Journal of Clinical InvestigationVol. 43, No. 7, 1964

Contractile Element Work: A Major Determinant of Myo-cardial Oxygen Consumption *

NAPHTALI A. BRITMAN t AND HERBERTJ. LEVINE(From the Pratt Clinic-New England Center Hospital and the Department of Medicine,

Tufts University School of Medicine, Boston, Mass.)

The study of the determinants of myocardialoxygen consumption during the past fifty yearshas formed an interesting historical sequence.In 1927 Starling and Visscher proposed that theenergy requirement of the heart was determinedby its initial fiber length (1), and this observationwas confirmed by others (2, 3). Rhode, on theother hand, stated that only ventricular pressureand heart rate determined the oxygen consump-tion of the heart (4). In an effort to resolve theimportance of both fiber length and pressuregenerated, stroke work was examined but foundby a number of workers to correlate poorly withoxygen consumption (1-3, 5-8). As early as1915, Evans and Matsuoka suggested that myo-cardial wall tension may be the major determin-ant of myocardial oxygen consumption (5).This thesis received some support from the workof Fischer, who found that oxygen consumptionvaried directly with isometric tension in isolatedskeletal muscle twitches (9).

In 1958 Sarnoff and associates (7) described aremarkably constant relationship between oxy-gen consumption and the area under the systolicportion of the arterial pressure curve (tension-time index). This measure of pressure and time(hereafter referred to as pressure-time perminute), however, did not bear a constant rela-tion to oxygen consumption during exercise innormal human subjects (10). As changes inventricular dimensions during exercise had beenreported (11), it was suggested that changes inradius and therefore of wall tension may havebeen responsible for the observed discrepancybetween pressure-time per minute and oxygenconsumption (10). Subsequently, oxygen con-sumption has been related to the product of meanmyocardial tensile force and the systolic ejection

* Submitted for publication December 4, 1963; acceptedFebruary 27, 1964.

This work was supported by U. S. Public Health Serviceresearch grant H-7139 from the National Heart Institute.

t Postdoctoral fellow of the National Heart Institute,U. S. Public Health Service.

period (force-time per minute). Despite thisconsideration, the relationship between force-time per minute and oxygen consumption was notalways found to be linear (12).

In terms of basic muscle mechanics, however,the concept of force-time per minute, like theother indexes mentioned, fails to consider thetotal contractile effort of the heart. It has longbeen considered that the contractile effort ofmuscle may be manifested either as fiber short-ening or as force generation brought about bythe stretching of a series elastic component (13,14). Since the energy requirement of the musclemust be governed by the contractile element it-self, a reasonable assumption is that both mani-festations of the contractile process should berepresented in a consideration of muscle ener-getics.

The purpose of this paper is to describe amethod for the calculation of total contractileelement work in the intact dog heart. Wefoundthat over a wide range of altered hemodynamics,contractile element work (CEW) bears a closerrelation to myocardial oxygen consumption thandoes the pressure-time per minute, force-time perminute, or left ventricular work.

MethodsMethods and experimental design. Thirty-four studies

were carried out in 23 mongrel dogs weighing from 13 to 24kg, anesthetized with either sodium pentobarbital, 25 mgper kg, with or without morphine sulfate premedication,3 mg per kg, or chloralose, 50 to 70 mg per kg, with mor-phine sulfate premedication. The details of the experi-mental design have been presented in the preceding paper(15). Obstruction of the proximal ascending aorta wasproduced by surgical coarctation (umbilical tape tourni-quet) in 8 animals and by inflation of an intra-aortic balloonin the remainder. The resultant gradient was utilized toderive instantaneous aortic flow rate (vide infra). Cathe-ters were placed in the left ventricle, aorta, pulmonaryartery, and great cardiac vein. Coronary flow was deter-mined by the nitrous oxide desaturation method (16).Systemic arterial, pulmonary arterial, and coronary venousoxygen contents were measured by the method of VanSlyke and Neill (17).

1397

NAPHTALI A. BRITMAN AND HERBERTJ. LEVINE

Left ventricular volume was determined by the thermaldilution technic (18). The error and reproducibility ofthis method have been presented (15).

Each study consisted of the simultaneous measurementof cardiac output, left ventricular and aortic pressures,heart rate, left ventricular volume and left ventricularcoronary blood flow, and oxygen extraction. Alterationsof the hemodynamic state were achieved by changing thedegree of aortic obstruction, volume loading by therapid infusion of 500 to 1,500 ml of whole blood or inotro-pism induced by the infusion of isoproterenol in a dose of1 to 5 ,Ag per minute.

At the conclusion of each experiment, the left ventriclewith the interventricular septum was dissected from theremainder of the heart and was weighed.

Definitions and calculations. All terms and measure-ments refer to the left ventricle. Stroke volume was de-rived from the cardiac output and heart rate, and with theratio of end-diastolic volume to end-systolic volume ob-tained from the thermal dilution curve, the end-diastolicchamber volume was calculated (18). Instantaneousaortic flow rate was derived as described in the precedingpaper (15). The instantaneous ventricular volume (V)at each 0.02-second interval during systole was derived byintegration of the flow rate curve up to that time and bysubtraction of this integral (the volume ejected) from theend-diastolic volume. The ventricle was assumed to bespherical, and the instantaneous radius, r, was obtainedfrom the formula V = 47rr3/3.

The circumferential fiber shortening rate (CFSR), de-fined as the rate of fiber shortening at the equator of asphere, was calculated at each 0.02-second interval duringsystole, as flow rate/2r2 (15) and is expressed as centimetersper second. Myocardial tensile force (F) was calculatedat similar intervals as F = irr2P', where F = total tangen-tial myocardial force in dynes, r = internal radius of theleft ventricle in centimeters, and P = intraventricularpressure in dynes per cm2. The rate of change of F(dF/dt)was derived at each 0.02-second interval by measuring theslope of the force-time plot.

In our analysis of the muscle mechanics of the heart, thethree-component model of Hill (13, 14) has been employed(see Figure 2, reference 15). Since it is apparent from thismodel that the contractile effort of the heart may be ex-pressed as either shortening of the muscle fiber or length-ening of the series elastic component (SEC), at any oneinstant the shortening velocity of the contractile element(CE) must be equal to the sum of the fiber shortening rate(CFSR) plus the lengthening velocity of the SEC (dl/dt).The latter, in turn, is responsible for force generation withinthe fiber and is related to the rate of force development

I From the Laplace equation, surface tension per unitlength = rP/2. Multiplying this by the total length alongwhich tension exists (27rr), total tension = (27rr) (rP/2)or 7rr2P. Hefner, Sheffield, Cobbs, and Klip have foundthis force to vary directly with the measured force neces-sary to keep together the two edges of a slit in the ventri-cular wall (19).

(dF/dt) by the stiffness of the SEC (dF/dl) as follows:d F/dt = (d F/dl) (dl/dt) (13, 14).

To derive dl/dt, both dF/dt and dF/dl must be known.Although dF/dt may be measured in these experiments asdescribed above, dF/dl must be estimated from in vitroexperiments of mammalian heart muscle. In the isolatedcat papillary muscle, Sonnenblick found that dF/dl in-creased linearly with increasing force and was independentof stimulation frequency, initial fiber length, and inotropicinterventions such as norepinephrine or calcium (20, 21).To estimate the dF/dl of the dog's left ventricle, the rela-tionship between dF/dl and F in the cat papillary musclewas normalized for unit dimensions and extrapolated to thespecific dimensions of each dog's left ventricle. Thisformula, which was derived in the preceding paper (15), isas follows: dF/dl (dynes per centimeter) = [28.8 X F(dynes)]/[10 (centimeters)] + [241,000 (dynes per centi-meter) X A, (cm2)]/[10 (centimeters)], where 10, themuscle length, was obtained as 27rr, where r0 is the smallestend-diastolic chamber radius measured in a given dog, andA0, the cross-sectional area of muscle, was derived as 27rrot,where t is the wall thickness at that end-diastolic chambersize. The smallest end-diastolic chamber size was used toapproximate the resting dimensions of the muscle. Wallthickness, t, was derived by the subtraction of r0 from theradius of a sphere whose volume was equal to the smallestend-diastolic chamber volume plus the left ventricularmuscle volume in milliliters (left ventricular weight ingrams).

Using the measured dF/dt and the above approximationof dF/dl, a value of dl/dt was obtained at each 0.02-secondinterval of systole. This dl/dt was then added to the CFSRto yield the contractile element velocity (Vce) at eachinterval.

Instantaneous shortening power in dyne-centimeters persecond was derived as the product of force (dynes) andshortening velocity (centimeters per second). Thus,shortening power of the muscle fiber was calculated as FX CFSR, whereas shortening power of the contractileelement was calculated as F X Vce. These shorteningpowers were then plotted against time for one completesystole. This plot for a typical experiment is shown inFigure 1. Since the area under a power-time curve repre-sents work done, the area under the fiber shortening powercurve (area B + area C) equals the fiber shortening work(FSWV) per beat, and the area under the contractile ele-ment power curve (area A + area B) equals the contractileelement work (CEW) per beat.

Fiber shortening work per minute was derived by multi-plying the heart rate times the directly planimetered areaunder the fiber shortening power curve (B + C) and isexpressed as dyne-centimeters per minute per 100 g leftventricle (LV).

Contractile element work per beat was derived as thesumi of area A + area B. Area B was obtained by directplanimetry, but because of the difficulties in accuratelydetermining the Vce during the isometric period (15), areaA, which represents the work done by the CE in stretchingin the SEC to peak force, was derived by mathematicalintegration as follows:

1398

CONTRACTILEELEMENTWORK

SHORTENINGPOWER

106 dyne-cm/sec

40V

log 3/4/63 (Ao.2)

SHORTENINGPOWEROF.

Muscle FiberContractile Element

301-

20-

10-

0 0 .02 .60 II4 ,.16_-.03 0 .02 .04 .06 .08 .10 .12 .14 .16

x-ISO/MTfRIC ok EMONo iTIME IN SECONDS

FIG. 1. TIME COURSEOF THE SHORTENINGPOWEROF THE CONTRACTILEELEMENTANDTHEMUSCLEFIBER. Contractile element shortening power (opencircles) and fiber shortening power (solid circles) are plotted throughout thecourse of one systole. The areas under these curves represent work (work= f power X dt). These two curves cross at the point where peak force isachieved, since at that point, dF/dt, and therefore dl/dt, are equal to zero, andthus fiber shortening velocity is equal to the contractile element velocity. Itfollows that the respective shortening powers would also be equal at that point.

From the onset of the isometric period until the point where the powercurves cross, the power of the contractile element exceeds that of the fiber byan amount used for lengthening of the SEC. Thus, area A represents the workdone by the contractile element in stretching the SECto peak force. Beyondthe point of crossing of the curves, the CEpower is less than that of fiber short-ening, since the recoiling SEC is now assisting the CE in shortening of thefiber. Beyond the point where the CE power falls to zero, the CE begins tolengthen, and the remaining fiber shortening is entirely performed by therecoiling SEC. Thus, area C represents the work done by the recoiling SECin shortening the fiber, whereas area B represents that portion of fiber short-ening work performed directly by the contractile element. Area A + area Brepresent the total work done by the contractile element, and area B + area Cequal the total fiber shortening work performed.

In stretching a spring from initial length 1i and force Fi,to peak length 4, and force Fp, work done = Edi. Forthe SEC, dF/dl = S X F + (dF/dl)0, where S = 28.8/lo(vide supra). Because the stiffness of the SECat zero load(dE/di). constitutes a small contribution to total dF/dl(except at very low force), it was ignored in this derivation.Thus dl = dF/(S X F), and the expression for work donebecomes

f FdF or IfdFpJ(F" S X F o S J F

By integration, work = I/S (F, - F,). Fi is equal to thefraction of the end-diastolic force at the onset of isometriccontraction borne by the SEC. Since most of the end-diastolic force is thought to be borne by the parallel elasticcomponent rather than by the SEC, and further, since thetotal end-diastolic force is small compared with the peakforce, F1 was ignored. Thus, the work performed instretching the SEC (area A) was calculated as F,/S.

Contractile element work (CEW) per minute was ob-tained by multiplying the heart rate times the CEWper

1399

NAPHTALI A. BRITMAN AND HERBERTJ. LEVINE

beat as derived above and is expressed as dyne-centinmetersper minute per 100 g LV.

Left ventricular work was derived as the product of LVsystolic mean pressure and cardiac output and is expressedas kilogram-meters per minute per 100 g LV. Mechanicalefficiency in per cent was obtained as the ratio of left ventri-cular work to the energy equivalent (2.06 kg-in per milli-liter 02) of left ventricular oxygen consumption minus 3 mlper minute per 100 g (the oxygen consumption of the beat-ing, nonworking heart) (22).

Pressure-time per minute (PTM) was calculated as theproduct of left ventricular systolic mean pressure and sys-tolic ejection period per minute and is expressed as mmHg-seconds per minute.

Force-time per minute (FTM) was derived by multi-plying heart rate times the directly planimetered areaunder the force-time curve during the ejection period of asingle systole and is expressed as dyne-seconds per minuteper 100 g LV.

Left ventricular oxygen consumption (LVqO2) was cal-culated as the product of the myocardial a-v oxygen differ-ence and the left ventricular coronary flow per 100 g and isexpressed as milliliters per minute per 100 g LV.

Results

Relationship of pressure-time per minute to leftventricular oxygen consumption. The relation-ship between PTMand LVqO2, shown in Figure2, has an r of 0.74 (p < 0.001). The regressionline for these points has a negative y intercept(-2.22 ml). When only those studies with aqO2 < 15 ml per minute per 100 g were analyzed(18 studies), an r of 0.81 (p < 0.001) was ob-tained, and the regression line for these pointshas a slope significantly different (p < 0.001)from the slope of the previous line, with a positivey intercept of 4.15 ml. Analysis of the remain-ing 16 studies with qO2 > 15 ml yielded nostatistically significant correlation (p > 0.10).

Relationship of force-time per minute to leftventricular oxygen consumption. The relation-ship of FTMand LVqO2, shown in Figure 3, hasan r of 0.74 (p < 0.001). The y intercept of thisregression line is +5.25 ml. In this case, nosignificant correlation was found for either thesubgroup with qO2 < 15 ml (p > 0.05) or thesubgroup with qO2 > 15 ml (p > 0.10). Four ofthe 5 isoproterenol studies lie above the regres-sion line.

Relationship of fiber shortening work per minuteto left ventricular oxygen consumption. Figure4 shows the relationship of FSWto LVqO2 (r=0.74; p < 0.001). The y intercept of this re-gression line is +6.75 ml. In this case, analysisof the population with qO2 < 15 ml yielded anr of 0.68 (0.001 < p < 0.01), but the slope was

not significantly different (p > 0.10). Thepoints with high qO2 yielded no significant cor-relation (p > 0.10). Four of the 5 isoproterenolpoints lie below the regression line.

Relationship of contractile element work to leftventricular oxygen consumption. Figure 5 showsthe relationship of CEWto LVqO2. The r forthis relationship is 0.91 (p < 0.001) and issignificantly better than each of the previouscorrelations (0.01 < p < 0.05). The y inter-cept of this regression line is +4.33 ml. Whenthe analysis was made of the point with qO2 > 15ml, a significant correlation was found (r = 0.74;p = 0.001). This is in contrast to the absenceof such a correlation in the case of the three previ-ous determinants. Analysis of those points withqO2 < 15 yielded an r of 0.77 (p < 0.001) and aslope not significantly different from that of theentire group. Despite the improved correlationof qO2 with CEW,4 of the 5 isoproterenol pointslie below the regression line.

Relationship of fiber shortening work to leftventricular work. Figure 6 shows the linear re-lationship between FSWper minute per 100 gLV and LV work per minute per 100 g LV. Thislinearity can be predicted from theoretical con-siderations. Per beat, FSW= f F X CFSRdt.As F = 7rr2 X P and CFSR= (d V/dt)/2r2, thisbecomes FSW= ir/2 fP X [(d V/dt)dt], or FSW= 7r/2 P dV. Since Pd V = stroke work, LVwork per minute = (2/7r) FSW per minute.Introducing the units conversion factor (0.0102kg-m per 106 dyne-cm), LV work (kilogram-me-ters per minute) = 0.00649 FSW(106 dyne-cm perminute). This shows excellent agreement withthe slope of the regression equation for the LV

2 The reason for the 2/r factor lies in the tacit assump-tion that the spheric muscular shell of radius r is equiva-lent to a sheet of muscle of width 2irr and length 27rr, and inthe fact that shortening in only one dimension was con-sidered. However, since the surface area of a sphere is47rr2, a more reasonable representation of the muscularshell would be a sheet of muscle of dimensions 2 fi rX 2 (fir r). From the law of Laplace, surface tension perunit length is given by (r X P)/2, where P is the intra-cavitary pressure. Thus the total tension (force) in onedirection would be (2 by r) X (rP/2) or 4Jw r2 X P. Ifwe now let the sphere contract so that the radius changesan increment dr and the volume changes d V, the side of theabove considered square would shorten a distance of 2 +/rdr, and the work done in one dimension would be (Air r2X P) X (2 fir dr) or P X 27rr2 dr. Since shorteningclearly occurs in two dimensions, the total true fiber short-ening work is P X 4 7rr2dr. Since, by differentiation,dV = 4xwr2dr, the total true fiber shortening work canreadily be seen to equal the pressure volume work (p dV).

1400

CONTRACTILEELEMENTWORK

PRESSURETIME PER MINUTEmmHg-nc/rrin

FIG. 2. RELATIONSHIP OF PRESSURE-TIME PER MINUTE TO LEFT VENTRICULAROXYGENCONSUMPTION(LVqO2). Two regression lines are shown, one obtained fromall points and one from only those points with qO2 < 15 ml per minute per 100 g(see text).-

-30 0.z74/Vj0.i17x*f5.25 0 /

25LVq02(Ecc/min /lOOm . E

20 -

15-.

10-* Aortic Obstruction Alone

ok ®>) Isoproterenol5 El Volume Loading

50 100 150 20CFORCE-TIME PER MINUTE

I6dyn-ssc/rmin/lOOgm LV.FIG. 3. RELATIONSHIP OF FORCE-TIME PER MINUTE

TO LV OXYGENCONSUMPTION.

1401

1402 NAPHTALI A. BRITMAN AND HERBERTJ. LEVINE

30 - r~o .74- yz O.O/57xt6.75

25_LVq02

cc/min /100gm20 _-

20~~~~~~~~

' 5

10 _ r/' ; * * * Aortic Obstruction Alone. Isoproterenol

5 E1 Volume Looding

, I I I , I , I . I *

200 400 600 800 1000 l1O0 1400FIBER SHORTENINGWORKPER MINUTE

106 dyne-cm/min/1OOgmL.V.

FIG. 4. RELATIONSHIP OF FIBER SHORTENINGWORKTO LV OXYGENCONSUMPTION.

rm 0.9/ 4Yz 0.0139xf 43355

25

LVqO2 @cc/min/100 gm E

CONTRACTILE ELEMENTWORKPER MINUTEI dyne-cm /min /O0 gm LV.

FIG. 5. RELATIONSHIP OF CONTRACTILEELEMENTWORK(CEW) TO LV OXYGENCONSUMPTION.

CONTRACTILEELEMENTWORK

FIBER SHORTENINGWORKlog dyne-cm /min /100 gm L.V.

FIG. 6. RELATIONSHIP OF LEFT VENTRICULARWORKTO FIBERSHORTENINGWORK(FSW).

work-FSW plot. Thus, the FSW-qO2 plot(Figure 4) reflects the relation of LV work tooxygen consumption, and the deviations of thepoints from the regression line represent varia-tions in mechanical efficiency.

Contractile element work index. Because thederivation of CEWinvolves laborious calcula-tions and further requires the measurement ofinstantaneous flow, an attempt was made toderive an index of CEW, which could be cal-culated from the readily obtainable parametersof heart rate (HR), stroke volume (SV), leftventricular systolic mean pressure (P), and leftventricular mean volume ('V). The last term isdefined as the volume when half of the strokevolume is ejected. The equation for this con--tractile element work index is as follows: CEWindex = [HR][P][SV + [V/9.6].

This index yielded an excellent linear correla-tion with the calculated CEW(r - 0.995), al-though the correlation between this index and thetrue CEWhas been tested only under the specificconditions of these experiments. This index wasderived in the following manner: CEWper beat= (FI/S) (area A, Figure 1) + FSW(area B +

area C) minus the work returned by the recoilingSEC (area C). Since area C is relatively smalland a relatively constant fraction of area A, anapproximation of A-C was made by using meanforce instead of peak force. Since S = 28.8/lo,lo = 27rr,, FSW= 7r/2(P X SV), and F is ap-proximately equal to 7rf2 x P, then CEWindex= [2'ir2 f2 ro P/28.81 + [r P (SV)/2]. Makingthe further approximation that ro = f and sinceV = 47rt3/3, this expression reduces to CEWindex = [3irVP]/2 (28.8)J + P SV/2 or [ErP/2][SV + (3 V/28.8)j per beat. Since this is anindex, the constant 7r/2 can be ignored, and thefinal form is P [SV + (V/9.6)] per beat or[HR][P] {SV + (V/9.6)] per minute.

Examination of this index shows that it iscomposed of two basic terms: 1) P X SV, repre-senting external stroke work, and 2) P X V7,representing internal pressure generation work.This index resembles in its general form a re-cently described expression for the total energyinvolved in cardiac contraction (23). This ex-pression was given as the sum of E1 and E2, whereE1 is the product of mean isometric pressure andleft ventricular end-diastolic volume,- and E2 is

LVWORK8Kg-M/min

per100 gm L.V.

6

1403

NAPHTALI A. BRITMAN ANDHERBERTJ. LEVINE

the conventional stroke work P X SV. Thissum of E1 and E2 was reported to correlate wellwith left ventricular oxygen consumption.

Discussion

Determinants of myocardial q02. That LVwork correlates poorly with myocardial oxygenconsumption has long been appreciated. (1-3,5-8). Our study again confirmed this observa-tion by the fact that fiber shortening work, whichis proportional to LV work, showed only a faircorrelation with LVqO2. Although other work-ers have demonstrated a remarkably constantrelationship between pressure-time per minuteand LVqO2 in the dog heart (7, 9, 24), in ourexperiments this relationship was observed tobe no better than that found for LV work. Theexplanation for this is not entirely clear, althoughcertain differences in experimental design may berelevant. Weattempted to produce wide vari-ations in end-diastolic volume and thus achievechanges in myocardial wall force that would notbe reflected in the PTMmeasurement. Similarlythe isoproterenol experiments were designed toproduce a high ratio of FSW/CEWin order thatthe energy cost of fiber shortening might beexamined more clearly.

Thus, although a good correlation betweenPTMand qO2 was observed at low LVqO2 values,no significant correlation was observed in thehigher range (LVqO2 > 15 ml). When force-time per minute was examined, again the cor-relation was not improved. In this case, how-ever, the spread was generalized, and no signifi-cant correlation could be obtained in either thelower oxygen consumption group or the higherone. Because in comparing hearts of differentsizes it is not the force alone that might reason-ably be expected to vary with energy utilization,but rather the product of force times the distancethrough which it is generated, we decided to ex-amine also the effect of multiplying the FTMby the mean chamber radius (radius when halfthe stroke volume has been ejected). However,this did not significantly improve the correlation(r = 0.78).

Contractile element work showed a signifi-cantly higher correlation with oxygen consump-tion than any of the other three determinantsstudied. In addition it was the only determinantyielding a significant correlation when only thosepoints with q02 sbove 15 ml were examined.

From a theoretical standpoint as well, con-tractile element work is a more satisfactory

determinant of oxygen consumption, since ittakes into account the total contractile effort ofthe heart muscle, namely, both force generationand fiber shortening. With the three-componentmodel as a dynamic representation of musclecontraction, the former may be considered as"internal work," whereas the latter representsthe "external work" of the heart. Just as con-sideration of only the external work (LV workor FSW) has not proved to be a satisfactorydeterminant of myocardial qO2, so too considera-tion of only the internal work (PTM and FTM)has its shortcomings. The relative success ofPTMand FTM as determinants of oxygen con-sumption may in part be due to the fact thatventricular pressure (or force) enters into thecalculation of both the internal and external workof the heart. Secondly, inherent in the deriva-tion of PTMand FTM is a consideration of theduration of systole, which in turn often variesdirectly with stroke volume and thereby exter-nal work.

Gorlin and his associates (25) have recentlyfound that with increased fiber shortening (ex-ternal work) induced by catecholamines in hu-man subjects, the observed oxygen consumptionwas greater than that which could be predictedfrom either pressure-time or force-time alone.Figure 3 shows a similar observation, in that 4 ofthe 5 isoproterenol studies lie above the regressionline, indicative of a higher oxygen consumptionthan that predicted by force-time per minute.In the case of the FSW, the fact that the majorityof isoproterenol points lie below the regressionline is in agreement with the well-known observa-tion that "flow work" is performed with rela-tively little oxygen cost (5). Sinice CEWtakesinto account both fiber shortening and forcegeneration, the relationship between qO2 andCEWwould be expected not to be altered by iso-proterenol. This was not the case, however, andthe observation that 4 of the 5 isoproterenolpoints still lie below the regression line must haveanother explanation (vide infra).

Efficiency considerations. If indeed it is thecontractile element work that determines myo-cardial oxygen consumption, then the observedexternal mechanical efficiency would be depend-ent on two factors: 1) the efficiency of the con-tractile element and 2) that portion of the totalcontractile effort expressed externally as fibershortening. In fact, mechanical efficiency obvi-ously = CEefficiency X FSW/CEW.

The average CE efficiency was obtained fromthe slope of the Q02-CEWregression line (Figure

1404

CONTRACTILEELEMENTWORK

5). Since the calculation of contractile elementwork is in error by virtue of the same considera-tions involved in the calculation of FSW (seefootnote 2), the true CEWin kilogram-metersper minute is equal to 0.00649 X CEWin 106dyne-centimeters per minute. Therefore, theCE efficiency is equal to the reciprocal of theqO2-CEW slope multiplied by 0.00649 anddivided by the mechanical equivalent of oxygen(2.06 kg-m per ml). This yielded an averageCE efficiency of 22.7%.

We then decided to examine the relationshipof external mechanical efficiency and the ratioFSW/CEW(Figure 7). This showed a signifi-cant correlation (r = 0.77; p < 0.001). SinceLV work and therefore external mechanicalefficiency fall to zero when FSWis zero, the plotwas regressed in such a manner as to force theregression line to pass through the origin of thegraph. When this was done, we found that aquadratic equation (y = bx + CX2) fit the pointssignificantly better (0.001 < p < 0.01) than alinear one (y = bx). Let us now examine thesignificance of this curvilinear relation betweenexternal mechanical efficiency and FSW/CEW.Figure 7 illustrates that as FSW/CEW in-creases, the ratio of external mechanical effici-ency to FSW/CEWincreases. This is to saythat the CEefficiency rises with increasing FSW/CEW. Indeed, a direct plot of (CEW/qO2)-4.333 and FSW/CEWshowed a significant cor-relation (r = 0.50; 0.001 < p < 0.01).

This increase in CE efficiency with increasingFSW/CEWexplains the location of most of theisoproterenol points below the regression lines inFigure 5, as the ratio FSW/CEWis markedlyincreased by isoproterenol.

If the CE itself is unable to distinguish betweenforce generation and fiber shortening, the impli-cation of this rise in CE efficiency with FSW/CEWis either that the fiber shortening work ofthe contractile element has been overestimated inthese studies or that the force generating work ofthe CE has been underestimated. Since FSWis equivalent to LV work and the error in itsmeasurement is small, that FSWhas been con-sistently overestimated is unlikely. Therefore,it would seem appropriate to examine the possi-ble causes of an underestimation of the forcegeneration work. A likely source of error is thegross approximation of the active stiffness, S (theslope of the dF/dl - F relationship), which wasderived by extrapolation from the isolated cat

8 4.33 = the y intercept of the CEW-qO2 line.

3CEXTERPMECHANEFFICIEI

(70) 2C

1C

ALYc 0.0298x *0a00247x '

MALIICAL . tINCY

.0

* *e~0 0 0* .0

l A , , , , , ,,110

0 20 40 60BW(%)

80 100

FIG. 7. RELATIONSHIP OF EXTERNALMECHANICALEFFICIENCY TO FSW/CEW.

papillary muscle to the intact dog heart. Sincethe force generation work was calculated asFp/S, an overestimation of S would lead directlyto an underestimation of the calculated forcegeneration work. A second possible explanationis the effect of the asynchronicity of cardiacmuscle contraction. In this instance, the non-contracting fibers act functionally as passiveelastic structures in series with the contractingfibers. Since the stiffness of resting muscle fiberis much less than that of the SEC, more workmight be involved in developing a given wallforce than that calculated on the basis of thestiffness of the SEC. A third consideration in-volves the role played by the fibrous mitral valve,which is in series with the muscle fibers. Thestiffness of fibrous tissue is constant (26) anddoes not increase with increasing load as in thecase of the SEC. The energy involved instretching such a spring is proportional to F,2 4and ignoring this factor would again lead to anunderestimation of force generation work.Lastly, the exact shape of the left ventricle mayplay a role. The work involved in generating agiven intraluminal pressure might be greater ina nonspherical one of the same volume.

The q02 of the beating, empty heart. The yintercepts of the regression lines of Figures 2 to 5represent the oxygen consumption of the heartwhen each parameter (PTM, FTM, FSW, orCEW) is zero, i.e., the beating, empty heart.Kohn (22) recently found the oxygen consump-tion in such hearts to be 3.0 ml per minute per

4dF/dl = k, dW= Fdl, or W= f FdF/k. Integrat-ing, this becomes (1/2k) (Fp,-F,'). Ignoring F, for thereasons discussed earlier, work = Fp'/2k.

1405

NAPHTALI A. BRITMAN AND HERBERTJ. LEVINE

100 g. The CEW-qO2 regression line yieldedthe y intercept closest to this value (4.33 ml perminute per 100 g). In the case of the PTM re-gression line, the y intercept was negative (-2.22ml), which is not meaningful in physiologic terms.This was also true of the results published byNeill, Levine, Wagman, and Gorlin (8).

Kohn further found that the oxygen consump-tion of the nonbeating heart (KCl asystole) wasonly 1.5 ml per minute per 100 g. The signifi-cance of this difference (1.5 ml) can be appreci-ated from a consideration of classical skeletalmuscle energetics. Heat studies of a twitchhave shown that a small amount of heat is liber-ated due to activation alone (27). Thus, thedifference between the oxygen consumption ofthe beating empty heart and that of the nonbeat-ing heart can be considered to reflect the energyof activation per minute (heart rate times acti-vation energy per beat).' From the stimulationfrequency used by Kohn, the activation energyper beat can be calculated to be 0.0125 ml perbeat per 100 g.

Since in our studies a wide range of heart rateswas observed (70 to 207), we decided to re-examine the CEW-LVqO2 data in terms of apossible additional effect of heart rate on thetotal oxygen consumption. To do this, we per-formed multiple regression for qO2 as a linearfunction of both CEWand heart rate (HR), asfollows: q02 = a + b (CEW) + c (HR), wherea = the oxygen consumption of the nonbeating,empty heart; b = qO2/CEW, or the reciprocalof CE efficiency; and c = the activation energyper beat. The result of this regression was asfollows: qO2 = 1.93 + 0.0129 CEW+ 0.0202HR. Thus the extrapolated oxygen consump-tion of the nonbeating, empty heart was 1.93 mlper minute per 100 g, fairly good agreement withKohn's figure of 1.5 ml, and the activation energyper beat was 0.0202 ml per beat per g, also show-ing reasonable agreement with that calculatedfrom Kohn's data. The coefficient of CEWwasnot much different from that obtained in theoriginal regression (0.0138, Figure 5). Statisti-cally, however, the addition of the heart rate termin the multiple regression analysis did not sig-nificantly add to the determination of qO2 byCEWalone (p > 0.20).

Fenn effect in the heart. The classic work of

5 When calculated in this way, activation energy in-cludes both the classical heat of activation (27) and theenergy consumed in overcoming the resistance of theheart wall to shortening.

Fenn (28) and Hill (13) has shown that onshortening, skeletal muscle liberates an addi-tional amount of heat that is directly propor-tional to the shortening distance (Fenn effect).Since the Fenn effect is considered to be a funda-mental property of the contractile process ofmuscle (13, 29), it follows that a considerationof the extra energy cost associated with short-ening should take into account the total short-ening of the contractile element, rather thanfiber shortening alone.

In shortening a distance d at a force F, thework done equals F X d, and the extra energycost of shortening equals a X d, where a = theshortening heat per unit distance. Thus, theefficiency of the shortening process would begiven by (F X d)/(Fd + ad), or 1/E1 + (a/F)].It is, therefore, necessary to examine the ratioa/F in order to assess the consequences of theFenn effect on CE efficiency, iLe., as a/F in-creases, CE efficiency would decrease.

The shortening heat constant a has not beenmeasured in cardiac muscle. There are, how-ever, good theoretical grounds for the belief thatthe heat constant a is identical to the constant aof Hill's classic force-velocity relation: (F + a)V = b(Fo - F) (13, 30). Further, in the frogsartorius muscle, the constant a was derived ex-perimentally from both heat and mechanicalstudies, and fairly good agreement was found(13).

The mechanical constant a has been studied inisolated cat papillary muscle, and the ratio a/F0(isometric tension) was found to be constant inthe face of inotropic interventions, differentstimulation frequencies, and different initialfiber lengths (21). If the constancy of this ratioholds for the intact dog heart, and further if themechanically derived constant a is assumed to beequivalent to the shortening heat constant a, thenthe ratio of F0 to F would also be an index ofshortening efficiency, since a varies as Fo. AsFO/F increases, efficiency would decrease.

In the case of cardiac contraction, contractileelement shortening occurs through a range offorce from Fj to Fp, so that the average forceshould be considered in the above evaluation ofCE efficiency. However, since Fj is generallyclose to zero, changes in average force will gen-erally be reflected by similar changes in peakforce, F,. Therefore, we may consider the ratioFo/Fp as an index of the theoretical CE short-ening efficiency.

In the studies described in this paper, force-velocity curves for the contractile element were

1406

CONTRACTILEELEMENTWORK

constructed from the instantaneous values offorce and contractile element velocity. Thesecurves and their interpretation form the subjectof the preceding paper (15). In 22 of the 34studies, the curves were well enough defined topermit a reasonably fair estimate of the projectedisometric force Fo. In these cases, the relation-ship between CE efficiency and the ratio FO/Fpwas examined, but no significant correlation wasfound. Thus, in these studies, we were unableto demonstrate a Fenn effect in the intact heart.However, this problem warrants further study.

It is reasonable to assume that ultimate com-prehension of the energetics of cardiac musclewill be predicated on an understanding of basicmuscle mechanics. Although our study suggeststhat CEWis the major determinant of myocard-ial oxygen requirements, the ultimate formula-tion of muscle energetics will include a consider-ation of the energy cost of resting cardiacmuscle, the activation energy per beat, and per-haps other factors such as the Fenn effect or therole played by the parallel elastic component.

Summary

Cardiac contraction in the intact dog heart hasbeen analyzed in terms of Hill's series elasticmodel for muscle, and the total work performedby the contractile element was calculated. Con-tractile element work was derived as the sum ofthe work done in stretching the series elasticcomponent to peak force, plus the work per-formed by the contractile element in shorteningof the muscle fiber. The latter quantity was cal-culated as the total fiber shortening work minusthe amount performed by the recoiling serieselastic component.

Over a wide range of altered hemodynamics,an excellent correlation between contractile ele-ment work and left ventricular oxygen consump-tion was observed (r = 0.91). This relationshipwas significantly better (p < 0.05) than thatfound between oxygen consumption and pressure-time per minute (r = 0.74), force-time perminute (r = 0.74), or fiber shortening work(r = 0.74).

An index of contractile element work was de-rived using only heart rate, left ventricular sys-tolic mean pressure, and mean left ventricularvolume and was shown to correlate well with thecalculated contractile element work (r = 0.995).

External mechanical efficiency depends on theproportion of total contractile element work thatis expressed as fiber shortening work. Fronm an

analysis of the contractile element work-oxygenconsumption relationship, the oxygen consump-tion of the beating empty dog heart has beenestimated to be 4.3 ml per 100 g per minute.Multiple regression of oxygen consumption as alinear function of both contractile element workand heart rate was also performed in an effort toexamine activation energy per beat as a possibledeterminant of myocardial oxygen consumption.In this manner the energy requirement of thenonbeating heart was estimated to be 1.9 ml per100 g per minute and the energy requirement ofactivation estimated to be 0.02 ml per beat per100 g.

A method is described by which the Fenneffect may be studied in the intact dog heart.Using this approach, our attempts to demon-strate the Fenn effect were unsuccessful.

References1. Starling, E. H., and M. B. Visscher. The regula-

tion of the energy output of the heart. J. Phys-iol. (Lond.) 1926, 62, 243.

2. Hemingway, A., and A. R. Fee. The relationshipbetween the volume of the heart and its oxygenusage. J. Physiol. (Lond.) 1927, 63, 299.

3. Decherd, G., and M. B. Visscher. The relative im-portance of the performance of work and the ini-tial fiber length in determining the magnitude ofenergy liberation in the heart. Amer. J. Physiol.1933, 103, 400.

4. Rhode, E. Uber den Einfluss der MechanischenBedingungen auf die Tatigkeit und den Sauer-stoffverbrauch der Warmbluterherzens. Naunyn-Schmiedeberg's Arch. exp. Path. Pharmak. 1912,68, 401.

5. Evans, C. L., and Y. Matsuoka. The effect of vari-ous mechanical conditions on the gaseous metabo-lism and efficiency of the mammalian heart. J.Physiol. (Lond.) 1915, 49, 378.

6. Katz, L. N. Analysis of the several factors regu-lating the performance of the heart. Physiol. Rev.1955, 35, 91.

7. Sarnoff, S. J., E. Braunwald, G. Welch, R. B.Case, W. N. Stainsby, and R. Marcruz. Hemo-dynamic determinants of the oxygen consumptionof the heart with special reference to the tension-time index. Amer. J. Physiol. 1958, 192, 148.

8. Neill, W. A., H. J. Levine, R. J. Wagman, and R.Gorlin. Left ventricular oxygen utilization inintact dogs: effect of systemic hemodynamic fac-tors. Circulat. Res. 1963, 12, 163.

9. Fischer, Ernst. The oxygen consumption of iso-lated muscles for isotonic and isometric twitches,Amer. J. Physiol. 1931, 96, 78.

10. Levine, H. J., and R. J. Wagman. Energetics of thehuman heart. Amer. J. Cardiol. 1962, 9, 372.

1407

NAPHTALI A. BRITMAN AND HERBERTJ. LEVINE

11. Braunwald, E., A. Goldblatt, and D. C. Harrison.Determinants of ventricular dimensions in intactunanesthetized man (abstract). J. dlin. Invest.1962, 41, 1347.

12. Rolett, E. L., P. M. Yurchak, L. S. Cohen, W. C.Elliott, and R. Gorlin. Relation between ventricu-lar force and oxygen consumption. Fed. Proc.1963, 22, part I, 345.

13. Hill, A. V. The heat of shortening and the dynamicconstants of muscle. Proc. roy. Soc. Lond. B1938, 126, 136.

14. Hill, A. V. The abrupt transition from rest to ac-tivity in muscle. Proc. roy. Soc. Lond. B 1949,136, 399.

15. Levine, H. J., and N. A. Britman. Force-velocityrelations in the intact dog heart. J. clin. Invest.1964, 43, 1383.

16. Goodale, W. T., and D. B. Hackel. Measurementof coronary blood flow in dogs and man from rateof myocardial nitrous oxide desaturation. Cir-culat. Res. 1953, 1, 502.

17. Peters, J. P., and D. D. Van Slyke. QuantitativeClinical Chemistry. Baltimore, Williams and Wil-kins, 1932, vol. 2, p. 321.

18. Bristow, J. D., R. E. Ferguson, F. Mintz, and E.Rapaport. Thermodilution studies of ventricularvolume changes due to isoproterenol and bleeding.J. appl. Physiol. 1963, 18, 129.

19. Hefner, L. L., L. T. Sheffield, G. C. Cobbs, and W.Klip. Relation between mural force and pressurein the left ventricle of the dog. Circulat. Res.1962, 11, 654.

20. Sonnenblick, Edmund H. Force-velocity relationsin mammalian heart muscle. Amer. J. Physiol.1962, 202, 931.

21. Sonnenblick, Edmund H. Implications of musclemechanics in the heart. Fed. Proc. 1962, 21, 975.

22. Kohn, R. M. Myocardial oxygen uptake during ven-tricular fibrillation and electromechanical dissoci-ation. Amer. J. Cardiol. 1963, 11, 483.

23. Fronek, A., 0. Hudlicka, and. C. Kubie. The esti-mation of total energy utilization of the leftventricle. Fed. Proc. 1963, 22, part I, 520.

24. Sugiura, M. Experimental studies on the regula-tory mechanisms of coronary circulation. Jap.Circulat. J. (Ni.) 1959, 23, 108.

25. Gorlin, R., P. M. Yurchak, E. L. Rolett, W. C. El-liott, and L. S. Cohen. Inferential evidence forthe Fenn effect in the human heart (abstract).J. dlin. Invest. 1963, 42, 938.

26. Krafka, J., Jr. Comparative study of the histo-physics of the aorta. Amer. J. Physiol. 1939, 125,1.

27. Hill, A. V. The heat of activation and the heat ofshortening in a muscle twitch. Proc. roy. Soc.Lond. B 1949, 136, 195.

28. Fenn, W. 0. A quantitative comparison between theenergy liberated and the work performed by theisolated sartorius muscle of the frog. J. Physiol.(Lond.) 1923, 58, 175.

29. Podolsky, Richard J. The mechanism of muscularcontraction. Amer. J. Med. 1961, 30, 708.

30. Podolsky, Richard J. Mechanochemical basis ofmuscular contraction. Fed. Proc. 1962, 21, 964.

1408