Ventricular performance measured during ejection: Studies in patients of the rate of change of ventricular power

Experimental and laboratory reports Ventricular performance measured during ejection: Studies in patients of the rate of change of ventricular power Paul D. Stein, M.D. Hani N. Sabbah, B.S. Oklahoma City, Okla.

The ejection rate of change of ventricular power has attributes which make it advantageous for the evaluation of ventricular performance. 1, ~ Its relation to ventricular energy gives it a fundamental fluid dynamic significance as well as a physiological meaning. Its derivation is free of assumptions; the expression, therefore, being firmly based upon theory. Of a practical nature, the ejection rate of change of power was shown in dogs to be sensitive to drug-induced alterations of the contractile state, yet affected little by alterations of preload or afterload. 1 For these reasons, the ejection rate of change of ventricular power appears to be a hemodynamic expression which merits evaluation in patients. Methods

Ventricular power is the product of ventricular pressure and flow. The rate of change of ventricular power is derived by differentiation of this product, and can be written as follows1: Rate of change of power = ~

__dP + P dt

dQ -dt

Where p =

intraventricular pressure (dynes cm.-2),

=

aortic flow (cm2 sec.-1), and d p / d t and d Q / d t are their respective rates of change.

(1)

From the Department of Medicine, University of Oklahoma College of Medicine and Veterans Administration Hospital, Oklahoma City, Okla. Supported in part by the American Heart Association (Grant No. 72927), National Institutes of Health (NHLI 72-2921-B), the VA Research Service, and the Oklahoma Heart Association. Received for publication Jan. 13, 1975. Reprint requests: Paul D. Stein, M.D., Veterans Administration Hospital, 921 N.E. 13th St., Oklahoma City, Okla. 73104.

May, 1976, Vol. 91, No. 5, pp. 599-606

The rate of change of power during ejection was calculated in 22 patients with angina during diagnostic cardiac catheterization. Patients were studied consecutively. All but one of the patients had coronary arterial disease, the severity of which varied; one patient had angina with arteriographically normal appearing vessels. Patients with valvular disease were excluded. Patients in whom ventriCular premature contractions occurred during ventriculography, or in whom reliable aortic velocities were not obtained were also excluded. All patients received light sedation with diazepam (Valium) and were studied in the postabsorptive state. Velocity was measured at the root of the aorta with a catheter-tip velocity sensor (Carolina M e d i c a l Electronics, King, N. C.). A tapered tip distal to the velocity sensor was passed across the aortic valve. This facilitated a reasonably straight alignment Of the catheter along the axial stream of flow. It also stabilized the tip of the catheter during diastole, thereby reducing artifact due to motion of the catheter. A sample of original data is shown (Fig. 1). Blood velocity showed some artifact due to 60 cycle interference in spite of the fact that a 30 Hz filter was utilized. However, these were high-gain tracings; the deflection of the original data was approximately 6 cm. The important data were derived from the upstroke of the velocity signal which was uniformly smooth and little affected by interference. The profile of flow was assumed to be flat, and the cross-sectional area of the aorta was assumed to be constant. The velocity signal, on this basis, would be identical to a flow signal. 3 The flow signal was calibrated by t h e measurement of cardiac output utilizing the indicator dilution technique with indocyanine green.

American Heart Journal

599

S~inand

Sabbah

an electronic digitizer ( N u m o n i c s Corp., N o r t h Wales, Pa.) on line with a H e w l e t t P a c k a r d 2100 A c o m p u t e r ( W a l t h a m , Mass.) T h e e q u a t i o n s descriptive of left v e n t r i c u l a r pressure a n d aortic flow were calculated by the C h e b y s h e v polynomial a p p r o x i m a t i o n t e c h n i q u e as previously described: From the c o m p u t e d m a t h e m a t i c a l equations descriptive of i n t r a v e n t r i c u l a r pressure and aortic flow, and with t h e aid of a c o m p u t e r , peak values of left v e n t r i c u l a r d p / d t , r a t e of change of flow, power, a n d t h e r a t e of change of

:~100E E LU nCO CO ILl n'Q.

0 FnO

power were calculated.* M a x i m u m d p / d t w a s P also obtained from the c o m p u t e r i z e d data. V m a x was calculated as the linear e x t r a p o l a t i o n of 10i -

0

/

E

nFZ

I

I I

U,I

0

o,

\

J

k_

\

o

I

!

0.5

SEC

Fig. 1. Samples of original data showing aortic pressure (top), left ventricular pressure (middle), and aortic velocity (bottom). The ECG is also shown.

Following m e a s u r e m e n t s of flow, pressures were m e a s u r e d in rapid s e q u e n c e w i t h a highfrequency m i c r o m a n o m e t e r (Millar I n s t r u m e n t s , Inc., H o u s t o n , T e x a s ) located a t the tip of a cardiac catheter. Pressure a n d flow were recorded on a p h o t o g r a p h i c recorder a t a p a p e r speed of 200 m m . per second. T h e tracings were digitized w i t h

600

d p / d t plotted with respect to i n t r a v e n t r i c u l a r P pressure. 4 D a t a corresponding to pressures of less t h a n 20 mm. H g was excluded because of i n h e r e n t inaccuracies related to c a l c u l a t i o n s of the ratios of small numbers. T h e n o n s i m u l t a n e o u s m e a s u r e m e n t of ventricular pressure and aortic flow would t e n d to reduce the precision of t h e m e a s u r e m e n t of the m a x i m u m r a t e of change of power. T h e m a x i m u m rate of change of power occurred during the blunt, slowly changing p e a k portion of the ventricular pressure curve, which m i n i m i z e d errors d u e to n o n s i m u l t a n e o u s m e a s u r e m e n t s . In this investigation, a s t e a d y s t a t e during the period of m e a s u r e m e n t s was assumed, and an effort was made to achieve such a s t e a d y state. C a t h e t e r s with a c o m b i n a t i o n of sensors are being developed which would p e r m i t s i m u l t a n e o u s pressure a n d velocity m e a s u r e m e n t s . S u c h a catheter, utilized with an analogue c o m p u t e r , would facilitate use of this index and p e r m i t m e a s u r e m e n t s u n d e r changing conditions. Both

Vmax

and

maximum

dp/dt were P calculated on the basis of t h e a c t u a l pressure. 4 All b u t one of the p a t i e n t s with p o o r v e n t r i c u l a r performance h a d either hypokinesis, akinesis, or dyskinesis. P r e s u m a b l y , therefore, n o n u n i f o r m contraction also occurred during isovolumic systole in all b u t one of the p a t i e n t s with

*The technique of the calculation of the p e a k r a t e of change of power from the equations descriptive of pressure a n d flow as described in this study is unnecessarily complex for o r d i n a r y clinical usage. A dedicated analogue c o m p u t e r would simplify s u c h calculations; s u c h a c o m p u t e r is now being constructed.

May, 1976, Vol. 91, No. 5

Ejection rate of change o[power XIO 5

XlO ~

14-

700

.3 1 2 -

600

/ ' ~ .-I 10 U,.

8

-{2

In0
8-

40O

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500

1400

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1200

30

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J= 0

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q

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- 200

er

10

20

|

I

30

40 TIME

50

6'0

70

0

0

IMSEC}

Fig. 2. I n s t a n t a n e o u s v a l u e s in a p a t i e n t w i t h n o r m a l v e n t r i c u l a r p e r f o r m a n c e of aortic flow. rate of c h a n g e of flow [d(flow)/dt], power, a n d t h e rate of c h a n g e of power [d(power)/dt]. Values are s h o w n as a f u n c t i o n of t i m e after t h e o n s e t of ejection. ( P a t i e n t D. B., T a b l e I).

Table I. Patients with normal performance (E. F. > 58 per cent, Vcr > 1.3 sac. -1, E D V I < 90 c m 2 / M2.)*

Cardia l I Peak Blood l I index| I geart ~ressure~ VED1~ (L./ |Ejection LVEDI I dp/dt [ rate |(ram. |(ram.| rain./|fraction VcF (em.V [ (mm. Patient I (b.p.m.)l Hg) I Hg) I M.9 I (%) I(sac'-9 M.9

B.J. W.N.

66 102 72

120/77 130/80 107/76 128/70 120/77 109/68 146/ 102 102/62 140/95 128/75

Mean _+ S.E.

79 5

123/78 5/4

E.S.

J.M. R.G. M.M. B.E. E.P. D.B. R.C,

60 94 72 92 60 90 78

I I I I Peak [ I Peak I(dp/dt) l |flow [ /p Vmax I (cm.V

I I power ]d(power) [ Peak I •215 [ d~/dt[ (dynes [ (dynes (cm.'V cm./ I crn./

l sec-'J I --c) I sec. I sec; l seo )

17 12 7 7 14 12 13

2.8 3.4 3.2 3.3 3.0 2.8 2.6

75 73 70 59 85 65 64

1.7 1.9 1.8 2.5 1.7 1.6 2.2

61 55 84 47 83 69 57

1,400 1,500 1,300 2,000 1,300 1,200 1,400

38 38 37 67 32 48 26

1.49 1.59 1.48 2.58 1.28 1.61 1.20

600 740 560 820 1000 630 540

13,000 780 15,000 1,100 19,000 800 24,000 1,300 21,000 1,600 14,000 830 12,000 920

19 23 27 39 28 18 20

9 14 9

2.6 2.8 2.7

66 63 70

1.4 2.4 1.5

81 71 85

1,300 3,200 1,300

35 53 50

1.53 2.15 1.52

930 650 600

17,000 1,200 14,000 1,280 16,000" 850

22 28 23

11 1

2.9 0.1

69 2

1.8 0.2"

69 4,

1,600 200

42 4

1.64 .1

700 51

16,500 1,200

25 2

1,100 90

*Key to Table I: E.F. = ejection fraction. VcF = mean velocity of circumferential fiber shortening. LVEDVI = left ventricular end-diastolic volume index. LVEDP ffi left ventricular end-diastolic pressure. dp/dt = rate of change of left ventricular pressure. d(~/dt = rate of change of flow. d(power)/dt = rate of change of power.

American Heart Journal

601

Stein and Sabbah

PERFORMANCE NORMAL

ABNORMAL

8

XlO 50

40

a UJ

u

0

o~ 9

30

~~

20

Results

Y

w

0 z

0 o k-

0

Y

!

p 4( . 0 0 1

"2e

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uJ "~ UJ

0O

.s

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Fig. 3 . Individual values of the rate of change of power [d(power)/dt] measured during ejection in patients with normal performance and patients with abnormal performance. a b n o r m a l p e r f o r m a n c e . Strictly speaking, V m a x would be theoretically invalid in these patients. Following the m e a s u r e m e n t of aortic velocity and i n t r a v e n t r i c u l a r pressure, a v e n t r i c u l o g r a m was p e r f o r m e d as previously described 6 f r o m which left v e n t r i c u l a r v o l u m e s were c a l c u l a t e d b y the single-plane a r e a - l e n g t h m e t h o d . 7 T h e ejection fraction was c a l c u l a t e d f r o m t h e ventriculog r a m s as the ratio of the v o l u m e ejected to enddiastolic volume. 8 T h e m e a n velocity of circumferential fiber shortening (VcF) was m e a s u r e d along the m i n o r axis of the ventricle as described b y K a r l i n e r and associates. 9 P a t i e n t s were categorized as h a v i n g n o r m a l ventricular p e r f o r m a n c e if t h e y h a d a n ejection fraction greater t h a n 58 per cent, 8 a m e a n velocity of circumferential fiber shortening 9 g r e a t e r t h a n 1.3 sec, I a n d a left v e n t r i c u l a r end-diastolic v o l u m e index 8 of less t h a n 90 c m 2 / m . ~ T h e r e were 10 such patients. P a t i e n t s were categorized as h a v i n g a b n o r m a l v e n t r i c u l a r p e r f o r m a n c e if their ejection fraction was less t h a n 50 per cent 1~ and their m e a n velocity of circumferential fiber shortening ~ was less t h a n 1.0 sec. -1 T h e r e were 12 such patients. P a t i e n t s in w h o m the ejection fraction was n o r m a l and the m e a n velocity of circumferential fiber shortening was a b n o r m a l , or vice

602

versa, were excluded f r o m the s t u d y because one could n o t categorize their p e r f o r m a n c e with certainty. I t is emphasized t h a t these groups were selected to ensure t h a t t h e v e n t r i c u l a r p e r f o r m ance of these p a t i e n t s was definitely either n o r m a l or a b n o r m a l . A strict classification is required in order to e x a m i n e the validity of this new h e m o d y n a m i c index of p e r f o r m a n c e , a n d to c o m p a r e it to previously derived indices.

Typical curves illustrative of t h e relation w i t h respect to t i m e of aortic flow, r a t e of change of flow, power, a n d the r a t e of c h a n g e of p o w e r are shown (Fig. 2). T h e r a t e of change of p o w e r reaches a p e a k during the early p o r t i o n of ejection and well before p e a k power. T h e r a t e of c h a n g e of power reaches p e a k within a few milliseconds of the peak r a t e of change of flow. In patients with n o r m a l p e r f o r m a n c e (characterized by a n o r m a l ejection f r a c t i o n a n d velocity of circumferential fiber s h o r t e n i n g in the presence of a n o r m a l end-diastolic v o l u m e index) t h e ejection rate of change of p o w e r was (25 _+ 2) • 108 dyne cm. sec. -~ ( m e a n _ S.E.). In p a t i e n t s w i t h a low ejection fraction a n d low velocity of circumferential fiber shortening, t h e ejection r a t e of change of power was (11 _ 1) • l0 s d y n e cm. sec. ~ (P < 0.001)* (Tables I a n d II). T h e r e was no overlap of values (Fig. 3). In p a t i e n t s w i t h n o r m a l v e n t r i c u l a r p e r f o r m a n c e , the p e a k r a t e of change of p o w e r ranged b e t w e e n 18 and 39 • 10 s d y n e cm. sec. 2 I t did n o t exceed 15 • 108 d y n e cm. sec. -2 in p a t i e n t s w i t h poor v e n t r i c u l a r performance. P e a k power during ejection, p e a k flow, a n d t h e p e a k rate of change of flow also showed a significant difference of the m e a n . T h e p e a k flow a n d the p e a k r a t e of change of flow showed s o m e overlap of values. T h e c o m m o n l y m e a s u r e d isovolumic indices (peak d p / d t ' m a x i m u m d p / d t , a n d P Vmax) showed m o r e overlap ( T a b l e s I a n d II). T h e peak ejection r a t e of change of p o w e r correlated well with the m e a n velocity of circumferential fiber shortening (r -- 0.86) (r = correlation coefficient). (Fig. 4). I t also correlated, b u t less closely, with the ejection fraction (r = 0.71) (Fig. 5). As would be predicted f r o m the fact t h a t the r a t e of change of flow is a c o m p o n e n t t e r m in *Unpaired t test.

May, 1976, Vol. 91, No. 5

Ejection rate of change of power X 10 s 50

I Y= 9.36X'6.21 R=0.86

kE3 er

O.

40-

I

I

I

I

I 1.2

I 1.$

2.0

30-

5 20o

g

9

10-

o

tU

I .4

0

I .8

VELOCITY OF CIRCUMFERENTIAL FIBER SHORTNING

I 2.4 (sEc-b

Fig. 4. Rate of change of power [d(power)/dt] measured during ejection shown in relation to the mean velocity of circumferential fiber shortening. Correlation coefficient (r) is shown.

Table

II.

Patients

with abnormal

performance

( E . F. 5 0

) e r c e n t , Vc~ 1.0 sac. -~)

Peak Peak i Blood | iCardiac index I Peak Peak Heart pressure~LVEDP (L./ Ejection i LVEDI dp/dt I(dp/dt flow d~/dt rate (ram. |(ram. rain.~ fraction VcF (cm2/ (ram. /19) ] Ymax (cm.3/ (cm.3/ Patient (b.p.m.) Hg) | Hg) M s) (%) (sac. 1) M 2) Ig/sec.) (sac. 1) (sac. l) sac.) sec'2)

t

R.G. B.L. R.L. W.H. R.W. R.Y. O.B. L. L.B. R.N. W.T. W.G. G.D.

84 83 73 80 76 64 60 92 72 64 88 72

Mean _+ S.D. *Probability

76 3 NS

104/71 92/65 110/70 115/82 105/74 90/63 100/70 135/87 134/88 100/67 88/65 129/73

13 20 10 16 12 14 8 15 15 25 24 7

109/73 15 5/2 2 < 0.05/ . NS NS

2.2 2.1 2.4 2.4 3.0 2.2 2.7 3.3 2.6 1.9 2.9 2.9

27 27 46 21 36 44 49 36 38 34 16 46

0.4 0.6 0.9 0.6 0.7 0.6 0.4 0.5 0.5 0.3 0.4 0.8

64 53 108 87 108 74 85 91 112 124 183 159

1,300 1,500 1,100 1,200 900 800 900 1,500 1,700 800 600 1,300

35" 38 30 25 23 25 33 49 34 18 15 37

1.57 1.62 1.70 1.36 L03 1.12 1.42 2.00 1.36 1.00 1.00 1.45

320 280 290 400 600 350 570 490 240 200 380 530

2.6 0.1 < 0.05

35 3 t

0.6 0.05 t

104 11 t

1,100 100 < 0.05

30 3 0.02

1.39 0.1 NS

390 40 0.001

<

<

Peak Peak power d(power) XlO 5 i/dt• ~ (dynes I (dynes I cm./ cm./ t sac.) see. "~)

7,000 6,500 5,100 11,000 9,000 8,200 10,000 1%000 5,700 6,900 11,000 i1,000

<

8,300 700 0.001

400 400 380 500 670 390 680 700 390 210 390 780

<

8 9 7 15 12 9 14 15 9 7 12 15

490 11 50 1 0.001 <0.001

*Probabilities (unpaired t test) refer to comparisons with comparable hemodynamic data listed in Table I. tThe means of E. F., VcF,and LVEDI differed significantly in patients with normal and abnormal performance; but patients were grouped on the basis of these indices.

the rate of change of power, a close correlation w a s o b s e r v e d b e t w e e n t h e s e t w o i n d i c e s ( r -- 0 . 9 5 ) (Fig. 6). Discussion

During the isovolumic portion of systole, press u r e is r e l a t e d t o t e n s i o n a l o n g t h e v e n t r i c u l a r wall as shown by the Laplace equation. Therefore, isovolumic indices which measure combina-

American Heart Journal

tions of ventricular pressure and its derivat i v e 4, 5, 11 h a v e t h e a d v a n t a g e o f r e f l e c t i n g t e n s i o n along the ventricular wall in an uncomplicated fashion. Such indices, therefore, may be advantageous for assessing the function of cardiac muscle. For purposes of assessing the function of the pump, however, it would seem appropriate to evaluate ventricularperformance during ejection. Several important indices of performance during

603

Stein and S a b b a h

xlo' 50

1

Ia 40

n-

o

~

3

o=

a.

I

1

1

1

Y = 0.300X'2.21 R = 0.71

I

I

1

I

9

3o

9

-

9

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~-

O

9

LLI - 1 0 ...) Inn

~

~ ~

8-.~e 9

j

10

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[

J

l

I

l

I

I

i

20

30

40

50

60

70

80

90

100

EJECTION FRACTION ( PER CENT |

Fig. 5. Rate of change of power shown in relation to the ejection fraction.

X 10 a 50 I,O tr

40

O

30

o.

I

I

I

1

I

Y = 0.0015X-2.18 R = 0.96

1

/o

20

uJ u,i

10

1 0

4000

I

L

I

i

8000

12000

I(K)OO

20000

RATE OF CHANGE OF FLOW

24000

MJSIEC2)

Fig. 6. Rate of change of power shown in relation to the rate of change of flow.

ejection have been utilized. These include cardiac output, 1~ ventricular work, 1~ ventricular power, ~ ventricular ejection rate/3 peak flow, ~4 peak rate of change of flow, ~'~ velocity of circumferential fiber shortening, ~ and the ejection fraction2 These are all useful and contribute prominently to the evaluation of the cardiac performance of patients. Even so, these indicators of cardiac function have shortcomings which warrant the continued exploration of methods for the evaluation of ventricular performance. TM Just as the peak rate of change of power distinguished between patients with normal and abnormal ventricular performance, peak flow, peak rate of change of flow, and peak power also distinguished between these two groups. Previous studies in dogs showed t h a t peak flow and peak power as well as the peak rate of change of power were responsive to drug-induced changes of the

604

contractile state. 1 However, peak flow and peak power also showed significant changes with preload which were not shown with the peak rate of change of power. Studies in dogs showed t h a t the peak rate of change of flow was the only ejection index, in addition to the peak rate of change of power, which responded to drug-induced changes of the contractile state and failed to respond significantly to changes of the preload and afterload. 1The peak rate of change of power, however, although more complex in its measurement t h a n the peak rate of change of flow, has advantages which recommend its utilization. These are its fluid dynamic basis, its physiological meaning, and its integrative characteristics. T he rate of change of power indicates an acceleration of energy expended upon the production of useful work by the ventricle during ejection. Since fluid dynamic systems are comprehensively described

May, 1976, Vol. 91, No. 5

Ejection rate of change of power

on the basis of considerations of the energy of the system, it is likely t h a t this acceleration of energy expenditure might be a useful expression. An advantageous feature of the r a t e of change of ventricular power is the encompassing character of the expression. It implies i n f o r m a t i o n related to ventricular work, v e n t r i c u l a r power, ventricular pressure, aortic flow, the rate of change of ventricular pressure, and the rate of change of aortic flow. B o t h v e n t r i c u l a r power and ventricular work can be derived from the expression by integration. Ventricular pressure, aortic flow, and their respective rates of change are components of the expression. E a c h of these expressions has been utilized previously for the evaluation of ventricular performance, ~2 14 ~ although d p / d t is best applied to the isovolumic period. It was previously shown t h a t the r a t e of change of power can be written in t e r m s of the length, tension, and velocity of muscle shortening. 1 This is possible because tension is related to pressure by the Laplace equation and circumferential fiber length and the velocity of fiber shortening are related to flow. T h e exact relation depends upon the shape of the ventricle. T h e rate of change of power, written in terms of tension, length, and velocity of shortening, in the p a r t i c u l a r case of an assumed spherically shaped ventricle, is: TM

Rate of change of power = 8~r

rT d~ + r dr dT + T ( dr~"~dt 2 dt dt \ dt/

(2)

where T = tension along the v e n t r i c u l a r wall (dynes/cm.), r = radius (cm.), d r / d t - rate of shortening of the radius (cm./sec.) and d2r/ dt ~ = acceleration of shortening of the radius (cm./sec.~). T h e relation of the ejection rate of change of power to tension, length, and velocity of shortening of the ventricular wall is of interest because these parameters are said to describe the contractile state of cardiac muscle p r e p a r a t i o n s . " T h e s e mechanical concepts have also been applied to the intact h e a r t and found to be useful. 3' 18 T h e interrelation of the rate of change of power and the velocity of shortening of the radius (and consequently circumference), shown in E q u a t i o n 2, explains the close correlation observed between the rate of change of power and the velocity of circumferential fiber shortening (Fig. 4).

American Heart Journal

T h e rate of change of power is an expression of physiological meaning t h a t can also be applied to the isovolumic period2. 19 Its form and derivation differ from the ejection rate of change of power, since no flow occurs during the isovolumic period. However, the concept of an acceleration of energy expenditure has meaning during b o t h the isovolumic phase of systole and the ejection phase, and a useful evaluation of ventricular p e r f o r m a n c e in patients has also resulted from the former2 T h e utility of the ejection rate of change of power in the presence of valvular disease has not yet been studied. This index seemingly would be valid in the presence of mitral v a l v u l a r disease and aortic regurgitation. Stenosis of the aortic valve would produce a n o n u n i f o r m profile of velocity across the aortic valve, which might produce uninterpretable results. It m a y be advantageous to present the rate of change of ventricular power in a relatively nondimensional fashion. This can be accomplished by normalizing it to i n s t a n t a n e o u s power. T h e ratio of the instantaneous r a t e of change of power to instantaneous power we have t e r m e d the fractional rate of change of power. ~ This has particular advantages, since this form of the e q u a t i o n is such t h a t changes of the cross-sectional area of the aorta can be neglected and aortic velocity can be utilized directly in the calculations. T h e form of the expression permits a simple relation to be shown between the velocity of circumferential fiber shortening, velocity of elongation of the series elastic, power, flow, and their rates of change, providing t h a t some assumptions are made. 2

Summary An expression indicative of the r a t e of change of ventricular power was derived a n d applied to the evaluation of left ventricular p e r f o r m a n c e of patients with angina. Patients were categorized as having normal or a b n o r m a l v e n t r i c u l a r performance on the basis of the ejection fraction, m e a n velocity of circumferential fiber shortening, and left ventricular end-diastolic v o l u m e index. In those with normal performance, the ejection r a t e of change of power was (25 z 2) x l0 s d y n e cm.sec.-2; in patients with a b n o r m a l p e r f o r m a n c e it was (11 _ 1) x 108 dyne cm.sec. -~ (P < 0.001). T h e r e was no overlap of values between categories of patients. Such a clear distinction between categories was not seen with any of t h e c o m m o n l y

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utilized isovolumic indices of performance. The rate of change of ventricular power measured d u r i n g e j e c t i o n is f r e e o f a s s u m p t i o n s , y e t h a s a fluid dynamic as well as a physiological meaning. It serves in an integrative fashion by incorporating terms previously shown to be of functional s i g n i f i c a n c e . P r e v i o u s s t u d i e s in d o g s s h o w e d t h a t it reflected alterations of the inotropic state, yet it was relatively independent of alterations of preload or afterload. It appears, therefore, that it is a n i n d i c a t o r o f v e n t r i c u l a r p e r f o r m a n c e t h a t has desirable characteristics. REFERENCES

1. Stein, P. D., and Sabbah, H. N.: Rate of change of ventricular power: An indicator of ventricular performance during ejection, AM. HEART J. 91:219, 1976. 2. Stein, P. D., and Blick, E. F.: A comprehensive characterization of the dynamics of ventricular performance, in Iberal, A. S., and Guyton, A. C., editors: Regulation and control in physiological systems, 1973, Pittsburgh, Instrument Society of America, p. 329-332. 3. Peterson, K. L., Uther, J. B., Shabetai, R., and Braunwald, E.: Assessment of left ventricular performance in man. Instantaneous tension-velocity-length relations observed with the aid of an electromagnetic velocity catheter in the ascending aorta, Circulation 47:924, 1973. 4. Mason, D. T., Spann, J. F., Jr., and Zelis, R.: Quantification of the contractile state of the human heart. Maximal velocity of contractile element shortening determined by the instantaneous relation between the rate of pressure rise and pressure in the left ventricle during isovolumic systole, Am. J. Cardiol. 26:248, 1970. 5. Nejad, N. S., Klein, M. D., Mirsky, I., and Lown, B.: Assessment of myocardial contractility from ventricular pressure recordings. Cardiovasc. Res. 5:15, 1971. 6. Stein, P. D., and Sabbah. H. N.: Ventricular performance in patients based upon the rate of change of power during isovolumic contraction, Am. J. Cardiol. 35:258, 1975.

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7. Hermann. H. J., and Bartle, S. H.: Left ventricular volumes by angiocardiography: Comparison of methods and simplification of techniques, Cardiovasc. Res. 4:404. 1968. 8. Dodge, H. T., and Baxley, W. A.: Left ventricular volume and mass and their significance in heart disease, Am. J. Cardiol. 23:528, 1969. 9. Karliner, J. S., Gault, J. H.. Eckberg, D., Mullins, C. B., and Ross, J., Jr.: Mean velocity of fiber shortening. A simplified measure of left ventricular myocardial contractility, Circulation 44:323, 1971. 10. Hugenholtz, P. G., Ellison, R. C., Urschel, C. W., Mirsky, I., and Sonnenblick, E. H.: Myocardial force velocity relationships in clinical heart disease. Circulation 41:191, 1970. 11. Gleason, W. L.. and Braunwald, E.: Studies on the first derivative of the ventricular pressure pulse in man, J. Clin. Invest. 41:80, 1962. 12. Rushmer, R. F.: Cardiovascular dynamics, ed. 3, Philadelphia, 1970, W. B. Saunders Company. 13. Levine, H. J., Neill, W. A., Wagman, R. J., Kasnow, N., and Gorlin, R.: The effect of exercise on mean left ventricular ejection rate in man, J. Clin. Invest. 41:1050, 1962. 14. Nutter, D. R., Noble, R. J., and Hurst, V. W., III: Peak aortic flow and acceleration as indices of ventricular performance in the dog, J. Lab. Clin. Med. 77:307, 1971. 15. Noble, M. I. M., Trenchard, D., and Guz, A.: Left ventricular ejection in conscious dogs. 1. Measurement and significance of the maximum acceleration of blood from the left ventricle, Circ. Res. 19:139, 1966. 16. Van Den Bos, G. C., Elzinga, G., Westerhof, N., and Noble, M. I. M.: Problems in the use of indices of myocardial contractility, Cardiovasc. Res. 7:834, 1973. 17. Sonnenblick, E. H.: Force-velocity relations in mammalian heart muscle, Am. J. Physiol. 202:931, 1962. 18. Fry, D. L., Griggs, D. M., Jr., and Greenfield, J. C., Jr.: Myocardial mechanics: Tension-velocity-length relations of heart muscle, Circ. Res. 14:73, 1964. 19. Stein, P. D., McBride, G. G., and Sabbah. H. N.: Ventricular performance and energy transfer, power, and rate of change of power during isovolumic contraction, Cardiovasc. Res. 9:29, 1975.

May, 1976, Vol. 91, No. 5