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Determination of the external work and power of the left ventricle in intact man
Determination of the external work power of the left ventricle in intact
and man
Robert E. Snell, M.D.* Peter C. Luchsinger, M.D.** Washington, D. C.
T
he external work of the left ventricle in man is usually calculated from mean pressure-volume measurements. Such estimates are deficient in at least two respects. First, some arithmetic error is introduced in determining the total work done, as demonstrated by Katz2 in 1932. Second, the use of mean data gives no information concerning the temporal pattern of work performance in a system in which pressure and flow are highly pulsatile. The development of the computed pressure gradient technique by Fry and his associates3 has made possible the measurement of instantaneous blood flow and velocity in the human ascending aorta. The use of this technique in conjunction with simultaneous determinations of instantaneous aortic pressure makes possible accurate computations of ventricular power and work in man4 that avoid the abovementioned deficiencies. The present study reports observations in individuals without known systemic cardiovascular disease, as well as in patients with nonvalvular
heart disease, during a control state. In addition, a group of subjects have been studied during the administration of a pressor amine. Method A. Theory. Work represents the product of a force by the distance over which the force acts; power is the time rate at which work is done. In hydraulic systems, in which the force is usually measured as a pressure, the equivalent expressions for work and power involve the pressure-volume and pressure-volume flow products, respectively. The external, or “useful,” work of the left ventricle is defined as the work required to maintain a pressure upon the volume of blood ejected into the ascending aorta, and to impart a velocity to it.5 Since the work done represents the temporal integral of the power provided to the flowing blood during the ejection period, external ventricular work may be computed from Equation (1) (see top of Page 530).
the sur.gid assistance of James M. Clements. M.D., Assistant Chief, Surgical Service, Veterans Administration Hospital, Washington, D. C.. and Clinical Instructor in Surgery, Georgetown University School of Medicine. From the Cardiopulmonary Research Laboratory, Veterans Administration Hospital, Washington, D. C., and the Department of Medicine. Georgetown University School of Medicine, Washington, D. C. A portion of this work was completed during Dr. Snell’s tenure as a. Trainee in Cardiovascular Physiology under Training Grant No. ST1 HE 5454 from the National Heart Institute. Reported in part at the 36th Scientific Sessions of the American Heart Association, Los Angeles, Calif., Oct. 25.27, 1963.1 Received for publication July 2, 1964. *Clinical Investigator. Veterans Administration Hospital, Washington. D. C., and Instructor in Medicine. Georgetown University School of Medicine. Address: VA Hospital, 2650 Wisconsin Ave., N. W.. Washington 7. D. C. **Chief, Cardiopulmonary Physiology Research, Veterans Administration Hospital, Washington, D. C., and Assistant Professor of Medicine, Georgetown University School of Medicine. With
529
1) where LVSW = left ventricular stroke work (Gm.M per beat); P = instantaneous aortic pressure (cm. HzO); Q = instantaneous aortic blood flow (c.c./sec.); v = instantaneous aortic blood velocity (cm.;‘sec); p = density of blood (average 1.057 Gm.,‘c.c.); g = gravitational constant (980 cnl./sec.2) ; and tc to tl = systolic ejection period (sec.).
The first term of Equation (1) is generally called the “ pressure” work, whereas the second represents the “kinetic,” or ” accelerative” work. This latter quantity represents the correction for the work done in moving the blood mass to the site of measurement in the ascending aorta. In the absence of values for instantaneous velocity and flow, external ventricular work has been approximated by the mean pressure-stroke volume product.
LVSW = (p) x (17)
(2
The accelerative term is generally ignored. If mean systolic pressure is used, results from Equation (2) will approximate those from Equation (1) with varying degrees of accuracy.6 Other investigators7,8 have used the difference between mean arterial pressure and left atria1 or left ventricular end-diastolic pressure as the first term on the right in Equation (2). B. Patient material. AA total of 19 male patients from the Veterans Administration Hospital, Washington, D. C., were studied (Table I). Eleven (Group I) had no evidence of systemic cardiovascular disease. The other 8 had clinical findings suggestive of primary myocardial disease (Group II). In this hospital, this diagnosis is applied to young adults who demonstrate cardiomegaly and symptoms and signs of lowoutput congestive heart failure in the absence of angina, persistent or significant hypertension, organic valvular disease, constrictive pericarditis, or evidence of systemic, neuromuscular or metabolic disease. At the actual time of study, only 1 patient was in congestive heart failure (J.A.C., No. 16); the other 7 had past histories of congestive failure, together with present evidence of cardiac enlargement and nonspecific electrocardiographic abnormalities.
Because of the variations in body size between and within the two groups, all values for work and power were expressed as indices, in order to facilitate comparison. .Lis indicated above, one individual had manifestations of overt cardiac failure at the time of study; accordingly, the expression of work in terms of body surface area in this subject may be falsely low, because of the retention of fluid. C. Experimental procedltre. All patients were studied in the fasting state without premeditation. Surgical exposure of the femoral artery was achieved under local anesthesia. A specially designed catheter* with two pairs of lateral openings separated by a distance of 5 cm. was introduced and advanced to the ascending aorta, under fluoroscopic control, just distal to the aortic valve. The final position of the catheter was documented by x-ray. Observations at rest were made over a period of approximately 30 minutes. Four subjects from Group 1 were also studied during the administration of I-norepinephrinet by intravenous infusion at a rate of 4 micrograms per minute. 1. PRESSPKEMEASCWMENT. The catheter lumina were connected to two strain gauges1 used in conjunction with chopperstabilized, low-level amplifiers.$ The systern was tested prior to each study, using a pneumatic sine wave generator,” to assure that dynamic imbalance was less than 5 per cent of the input pressures at 1.5 cycles per second, and that the dynamic single-ended response was uniform (A 5 per cent) over the same frequency range. *U.S. Catheter and Instrument Company, Glens Falls, N. Y. tlevophed. Winthrop Laboratories. New York. N. Y. IModel P23Db. Statham Transducers, Inc.. Hato Rey. Puerto Rico. $Model350-4-1500. Sanborn Co.. Wnltbam. Ma-. “National Instrument Laboratories. Kensington. Md.
Volume Number
69 4
Determination
of external work and power of LV in man
Phase lag was linear through 15 cycles per second and approximated 1 degree per cycle per second. The static imbalance was less than 0.1 per cent over a pressure range of 300 cm. HZO. These are the minimum requirements listed by Greenfield and Fry9 for the measurement of aortic blood velocity by the computed pressure gradient technique. 2.
VELOCITY
AND
FLOW
Table I. Physical characteristics of patients studied
Group
Group
BSA CM.9
I. No cardiovascular H.L.B. (10) A.P. (13) J.A. (26) W.H.P. ( 7) J.Mc. (30) J.W.B. (12) W.A.H. (11) B.W. (19) C.A. (18) R.L.E. ( 9) I.C. (29) II. E.S. M.P. H.S.P. J.W.C. H.Mc. R.M.C. J.A.C. J.M.
Myocardial
(25) (24) (22) (17) (21) (20) (16) (23)
300 Flow cc.lscc.
MEASUREMENT.
Instantaneous velocity measurements were made by the method described by Fry and his co-workers,3 Barnett, Greenfield, and Fox,‘O and Snell and associates,ll using a Donner analog computer. A calibration of the instantaneous velocity tracing in terms of flow was obtained by first determining the mean velocity by planimetry. Three to five consecutive cardiac cycles at the time of the determination of cardiac output by the dye-dilution technique were used for this purpose. The mean height of the velocity curve was then set equal to the mean flow obtained by the dye-dilution technique, resulting in a flow calibration of the velocity tracing. In the four studies employing l-norepinephrine, dye curves were repeated
Patient (Number)
531
disease 41 33 37 36 42 43 40 31 44 47 37
1.70 1.90 1.67 1.86 1.66 1.99 1.57 1.56 1.72 1.52 1.99
44 37 36 44 40 34 49 47
1.89 1.76 1.95 2.05 1.75 2.18 1.90 1.60
disease
0
I
Time (sec.1
I
I
0.25
Fig. 1. Recordings of pressure obtained in the ascending aorta cardiovascular disease (J. MC.,
0.75
and velocity of a subject No. 30).
(flow) without
during administration of the drug, and the calibration procedure was repeated. In all instances this second calibration agreed within 5 per cent with that obtained during the control period. This method of flow calibration neglects changes in radius during the cardiac cycle, which normally approximate 5 per cent in the ascending aorta. It also assumes that ilow in the ascending aorta becomes zero at end-diastole, as demonstrated by Spencer and Denison.12 Cardiac outputs were determined by the dye-dilution technique using a cuvette densitometer* and a fixed-speed withdrawal pump.t Duplicate measurements of cardiac output made with this technique are reproducible to l t5 per cent in this laboratory. 3. WORK COMPUTATION. Representative pressure and velocity (flow) curves obtained in one individual are shown in Fig. 1. Measurements for work computation commenced with the initial upstroke of the pressure wave and terminated at the incisura. Tracings were obtained at a paper speed of 100 mm. per second, and ordinate values were determined at O.Olsecond intervals. Computations of work from Equation (1) were accomplished *Model 103-IR. Gilford Instrument Oberlin. Ohio. tHarvard Instrument Co., Dover, Mass.
Laboratories,
Inc.,
r
Fig. 2. .,I. Ventricular estcrnal power output, as a function of time, in a subject from Group 1 (A.P., iVo. 13). H, ‘I‘hc temporal pattern of work performance in the subjects of Group I. The individual points represent average values for instantaneous power obtained in 11 individuals, and the \,ertical lines define the standard error of the mean. The abscissa has been r~ondimerrsiol~alized and expressed as per cent duration systolic ejection.
using digital coll~putation with card-punch input.* Average stroke work values were also obtained front Equation (2), using values for mean systolic pressure and mean flow obtained by computer integration of the area under the curves. Results
Table II lists the mean values for heart rate, aortic pressure, cardiac index, and stroke and minute work indices in the individuals without cardiovascular disease (Group If. In 2 of these subjects (R.L.E.~ So. 9, and I.C., No. 29) the resting heart rate was above 100 during repeated measurements. Since no cause for this sinus tachycardia was evident, other than anxiety, they were retained in the control group. The resting stroke work index ranged from 51 to 90 Grn.M.jM.’ per beat, with the lowest values being found in the patients with rapid heart rates. The kinetic fraction of the total work was small, never exceeding 3 per cent of the total work output. Even at peak ejection, that fraction of instantaneous power related to the accelerative force never exceeded 5 per cent. Fig. 2,,4 shows a typical representation of the temporal pattern of work performance obtained in one of the subjects in Group 1. The illustration represents a1-1 average of five separate pressure and flow curves recorded at rest. To obtain a com-
posite “power curve” for the 11 subjects, the abscissa was nondiInensionalized in all and expressed as per cent duration systolic ejection. The individual values were then averaged at 21 points during the ejection period, and the result appears in Fig. 2,N. Salient features of this representation are a rapid rise to peak power values during the first third of ejection, then maintenance of power output at a high level until half of the ejection period has been completed, and a subsequent slow decline in power
POWER CM.%!./
M?/rec.
l -.---
Control
x-
L- Norepinsphrinc
500
250
SYSTOLIC
EJECTION
(rec.1
Determination
H.L.B. A.P. J.A. W.H.P. J.Mr. J.\V.B. W.A.H. B.W. CA. R.L.E. I.C.
(10) (13) (26) ( 7) (30) (12) (11) (19) 118) ( 9) (29)
.qverage
533
of external work and power of LV in man
58 65 66 68 69 71 75 76 79 106 112
133/80 127/84 136/79 102167 11 l/63 112/69 116/69 110174 m/79 124/85 112/70
3.35 2.94 3.53 3.85 3.20 3.08 3.78 3.47 3.84 3.36 3.80
88 73 88 74 64 60 71 60 70 50 50
76.8
119/74
3.47
68.0
1.5 1.3 1.1 0.9 1.6 0.7 0.9 0.8 1.9 1.1 1.0
+2
90 74 89 7s 66 61 72 ;:
1.2 SD.
51 51
5,220 4,810 5,874 5,100 4,554 4,331 5,400 4,636 5,688 5,406 5,712
83 71 85 74 62 58 48 60 75 50 48
69.2 25.6
5,151 1,037
66.7
*Indi~,idua~ values reported here and in succeeding tables represent the mean of several observations. HR; Heart rate. P: Aortic pressure (mm. Hg). Cf: Cardiac index (L./‘min. per M.2). PA’: “Pressure” work (first term of Equation t) (Gm.M./M.z per heat). KW: “Kinetic” work (second term of Equation I) (Gm.MJM.2 per beat). LVSU: Left ventricular stroke work index (from Equation 1) (Gm.M./M.* per beat). LVC’MW: Left ventricular minute work index (Gm.MJM.2 per minute). LVSW:
Stroke work index from product
of mean systolic
pressure and stroke volume
(Equation
2;.
Putient (Number) J&k. B.W. CA. I.C.
(30) (19) (18) (29)
60 66 69 75
.qverage Per cent
change*
*Comparison of average For key to abbreviations
143/80 157/94 16.5’100 1sy90
2.96 3.11 3.33 3.71
80 86 95 95
67.5
1x/91
3.28
89.0
-20
f36/26
-8
+45
values for the 4 subjects see Table II.
at rest and during
values over the last half of systole. Although variations in the actual magnitudes of power output were found among individuals, this temporal pattern of work performance was consistent, and apparently unaltered by differences in heart rate. Values for rate, pressure, flow, and work obtained during the adlninistration of I-norepinephrine are presented in Table III. Increases in the stroke work index ranged from 24 to 90 per cent. Because of the attendant bradycardia, there was a lesser increase in minute work. The kinetic
administration
1.5 0.7 1.3 1.7
82 87 96 97
4,920 5,742 6,624 7,275
1 3
90.3
6,140
0
+45
119
of the drug.
fraction of the total work remained less than 2 per cent in these subjects. Ac~oi~panying the rise in stroke work with the pressor agent was a significant alteration in the temporal pattern of work performance. Changes found in one subject are shown in Fig. 3, whereas in Fig. 4 the values for instantaneous power obtained in 4 individuals during infusion of the drug have been averaged and compared with their corresponding control observations. With infusion of the drug, the initial rise to peak power levels appears to be slightly delayed, and values for peak
Group IIA* M.P. H.S.P. J.N’.C. H.Mc. 1Z.M.C.
(2-i) (221 117) (21) (20)
Average
73 78 79 80 81
m/70 129/84 153/83 135/82 137/99
.z .35 2.76 .z 16 .i 3.3 2.53
66 59 74 68 63
0.5 1.7 0.8 0 Y 1.0
67 61 75 69 6-L
4,8Yl 4,758 5.925 5,520 5.181
78.2
136/84
.z. 1s
66.0
1.0
67.0
5,256
107/69 102/77 104/70
2.43 1.96 2.71
45 32 31
0.4 1.5 0.6
4s 34 3.5
3,195 2,924 3,220
10-r/72
2.37
37.0
0.8
37,x
.3.113
c;rot1p rrut ;2c. J.M. A%verage
::i; (23)
71 86 92 83.0
*Five patients with stroke work values within the range encountered iThree patients with stroke work values lower than any encountered
power output to be moderately increased. The most prominent alteration is the maintenance of external power at a high level during the second half of systole. Expressed in a different manner, this means that, with infusion of the drug, approximately 11 per cent more of the total external work was a~cotllplished during the latter half of systolic ejection (Fig. 5). Results obtained in the 8 individuals with heart disease (Group II) are presented in Table IV. These patients were further subdivided on the basis of values for total work. In 5 (Group IN), mean pressures were generally higher and flows lower than those found in the control group. Work indices were consequently within the range encountered in Group I. The other 3 patients (Group IIB) had decreased values for both pressure and flow, and the work accomplished was less than 50 Gm.M./M.2 per beat in all. One of the subjects in this last group was in congestive failure at the time of study; review of the clinical data in the other 2 patients revealed no obvious distinguishing characteristics at the time of study. Composite “power curves” were also different in the two subgroups (Fig. 6). The pattern of work performance in those individuals in Group IL4 resembles that
in the control group. in the control group.
seen with the administration of l-norepinephrine, with power output being maintained higher than in the normal subjects during the latter half of ejection. On the other hand, the Group IIB patients demonstrate a diminution in the absolute values for power output throughout. This decrease is relatively greater in the first haIf of the ejection period, however, as can be seen from the comparisons of fractional work accomplishment in Fig. 7. Discussion
Katz,2 in studies on the isolated turtle heart, demonstrated that significant inaccuracy could arise from the use of mean pressure-volume data to estimate stroke work. Remington and Hamilton6 found that the product of mean systolic pressure and stroke volume generally underestimated true ventricular work, with the discrepancy usually being less than 12 per cent. This is in agreement with the present study. The difference is related to the contour of the pressure and Row wave forms and to neglect of the kinetic term. In the limited range of stroke volumes and heart rates encountered in the present study, the latter factor was not significant. Under different circumstances, particularly in the calculation of the work of the right ventricIe, this may not hold true.‘”
Volwne Number
69 4
Determination
of external work and power of LV in man
535
POWER GM. M./M?lsec.
..“.‘. X-
% DURATION
Fig. 4. External I-norepinephrine. lines indicate the of the drug differ cent of ejection.
power output in The abscissa has standard error of significantly (p <
SYSTOLIC
Control l? -Norepinephrine
EJECTION
4 subjects at rest, and during infusion of been nondimensionalized, and the vertical the mean. Values obtained during infusion 0.05) from the control over the last 55 per
Factors governing the mechanical performance of cardiac muscle have recently been reviewed. These include the muscle’s resting length, force-velocity relationships, and afterload. In the isolated cat papillary muscle, I-norepinephrine increases work and power for any given initial length and afterload mainly by increasing the maximal velocity of shortening.14 Presumably analogous relationships will determine the mechanical performance of the intact ventricle.5J5 At any given heart rate, the instantaneous power developed by the ventricle should be a function of end-diastolic volume, the inotropic state of the myocardium, and the output load imposed by the arterial system. Burch and his associates16,17 have considered the variations in power output to be expected from alterations in heart rate occurring at constant levels of pressure and cardiac output. In the intact subject, such relationships become less easy to define. In the present study, an increase in the mean aortic pressure-mean flow ratio was common to those individuals receiving l-norepinephrine and to the patients with heart disease, when compared with the control group. It is possible that this increase in resistive output load, rather than myocardial disease as such, is re-
sponsible for the relative increase in the levels of power during late systole. The lack of information concerning changes in ventricular filling pressure and contractile force, however, prohibits a satisfactory explanation of these alterations at this time. What is evident from the present study is that ventricular mechanical performance must be judged not only by the total work done, but also by the temporal pattern of work accomplishment. CONTROL
Fig. 5. Fractional work accomplishment during the first (shaded bars) and second (solid bars) halves of systohc ejection,’ before and ~ during infusion of I-norepinephrine. The relative increase in work performed during the second half of the ejection period is statistically significant (p < 0.05).
x-
% DURATION
SYSTOLIC
ClOlJl, I
O----
Group
UA
. .....I
Group
IIS
EJECTION
Fig. 6. Exterual power output in subjects without cardiovascular disease (Group I) and in those with primary myocardial disease (Group If). T’alues for stroke work were above 60 Gm.M./M.* per beat in the 5 patients in Group IIA and below 50 Gm.M./M.2 per beat in the 3 subjects iu Group IIB. Vertical lines represent the standard error of the mean.
Finally, it should be mentioned that a portion of the output load faced by the ventricle is nonresistive in nature and reflects the inertial and compliant properties of the system upon which work is being done. This means that not only the dissipation of power, but also the storage of energy may take place. In the steady state, the power stored would not influence the total external work done by the ventricle, but could alter the temporal manner of
G@O”PI
‘n
B
Fig. 7. Fractional work accomplishmeIlt during the first (shaded bars) and second (sofa bnrs) halves of ejection in Groups i and II. The difference between the control group and the two groups with heart disease is statistically significant (p < 0.02).
its accomplishment. The effect of the complex output load on ventricular power output is difficult to analyze in terms of the temporal pressure-flow product; an approach based on the study of the transmission of power in the ascending aorta has been presented in a preliminary rep0rt.l Summary
1. Measurements of the external work and power of the left ventricle have been made in 19 subjects. Computations were based on instantaneous measurements of pressure, velocity, and flow in the ascending aorta. 2. In 11 subjects without known cardiovascular disease the resting stroke work index ranged from 51 to 90 Gm.M./M.” per beat. The average minute work indes was 5.2 Kg.M./M.2 per minute in the same group. 3. The administration of l-norepinephrine produced not only a rise in the total work performed, but also a change in the temporal pattern of work accomplishment whereby the increase in power output was most pronounced during the latter half of the ejection period. 4. In 6 individuals with nonvalvular heart disease but normal external work
output, increases in external power during late systole, relative to the normal, were found. In 3 subjects with work values below 50 Gnl.M./M.2 per beat, there was both a general diminution in the levels of power achieved and an altered pattern of work performance. 5. The factors relating to the manner of work ~~ccomplishnlent by the intact ventricle have been discussed. The helpful suggestions Shugoll in regard to this knowledged.
received study
from Dr. Gerald are gratefully ac-
REFERENCES 1.
2.
.*3
4.
5.
6.
7.
Snell, R. E., and Luchsinger, P. C.: Determination of left ventricular stroke work and power in intact man, Circulation 28:809, 1963. Katz, L. N.: Observations on the external work of the isolated turtle heart, Am. J. Physiol. 99:579, 1932. Fry, D. L., Mallos, A. J., and Casper, A. G. T.: A catheter tip method for measurement of the instantaneous aortic blood velocity, Circulation Res. 4:627, 1956. Rudewaid, B.: Hemodynamics of the human ascending aorta as studied by means of a differential pressure technique, Acta physiol. scandinav. a: (Suppl. 187) 1, 1962. Landowne, M., and Katz, L. N.: Circulatory system: Heart: work and failure, in 0. Glasser, editor: Medical physics, Chicago, 1950, Yearbook Publishers, Inc., Vol. 2, p. 194. Remington, J. W., and Hamilton, W. F.: The evaluation of the work of the heart, Am. J. Physiol. 150:292, 1947. Sarnoff, S. J., and Berglund, I?.: Ventricular function. I. Starling’s law of the heart studied by means of simultaneous right and left ventricular function curves in the dog, Circulation 9:706, 19.54.
8.
Ferguson, T. B., Shadle, 0. W., and Gregg, D. E.: Effect of blood and saline infusion on ventricular end-diastolic pressure, stroke work, stroke volume and cardiac output in the open and closed chest dog, Circulation Res. 1:62, 1953. 9. GreenfieId, J. C., and Fry, D. L.: Measurement errors in estimating aortic blood velocity by pressure gradient, J. Appl. Physiol. 17:1013, 1962. 10. Barnett, G. O., Greenfield, J. C., and Fox, S. M.: The technique of estimating the instantaneous aortic blood velocity in man from the pressure gradient, AM. HEARTJ. 62:359, 1962. R. E., Clements, J. M., Pate& D. J., 11. Snell, Fry, D. L., and Luchsinger, P. C.: Instantaneous blood flow in the human aorta, J. Appl. Physiol. (Accepted for publication. 12. Spencer, M. P., and Denison, A. B., Jr.: Pulsatile blood flow in the vascular system, in Hamilton, W. F., editor: Handbook of physiology. Section 2: Circulation, Washington, D. C., 1963, American Physiological Society, Vol. 2, p. 839. 13. Prec, O., Katz, L. N., Sennett, L., Rosenman, R. H., Fishman, A. P., and Hwang, W.: Determination of kinetic energy of the heart in mart, Am. J. Physiol. 159:483, 1949. 14. Sonnenblick, E. H.: Implications of muscle mechanics in the heart, Fed. Proc. 22:975, 1962. 1.5. Fry, D. L., Griggs, D. M., Jr., and Greenfield, 1. C.. .Tr.: Mvocardial mechanics: tensionvelocity-length relationships of heart muscle, Circulation Res. 14:73, 1964. 16. Burch, G. E., Ray, C. T., and Cronvich, J. C.: George Fahr lecture. Certain mechanical pecularities of the human cardiac pump in normal and diseased states, Circulation 5:504, 1952. 17. Burch, G. E.: Relationship of heart rate to cardiac output, work, power and tension in man, J.A.M.A. 182:340, 1962.
and man
Robert E. Snell, M.D.* Peter C. Luchsinger, M.D.** Washington, D. C.
T
he external work of the left ventricle in man is usually calculated from mean pressure-volume measurements. Such estimates are deficient in at least two respects. First, some arithmetic error is introduced in determining the total work done, as demonstrated by Katz2 in 1932. Second, the use of mean data gives no information concerning the temporal pattern of work performance in a system in which pressure and flow are highly pulsatile. The development of the computed pressure gradient technique by Fry and his associates3 has made possible the measurement of instantaneous blood flow and velocity in the human ascending aorta. The use of this technique in conjunction with simultaneous determinations of instantaneous aortic pressure makes possible accurate computations of ventricular power and work in man4 that avoid the abovementioned deficiencies. The present study reports observations in individuals without known systemic cardiovascular disease, as well as in patients with nonvalvular
heart disease, during a control state. In addition, a group of subjects have been studied during the administration of a pressor amine. Method A. Theory. Work represents the product of a force by the distance over which the force acts; power is the time rate at which work is done. In hydraulic systems, in which the force is usually measured as a pressure, the equivalent expressions for work and power involve the pressure-volume and pressure-volume flow products, respectively. The external, or “useful,” work of the left ventricle is defined as the work required to maintain a pressure upon the volume of blood ejected into the ascending aorta, and to impart a velocity to it.5 Since the work done represents the temporal integral of the power provided to the flowing blood during the ejection period, external ventricular work may be computed from Equation (1) (see top of Page 530).
the sur.gid assistance of James M. Clements. M.D., Assistant Chief, Surgical Service, Veterans Administration Hospital, Washington, D. C.. and Clinical Instructor in Surgery, Georgetown University School of Medicine. From the Cardiopulmonary Research Laboratory, Veterans Administration Hospital, Washington, D. C., and the Department of Medicine. Georgetown University School of Medicine, Washington, D. C. A portion of this work was completed during Dr. Snell’s tenure as a. Trainee in Cardiovascular Physiology under Training Grant No. ST1 HE 5454 from the National Heart Institute. Reported in part at the 36th Scientific Sessions of the American Heart Association, Los Angeles, Calif., Oct. 25.27, 1963.1 Received for publication July 2, 1964. *Clinical Investigator. Veterans Administration Hospital, Washington. D. C., and Instructor in Medicine. Georgetown University School of Medicine. Address: VA Hospital, 2650 Wisconsin Ave., N. W.. Washington 7. D. C. **Chief, Cardiopulmonary Physiology Research, Veterans Administration Hospital, Washington, D. C., and Assistant Professor of Medicine, Georgetown University School of Medicine. With
529
1) where LVSW = left ventricular stroke work (Gm.M per beat); P = instantaneous aortic pressure (cm. HzO); Q = instantaneous aortic blood flow (c.c./sec.); v = instantaneous aortic blood velocity (cm.;‘sec); p = density of blood (average 1.057 Gm.,‘c.c.); g = gravitational constant (980 cnl./sec.2) ; and tc to tl = systolic ejection period (sec.).
The first term of Equation (1) is generally called the “ pressure” work, whereas the second represents the “kinetic,” or ” accelerative” work. This latter quantity represents the correction for the work done in moving the blood mass to the site of measurement in the ascending aorta. In the absence of values for instantaneous velocity and flow, external ventricular work has been approximated by the mean pressure-stroke volume product.
LVSW = (p) x (17)
(2
The accelerative term is generally ignored. If mean systolic pressure is used, results from Equation (2) will approximate those from Equation (1) with varying degrees of accuracy.6 Other investigators7,8 have used the difference between mean arterial pressure and left atria1 or left ventricular end-diastolic pressure as the first term on the right in Equation (2). B. Patient material. AA total of 19 male patients from the Veterans Administration Hospital, Washington, D. C., were studied (Table I). Eleven (Group I) had no evidence of systemic cardiovascular disease. The other 8 had clinical findings suggestive of primary myocardial disease (Group II). In this hospital, this diagnosis is applied to young adults who demonstrate cardiomegaly and symptoms and signs of lowoutput congestive heart failure in the absence of angina, persistent or significant hypertension, organic valvular disease, constrictive pericarditis, or evidence of systemic, neuromuscular or metabolic disease. At the actual time of study, only 1 patient was in congestive heart failure (J.A.C., No. 16); the other 7 had past histories of congestive failure, together with present evidence of cardiac enlargement and nonspecific electrocardiographic abnormalities.
Because of the variations in body size between and within the two groups, all values for work and power were expressed as indices, in order to facilitate comparison. .Lis indicated above, one individual had manifestations of overt cardiac failure at the time of study; accordingly, the expression of work in terms of body surface area in this subject may be falsely low, because of the retention of fluid. C. Experimental procedltre. All patients were studied in the fasting state without premeditation. Surgical exposure of the femoral artery was achieved under local anesthesia. A specially designed catheter* with two pairs of lateral openings separated by a distance of 5 cm. was introduced and advanced to the ascending aorta, under fluoroscopic control, just distal to the aortic valve. The final position of the catheter was documented by x-ray. Observations at rest were made over a period of approximately 30 minutes. Four subjects from Group 1 were also studied during the administration of I-norepinephrinet by intravenous infusion at a rate of 4 micrograms per minute. 1. PRESSPKEMEASCWMENT. The catheter lumina were connected to two strain gauges1 used in conjunction with chopperstabilized, low-level amplifiers.$ The systern was tested prior to each study, using a pneumatic sine wave generator,” to assure that dynamic imbalance was less than 5 per cent of the input pressures at 1.5 cycles per second, and that the dynamic single-ended response was uniform (A 5 per cent) over the same frequency range. *U.S. Catheter and Instrument Company, Glens Falls, N. Y. tlevophed. Winthrop Laboratories. New York. N. Y. IModel P23Db. Statham Transducers, Inc.. Hato Rey. Puerto Rico. $Model350-4-1500. Sanborn Co.. Wnltbam. Ma-. “National Instrument Laboratories. Kensington. Md.
Volume Number
69 4
Determination
of external work and power of LV in man
Phase lag was linear through 15 cycles per second and approximated 1 degree per cycle per second. The static imbalance was less than 0.1 per cent over a pressure range of 300 cm. HZO. These are the minimum requirements listed by Greenfield and Fry9 for the measurement of aortic blood velocity by the computed pressure gradient technique. 2.
VELOCITY
AND
FLOW
Table I. Physical characteristics of patients studied
Group
Group
BSA CM.9
I. No cardiovascular H.L.B. (10) A.P. (13) J.A. (26) W.H.P. ( 7) J.Mc. (30) J.W.B. (12) W.A.H. (11) B.W. (19) C.A. (18) R.L.E. ( 9) I.C. (29) II. E.S. M.P. H.S.P. J.W.C. H.Mc. R.M.C. J.A.C. J.M.
Myocardial
(25) (24) (22) (17) (21) (20) (16) (23)
300 Flow cc.lscc.
MEASUREMENT.
Instantaneous velocity measurements were made by the method described by Fry and his co-workers,3 Barnett, Greenfield, and Fox,‘O and Snell and associates,ll using a Donner analog computer. A calibration of the instantaneous velocity tracing in terms of flow was obtained by first determining the mean velocity by planimetry. Three to five consecutive cardiac cycles at the time of the determination of cardiac output by the dye-dilution technique were used for this purpose. The mean height of the velocity curve was then set equal to the mean flow obtained by the dye-dilution technique, resulting in a flow calibration of the velocity tracing. In the four studies employing l-norepinephrine, dye curves were repeated
Patient (Number)
531
disease 41 33 37 36 42 43 40 31 44 47 37
1.70 1.90 1.67 1.86 1.66 1.99 1.57 1.56 1.72 1.52 1.99
44 37 36 44 40 34 49 47
1.89 1.76 1.95 2.05 1.75 2.18 1.90 1.60
disease
0
I
Time (sec.1
I
I
0.25
Fig. 1. Recordings of pressure obtained in the ascending aorta cardiovascular disease (J. MC.,
0.75
and velocity of a subject No. 30).
(flow) without
during administration of the drug, and the calibration procedure was repeated. In all instances this second calibration agreed within 5 per cent with that obtained during the control period. This method of flow calibration neglects changes in radius during the cardiac cycle, which normally approximate 5 per cent in the ascending aorta. It also assumes that ilow in the ascending aorta becomes zero at end-diastole, as demonstrated by Spencer and Denison.12 Cardiac outputs were determined by the dye-dilution technique using a cuvette densitometer* and a fixed-speed withdrawal pump.t Duplicate measurements of cardiac output made with this technique are reproducible to l t5 per cent in this laboratory. 3. WORK COMPUTATION. Representative pressure and velocity (flow) curves obtained in one individual are shown in Fig. 1. Measurements for work computation commenced with the initial upstroke of the pressure wave and terminated at the incisura. Tracings were obtained at a paper speed of 100 mm. per second, and ordinate values were determined at O.Olsecond intervals. Computations of work from Equation (1) were accomplished *Model 103-IR. Gilford Instrument Oberlin. Ohio. tHarvard Instrument Co., Dover, Mass.
Laboratories,
Inc.,
r
Fig. 2. .,I. Ventricular estcrnal power output, as a function of time, in a subject from Group 1 (A.P., iVo. 13). H, ‘I‘hc temporal pattern of work performance in the subjects of Group I. The individual points represent average values for instantaneous power obtained in 11 individuals, and the \,ertical lines define the standard error of the mean. The abscissa has been r~ondimerrsiol~alized and expressed as per cent duration systolic ejection.
using digital coll~putation with card-punch input.* Average stroke work values were also obtained front Equation (2), using values for mean systolic pressure and mean flow obtained by computer integration of the area under the curves. Results
Table II lists the mean values for heart rate, aortic pressure, cardiac index, and stroke and minute work indices in the individuals without cardiovascular disease (Group If. In 2 of these subjects (R.L.E.~ So. 9, and I.C., No. 29) the resting heart rate was above 100 during repeated measurements. Since no cause for this sinus tachycardia was evident, other than anxiety, they were retained in the control group. The resting stroke work index ranged from 51 to 90 Grn.M.jM.’ per beat, with the lowest values being found in the patients with rapid heart rates. The kinetic fraction of the total work was small, never exceeding 3 per cent of the total work output. Even at peak ejection, that fraction of instantaneous power related to the accelerative force never exceeded 5 per cent. Fig. 2,,4 shows a typical representation of the temporal pattern of work performance obtained in one of the subjects in Group 1. The illustration represents a1-1 average of five separate pressure and flow curves recorded at rest. To obtain a com-
posite “power curve” for the 11 subjects, the abscissa was nondiInensionalized in all and expressed as per cent duration systolic ejection. The individual values were then averaged at 21 points during the ejection period, and the result appears in Fig. 2,N. Salient features of this representation are a rapid rise to peak power values during the first third of ejection, then maintenance of power output at a high level until half of the ejection period has been completed, and a subsequent slow decline in power
POWER CM.%!./
M?/rec.
l -.---
Control
x-
L- Norepinsphrinc
500
250
SYSTOLIC
EJECTION
(rec.1
Determination
H.L.B. A.P. J.A. W.H.P. J.Mr. J.\V.B. W.A.H. B.W. CA. R.L.E. I.C.
(10) (13) (26) ( 7) (30) (12) (11) (19) 118) ( 9) (29)
.qverage
533
of external work and power of LV in man
58 65 66 68 69 71 75 76 79 106 112
133/80 127/84 136/79 102167 11 l/63 112/69 116/69 110174 m/79 124/85 112/70
3.35 2.94 3.53 3.85 3.20 3.08 3.78 3.47 3.84 3.36 3.80
88 73 88 74 64 60 71 60 70 50 50
76.8
119/74
3.47
68.0
1.5 1.3 1.1 0.9 1.6 0.7 0.9 0.8 1.9 1.1 1.0
+2
90 74 89 7s 66 61 72 ;:
1.2 SD.
51 51
5,220 4,810 5,874 5,100 4,554 4,331 5,400 4,636 5,688 5,406 5,712
83 71 85 74 62 58 48 60 75 50 48
69.2 25.6
5,151 1,037
66.7
*Indi~,idua~ values reported here and in succeeding tables represent the mean of several observations. HR; Heart rate. P: Aortic pressure (mm. Hg). Cf: Cardiac index (L./‘min. per M.2). PA’: “Pressure” work (first term of Equation t) (Gm.M./M.z per heat). KW: “Kinetic” work (second term of Equation I) (Gm.MJM.2 per beat). LVSU: Left ventricular stroke work index (from Equation 1) (Gm.M./M.* per beat). LVC’MW: Left ventricular minute work index (Gm.MJM.2 per minute). LVSW:
Stroke work index from product
of mean systolic
pressure and stroke volume
(Equation
2;.
Putient (Number) J&k. B.W. CA. I.C.
(30) (19) (18) (29)
60 66 69 75
.qverage Per cent
change*
*Comparison of average For key to abbreviations
143/80 157/94 16.5’100 1sy90
2.96 3.11 3.33 3.71
80 86 95 95
67.5
1x/91
3.28
89.0
-20
f36/26
-8
+45
values for the 4 subjects see Table II.
at rest and during
values over the last half of systole. Although variations in the actual magnitudes of power output were found among individuals, this temporal pattern of work performance was consistent, and apparently unaltered by differences in heart rate. Values for rate, pressure, flow, and work obtained during the adlninistration of I-norepinephrine are presented in Table III. Increases in the stroke work index ranged from 24 to 90 per cent. Because of the attendant bradycardia, there was a lesser increase in minute work. The kinetic
administration
1.5 0.7 1.3 1.7
82 87 96 97
4,920 5,742 6,624 7,275
1 3
90.3
6,140
0
+45
119
of the drug.
fraction of the total work remained less than 2 per cent in these subjects. Ac~oi~panying the rise in stroke work with the pressor agent was a significant alteration in the temporal pattern of work performance. Changes found in one subject are shown in Fig. 3, whereas in Fig. 4 the values for instantaneous power obtained in 4 individuals during infusion of the drug have been averaged and compared with their corresponding control observations. With infusion of the drug, the initial rise to peak power levels appears to be slightly delayed, and values for peak
Group IIA* M.P. H.S.P. J.N’.C. H.Mc. 1Z.M.C.
(2-i) (221 117) (21) (20)
Average
73 78 79 80 81
m/70 129/84 153/83 135/82 137/99
.z .35 2.76 .z 16 .i 3.3 2.53
66 59 74 68 63
0.5 1.7 0.8 0 Y 1.0
67 61 75 69 6-L
4,8Yl 4,758 5.925 5,520 5.181
78.2
136/84
.z. 1s
66.0
1.0
67.0
5,256
107/69 102/77 104/70
2.43 1.96 2.71
45 32 31
0.4 1.5 0.6
4s 34 3.5
3,195 2,924 3,220
10-r/72
2.37
37.0
0.8
37,x
.3.113
c;rot1p rrut ;2c. J.M. A%verage
::i; (23)
71 86 92 83.0
*Five patients with stroke work values within the range encountered iThree patients with stroke work values lower than any encountered
power output to be moderately increased. The most prominent alteration is the maintenance of external power at a high level during the second half of systole. Expressed in a different manner, this means that, with infusion of the drug, approximately 11 per cent more of the total external work was a~cotllplished during the latter half of systolic ejection (Fig. 5). Results obtained in the 8 individuals with heart disease (Group II) are presented in Table IV. These patients were further subdivided on the basis of values for total work. In 5 (Group IN), mean pressures were generally higher and flows lower than those found in the control group. Work indices were consequently within the range encountered in Group I. The other 3 patients (Group IIB) had decreased values for both pressure and flow, and the work accomplished was less than 50 Gm.M./M.2 per beat in all. One of the subjects in this last group was in congestive failure at the time of study; review of the clinical data in the other 2 patients revealed no obvious distinguishing characteristics at the time of study. Composite “power curves” were also different in the two subgroups (Fig. 6). The pattern of work performance in those individuals in Group IL4 resembles that
in the control group. in the control group.
seen with the administration of l-norepinephrine, with power output being maintained higher than in the normal subjects during the latter half of ejection. On the other hand, the Group IIB patients demonstrate a diminution in the absolute values for power output throughout. This decrease is relatively greater in the first haIf of the ejection period, however, as can be seen from the comparisons of fractional work accomplishment in Fig. 7. Discussion
Katz,2 in studies on the isolated turtle heart, demonstrated that significant inaccuracy could arise from the use of mean pressure-volume data to estimate stroke work. Remington and Hamilton6 found that the product of mean systolic pressure and stroke volume generally underestimated true ventricular work, with the discrepancy usually being less than 12 per cent. This is in agreement with the present study. The difference is related to the contour of the pressure and Row wave forms and to neglect of the kinetic term. In the limited range of stroke volumes and heart rates encountered in the present study, the latter factor was not significant. Under different circumstances, particularly in the calculation of the work of the right ventricIe, this may not hold true.‘”
Volwne Number
69 4
Determination
of external work and power of LV in man
535
POWER GM. M./M?lsec.
..“.‘. X-
% DURATION
Fig. 4. External I-norepinephrine. lines indicate the of the drug differ cent of ejection.
power output in The abscissa has standard error of significantly (p <
SYSTOLIC
Control l? -Norepinephrine
EJECTION
4 subjects at rest, and during infusion of been nondimensionalized, and the vertical the mean. Values obtained during infusion 0.05) from the control over the last 55 per
Factors governing the mechanical performance of cardiac muscle have recently been reviewed. These include the muscle’s resting length, force-velocity relationships, and afterload. In the isolated cat papillary muscle, I-norepinephrine increases work and power for any given initial length and afterload mainly by increasing the maximal velocity of shortening.14 Presumably analogous relationships will determine the mechanical performance of the intact ventricle.5J5 At any given heart rate, the instantaneous power developed by the ventricle should be a function of end-diastolic volume, the inotropic state of the myocardium, and the output load imposed by the arterial system. Burch and his associates16,17 have considered the variations in power output to be expected from alterations in heart rate occurring at constant levels of pressure and cardiac output. In the intact subject, such relationships become less easy to define. In the present study, an increase in the mean aortic pressure-mean flow ratio was common to those individuals receiving l-norepinephrine and to the patients with heart disease, when compared with the control group. It is possible that this increase in resistive output load, rather than myocardial disease as such, is re-
sponsible for the relative increase in the levels of power during late systole. The lack of information concerning changes in ventricular filling pressure and contractile force, however, prohibits a satisfactory explanation of these alterations at this time. What is evident from the present study is that ventricular mechanical performance must be judged not only by the total work done, but also by the temporal pattern of work accomplishment. CONTROL
Fig. 5. Fractional work accomplishment during the first (shaded bars) and second (solid bars) halves of systohc ejection,’ before and ~ during infusion of I-norepinephrine. The relative increase in work performed during the second half of the ejection period is statistically significant (p < 0.05).
x-
% DURATION
SYSTOLIC
ClOlJl, I
O----
Group
UA
. .....I
Group
IIS
EJECTION
Fig. 6. Exterual power output in subjects without cardiovascular disease (Group I) and in those with primary myocardial disease (Group If). T’alues for stroke work were above 60 Gm.M./M.* per beat in the 5 patients in Group IIA and below 50 Gm.M./M.2 per beat in the 3 subjects iu Group IIB. Vertical lines represent the standard error of the mean.
Finally, it should be mentioned that a portion of the output load faced by the ventricle is nonresistive in nature and reflects the inertial and compliant properties of the system upon which work is being done. This means that not only the dissipation of power, but also the storage of energy may take place. In the steady state, the power stored would not influence the total external work done by the ventricle, but could alter the temporal manner of
G@O”PI
‘n
B
Fig. 7. Fractional work accomplishmeIlt during the first (shaded bars) and second (sofa bnrs) halves of ejection in Groups i and II. The difference between the control group and the two groups with heart disease is statistically significant (p < 0.02).
its accomplishment. The effect of the complex output load on ventricular power output is difficult to analyze in terms of the temporal pressure-flow product; an approach based on the study of the transmission of power in the ascending aorta has been presented in a preliminary rep0rt.l Summary
1. Measurements of the external work and power of the left ventricle have been made in 19 subjects. Computations were based on instantaneous measurements of pressure, velocity, and flow in the ascending aorta. 2. In 11 subjects without known cardiovascular disease the resting stroke work index ranged from 51 to 90 Gm.M./M.” per beat. The average minute work indes was 5.2 Kg.M./M.2 per minute in the same group. 3. The administration of l-norepinephrine produced not only a rise in the total work performed, but also a change in the temporal pattern of work accomplishment whereby the increase in power output was most pronounced during the latter half of the ejection period. 4. In 6 individuals with nonvalvular heart disease but normal external work
output, increases in external power during late systole, relative to the normal, were found. In 3 subjects with work values below 50 Gnl.M./M.2 per beat, there was both a general diminution in the levels of power achieved and an altered pattern of work performance. 5. The factors relating to the manner of work ~~ccomplishnlent by the intact ventricle have been discussed. The helpful suggestions Shugoll in regard to this knowledged.
received study
from Dr. Gerald are gratefully ac-
REFERENCES 1.
2.
.*3
4.
5.
6.
7.
Snell, R. E., and Luchsinger, P. C.: Determination of left ventricular stroke work and power in intact man, Circulation 28:809, 1963. Katz, L. N.: Observations on the external work of the isolated turtle heart, Am. J. Physiol. 99:579, 1932. Fry, D. L., Mallos, A. J., and Casper, A. G. T.: A catheter tip method for measurement of the instantaneous aortic blood velocity, Circulation Res. 4:627, 1956. Rudewaid, B.: Hemodynamics of the human ascending aorta as studied by means of a differential pressure technique, Acta physiol. scandinav. a: (Suppl. 187) 1, 1962. Landowne, M., and Katz, L. N.: Circulatory system: Heart: work and failure, in 0. Glasser, editor: Medical physics, Chicago, 1950, Yearbook Publishers, Inc., Vol. 2, p. 194. Remington, J. W., and Hamilton, W. F.: The evaluation of the work of the heart, Am. J. Physiol. 150:292, 1947. Sarnoff, S. J., and Berglund, I?.: Ventricular function. I. Starling’s law of the heart studied by means of simultaneous right and left ventricular function curves in the dog, Circulation 9:706, 19.54.
8.
Ferguson, T. B., Shadle, 0. W., and Gregg, D. E.: Effect of blood and saline infusion on ventricular end-diastolic pressure, stroke work, stroke volume and cardiac output in the open and closed chest dog, Circulation Res. 1:62, 1953. 9. GreenfieId, J. C., and Fry, D. L.: Measurement errors in estimating aortic blood velocity by pressure gradient, J. Appl. Physiol. 17:1013, 1962. 10. Barnett, G. O., Greenfield, J. C., and Fox, S. M.: The technique of estimating the instantaneous aortic blood velocity in man from the pressure gradient, AM. HEARTJ. 62:359, 1962. R. E., Clements, J. M., Pate& D. J., 11. Snell, Fry, D. L., and Luchsinger, P. C.: Instantaneous blood flow in the human aorta, J. Appl. Physiol. (Accepted for publication. 12. Spencer, M. P., and Denison, A. B., Jr.: Pulsatile blood flow in the vascular system, in Hamilton, W. F., editor: Handbook of physiology. Section 2: Circulation, Washington, D. C., 1963, American Physiological Society, Vol. 2, p. 839. 13. Prec, O., Katz, L. N., Sennett, L., Rosenman, R. H., Fishman, A. P., and Hwang, W.: Determination of kinetic energy of the heart in mart, Am. J. Physiol. 159:483, 1949. 14. Sonnenblick, E. H.: Implications of muscle mechanics in the heart, Fed. Proc. 22:975, 1962. 1.5. Fry, D. L., Griggs, D. M., Jr., and Greenfield, 1. C.. .Tr.: Mvocardial mechanics: tensionvelocity-length relationships of heart muscle, Circulation Res. 14:73, 1964. 16. Burch, G. E., Ray, C. T., and Cronvich, J. C.: George Fahr lecture. Certain mechanical pecularities of the human cardiac pump in normal and diseased states, Circulation 5:504, 1952. 17. Burch, G. E.: Relationship of heart rate to cardiac output, work, power and tension in man, J.A.M.A. 182:340, 1962.