase, and the end-systolic pressure-volume points would fall on ESPVRsthat are shifting slightly to the right. This would resultin a steeper ESPVR than that obtained at any of theafterloads at steady state with use of preload reductionas the means of constructing the ESPVR (figure 5).Such a phenomenon has been recently demonstratedby Baan and van der Veldel° for canine ventricles insitu.

Afterload influences on ESPVR are consistent withdata from papillary muscle and whole hearts for whichgreater shortening from the same starting length orvolume results in a force-length (or pressure-volume)trajectory that falls short of the end-systolic pointachieved by isometric (or isovolumetric) contrac-tion.", 43' Some of this reduction has been attributed

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to a ventricular internal resistance,26 27 as well as short-ening deactivation. 43 Recent studies have furthersuggested potential positive effects of ejection on end-systolic pressure under certain conditions. This posi-tive effect may relate to the total integrated time spentat longer muscle lengths for ejecting beats (particularlythose at high afterloads), thereby enhancing contractilestate via length-dependent Ca2' activation.45

Since ejection history dependence is likely to influ-ence the ESPVR more if differently afterloaded beatsare used, these results support a preference for the useof preload reduction to determine the ESPVR. It re-mains possible that there are significant differencesbetween man and canine preparations regarding theinfluence of afterload on ESPVR. In this regard, sever-al clinical studies we have performed have failed todemonstrate any significant ESPVR shift or alterationbetween relations generated during IVC occlusion vsincreased afterload produced by isometric handgrip(figure 6, A). Thus, despite the potential load depend-ence, changes in pressure-volume relations due tophysiologic alterations in load have thus far appearedtiny compared with the substantial changes broughtabout by varying inotropic state (figure 6, B).

Statistical uncertainties. Assessment of ESPVR in situmay yield data limited to a relatively small range ofaltered loading, with few individual cardiac cycles.This is particularly true for patient studies, in whichmany ESPVRs first reported were based on 2 or atmost 3 beats. Even now, studies are performed inwhich the Ees parameter is based on limited data.Clearly, the statistical confidence of a given slope willbe poor if only a few points are determined over alimited range. Even a small degree of noise in thepressure or volume data can yield different estimatesfor Ees and Vo. Reliance on a given slope and interceptas if they were exact measured parameters can easilymislead us.Some investigators,' ` have expressed concern over

the statistical difficulties surrounding ESPVR charac-terization. They emphasize that as the range of alteredend-systolic pressures and volumes is fairly small withthe usually obtainable range of data in situ, the rela-tionship is difficult to characterize in a statisticallymeaningful way. While true to some extent, it is oftenthis attempt to boil down the description of an ESPVRinto two linear parameters that can obscure clear differ-ences between pressure-volume relations. Instead offixating on a slope and intercept, the actual pressure-volume data should be more frequently displayed. Asmany individual cardiac cycles as possible should beused over as wide a loading range as practically obtain-

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VOLUME (ml)FIGURE 6. A, Pressure-volume relations obtained by conductancecatheter technique in a patient. Solid loops were determined duringpreload reduction by IVC occlusion (decrease in systolic pressure withdecrease in end-diastolic volume), while dashed loops were obtainedduring the increase in afterload induced by isometric hand grip (increasein pressure with little change in end-diastolic volume). Despite the verydifferent loading patterns, ESPVRs fell along a single slightly curvilin-ear relationship. B, In contrast to the minimal alteration in ESPVR withdifferent loading patterns, the effect of an inotropic intervention is oftenquite clear. Control pressure-volume loops and ESPVR in a patient areshown by dashed lines. With intravenous dobutamine, the ESPVRshifted markedly to the left, and became much steeper (solid lines).

able. Alternative statistical approaches such as analy-sis of covariance, or comparisons of Ves measuredwithin the data range (rather than Vo) should be used.Assuming the data are not exceedingly corrupted bynoise, the end-systolic pressure-volume points, wheth-er linear or not, provide important information con-cerning the limits of systolic performance for a givenheart. The ability to reasonably distill the data into twoparameters with a high degree of statistical confidenceis certainly convenient, but not a necessity.

Contractility: alternative views. The slope of the ESPVRprovides a measure of the end-systolic chamber stiff-ness over a given loading range; however, whetherchamber stiffness is what we mean by "'contractile

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state" remains debatable. Certainly end-systolic elas-tance can be influenced by chamber geometry, againstressing that the variable assesses a chamber and not amuscle property. Several attempts have been made tonormalize Ees by muscle mass and/or cavity vol-ume. 17 18 However, while these "corrections" may beapplicable under controlled conditions, it is unlikelythat given the wide clinical spectrum of myocardialdisease, large ventricles, for example, will alwayshave lower Ees values (see example in figure 8, B).

In isolated hearts with homogeneous wall proper-ties, the end-systolic elastance is highly correlatedwith inotropic state. However, in regionally ischemic22or locally paced ventricles,46 heterogeneity of me-chanical properties or systolic timing can render thecorrelation between net chamber contractility and Eesmuch less direct. A rightward shift of ESPVR place-ment, for example, certainly indicates reduced me-chanical performance in that lower end-systolic pres-sures and stroke work are obtained for any givenstarting volume. However, the end-systolic elastancecan appear unchanged (figure 3, bottom).The potentially complex relationship between

ESPVR and contractile state is not unique to this mea-surement. Another measure of systolic chamber func-tion is the slope of the relation between the maximalvalue of the first derivative of left ventricular pressure(dP/dtmn) and end-diastolic volume.47 It is fairly simpleto predict a correlation between this slope and Ees, andit is thus not surprising that interventions that shiftESPVR without altering Ees have been found to alsoshift the dP/dtmax-end-diastolic relation without alter-ing its slope.48

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Yet another proposed measure of chamber contrac-tile state is the preload-recruitable stroke work(PRSW), or the slope of the stroke work-end-diastolicrelationship. First suggested by Sarnoff and Mitchell,49this relation was recently demonstrated in closed-chestdogs by Glower et al.5` The PRSW is attractive forseveral reasons. It is quite linear over a wide range ofphysiologic conditions. The dependent variable(stroke work) varies more with changes in end-diastol-ic volume than end-systolic pressure does with end-systolic volume; therefore, from a statistical stand-point, this relation may be easier to quantify in situ.Despite the clear potential for afterload sensitivity(stroke work declines to zero at both no load and infi-nite load), PRSW is quite stable over a range of phys-iologic afterloads.

However, PRSW does not separate systolic and dia-stolic properties, but rather integrates them. In animalstudies, in which the greatest degree of testing ofPRSW has been done, EDPVRs are generally so flatthat this interdependence is of little significance. How-ever, in patients with chronic hypertrophy in whomdiastolic properties may be very abnormal, the inter-play between systolic and diastolic properties may ren-der PRSW difficult to interpret as a pure systolic in-dex. In addition, stroke work is at some levelejection-history dependent, and some care should betaken to derive PRSW from cardiac cycles under dif-ferent preloads but with relatively stable ejectionpatterns. We emphasize that all of the indexes dis-cussed above are easily obtainable from the same set ofpressure-volume data used in assessing the ESPVR(figure 7).

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The pressure-volume diagram: a broader view. Thus farwe have concentrated on several of the issues andcontroversies surrounding ESPVR and Ees as assess-ments of ventricular contractile state. However, thestrengths of the pressure-volume description of ven-tricular performance do not depend on a complete reso-lution of these issues. The preoccupation with makingEes the ultimate index of contractility as sort of a "holygrail" is unfortunate. What is important, however, isthat the steepness of an ESPVR combined with theEDPVR enables the clinician to appreciate the influ-ence of afterload changes on systolic pressure andstroke volume, or the dependence of both variables onchanges in ventricular filling. Focusing on the entirepressure-volume description, particularly on the inter-relation between diastolic and systolic properties, rath-er than on the determination of Ees alone, is muchmore likely to provide clinically useful insights intocardiac function and the outcome of drug therapy.Two clinical examples drawn from recent patient

studies are shown to demonstrate this utility (figure 8).Left ventricular pressure-volume relationships wereobtained by use of a multielectrode conductance cath-eter system, while loading was again rapidly (and re-versibly) altered by transient IVC occlusion.

Both patients had a 1 year history of dyspnea onexertion, without any coronary or valvular disease.Cardiac catheterization confirmed normal coronaryarteries, and ventriculography demonstrated diffusehypokinesis with cavity enlargement. Patient A hadnormal systolic pressures (100 mm Hg), while patient

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B had high pressures (180 mm Hg). Thus, patient Bmight have been anticipated to respond more to vasodi-lator therapy (with an improvement in stroke volume)than patient A; however, the exact opposite provedtrue. Patient A had a very shallow ESPVR, and thusthe reduction in afterload (solid lines) would have sub-stantially improved forward output (by 30% in thiscase). However, the left ventricle in patient B, whiledilated, had a very steep ESPVR, and similar afterloadreduction would not have substantially improvedstroke volume ( + 10% at most). Furthermore, hewould be unlikely to benefit from inotropic agents,since his ESPVR was already quite steep, while patientA might benefit a great deal. This was confirmed byadministering dobutamine to patient A (figure 9),which produced a marked leftward shift and steepen-ing of the ESPVR, increasing stroke volume at anygiven preload. Neither patient had significant preloadreserve, because both were operating at end-diastolicpressures of 20 to 22 mm Hg. Thus, simply by generat-ing the diastolic and systolic pressure-volume rela-tions, a much more precise characterization of cardiacperformance was obtained, and pharmacologic therapywas better targeted.

In this perspective, we have tried to review the stat-us of the ESPVR and pressure-volume relations for thecharacterization of ventricular performance. Many ofthe current concerns regarding ESPVR primarily im-pact on attempts to reduce pressure-volume data to asingle number, Ees, as an index of contractility. Ratherthan dwell on these issues, we believe the focus should

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VOLUME (ml) VOLUME (ml)FIGURE 8. Example of use of pressure-volume relations and ESPVR to predict response to vasodilator therapy in two patientswith dilated cardiomyopathy. Patient A demonstrated a shallow ESPVR slope (1.3 mm Hg/ml), and a 35% reduction in afterloadresistance (solid lines) predicted a near 30% increase in stroke volume (indicated by solid brackets above the loops), with littlechange in systolic pressure. Patient B, on the other hand, displayed a very steep ESPVR (6.9 mm Hg/ml), and similar afterloadreduction predicted a less than 10% change in stroke volume, with a much greater effect on systolic pressures.

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be reoriented toward use of the entire pressure-volumedescription for its many strengths: (1) that it provides acharacterization of pump performance that allowsloading factors to be reasonably separated from ven-tricular properties, (2) that it identifies both diastolicand systolic properties in common terms and thereforehelps clarify their interrelationship, and (3) that it pro-vides a description of coupling between ventricle andvasculature, which enables predictions of stroke vol-ume and stroke work response to various loading inter-ventions.

We thank Dr. Kiichi Sagawa for his thoughtful insights,suggestions, and encouragement in the writing of this perspec-tive.

References1. Katz A: Influence of altered inotropy and lusitropy on ventricular

pressure-volume loops. J Am Coll Cardiol 11: 438, 19882. Suga H, Sagawa K: Instantaneous pressure-volume relationships

and their ratio in the excised, supported canine left ventricle. CircRes 35: 117, 1974

3. Suga H, Sagawa K, Shoukas AA: Load independence of the instan-taneous pressure-volume ratio of the canine left ventricle and ef-fects of epinephrine and heart rate on the ratio. Circ Res 32: 314,1973

4. Sagawa K, Suga H, Shoukas AA, Bakalar KM: End-systolic pres-sure-volume ratio: A new index of contractility. Am J Cardiol 40:748, 1979

5. Suga H, Hayashi T, Shirahata M: Ventricular systolic pressurevolume area as predictor of cardiac oxygen consumption. Am JPhysiol 240(Heart Circ Physiol 9) H320, 1981

6. Suga H, Hayashi T, Suehiro S, Hisano R, Sirahata M, Ninomiya I:Equal oxygen consumption rates of isovolumic and ejecting con-tractions with equal systolic pressure volume areas in canine leftventricle. Circ Res 49: 1082, 1981

7. Sunagawa K, Maughan WL, BurkhoffD, Sagawa K: Left ventricu-lar interaction with arterial load studied in isolated canine ventricle.Am J Physiol 245(Heart Circ Physiol 14): H773, 1983

8. Sunagawa K, Sagawa K, Maughan WL: Ventricular interactionwith the vascular system in terms of pressure-volume relationships.

In Yin FCP, editor: Ventriculo-vascular coupling: clinical, physio-logic, and engineering aspects. 1987, New York, Springer Verlag,pp 210-239

9. Freeman GL, Little WC, O'Rourke RA: The effect of vasoactiveagents on the left ventricular end-systolic pressure-volume relationin closed-chest dogs. Circulation 74: 1107, 1986

10. Baan J, van der Velde E: Sensitivity of left ventricular end-systolicpressure-volume relation to the type of loading intervention indogs. Circ Res (in press)

11. Spratt JA, Tyson GS, Glower DD, David JW, Muhlbaier LH,Olsen CO, and Rankin JS: The end-systolic pressure-volume rela-tionship in conscious dogs. Circulation 75: 1295, 1987

12. Maughan WL, Sunagawa K, Burkhoff D, Sagawa K: Effect ofarterial impedance changes on the end-systolic pressure-volumerelation. Circ Res 54: 595, 1984

13. Crottogini AJ, Willshaw P, Barra JG, Armentano R, Eng B, Fi-scher C, Pichel RH: Inconsistency of the slope and the volumeintercept of the end-systolic pressure-volume relationship as indi-vidual indexes of inotropic state in conscious dogs: presentation ofan index combining both variables. Circulation 76: 1115, 1987

14. Burkhoff D, Sugiura S, Yue DT, Sagawa K: Contractility-depen-dent curvilinearity of end-systolic pressure-volume relations. Am JPhysiol 252(Heart Circ Physiol 21): H1218, 1987

15. Mirsky I, Tajimi T, Peterson KL: The development of the entireend-systolic pressure-volume and ejection-fraction-afterload rela-tions: a new concept of systolic myocardial stiffness. Circulation76: 343, 1987

16. Kass DA, Beyar R, Heard M, Maughan WL, Sagawa K: Curvilin-ear ESPVR in situ can yield negative estimated volume intercept(Vo) and Vo change with inotropic state. Circulation 76(suppl IV):IV-428, 1987 (abst)

17. Suga H, Hisano R, Goto Y, Hamada 0: Normalization of end-systolic pressure-volume relation and Emax of different sizedhearts. Jpn Circ J 48: 136, 1984

18. Belcher P, Boerboom LE, Olinger GN: Standardization of end-systolic pressure-volume relation in the dog. Am J Physiol249(Heart Circ Physiol 18): H547, 1985

19. Hanson DE, Cahill PD, DeCampli WM, Harrison DC, Derby GC,Mitchell RS, Miller DC: Valvular-ventricular interaction: impor-tance of the mitral apparatus in canine left ventricular systolicperformance. Circulation 73: 1310, 1986

20. Kass DA, Yamazaki T, Burkhoff D, Maughan WL, Sagawa K:Determination of left ventricular end-systolic pressure-volume re-lationships by the conductance (volume) catheter technique. Circu-lation 73: 586, 1986

21. Kass DA, Midei M, Graves W, Brinker JA, Maughan WL: Use of aconductance (Volume) catheter and inferior vena caval occlusionfor rapid determination of pressure-volume relationships in man.Cathet Cardiovasc Diagn (in press)

22. Sunagawa K, Maughan WL, Sagawa K: Effect of regional ische-mia on the left ventricular end-systolic pressure-volume relation-ship of isolated canine hearts. Circ Res 52: 170, 1983

23. Sagawa K, Sunagawa K, Maughan WL: Ventricular end-systolicpressure-volume relations. In Levine HJ, Gaasch WH, editors: Theventricle. Boston, 1985, Martinus Nijhoff, pp 79-82

24. Maughan WL, Sunagawa K, Hunter WC, Sagawa K: Instantaneousbut not end-systolic pressure-volume relationship (ESPVR) de-pends on afterload. Fed Proc 44: 1017, 1985 (abst)

25. Hunter WC, Janicki JS, Weber KT, Noordergraaf A: Systolic me-chanical properties of the LV: effects of volume and contractilestate. Circ Res 52: 319, 1983

26. Schroff SG, Janicki JS, Weber KT: Evidence and quantification ofleft ventricular systolic resistance. Am J Physiol 249(Heart CircPhysiol 18): H353, 1985

27. Campbell KB, Ringo JA, Knowlen GG, Kirkpatrick RD, SchmidtSL: Validation of optimal elastance-resistance left ventricularpump models. Am J Physiol 251(Heart Circ Physiol 20): H382,1986

28. Little WC, Freeman GL: Description of LV pressure-volume rela-tions by time-varying elastance and source resistance. Am J Phys-iol 253(Heart Circ Physiol 22): H83, 1987

29. Maughan WL, Kass DA, Heard M, Sagawa K: Erroneous estima-tion of the end-systolic pressure-volume relationship from time-varying elastance in patients. Circulation 76(suppl IV): IV-545,1987

Vol. 77, No. 6, June 1988 1211

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KASS and MAUGHAN

30. Grossman W, Braunwald E, Mann T, McLaurin LP, Green L:Contractile state of the left ventricle in man as evaluated from end-systolic pressure-volume relations. Circulation 56: 845, 1977

31. Mehmel HC, Stockinsk B, Ruffnamm K, Olshuausen KV, SchulerG, Kobler W: The linearity of the end-systolic pressure-volumerelationship in man and its sensitivity for assessment of left ventric-ular function. Circulation 63: 1216, 1981

32. McKay RG, Aroesty JM, Heller GV, Royal HD, Warren WE,Grossman W: Assessment of the end-systolic pressure-volume re-lationship in human beings with the use of a time varying elastancemodel. Circulation 74: 97, 1986

33. Allen DG, Jewell BR, Murray JW: The contribution of activationprocesses to the length-tension relation of cardiac muscle. Nature248: 606, 1974

34. Kentish JC, ter Keurs HEDJ, Ricciardi L, Bucx JJJ, Nobel MIM:Comparison between sarcomere length-force relations of intact andskinned trabeculae from rat right ventricle. Circ Res 58: 755, 1986

35. Lakatta EG, Jewell BR: length-dependent activation: its effect onthe length-tension relation in cat ventricular muscle. Circ Res 40:251, 1977

36. Hibberd MG, Jewell BR: Calcium and length dependent forceproduction in rat ventricular muscle. J Physiol 329: 527, 1982

37. Nichols CG: The influence of 'diastolic' length on the contractilityof isolated cat papillary muscle. J Physiol 361: 269, 1985

38. Allen DG, Kurihara S: Calcium transients in mammalian ventricu-lar muscle. Eur Heart J 1(suppl A): 5, 1980

39. Frank 0: Zur Dynamik des Herzmuskels. Z Biol 32: 370, 189540. Monroe RG, French GN: Left ventricular pressure-volume rela-

tionships and myocardial oxygen consumption in the isolated heart.Circ Res 9: 362, 1961

41. Weber KT, Janicki JS, Hefner LL: Left ventricular force-length

relations of isovolumic and ejecting contractions. Am J Physiol231: 337, 1976

42. Suga H, Kitabatake A, Sagawa K: End-systolic pressure deter-mines stroke volume from fixed end-diastolic volume in the isolat-ed canine left ventricle under a constant contractile state. Circ Res44: 238, 1979

43. Suga H, Sagawa K, Demer L: Determinants of instantaneous pres-sure in canine left ventricle: time and volume specification. CircRes 46: 256, 1980

44. Taylor R: Active length-tension relations compared in isometric,afterloaded and isotonic contractions of cat papillary muscles: theirdependence on inotropic state. Circ Res 26: 279, 1980

45. Hunter WC, Burkhoff D, Oikawa R, Sagawa K: Evidence for amechanisms opposing deactivation during ejection in canine leftventricles. Fed Proc 44: 1736, 1985 (abst)

46. Park RC, Little WC, O'Rourke RA: Effect of alteration of leftventricular activation sequence on the left ventricular end-systolicpressure-volume relation in closed-chest dogs. Circ Res 57: 706,1985

47. Little WC: The left ventricular dP/dtmax-end-diastolic volume re-lation in closed-chest dogs. Circ Res 56: 808, 1985

48. Little WC, Park RC, Freeman GL: Effects of regional ischemia andventricular pacing on LV dP/dt..ax-end-diastolic volume relation.Am J Physiol 252(Heart Circ Physiol 21): H993, 1987

49. Sarnoff SJ, Mitchell JH: The regulation of the performance of theheart. Am J Med 30: 747, 1961

50. Glower DD, Spratt JA, Snow ND, Kabas JS, Davis JW, Olsen CO,Tyson GS, Sabiston DC, Rankin JS: Linearity of the Frank-Starlingrelationship in the intact heart: the concept of preload recruitablestroke work. Circulation 71: 994, 1985

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