Download Single-Beat Estimation of the Slope of the End

202
Single-Beat Estimation of the Slope of the
End-Systolic Pressure-Volume Relation in the
Human Left Ventricle
Motoshi Takeuchi, MD; Yuichiro Igarashi, MD; Shinobu Tomimoto, MD;
Michio Odake, MD; Takatoshi Hayashi, MD; Takuya Tsukamoto, MD; Katsuya Hata, MD;
Hideyuki Takaoka, MD; and Hisashi Fukuzaki, MD
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This study assessed a new method of estimating the slope (Ees) of the end-systolic pressurevolume relation (ESPVR) from a single beat of the human heart. Left ventricular pressure was
recorded with a high-fidelity micromanometer in patients with heart disease during left
ventriculography. Peak isovolumic pressure at the end-disastolic volume was estimated by a
curve-fitting technique from an isovolumic left ventricular pressure curve. The ESPVR line was
drawn from the estimated peak isovolumic pressure-volume point tangential to the left upper
corner of the pressure-volume loop. The slope of this estimated ESPVR line from single-beat
analysis was compared with the slope of the ESPVR line obtained from three pressure-volume
loops in 16 patients given angiotensin II or nitroglycerin infusion. The estimated Ees was 5.0±2.2
mm Hg/m1/m2, and the conventional Ees was 4.9+2.7 mm Hg/mlm2. The estimated Ees showed
a positive correlation with the conventional Ees (r=0.91, p<0.001, SEE= 1.2 mm HgImlIm2). In
the other 13 patients, after dobutamine infusion (5 ,ug/kg/min i.v.) the estimated Ees increased
significantly from 5.6±1.4 to 7.4±2.0 mm Hg/ml/m2 (p<0.01). Thus, the estimated Ees
approximated the conventional Ees and was sensitive to a positive inotropic intervention. We
conclude that this single-beat analysis method facilitates assessment of the beat-by-beat ESPVR
of the human heart. (Circulation 1991;83:202-212)
A ssessment of the left ventricular contractile
state is important in both clinical practice
and physiological investigation.1 The endsystolic pressure-volume relation (ESPVR) has been
shown to be almost independent of preload, afterload, and heart rate in a given constant contractile
state in the isolated left ventricle.2-8 ESPVR is
approximately linear throughout the physiological
range, and the slope (Ees) of the ESPVR has been
proposed as an index of ventricular contractility.2-8
Many studies reported similar results in intact animals and humans.9-14 Previous investigations showed
that Ees in patients exhibiting normal contractions
was steeper than that in patients with poorly contracting left ventricles.910 Therefore, the ESPVR and
Ees are useful for a better understanding of ventricular mechanics under changing physiological and
inotropic conditions. To evaluate the Ees, however,
From The First Department of Internal Medicine, Kobe University School of Medicine, Kobe, Japan.
Address for correspondence: Motoshi Takeuchi, The First Department of Internal Medicine, Kobe University, School of Medicine, 7-5-2 Kusunoki-cho. Chuo-ku, Kobe, 650, Japan.
Received June 27, 1989; revision accepted September 11, 1990.
one needs at least two pressure-volume loops with
fairly different end-systolic pressures in a constant
inotropic state.9 The complexities of the method may
decrease the clinical usefulness of ESPVR and Ees
for assessing left ventricular contractility.
Accordingly, this study proposes and assesses a
new method of estimating Ees from a single pressure-volume loop in human hearts. To this end, left
ventricular pressure and volume were measured simultaneously in patients with heart disease. Estimated peak isovolumic pressure [Pmax(E)] at enddiastolic volume was derived from instantaneous
pressure of an ejecting contraction by a curve-fitting
technique according to Sunagawa et al.15 Assuming
the linearity of the ESPVR curve, an ESPVR line
was drawn from the Pmax(E)-volume point tangential to the left upper corner of the pressure-volume
loop of a real ejecting beat from which Pmax(E) was
obtained according to the method of Igarashi and
Suga.16 The slope [Ees(E)] of this estimated ESPVR
line was compared with the conventional Ees obtained by three pressure-volume loops under different loading conditions in the respective patients.
In addition, we studied the effect of positive inotropic
Takeuchi et al Single-Beat Estimation of Contractility
intervention on the slope of this estimated ESPVR
line. Assessment of the reliability of this single-beat
analysis is an indispensable step toward examining
whether the new method of estimating contractile
changes on a beat-by-beat basis is better than other
invasive, complex, and time-consuming conventional
methods used in the clinical setting.
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Methods
Study Patients
We studied 29 patients (24 men and five women);
25 patients had coronary artery disease (eight with
two-vessel and 17 with one-vessel disease), two patients had dilated cardiomyopathy, and two patients
had chest-pain syndrome. Their mean age was 57
years (range, 33-71 years). Eleven of the 25 patients
with coronary artery disease and prior myocardial
infarction had regional wall motion abnormalities on
the biplane left ventriculogram under control conditions. We excluded patients with unstable angina, left
main trunk or three-vessel disease, congestive heart
failure, and valvular heart disease. None of the
patients exhibited any sign of chest pain, electrocardiographic change, or a new onset of asynergy in the
biplane left ventriculogram throughout the study.
Complete, informed, and written consent was obtained from each patient, and no unfavorable complications occurred as a result of this study.
Procedures and Measurements
Cardiac catheterization was performed by the femoral approach in a fasting state under mild sedation
as previously reported in detail.17-20 This study was
performed at least 48 hours after cessation of treatment with calcium channel blockers and nitroglycerin
therapy. Left ventricular cineangiography was performed with biplane 35-mm cineangiography in the
right (300) and left (600) anterior oblique projections
(Poly-Diagnost C, Philips, The Netherlands). A bolus
of 35 ml contrast agent (Omnipaque, lohexol, Japan)
was injected through an 8F pig-tail catheter at a rate
of 12 ml/sec with cinefilm exposed at 60 frames/sec.
Simultaneously, high-fidelity left ventricular pressure
(SPC-370, 7F, Millar Instruments) and the first derivative of pressure (dP/dt) were recorded during
breath holding at midinspiration and were calculated
with a computer system (ACS, Philips).
Protocol
In addition to the control condition, angiotensin 11
(beginning with 4 ng/kg/min) was administered intravenously to increase the afterload in eight patients. The infusion rate was held constant with a
Harvard pump (Harvard Apparatus, South Natick,
Mass.). When the mean aortic pressure increased by
20 mm Hg and then by 30-40 mm Hg and became
stable at each level, left ventriculography was repeated. Therefore, the angiotensin II study consisted
of three loaded conditions, that is, the control, mildly
increased, and largely increased afterload conditions.
203
In the other eight patients, nitroglycerin (beginning with 10 jug/min) was administered intravenously
to decrease the afterload. When the mean aortic
pressure decreased by 10-20 mm Hg and then by
30-40 mm Hg and became stable at each level, left
ventriculography was repeated. Therefore, the nitroglycerin study also consisted of three conditions, that
is, the control, mildly reduced, and largely reduced
afterload conditions. Table 1 summarizes the clinical
and hemodynamic data during the control state and
two different loading conditions in both angiotensin
II and nitroglycerin studies.
In the remaining 13 patients, dobutamine was
administered intravenously at a rate of 5 gg/kg/min
to increase the contractility. When a new steady state
was achieved 10 minutes after dobutamine administration, left ventriculography was repeated with the
simultaneous measurement of left ventricular pressure. Therefore, in these 13 patients, two ventriculographies were performed, once during control conditions and once after dobutamine administration.
The total amount of contrast agent administered
was less than 105 ml in each patient. To dissipate the
effects of the contrast agent, a second and third
angiogram were performed 30 minutes apart. A
bipolar electrode catheter was positioned in the high
right atrium for pacing. Heart rate was maintained
constant at 86±9 beats/min (range, 73-105 beats/
min) in each patient throughout the study.
Data Analysis
For the evaluation of left ventricular volume, cinefilms were projected through a video camera, and
ventricular silhouettes were obtained with a light pen
on a video screen. A computer system (LVV100,
Philips) was used to calculate the volume from the
single-plane cineventriculogram by applying the arealength method of Kennedy et al.21 The volume variable
was corrected for overestimation and normalized with
respect to body surface area.2' All extrasystolic and
postextrasystolic beats were excluded, and only the
atrial paced beats were subjected to analysis. Pressurevolume loops were plotted using synchronous pressure
and volume data. The angiographic ejection fraction
was calculated according to the standard formula.
Ees and Pmax
The end-systolic pressure-volume point was identified as the left upper corner of the pressure-volume
trajectory.8 The set of three end-systolic pressurevolume points in each patient was subjected to a
linear regression analysis. This regression line indicated the conventional ESPVR, and the slope of this
line was the conventional Ees. The volume axis
intercept (Vo) of the ESPVR line was obtained
(Figure 1A). We designated the Pmax(E) at each
end-diastolic volume obtained as the intersection of
the ESPVR and the vertical line at the end-diastolic
volume Pmax. Figure 1A shows a schematic of a
conventional ESPVR line determined by a set of
three pressure-volume loops. Each ejecting contrac-
204
Circulation Vol 83, No 1, January 1991
TABLE 1. Summary of Clinical and Catheterization
HR
(beats/min)
DiagPatient Age Sex nosis
1
2
3
1
Angiotensin 11
1
59
M CPS
92 92 92 110
2
63
F DCM 81 81 73 108
F DCM 91
91
3
68
91 125
4
58
M CAD
90 90 90 97
33
M CAD
92 85 84 108
5
M CAD
6
48
83 82 80 94
M CAD
7
61
79 79 72 106
M CAD
81 78 78 100
8
45
54
86 85 83 109
Mean
6
8 12
SD
11
6
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Nitroglycerin
9
59
10
65
11
62
12
13
14
15
16
Mean
53
58
49
64
70
60
7
M
M
M
M
M
M
F
F
CPS
CAD
CAD
CAD
CAD
CAD
CAD
CAD
101
82
105
80
86
86
73
79
87
11
102
81
105
80
100
85
73
79
88
12
105
81
104
78
92
83
75
79
87
138
188
178
173
192
155
152
130
163
23
Data
ESP
(mm Hg)
2
3
124
147
135
131
111
102
118
107
124*
16
128
149
155
148
162
145
134
111
142
155
176
164
156
142
145
125
153t
16
118
146
123
144
135
136
104
86
EDP
(mm Hg)
1
2
3
ESV
EDV
(mi/Mr)
(mi/mr')
1
2
3
1
27
81
36
44
39
32
59
33
60
105
49
49
65
6 8
9 11
8 9
10 10
9 10
7 8
9 11
8 10
8 10t
1
1
9 21
14 49
16 26
14 25
13 31
12 23
16 44
10 28
13t 30
3
8
25
67
32
30
31
25
52
30
33*
9
14 10
12 8
14 12
17 12
20 16
14 8
12 10
7 6
14 10t
4 3
6
6
12
12
12
8
8
6
30
27
19
21
27
24
28
45
9t 28
3
8
28
19
17
18
23
22
21
38
23*
7
41t
12
25
18
15
16
17
19
15
29
EF
(%)
2
3
1
66
118
59
60
69
61 66
91 89
74 89
70 74t
17
14
68
119
66
78
79
82
95
93
84t
16
65
53
47
50
52
63
52
63
58
7
63
43
45
51
54
62
42
67
56
9
75
73
46
54
72
71
72
80
68
12
62
62
37
46
46
66
53
58
60
63
59
61
71
66
60
43
54t 60
10
8
59
71
62
64
72
69
69
45
64*
9
2
68
65
44
50
59
70
68
68
61*
10
3
60
32
45
43
51
61
37
65
52t
11
60
72
59
64
73
72
72
50
65
8
142t 124t
19t
11
16
SD
21
5
heart
HR,
rate; ESP, end-systolic pressure; EDP, end-diastolic pressure; ESV, end-systolic volume; EDV, end-diastolic volume; EF, left
ventricular ejection fraction; CPS, chest pain syndrome; DCM, dilated cardiomyopathy; CAD, coronary artery disease; 1, control state; 2 and
3, alteration of loading condition.
*p<0.01, tp<0.001, tp<0.05 compared with control state.
tion had its Pmax; therefore, each of the angiotensin
II and nitroglycerin studies had three different Pmax
values but only a single Ees.
Pmax(E)
The left ventricular pressure was input to an
analog-to-digital converter (ADTEC, AB98- 05A)
and stored in a digital computer (NEC PC9801VX21) to be processed later. The digital data
were analyzed using software developed in our laboratory for the personal computer. To estimate the
pressure curve [P(t)] of an isovolumic contraction at
an end-diastolic volume of an ejecting contraction, a
nonlinear least-squares approximation technique was
used15; the P(t) we used was the same that Sunagawa
et al15 used:
P(t) = 1/2Pmax(E)[1 - cos(wt + C)] + EDP
where Pmax(E) is an estimated peak isovolumic
pressure point, w is an angular frequency, C is a
phase shift angle of the sinusoidal curve, and EDP is
the left ventricular end-diastolic pressure. Figure 2
schematically represents the relation between the
ejecting contraction and the estimated isovolumic
contraction in the pressure-time diagram. P(t) was
obtained by fitting the measured left ventricular
pressure curve segments from the end-diastolic pressure point to the peak positive dP/dt and from the
pressure point of the peak negative dP/dt to the same
level as the end-diastolic pressure of the preceding
beat. The left ventricular end-diastolic point was
defined as the pressure at which dP/dt first exceeded
200 mm Hg/sec.17-20
Ees(E)
The straight line was drawn from the Pmax(E)volume point tangential to the left upper corner of
the real pressure-volume loop of the ejection contraction (Figure IB). This tangential line was defined
as the estimated ESPVR line. The slope of this
estimated line was Ees(E), and the volume axis
intercept of the estimated ESPVR line was Vo(E).
Pmax(E) and Ees(E) were obtained under three
different loading conditions in both the angiotensin
II and nitroglycerin studies. Pmax(E) and Ees(E)
were also obtained under control and increased
inotropic states.
Statistical Analysis
The correlation between the conventional Ees and
Ees(E) in the respective patients was obtained by
least-squares regression analysis. The correlation be-
Takeuchi et al Single-Beat Estimation of Contractility
205
loading conditions in both the angiotensin II and
nitroglycerin studies. All results are summarized as
mean±SD, and a significant difference was assumed
to be present at a probability of less than 0.05.
To test the reproducibility of Pmax(E), we compared Pmax(E) among five consecutive beats under
control and increased inotropic states in the 13
patients with heart disease. The variation was assessed using the coefficient of variation calculated as
the standard deviation divided by the mean, expressed as a percentage.
A
W
X
&D
Volume (mt)
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B
-
0
02
Volume (.d)
FIGURE 1. Panel A: Schematic of the conventional endsystolic pressure-volume relation (ESPVR) line determined by
a set of three pressure-volume loops. Pmax is the peak
isovolumic pressure at end-diastolic volume. Ees is the slope of
ESPVR. Panel B: Schematic of a method for determining the
ESPVR line from a single ejecting beat. Pmax(E) at enddiastolic volume was estimated by a curve-fitting technique.
ESPVR (estimated ESPVR) line was drawn from the
Pmax(E) -volume point tangential to the left upper comer of
the pressure-volume loop. Slope of this line is the estimated
Ees [Ees(E)], and the volume axis intercept of the estimated
ESPVR line is the estimated Vo [Vo(E)].
tween the Pmax and Pmax(E) and the correlation
between the conventional Vo and Vo(E) were also
obtained by least-squares regression analysis. The
individual data points, regression lines, correlation
coefficients, and standard errors of the estimates are
shown in Figures 3-5. Multiple comparisons were
performed by analysis of variance. Intergroup comparisons were performed by paired t tests with an
appropriate correction for the performance of multiple comparisons with Bonferroni's inequality. Analysis of covariance was used to compare slopes of the
regression lines between the control and pressure-
Results
Reproducibility of Pmax(E)
The reproducibility of measures of Pmax(E) was
tested under control and increased inotropic states in
the 13 patients with heart disease. The mean percent
standard deviation of the estimate was 7.3% and
6.9% in control and increased inotropic states, respectively. There were no significant differences of
mean percent standard deviation of the estimate
between control and increased inotropic states.
Angiotensin II and Nitroglycerin Studies
Table 2 lists Pmax and Pmax(E) of all patients
subjected to the angiotensin II and nitroglycerin
studies. There were no significant differences between Pmax and Pmax(E) at each level of loading
conditions in both angiotensin II and nitroglycerin
studies. Figure 3A shows the relation between Pmax
and Pmax(E) under three different loading levels in
the angiotensin II study, In the angiotensin II study,
Pmax(E) correlated with Pmax under the control
condition [Pmax(E) =0.96Pmax+ 18.0;r= 0.86,
p<0.01, SEE=37.0 mm Hg], under the mildly increased afterload condition [Pmax(E)=0.72 Pmax+
90.7; r=0.89, p<0.01, SEE=29.7 mm Hg], and under
the largely increased afterload condition
[Pmax(E)=0.87Pmax+64.2; r=0.89, p<0.01, SEE=
40.4 mm Hg].
Figure 3B shows the relation between Pmax(E) and
Pmax under three different loading levels in the
nitroglycerin study. In the nitroglycerin study,
Pmax(E) correlated with Pmax under the control
condition [Pmax(E) =0.68Pmax+ 123, p <0.01; r=0.89,
SEE=36.5 mm Hg], under the mildly reduced afterload condition [Pmax(E)=0.49Pmax+ 169, p <0.01;
r=0.72, SEE=47.2 mm Hg], and under the largely
reduced afterload condition [Pmax(E)=0.81Pmax+76,
p<O.Ol; r=0.87, SEE=38.9 mm Hg]. The slope of the
regression line was not changed significantly by changes
in loading conditions.
Table 2 also lists Ees, Ees(E), Vo, and Vo(E) of all
patients in the angiotensin II and nitroglycerin studies. One-way analysis of variance indicated that there
were no significant differences between Ees and any
Ees(E), although Ees(E) tended to increase with an
increasing afterload in the angiotensin II study. Figure 4A shows the relation between the conventional
Ees and Ees(E) under three different loading levels
Circulation Vol 83, No 1, January 1991
206
o
peak positive dp/dt
1600
a)
m- I
0
_E1600
300
peak negative dp/dt
r
a)
L
-
left ventricular pressure
Ut)
Ur)
a1)
--
estimated isovolumic pressure
L-
J
L-
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c
(D
pressure (EDP) to peak positive
dp/dt and from the point of peak
negative dp/dt to the level of EDP of
the preceding beat. Pmax(E), estimated peak isovolumic pressure; t,
time after the onset of pressure rise;
dotted curve, phase shift angle of the
sinusoidal curve for the isovolumic
pressure; T, duration of contraction
(T = 21T/o; , angular frequency).
200 V
CL
I
E
E
100
FIGURE 2. Schematic of the curvefittinig method for obtaining the estimated pressure curve [P(t)]. P(t)
was fitted by left ventricularpressure
curve segments from end-diastolic
F
(L)
-J
0
a
0
0.2
1
0.4
a~
a
0.6
sec
in the angiotensin II study. In the angiotensin II study,
Ees(E) correlated with the conventional Ees under the
control condition [Ees(E)=1.01 Ees+0.1; r=0.88,
p<0.Ol, SEE=0.94 mm Hg/mr2], under the mildly
increased afterload condition [Ees(E)=0.92 Ees+0.70;
r=0.82,p<0.01, SEE=1.09 mm Hg/mi/M2], and under
the largely increased afterload condition [Ees(E) =
0.93 Ees + 0.92; r=0.83,p<0.01, SEE=1.06 mm Hg/
mI/M2].
Figure 4B shows the relation between the conventional Ees and Ees(E) under three different loading
levels in the nitroglycerin study. In the nitroglycerin
study, Ees(E) correlated well with the conventional Ees
under the control condition [Ees(E)=0.67 Ees+1.90;
r=0.93,p<0.001, SEE=1.35 mm Hg/m/rn2], under the
mildly reduced afterload condition [Ees(E)=0.45
Ees+2.90; r=0.79,p<0.05, SEE=1.28 mm Hg/mi/M2],
and under the largely reduced afterload condition
[Ees(E)=0.81 Ees+1.70; r=0.92,p<0.001, SEE=1.27
mm Hg/mi/r2]. The slope of the regression line was not
changed significantly by changes in loading conditions.
There were no significant differences between
Vo(E) of the estimated ESPVR and Vo of the
conventional ESPVR in each loading condition. Figure 5 shows the relation between Vo and Vo(E)
under the control loading condition in the angiotensin II and nitroglycerin studies. Under the control
condition, Vo(E) correlated well with Vo in the
angiotensin II study (r=0.94, p<0.001, SEE=5.48
ml), and under the control condition, it correlated
poorly with Vo in the nitroglycerin study (r=0.62,
p<0.09, SEE=6.27 ml).
Effect of Dobutamine
Table 3 lists the effect of dobutamine infusion on
hemodynamic variables and ESPVR. The administration of dobutamine resulted in an increase in
end-systolic pressure, ejection fraction, and Pmax.
Peak positive dP/dt increased from 1,667±343 to
2,320+451 mm Hg/sec, and the ESPVR increased
from 3.9+1.6 to 5.7+2.4 mm Hg/mi/mi2 (p<0.01).
Figure 6 shows Ees(E) values before and after dobutamine infusion in 13 patients. Ees(E) increased from
5.6± 1.4 to 7.4±2.0 mm Hg/mI/M2 (p<0.01), resulting
in a mean increase of 32%.
Discussion
The aim of this study was to assess the feasibility of
the method to estimate the Ees of the ESPVR from
a single pressure-volume loop of the human heart.
We obtained Pmax(E) by a curve-fitting technique
from the left ventricular pressure curve.15 A straight
line was drawn from the Pmax(E)-volume point
tangential to the left upper corner of the original
pressure-volume loop.16 This tangential line was the
estimated ESPVR line, and the slope of this estimated line was [Ees(E)]. We found that Ees(E) was
close to the conventional Ees value obtained from
Takeuchi et al Single-Beat Estimation of Contractility
TABLE 2. Summary of End-Systolic Pressure-Volume Relation
Pmax
Pmax(E)
Ees
Vo
(mm Hg)
( H
(mm Hg)
2
2
1
3
Patient
1
3
m/lmn2)
(mi/M2)
Angiotensin II
338
346
5.1
-0.4
240
290
320
1
308
192
194
-23.0
229
1.5
181
231
2
176
312
1.2
324
230
277
4.8
254
339
3
276
3.3
-6.9
191
255
317
4
183 220
390
5.8
12.2
339
358
484
307
328
5
327
5.4
5.9
288
299
431
299
415
6
2.6
3.9
248
240
270
224
220
234
7
429
5.1
8.5
383
404
401
408
8
335
4.2
0.2
266
300
349
289*
325*
Mean
258
84
74
86
1.6
11.0
69
60
62
SD
Ees(E)
207
Vo(E)
(mi/M2)
(mm Hg/ml/m2)
1
2
3
1
2
3
3.4
1.3
5.6
3.8
6.8
5.1
3.0
6.0
4.4
1.8
4.0
1.7
7.1
4.1
6.7
4.8
3.3
5.0
4.6
1.8
4.3
2.2
-10.6
-33.3
3.2
-0.6
15.1
4.4
8.4
10.9
-0.3
15.4
-6.1
-17.6
12.9
-2.6
14.8
4.4
15.6
8.2
3.7
11.7
-5.9
12.9
4.6
9.0
19.9
7.0
18.5
5.3
8.9
8.3
5.5
4.6
8.1
5.7
3.5
4.6
4.8
1.8
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Nitroglycerin
4.0
-4.8
292
274
277
3.4
3.6
-7.6
-2.4
9
313
289
265
4.3
-10.7
-12.6
367
4.8
416
338
336
5.0
4.1
4.3
-10.3
-17.7
-16.7
10
406
355
424
13.8
6.0
469 377
385
10.8
12.1
4.9
576
518
8.3
2.5
-2.0
11
7.8
7.7
-1.4
322
6.0
-7.5
426 396
382
8.0
-1.2
-1.5
12
366 345
373
5.4
6.7
5.8
-5.7
436 404
8.4
-8.6
1.3
- 1.0
449
374
295
13
-17.2
377
352
4.9
4.9
4.6
-8.0
-11.1
311
3.7
383
-7.9
14
328 325
310
296
260
3.7
3.5
4.1
-13.3
3.7
-14.2
-17.6
-10.7
314
300
246
15
3.9
3.3
13.1
9.4
2.9
267
283
4.0
2.8
-2.3
232
194
165
16
225
5.6
5.3
6.1
-4.6
-5.7
-4.2
-7.3
375
298*
5.5
368
339*
337t 319*
Mean
9.1
7.4
75
63
72
2.5
1.9
3.1
8.8
7.7
77
3.5
99
92
SD
Pmax, peak isovolumic pressure point of end-systolic pressure-volume relation (ESPVR) line; Ees, slope of ESPVR; Vo, intercept on the
x axis of the ESPVR; Pmax(E), peak isovolumic pressure from the curve-fitting technique; Ees(E), Ees from single-beat analysis; Vo(E),
intercept from single-beat analysis; 1, control state; 2 and 3, alteration of loading condition.
*p<0.001, tp<0.05 compared with control state.
three pressure-volume loops under different loading
conditions and that Ees(E) increased significantly
after dobutamine administration. The values for
Ees(E) (mean, 5.0+2.2 mm Hg/ml/m ) in the subjects
in this study are comparable with those for Ees
determined in humans by the conventional method
reported in the literature.9,10
To obtain Pmax(E), we used the method originally
described by Sunagawa et al,15 as mentioned in the
"Methods." However, Pmax(E) may have been influenced by the chosen range of the isovolumic phase
for the curve fitting. To study this possibility, we
compared three estimated isovolumic pressure
curves from the same ejecting pressure curve by using
three different end-diastolic points identified as the
pressure points at dP/dt values of 200, 300, and 400
mm Hg/sec. The goodness of fit of the nonlinear
least-squares approximation technique, which fitted
the isovolumic phase with the equation of P(t) described in the "Methods," was assessed statistically
by the correlation coefficients and standard error of
the estimate as previously described. The correlation
coefficients were extremely high (0.999-1.000), and
there were no significant differences among the three
chosen ranges of isovolumic pressure curve fitting.
However, the standard errors of the estimate were
0. 18+0.12, 0.27+0.12, and 0.37+0.11 mm Hg, respec-
tively. The isovolumic pressure curve with end-diastolic point at the dP/dt value of 200 mm Hg/sec had
the smallest standard error of the estimate. Thus, the
chosen range of isovolumic pressure curve fitting in
this study seems to be most appropriate for Pmax(E).
Recent studies revealed nonlinearity of ESPVRs
under a variety of conditions. Burkhoff et al22 reported that the ESPVR of the isovolumically beating
isolated canine left ventricle contained systematic
nonlinearity when assessed throughout a wide range
of the left ventricular contractile state. Kass et a123
also reported that in situ ESPVRs determined rapidly throughout a sufficiently wide range of loads
were frequently curvilinear. However, Little et a124
observed that this nonlinearity, present in all inotropic states, did not prevent the ESPVR from being
well approximated by a straight line or the Ees from
providing a sensitive and consistent index of the
contractile state. Moreover, Igarashi et a125 reported
for isolated dog heart preparations that the slope of
the ESPVR line determined from the aortic occlusion method for middle ejection fraction was close to
the slope of the ESPVR line determined from five
steady-state contractions.
Although ESPVR throughout a wide pressurevolume range may be nonlinear even in the human
heart, our method could estimate the slope of
Circulation Vol 83, No 1, Januarv 1991
208
A.
Angiotensin 11 Study
A.
Angiotensin 11 Study
500
400
E
CD
rs
E
I
E
x
0.CL
E
300
E
U)
200
100
Pmax
Ees
(mmHg)
W
Downloaded from http://circ.ahajournals.org/ by guest on April 28, 2017
Nitroglycerin Study
B.
B.
(mmHg/milm 2)
Nitroglycerin Study
600
500
"E
m
1-
E
E
400
FE
300
W
0.
0
w)
200
100
100
200
300
Pmax
400
500
2
600
(mmHg)
4
6
Ees
8
10
12
14
(mmHglml/m 2)
FIGURE 4. Panel A: Plot of relation between conventional slope
of the end-systolic pressure-volume relation (Ees) and the
estimated slope [Ees(E)] under three different loading levels in
angiotensin II study. *, under the control condition [Ees vs.
Ees(E) -1; r=0.87, p<0.01, SEE=0.94 mm Hg/mll. 0, mildly
increased afterload condition [Ees vs. Ees(E)-2; r=0.82,
p<O.O1, SEE=1.09 mm Hg/mli. x, largely increased afterload
condition [Ees vs. Ees(E) -3; r = 0.83, p<0.01, SEE= 1.06
mm Hg/mli. Panel B: Plot of relation between conventional
Ees and Ees(E) under three different loading levels in nitroglycerin study. *, under the control condition [Ees vs. Ees(E) -1;
r=0.93, p<0.01, SEE=1.35 mm Hg/mli. 0, mildly reduced
afterload condition [Ees vs. Ees(E)-2; r=0.79, p<0.005,
SEE=1.28 mm Hg/ml. x, largely reduced afterload condition [Ees vs. Ees(E) -3; r=0. 92, p<0. 001, SEE=1.27 mm
FIGURE 3. Panel A: Plot of relation between peak isovolumic
(Pmax) and estimated pressure [Pmax(E)] under three
under the
different loading levels in angiotensin II study.
control condition [Pmax vs. Pmax(E)-1; r=0.86, p<0.01,
SEE=37.0 mm Hg]. 0, mildly increased afterload condition
[Pmax vs. Pmax(E) -2; r=0.89, p<0.01, SEE =29.7mm Hg].
x, largely increased afterload condition [Pmax vs.
Pmax(E) - 3; r = 0. 89, p < 0. 01, SEE = 40.3 mm Hg]. Panei B:
Plot of relation between Pmax and Pmax(E) under three
different loading levels in nitroglycerin study. *, under the
control condition [Pmax vs. Pmax(E)-1; r=0.89, p<0.01,
SEE=36.5 mm Hg], 0, mildly reduced afterload condition
[Pmax-Pmax(E)-2; r=0.72, p<0.01, SEE=47.2 mm Hg].
x, largely reduced afterload condition [Pmax versus
Pmax(E) -3; r=0.87, p<0.01, SEE=38.9 mm Hg].
Hg/mli.
ESPVR throughout a physiological range. The evaluation of Ees(E) in this study was not based on the
assumed linearity outside the operational pressurevolume range but within the operational pressurevolume range. Figure 7 presents the schematic of the
relation between "true" ESPVR, indicated by a solid
line, and our estimated linear ESPVR, indicated by a
broken line. This broken line is close to the "true"
ESPVR within the physiological range.
In the present study, conventional Pmax, by a set of
three pressure-volume loops, correlated with
Pmax(E) by a curve-fitting technique using the left
ventricular pressure curve, as shown in the "Results." This agreement indicates that the two different methods estimated similar isovolumic pressures for individual ejecting contractions. But "true"
Pmax at end-diastolic volume may be different from
our conventional Pmax(E), owing to the nonlinear
pressure
Takeuchi et al Single-Beat Estimation of Contractility
20
209
19
. £ -.
-
p<O.001
10 .j
E 100)
0.
-10
E
E
.
W
-20 .
0)
w
6-
-30 .
4-
{
i
-40 .
.40
-30
-10
-20
Vo
0
10
20
(ml)
Downloaded from http://circ.ahajournals.org/ by guest on April 28, 2017
FIGURE 5. Plot of relation between the volume axis intercept (Vo)
and the estimated intercept [Vo(E)l under the control loading
condition in angiotensin II (r=0.94, p<0.001, SEE=5.48 ml)
and nitroglycerin (r=O.62, p<0.09, SEE=6.27) studies.
ESPVR outside the operational pressure-volume
range. In the present study, conventional Ees also
correlated well with Ees(E) under each level of
loading condition, and Ees(E) was sensitive to a
positive inotropic intervention. Thus, Ees(E) can
estimate Ees throughout a physiological range and
detect the change of contractility in human hearts.
Our major concern is a simple estimation of the slope
of the ESPVR throughout a physiological range but
not an estimation of "true" Pmax.
71
Control
Dobutamine
FIGURE 6. Plot of the estimated slope of the end-systolic
pressure-volume relation before and after administration of
dobutamine. Mean +SD ofindividual mean Ees(E) values are
indicated by vertical bars.
There are several limitations in this study intrinsic
to the human heart. To obtain the three pressurevolume loops, we changed the loading condition. It
has been known that alterations in afterload can
change the ESPVR. Several investigative teams
showed parallel leftward shifts of ESPVR with increased resistance.1126-27 They suggested that the
volume intercept is dependent on the changes in
afterloads and that the slope of ESPVR is insensitive
to a wide range of changes in afterload. Freeman et
TABLE 3. Effect of Dobutamine Infusion on Hemodynamic Variables and End-Systolic Pressure-Volume Relations
HR
Ees(E)
ESP
EDP
ESV
EDV
Pmax
(mm Hg/
Vo(E)
(beats/
min) (mm Hg) (mm Hg) (mi/m2) (mi/M2) EF (%) (mm Hg)
(mi/m2)
mi/M2)
Diag
D C
D
C D
D
C D
D
D
C
C
C
C
D
Patient Age Sex nosis C D C
64
118
11
44
51
M CAD 92 92 116
12
53 114 109
293 343 3.6 4.0 31.3 23.5
71
1
11 54 47
89 92 40 50 294 407 5.0 6.2
M CAD 99 99 119 125 9
2
45
2.7 26.2
M CAD 78 78 128 162 0
12 29 23
66 67 57 66 355 550 6.0 8.8
7.4
4.3
50
3
M CPS 92 92 155 150 9
13 25 18
57 53 57 67 353 435 6.2 8.0 -0.7 - 1.0
4
40
M CAD 82 86 100 125 13
10 68 156
103 100 34 44 242 317 4.0 4.4 42.6 27.9
62
5
8 21 15
65 62 68 77 320 529 4.6 8.0 -4.9 -4.1
53
M CAD 82 82 118 149 9
6
34 41 29
M CAD 60 57 130 154 12
93 85 56 66 453 619 6.2 8.2 20.5
9.9
7
68
54 54 56 60 331 410 6.9 8.7
13 24 22
M CAD 93 89 123 127 13
6.0
7.4
8
70
12 25 22
77 86 67 75 350 575 5.0 6.6
6.2 -1.7
M CAD 88 88 96 154 8
9
45
77 78 65 70 425 569 6.1 8.1
6.7
7.8
M CAD 92 92 123 125 8 -11 27 23
55
10
7 23 19
70 64 67 70 473 605 7.3 10.4
5.4
5.7
M CAD 80 82 130 143 12
51
11
61
56 54 56 399 460 8.1 9.8
11.2
9.6
8 28 25
F CAD 90 98 133 151 14
12
68
73
63
220
365
4.2
5.4
5.9
82
115
12
14
38
27
73
48
20.3
74
75
M
CAD
13
58
9.3
11 36 29*
77 75 55 63* 347 476* 5.6 7.4* 14.0
57
85 86 119 138 10
Mean
76 104
1.4 2.0
13.9 10.4
9 16 14
18 18 11 10
10 11 20 16 4
10
SD
HR, heart rate; ESP, end-systolic pressure; EDP, end-diastolic pressure; ESV, end-systolic volume; EF, ejection fraction; Pmax, peak
isovolumic pressure point of end-systolic pressure-volume relation (ESPVR); Ees(E), slope of the ESPVR from single-beat analysis; Vo(E),
intercept from single-beat analysis; C, control; D, dobutamine administration.
*p<0.001 compared with control.
Circulation Vol 83, No 1, January 1991
210
during acute variation in arterial pressure loading.32
"true` peak isovolumic
a
~~~~~~~~~~pressure
i)
E
_
Volume
(ml)
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FIGURE 7. Schematic of the relation between the "true"endsystolic pressure-volume relation (ESPVR), indicated by solid
line, and our estimated linear ESPVR, indicated by dashed
line. *, "true" peak isovolumic pressure point; 0, peak isovolumic pressure points obtained as the intersection of the
estimated linear ESPVR from a set of three end-systolic
volume points and the vertical line at end-diastolic volume.
a128 reported that the composite ESPVRs under
angiotensin II and nitroprusside interventions had
steeper slopes and were shifted to the right compared
with those generated by vena caval occlusion in the
animals. Baan and Van der Velde29 reported the
dependency of the ESPVR on the type of loading
intervention. However, several clinical studies30 have
failed to demonstrate any significant ESPVR shift of
alteration between relations generated by increased
afterload compared with those generated during
vena caval occlusion. Kass and Maughan30 suggested
the potential differences of the influence of afterload
on ESPVR between human and canine preparations.
Our present study indicates that there were no
significant differences of the relation of conventional
Ees compared with Ees(E) under each loading condition between the angiotensin II and nitroglycerin
studies. Thus, although ESPVR may be dependent
on the way in which the loading condition is altered,
changes in pressure-volume relations caused by alterations in load seemed to be smaller than those
caused by varying inotropic state in the human
heart.30
The changes in arterial pressure can also activate
the baroreceptor reflex.31 Because we maintained a
constant heart rate using atrial pacing, the contribution of chronotrophic changes to contractility was
absent. Suga et a13' reported the effect of the carotid
sinus baroreflex changes on the instantaneous pressure-volume ratio, Emax. The end-systolic pressure
changed by about + 15% with a +50% change in the
mean pressure at about 100 mm Hg.31 In the present
study, a +40% change in the mean aortic pressure by
two interventions may have altered the end-systolic
pressure by only about
12%. Other data have
suggested that sympathetically mediated reflexes
contribute minimally to left ventricular contractility
However, our data cannot entirely exclude the possible effect of changes in the loading condition on the
linearity of the ESPVR line and contractility through
autonomic reflexes.
Vo of the ESPVR line was obtained by linear
extrapolation. Vo may be considered as the volume
to which the ventricle would contract if it were totally
unloaded, and negative Vo values would be physiologically impossible. In the present study, however,
apparent negative Vo and Vo(E) values were obtained, and the relation between Vo and Vo(E)
showed substantial variances. Similar negative Vo
values have been reported in experimental and clinical studies.1014 Vo was obtained by extrapolation,
and the extrapolation of the linear ESPVR may yield
negative Vo axis intercepts. Negative Vo values may
also possibly be related to the reduced slope values
resulting from pharmacological intervention.
All of the indexes of contractile function demonstrated a significant increase with positive inotropic
stimulation. Peak positive dP/dt is as effective for
defining increases in contractility as is the ESPVR.
However, peak positive dP/dt may be augmented by
increases in heart rate, preload, or afterload. Several
investigations33-35 reported that a single measurement of the end-systolic pressure-volume relation
can be a useful index of left ventricular performance.
Only when the volume intercept of ESPVR is zero is
the pressure-volume relation a reliable index of
myocardial contractility. The pressure-volume relation may also be dependent on afterload.36 Kass et
a137 examined the influence of alteration in preload
and afterload on indexes of contractile function and
conclude that any advantage of the ESPVR will
derive not from the magnitude of its responses to
inotropic change, which is smaller than most other
indexes, but from its relative insensitivity to load
alteration throughout a wide range of load. Therefore, we considered that our method of assessing
contractility on a beat-by-beat basis may be better
than other indexes.
In summary, we examined the clinical applicability
of Ees by a single-beat analysis. Pmax(E) was extrapolated by curve fitting, and the ESPVR line was
obtained from the Pmax(E)-volume point tangential
to the left upper corner of the pressure-volume
loops. We were able to estimate the single-beat Ees
by the slope of this ESPVR line, and we found that
Ees(E) was reasonably close to the conventionally
obtained Ees and was sensitive to a positive inotropic
intervention. We conclude that Ees(E) obtained by
the single-beat analysis method facilitates assessment
of the beat-by-beat ESPVR and the ventricular contractile state of the human heart.
Appendix
We calculated the sum of the squares of the
difference between observed and predicted pressures
during isovolumic left ventricular pressure. The fraction of the residual sum of squares to the number of
Takeuchi et al Single-Beat Estimation of Contractility
points analyzed, that is, the standard error of estimate (SEE), was used to evaluate the goodness of fit
according to the following equation:
15.
/N
SEE=-/N
Z [Pi(ob)-Pi(pre)12
16.
i=i
Downloaded from http://circ.ahajournals.org/ by guest on April 28, 2017
where Pi(ob) is observed pressure, Pi(pre) is predicted pressure, and N is the number of pressure
points analyzed.
17.
Acknowledgments
We gratefully thank Dr. Hiroyuki Suga, National
Cardiovascular Center Research Institute, Osaka,
Japan, for his critical review of the manuscript and
Masaaki Baba, PhD, for his excellent assistance with
computer analysis of pressure waves. We also acknowledge Dr. Yoshio Ohnishi, Dr. Kenici Hirata,
Dr. Shusuke Miwa, and Dr. Yuichi Matsuda for their
support in our cardiac catheterization laboratory.
18.
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KEY WORDS
* left ventricular function *
isovolumic
contraction * pressure-volume loop * single ejecting beat
Downloaded from http://circ.ahajournals.org/ by guest on April 28, 2017
Single-beat estimation of the slope of the end-systolic pressure-volume relation in the
human left ventricle.
M Takeuchi, Y Igarashi, S Tomimoto, M Odake, T Hayashi, T Tsukamoto, K Hata, H Takaoka
and H Fukuzaki
Downloaded from http://circ.ahajournals.org/ by guest on April 28, 2017
Circulation. 1991;83:202-212
doi: 10.1161/01.CIR.83.1.202
Circulation is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
Copyright © 1991 American Heart Association, Inc. All rights reserved.
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