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Clinical experience with the use of computers for calculation of cardiac output
New Method Clinical Experience with the Use of Computers for Calculation ALBERTO
BENCHIMOL, M.D., F.A.c.c.,
PHILIP
R.
La Jolla,
S
AKRE,
M.D. and E.
GREY
DIMOND, M.D., F.A.C.C .
California
studied separately with the sole purpose of obtaining dye curves which were expected to have a low cardiac output with either a markedly prolonged disappearance time or an early curve of intracardiac shunt. It is well known that under these circumstances the calculation of the cardiac output is grossly inaccurate by any method. Several methods were used to induce changes in the cardiac output. Exercise was used in 2 cases, pacing of the heart with an external pacemaker in 2 cases, administration of nitroglycerin in 1 and conversion of atrial fibrillation to sinus rhythm in 3 cases. Cardiac outputs were determined with the indicatordilution technic using indocyanine green (CardioGreen@) as an indicator. Detailed description of our technic has been presented in previous reports.lOJ1 Briefly, the technic consists of injecting 6.25 mg. of the indicator (indocyanine green) into the vein followed by flush of the tube containing the dye with 15 ml. of 5% dextrose. The blood is withdrawn from the artery at a constant rate of 38.2 ml./min. All injections were made into the medial antecubital vein through a No. 18 Cournand needle. Sampling was from the brachial artery through a No. 18 Cournand needle in 10 cases and from the central circulation in 7 cases. A Gilford cuvette densitometer (Model 103 IR) was used to detect the injected dye. Calibration Procedure: Prior to the injection of any dye 50 ml. of arterial blood is withdrawn and placed in a flask containing 50 mg. of heparin. A standard (blood without dye) and four solutions containing 1, 2, 3 and 5 mg. of dye per liter of blood were used for calibration purposes. The solutions were then withdrawn through the cuvette using the same attenuation and flow rates as were used throughout the study. A dye factor was then obtained. The curves were recorded on the Electronics for Medicine (DR-8 Model) oscilloscopic
methods have been suggested to calculate the cardiac output from indicatordilution curves. The Hamilton formula1~2 has been used for many years for that purpose and the results have been quite satisfactory. At its best, this is a time-consuming technic requiring replotting of the curves on semilogarithmic paper followed by the calculation of the area under the curve by hand methods or by a planimeter. Simplifications of this original formula have been suggested with variable results.*-’ With the development of computers and their use in medicine, it became clear that these instruments could be used to integrate the area under the dye curve, thus providing a quick way to calculate the cardiac output. Preliminary reports on this subject have been reported by Moody et a1.8 and by Hara and Belville.g This study was undertaken in order to test the usefulness of the dye-dilution computer in the routine clinical determinations of cardiac output. EVERAL
MATERIALS
of Cardiac Output*
AND METHODS
One-hundred and seventeen indicator-dilution curves were obtained in 12 consecutive patients. The patients were selected at random disregarding the presence or absence of cardiac or circulatory abnormalities. There were two normal subjects, 7 with arteriosclerotic heart disease, 2 with pulmonary diseases and 1 with subaortic stenosis. In addition, 63 curves were obtained in 5 other patients. Three of them were in marked congestive heart failure ; 1 had severe mitral valve disease; and 1 had pentalogy of Fallot. These patients were
* From the Institute of CardioPulmonary Diseases, Scripps Clinic and Research Foundation, La Jolla, Calif. This study was supported in part by National Institutes of Health Research Grant HE-07983-01, Graduate Training Grant HTS-5513 and by the Timkin-Sturgis Foundation. VOLUME 15, FEBRUARY 1965
213
214
Benchimol, Cardiac Output
in L./min.
TABLE I with Hamilton’s Method
Calculated
H
C
H
1 2 3 4 5 6 7 8 9 10 11 12
4.24 5.20 5.29 3.78 6.31 3.50 4.00 2.81 3.55 7.73 4.91 3.63
4.47 5.64 5.85 4.18 5.97 3.62 4.40 2.99 3.92 7.80 4.74 3.72
4.50 5.29 3.85 4.43 6.47 3.67 4.06 2.25 3.78 7.48 4.66 4.85
and with the dye-dilution
2
3
C.O. -
FIG. 1. Hamilton
L. /m1n.
4
5
H
C
H
C
H
C
4.58 5.98 4.33 4.71 6.20 3.83 4.44 2.61 4.21 8.19 4.60 5.24
4.92 5.79 4.83 4.80 6.25 3.47 4.17 3.00 3.76 7.91 4.99 5.93
5.83 5.30 5.19 4.65 6.74 3.75 4.62 3.14 4.09 7.21 4.72 7.35
5.44 4.23 6.09 3.58 4.36 3.01 3.86 6.42 4.87 7.35
5.51 4.78 6.05 3.94 4.82 3.12 4.26 6.93 4.90 7.68
5.01 4.05 6.90 4.55 4.25 3.27 3.97 6.76 5.25 5.86
5.92 4.27 6.63 4.82 4.91 3.61 4.47 6.61 5.35 5.95
photographic recorder at a paper speed of 5 mm./sec. with one second time lines. A Sanborn computer (Model 130) was connected to the output of the densitometer. The sensitivity knob of the computer was set to the high position because the output of the Gilford densitometer is 0.5 v. The delay knob was set according to the appearance time of the dye and set to approximately 3 sec. prior A shorter delay was set for to the appearance time. the first curve. The cardiac output was calculated with the use of the Hamilton formula: =
Computer
C
* Numbers 1 through 10 represent the number of determinations. 10 determinations WA included. H = Hamilton method. C = computer.
C.O. (L./min.)
and with the Dye-Dilution 4
3
2
1* Case
Akre and Dimond
For the sake of simplification
only a maximum
of
0
*em
60 X 2 X dye factor area of curve in mm*. computer.
5
6
7
6
COMPUTER
Cardiac output (C.O.) calculated with the method and with the dye-dilution computer.
FIG. 2. Percentage difference between the cardiac output calculated with the Hamilton method and with the dye-dilution computer. THE AMERICANJOURNAL OF CARDIOLOGY
215
Computers for Calculation of Cardiac Output TABLE
6
I
(continued)
a
7
9
10
H
C
H
C
H
C
H
c
H
C
3.97 4.66 2.79 4.37 5.36 5.46 5.59
4.17 5.31 3.07 4.63 5.51 5.16 5.80
3.84 5.74 2.89 3.84 5.59 5.30 5.41
4.21 6.11 3.27 4.26 4.70 5.36 5.64
3.59 6.20 3.23 4.31 4.59 5.71 5.96
4.04 6.90 3.43 4.66 5.32 5.85 6.09
3.88 5.39 2.91 3.98 4.73 5.17 4.34
4.23 5.97 3.19 4.28 5.32 5.54 4.73
3.03 4.62 5.66 5.79 5.14
3.50 4.71 6.22 5.94 5.27
The corn&&r directly measures the area under the curve from the initial upward deflection until a point in the descending limb is reached which corresponds to 60 per cent of the peak concentration. From there the computer calculates the remainder of the area, assuming an exponential rate of fall. The figure obtained is then used in the following formula: CO. (L./min.)
=
60 X 1 (N,, -
N6)
c X ND
where Z = amount of dye injected into patient. NM = counts obtained from computer for calibration with a known concentration of blood-dye mixture. = counts obtained from computer for calibra& tion of blood without dye. c = amount of dye in mg./L. of blood used to obtain Nbd. ND ‘= counts obtained from computer during the actual run of the dye curve.
It was interesting to note that the values obtained with the computer were slightly higher than those obtained by the hand method for the majority of curves (Fig. 2). Although
this difference was within the acceptable margin of error, it was thought to be due to the calibration factor. The calibration curves are illustrated in Figure 3 where the linearity of the system can be easily demonstrated. Changes in the cardiac output were provoked by exercise, by changes in the heart rate with an external pacemaker and by the administration of drugs. 160.. A
.
In a few cases the curves were analyzed by six observers; the results are described in the next section. The data obtained from 117 cardiac output determinations in 12 patients were analyzed by estimating the standard deviation by means of within-group variance. In this manner, the error in calibration between the 12 different patients was systematically excluded (Table I).
I
A .
.
a
RESULTS In 117 curves obtained in 12 cases there was good agreement between the cardiac output calculated with the Hamilton formula and with The average of the percentage the computer. difference was 8 per cent with a standard deviation of the difference of 4.2 per cent (Fig. 1). VOLUME
15,
FEBRUARY
1965
1 :
I
I
3 I 2 0 CAL/BRAT/ON- mg of dye /L . bfood
FIG 3. Calibration curves obtained with the dye-dilution computer with blood-dye mixture of 1, 2 and 3 mg. of dye per liter of blood.
216
Benchimol,
Akre and Dimond
5.0
4.5 .t : j 4.5
4.0 I
w
i Hamilton
-
=computer
0: u
3.5
I I
C
3
I
2
4
4
IO
Hinuhs2
DURING
AFTER
EXERCISE
EXERCISE
Case 10. Effect of exercise on the cardiac output calculated by the computer and by the Hamilton method. Note a rise in the cardiac output during exercise recorded with both technics.
3.0
FIG. 4.
, I
I I
I I
I
2
3
Curve No. ?.5--
FIG. 6. Cardiac output determinations obtained in one patient calculated by the Hamilton formula by six observers. A slight difference is present for the same curve calculated by different observers (see Fig. 7).
6.5--
$ j
5.5-I
0: 6
4.5--
3.5--
2-Op40 * HEART
1
60
-
60
’
loo
1
120
’
100
’
60
r
M)
RATE - MIN.
FIG. 5. Case 12. Cardiac output determined with the use of Hamilton’s formula and with the computer in a patient with complete heart block. The heart rate was controlled by means of a pacemaker catheter placed in the right ventricle. Note the close relation of the figures obtained in both methods.
The cardiac output increased with exercise, and this change was detected by both technics. The small difference between the two methods at rest was maintained during exercise, thus providing further evidence that the calibration factor may be the dominant factor in explaining this small discrepancy (Fig. 4). The same type of response was seen when the heart rate was changed with the use of an external pacemaker in patients with heart block (Fig. 5). The reproducibility of the hand method is demonstrated in Figure 6. Six trained observers calculated several dye curves, and the measurements are illustrated in Figure 7. The difference found ranged from 1 to 7 per cent for the same curve calculated by the six observers.
It should be emphasized, however, that these measurements were made on sharp curves and in patients with normal cardiac output (Fig. 7). However, when curves with prolonged clearance time were measured by the same six observers, the difference was much greater, being 2 to 16 per cent (Fig. 8). In 1 case, two computer units were connected in parallel to the output of the densitometer in order to test the reproducibility of the computed area ; five curves were obtained. The results of these measurements are illustrated in Figure 9, the difference between the computers for the same dye curve being 2, 2,1,1, and 5 per cent. In addition, the difference for the calculated cardiac output made by the two computers with the hand method was 5, 4, 8, 0.6 and 4 per cent. Figure 10 illustrates the correlation between the area under the dye curve measured with the computer and with the Hamilton formula. In the additional 5 cases (63 curves) the curves were markedly abnormal, having a low peak concentration, a prolonged build-up time and disappearance time and a clearance time greater than 50 sec. These cases were included in the study with the idea of evaluating the usefulness of the computer in cases with prolonged clearance time and abnormally shaped curves. The average of the percentage difference was 25.2 per cent with a standard deviation of 11.0 per cent. The discrepancy between the two methTHE
AMERICAN
JOURNAL
OF
CARDIOLOGY
217
Computers for Calculation of Cardiac Output
No. 1 Observer 1 2 3 4 5 6 Computer
C.O. (L./mm.) 3.64 3.64 3.50 3.61 3.46 3.66 3.75
No. 2
No. 3
C.O. Obsy (L./min.) 3.57 2 3.56 3 3.50 4 3.83 5 3.58 6 3.72 Computer 3.94
C.O. (L./min.) Observer 1 4.52 2 4.58 3 4.64 4 4.67 5 4.82 6 4.55 Computer 4.82
FIG. 7. Dye-dilution curves from which calculations of the cardiac output were made by the Hamilton method illustrated in Figure 6.
ods was very large, as predicted, thus confirming the initial assumption that the computer should not be used to calculate curves with these characteristics (Fig. 8). This is often due to the fact that the descending limb does not fall in an exponential decay. Since the hand method is also inaccurate in estimating the area of these curves, it is concluded that both technics should be used with great caution in curves with a clearance time above 50 sec. The computer was also of no value in cases with curves with low peak concentration, thus indicating that one should attempt to obtain curves with great amplification. Smoothness of the baseline from the moment of injection to the appearance of the dye is also important since artifacts of this nature can alter the counts of the computer. A good, free arterial flow and a rigid plastic tube are the most important factors in the elimination of these artifacts. In addition, the delay control in the computer should be set as nearly as possible to the appearance of the dye, thus providing a better control for the elimination of the baseline artifacts. DISCUSSION The data presented indicate that the dyedilution computer is a useful and reliable method to estimate the area under the dye curve. Its main advantage is the timeVOLUME 15, FEBRUARY 1965
saving factor, providing a quick way to calculate the cardiac output, usually within 3 to 5 min., as compared with 30 to 60 with the hand method. This is particularly important in cases in which a large number of determinations 3.5 -’
e 4 I
3.0 -’
0’ G
‘“*
2
3
Curve No. FIG. 8. Cardiac output calculated on three curves with long clearance time by five observers (compare with Fig. 6 and 7).
218
Benchimol,
3
2
I
Curve
Akre and Dimond
4
5
No.
KG. 9. Case 5. Five determinations of the cardiac output calculated by the Hamilton method plus two computers in a patient with normal cardiac output. Observe the similarity of results. 2000 =!
,600
.
. .
s 9
with normal and abnormal cardiovascular systems. The dye curves were calculated by the hand method of Hamilton and with the use of a dye-dilution analog computer. 3 I. There was a good agreement between the two methods with an average of the percentage difference of 8 per cent and with a standard deviation of 4.2 per cent. In curves with prolonged clearance time and low peak concentration, the average difference was 25.2 per cent with a standard deviation of 11 .O per cent. 3. Changes in the cardiac output provoked by exercise, change in heart rate and by administration of drugs were adequately detected by the computer technic. 4. It was found that the cardiac output computer is a time-saving, reliable and reproducible instrument in the calculation of the cardiac output. 5. The computer should not be used in cases with low peak concentration, prolonged clearance time and in cases with any form of intracardiac shunt. ACKNOWLEDGMENTS
aimI-l00 Area
of
I
,600
I
2000
I
2400
I
2600
-
32ko
3600
COMPUTER
FIG. 10. Correlation of the area under the dye curve measured with the computer and with the Hamilton method.
contemplated since the results of the hand methods will not be available for several days or weeks. Once-the calibration factor is obtained, several hundred curves can be calculated in one day, at a rate of 2 min’curve. The computer also eliminates the subjective influence of the observer who is calculating the curves by the One possible disadvantage of hand method. this instrument is that it does not “recognize” a “bad” curve from a “good” curve; the hand method can provide this information. This technic should be used with great caution in curves with a low peak concentration, a clearance ti.me. greater than 50 sec. and in cases with either left to right or right to left shunts. In addition, this particular unit does not help in the calculation of the mean transit time or central blood volume. are
SUMMARY 1. One hundred and seventeen cardiac output determinations were obtained in 12 patients
We wish to thank Mrs. Mary Vensel, Miss Marilyn Hanna, Miss Shirley Cardwell and Miss Ann Wall for their technical assistance. We are grateful to Dr. David Rogers for his help in the statistical analysis of the data.
REFERENCES I. STEWART, G. N. The pulmonary circulation time, the quantity of blood in the lungs and the output of the heart. Am. J. Physiol., 58: 20, 1921. 2. HAMILTON,W. F., MOORE, J. W., KINSMAN,J. M. and SPURLING, R. G. Studies on the circulation. IV. Further analysis of the injection method and of changes in hemodynamics under physiological and pathological conditions. Am. J. Physiol., 99: 534, 1932. 3. WARNER, H. R. and WOOD, E. H. Simplified calculation of the cardiac output from dye-dilution curves recorded by oximeter. J. Appl. Physiol., 5: 111, 1952. 4. Dow, P. Dimensional relationships in dye-dilution curves from humans and dogs, with an empirical formula for certain troublesome curves. J. A#@. Physiol., 7: 399, 1955. 5. HETZEL, P. S., RAMINEZ DE ARELLANO, A. A. and WOOD, E. H. Estimation of cardiac output from the initial portion of arterial indicator-dilution curves. Fed. Proc., 14: 72, 1955. 6. HETZEL, P. S., SWAN, H. J. C., RAMIREZ DE ARELLANO, A. A. and WOOD, E. H. Estimation of cardiac output from fuxt part of arterial dye-dilution curves. J. A@[. Physiol., 13: 92, 1958. 7. BENCHIMOL,A., DIMOND, E. G., CARVALHO, F. R. and ROBERTS, M. W. The forward triangle formula for calculation of the cardiac output. The indicator-dilution technique. Am. J. Cardiol., 12: 119, 1963. THE AMERICANJOURNAL OF CARDIOLOGY
Computers for Calculation of Cardiac Output N. F., BARBER, H. D., HOLMLUND,B. A. and MERRIMAN,J. E. A cardiac output computer for the rapid analysis of indicator-dilution curves. Digest of the 1961 International Conf. of Med. Electronics, p. 179, 1961. 9. HARA, H. H. and BELVILLE, J. W. On-line computation of cardiac output from dye-dilution curves. Circulation Res., 12: 379, 1963.
8.
MOODY,
VOLUME
15,
FEBRUARY
1965
219
IO. BENCHIMOL,A., Lx, Y. B., LEOLER, J. F. and DIMOND, E. G. Rapidly repeated determinations of the cardiac output with the indicator-dilution technic. Am. J. Cardiol., 13: 790, 1964. Il. BENCHIMOL, A., Lx, Y. B., DIUOND, E. G., VOTH, R. B. and ROLAND, A. S. Effect of heart rate, exercise and nitroglycerin on the cardiac dynamics in complete heart block. Circulation, 28: 510, 1963.
BENCHIMOL, M.D., F.A.c.c.,
PHILIP
R.
La Jolla,
S
AKRE,
M.D. and E.
GREY
DIMOND, M.D., F.A.C.C .
California
studied separately with the sole purpose of obtaining dye curves which were expected to have a low cardiac output with either a markedly prolonged disappearance time or an early curve of intracardiac shunt. It is well known that under these circumstances the calculation of the cardiac output is grossly inaccurate by any method. Several methods were used to induce changes in the cardiac output. Exercise was used in 2 cases, pacing of the heart with an external pacemaker in 2 cases, administration of nitroglycerin in 1 and conversion of atrial fibrillation to sinus rhythm in 3 cases. Cardiac outputs were determined with the indicatordilution technic using indocyanine green (CardioGreen@) as an indicator. Detailed description of our technic has been presented in previous reports.lOJ1 Briefly, the technic consists of injecting 6.25 mg. of the indicator (indocyanine green) into the vein followed by flush of the tube containing the dye with 15 ml. of 5% dextrose. The blood is withdrawn from the artery at a constant rate of 38.2 ml./min. All injections were made into the medial antecubital vein through a No. 18 Cournand needle. Sampling was from the brachial artery through a No. 18 Cournand needle in 10 cases and from the central circulation in 7 cases. A Gilford cuvette densitometer (Model 103 IR) was used to detect the injected dye. Calibration Procedure: Prior to the injection of any dye 50 ml. of arterial blood is withdrawn and placed in a flask containing 50 mg. of heparin. A standard (blood without dye) and four solutions containing 1, 2, 3 and 5 mg. of dye per liter of blood were used for calibration purposes. The solutions were then withdrawn through the cuvette using the same attenuation and flow rates as were used throughout the study. A dye factor was then obtained. The curves were recorded on the Electronics for Medicine (DR-8 Model) oscilloscopic
methods have been suggested to calculate the cardiac output from indicatordilution curves. The Hamilton formula1~2 has been used for many years for that purpose and the results have been quite satisfactory. At its best, this is a time-consuming technic requiring replotting of the curves on semilogarithmic paper followed by the calculation of the area under the curve by hand methods or by a planimeter. Simplifications of this original formula have been suggested with variable results.*-’ With the development of computers and their use in medicine, it became clear that these instruments could be used to integrate the area under the dye curve, thus providing a quick way to calculate the cardiac output. Preliminary reports on this subject have been reported by Moody et a1.8 and by Hara and Belville.g This study was undertaken in order to test the usefulness of the dye-dilution computer in the routine clinical determinations of cardiac output. EVERAL
MATERIALS
of Cardiac Output*
AND METHODS
One-hundred and seventeen indicator-dilution curves were obtained in 12 consecutive patients. The patients were selected at random disregarding the presence or absence of cardiac or circulatory abnormalities. There were two normal subjects, 7 with arteriosclerotic heart disease, 2 with pulmonary diseases and 1 with subaortic stenosis. In addition, 63 curves were obtained in 5 other patients. Three of them were in marked congestive heart failure ; 1 had severe mitral valve disease; and 1 had pentalogy of Fallot. These patients were
* From the Institute of CardioPulmonary Diseases, Scripps Clinic and Research Foundation, La Jolla, Calif. This study was supported in part by National Institutes of Health Research Grant HE-07983-01, Graduate Training Grant HTS-5513 and by the Timkin-Sturgis Foundation. VOLUME 15, FEBRUARY 1965
213
214
Benchimol, Cardiac Output
in L./min.
TABLE I with Hamilton’s Method
Calculated
H
C
H
1 2 3 4 5 6 7 8 9 10 11 12
4.24 5.20 5.29 3.78 6.31 3.50 4.00 2.81 3.55 7.73 4.91 3.63
4.47 5.64 5.85 4.18 5.97 3.62 4.40 2.99 3.92 7.80 4.74 3.72
4.50 5.29 3.85 4.43 6.47 3.67 4.06 2.25 3.78 7.48 4.66 4.85
and with the dye-dilution
2
3
C.O. -
FIG. 1. Hamilton
L. /m1n.
4
5
H
C
H
C
H
C
4.58 5.98 4.33 4.71 6.20 3.83 4.44 2.61 4.21 8.19 4.60 5.24
4.92 5.79 4.83 4.80 6.25 3.47 4.17 3.00 3.76 7.91 4.99 5.93
5.83 5.30 5.19 4.65 6.74 3.75 4.62 3.14 4.09 7.21 4.72 7.35
5.44 4.23 6.09 3.58 4.36 3.01 3.86 6.42 4.87 7.35
5.51 4.78 6.05 3.94 4.82 3.12 4.26 6.93 4.90 7.68
5.01 4.05 6.90 4.55 4.25 3.27 3.97 6.76 5.25 5.86
5.92 4.27 6.63 4.82 4.91 3.61 4.47 6.61 5.35 5.95
photographic recorder at a paper speed of 5 mm./sec. with one second time lines. A Sanborn computer (Model 130) was connected to the output of the densitometer. The sensitivity knob of the computer was set to the high position because the output of the Gilford densitometer is 0.5 v. The delay knob was set according to the appearance time of the dye and set to approximately 3 sec. prior A shorter delay was set for to the appearance time. the first curve. The cardiac output was calculated with the use of the Hamilton formula: =
Computer
C
* Numbers 1 through 10 represent the number of determinations. 10 determinations WA included. H = Hamilton method. C = computer.
C.O. (L./min.)
and with the Dye-Dilution 4
3
2
1* Case
Akre and Dimond
For the sake of simplification
only a maximum
of
0
*em
60 X 2 X dye factor area of curve in mm*. computer.
5
6
7
6
COMPUTER
Cardiac output (C.O.) calculated with the method and with the dye-dilution computer.
FIG. 2. Percentage difference between the cardiac output calculated with the Hamilton method and with the dye-dilution computer. THE AMERICANJOURNAL OF CARDIOLOGY
215
Computers for Calculation of Cardiac Output TABLE
6
I
(continued)
a
7
9
10
H
C
H
C
H
C
H
c
H
C
3.97 4.66 2.79 4.37 5.36 5.46 5.59
4.17 5.31 3.07 4.63 5.51 5.16 5.80
3.84 5.74 2.89 3.84 5.59 5.30 5.41
4.21 6.11 3.27 4.26 4.70 5.36 5.64
3.59 6.20 3.23 4.31 4.59 5.71 5.96
4.04 6.90 3.43 4.66 5.32 5.85 6.09
3.88 5.39 2.91 3.98 4.73 5.17 4.34
4.23 5.97 3.19 4.28 5.32 5.54 4.73
3.03 4.62 5.66 5.79 5.14
3.50 4.71 6.22 5.94 5.27
The corn&&r directly measures the area under the curve from the initial upward deflection until a point in the descending limb is reached which corresponds to 60 per cent of the peak concentration. From there the computer calculates the remainder of the area, assuming an exponential rate of fall. The figure obtained is then used in the following formula: CO. (L./min.)
=
60 X 1 (N,, -
N6)
c X ND
where Z = amount of dye injected into patient. NM = counts obtained from computer for calibration with a known concentration of blood-dye mixture. = counts obtained from computer for calibra& tion of blood without dye. c = amount of dye in mg./L. of blood used to obtain Nbd. ND ‘= counts obtained from computer during the actual run of the dye curve.
It was interesting to note that the values obtained with the computer were slightly higher than those obtained by the hand method for the majority of curves (Fig. 2). Although
this difference was within the acceptable margin of error, it was thought to be due to the calibration factor. The calibration curves are illustrated in Figure 3 where the linearity of the system can be easily demonstrated. Changes in the cardiac output were provoked by exercise, by changes in the heart rate with an external pacemaker and by the administration of drugs. 160.. A
.
In a few cases the curves were analyzed by six observers; the results are described in the next section. The data obtained from 117 cardiac output determinations in 12 patients were analyzed by estimating the standard deviation by means of within-group variance. In this manner, the error in calibration between the 12 different patients was systematically excluded (Table I).
I
A .
.
a
RESULTS In 117 curves obtained in 12 cases there was good agreement between the cardiac output calculated with the Hamilton formula and with The average of the percentage the computer. difference was 8 per cent with a standard deviation of the difference of 4.2 per cent (Fig. 1). VOLUME
15,
FEBRUARY
1965
1 :
I
I
3 I 2 0 CAL/BRAT/ON- mg of dye /L . bfood
FIG 3. Calibration curves obtained with the dye-dilution computer with blood-dye mixture of 1, 2 and 3 mg. of dye per liter of blood.
216
Benchimol,
Akre and Dimond
5.0
4.5 .t : j 4.5
4.0 I
w
i Hamilton
-
=computer
0: u
3.5
I I
C
3
I
2
4
4
IO
Hinuhs2
DURING
AFTER
EXERCISE
EXERCISE
Case 10. Effect of exercise on the cardiac output calculated by the computer and by the Hamilton method. Note a rise in the cardiac output during exercise recorded with both technics.
3.0
FIG. 4.
, I
I I
I I
I
2
3
Curve No. ?.5--
FIG. 6. Cardiac output determinations obtained in one patient calculated by the Hamilton formula by six observers. A slight difference is present for the same curve calculated by different observers (see Fig. 7).
6.5--
$ j
5.5-I
0: 6
4.5--
3.5--
2-Op40 * HEART
1
60
-
60
’
loo
1
120
’
100
’
60
r
M)
RATE - MIN.
FIG. 5. Case 12. Cardiac output determined with the use of Hamilton’s formula and with the computer in a patient with complete heart block. The heart rate was controlled by means of a pacemaker catheter placed in the right ventricle. Note the close relation of the figures obtained in both methods.
The cardiac output increased with exercise, and this change was detected by both technics. The small difference between the two methods at rest was maintained during exercise, thus providing further evidence that the calibration factor may be the dominant factor in explaining this small discrepancy (Fig. 4). The same type of response was seen when the heart rate was changed with the use of an external pacemaker in patients with heart block (Fig. 5). The reproducibility of the hand method is demonstrated in Figure 6. Six trained observers calculated several dye curves, and the measurements are illustrated in Figure 7. The difference found ranged from 1 to 7 per cent for the same curve calculated by the six observers.
It should be emphasized, however, that these measurements were made on sharp curves and in patients with normal cardiac output (Fig. 7). However, when curves with prolonged clearance time were measured by the same six observers, the difference was much greater, being 2 to 16 per cent (Fig. 8). In 1 case, two computer units were connected in parallel to the output of the densitometer in order to test the reproducibility of the computed area ; five curves were obtained. The results of these measurements are illustrated in Figure 9, the difference between the computers for the same dye curve being 2, 2,1,1, and 5 per cent. In addition, the difference for the calculated cardiac output made by the two computers with the hand method was 5, 4, 8, 0.6 and 4 per cent. Figure 10 illustrates the correlation between the area under the dye curve measured with the computer and with the Hamilton formula. In the additional 5 cases (63 curves) the curves were markedly abnormal, having a low peak concentration, a prolonged build-up time and disappearance time and a clearance time greater than 50 sec. These cases were included in the study with the idea of evaluating the usefulness of the computer in cases with prolonged clearance time and abnormally shaped curves. The average of the percentage difference was 25.2 per cent with a standard deviation of 11.0 per cent. The discrepancy between the two methTHE
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Computers for Calculation of Cardiac Output
No. 1 Observer 1 2 3 4 5 6 Computer
C.O. (L./mm.) 3.64 3.64 3.50 3.61 3.46 3.66 3.75
No. 2
No. 3
C.O. Obsy (L./min.) 3.57 2 3.56 3 3.50 4 3.83 5 3.58 6 3.72 Computer 3.94
C.O. (L./min.) Observer 1 4.52 2 4.58 3 4.64 4 4.67 5 4.82 6 4.55 Computer 4.82
FIG. 7. Dye-dilution curves from which calculations of the cardiac output were made by the Hamilton method illustrated in Figure 6.
ods was very large, as predicted, thus confirming the initial assumption that the computer should not be used to calculate curves with these characteristics (Fig. 8). This is often due to the fact that the descending limb does not fall in an exponential decay. Since the hand method is also inaccurate in estimating the area of these curves, it is concluded that both technics should be used with great caution in curves with a clearance time above 50 sec. The computer was also of no value in cases with curves with low peak concentration, thus indicating that one should attempt to obtain curves with great amplification. Smoothness of the baseline from the moment of injection to the appearance of the dye is also important since artifacts of this nature can alter the counts of the computer. A good, free arterial flow and a rigid plastic tube are the most important factors in the elimination of these artifacts. In addition, the delay control in the computer should be set as nearly as possible to the appearance of the dye, thus providing a better control for the elimination of the baseline artifacts. DISCUSSION The data presented indicate that the dyedilution computer is a useful and reliable method to estimate the area under the dye curve. Its main advantage is the timeVOLUME 15, FEBRUARY 1965
saving factor, providing a quick way to calculate the cardiac output, usually within 3 to 5 min., as compared with 30 to 60 with the hand method. This is particularly important in cases in which a large number of determinations 3.5 -’
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Curve No. FIG. 8. Cardiac output calculated on three curves with long clearance time by five observers (compare with Fig. 6 and 7).
218
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.
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with normal and abnormal cardiovascular systems. The dye curves were calculated by the hand method of Hamilton and with the use of a dye-dilution analog computer. 3 I. There was a good agreement between the two methods with an average of the percentage difference of 8 per cent and with a standard deviation of 4.2 per cent. In curves with prolonged clearance time and low peak concentration, the average difference was 25.2 per cent with a standard deviation of 11 .O per cent. 3. Changes in the cardiac output provoked by exercise, change in heart rate and by administration of drugs were adequately detected by the computer technic. 4. It was found that the cardiac output computer is a time-saving, reliable and reproducible instrument in the calculation of the cardiac output. 5. The computer should not be used in cases with low peak concentration, prolonged clearance time and in cases with any form of intracardiac shunt. ACKNOWLEDGMENTS
aimI-l00 Area
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FIG. 10. Correlation of the area under the dye curve measured with the computer and with the Hamilton method.
contemplated since the results of the hand methods will not be available for several days or weeks. Once-the calibration factor is obtained, several hundred curves can be calculated in one day, at a rate of 2 min’curve. The computer also eliminates the subjective influence of the observer who is calculating the curves by the One possible disadvantage of hand method. this instrument is that it does not “recognize” a “bad” curve from a “good” curve; the hand method can provide this information. This technic should be used with great caution in curves with a low peak concentration, a clearance ti.me. greater than 50 sec. and in cases with either left to right or right to left shunts. In addition, this particular unit does not help in the calculation of the mean transit time or central blood volume. are
SUMMARY 1. One hundred and seventeen cardiac output determinations were obtained in 12 patients
We wish to thank Mrs. Mary Vensel, Miss Marilyn Hanna, Miss Shirley Cardwell and Miss Ann Wall for their technical assistance. We are grateful to Dr. David Rogers for his help in the statistical analysis of the data.
REFERENCES I. STEWART, G. N. The pulmonary circulation time, the quantity of blood in the lungs and the output of the heart. Am. J. Physiol., 58: 20, 1921. 2. HAMILTON,W. F., MOORE, J. W., KINSMAN,J. M. and SPURLING, R. G. Studies on the circulation. IV. Further analysis of the injection method and of changes in hemodynamics under physiological and pathological conditions. Am. J. Physiol., 99: 534, 1932. 3. WARNER, H. R. and WOOD, E. H. Simplified calculation of the cardiac output from dye-dilution curves recorded by oximeter. J. Appl. Physiol., 5: 111, 1952. 4. Dow, P. Dimensional relationships in dye-dilution curves from humans and dogs, with an empirical formula for certain troublesome curves. J. A#@. Physiol., 7: 399, 1955. 5. HETZEL, P. S., RAMINEZ DE ARELLANO, A. A. and WOOD, E. H. Estimation of cardiac output from the initial portion of arterial indicator-dilution curves. Fed. Proc., 14: 72, 1955. 6. HETZEL, P. S., SWAN, H. J. C., RAMIREZ DE ARELLANO, A. A. and WOOD, E. H. Estimation of cardiac output from fuxt part of arterial dye-dilution curves. J. A@[. Physiol., 13: 92, 1958. 7. BENCHIMOL,A., DIMOND, E. G., CARVALHO, F. R. and ROBERTS, M. W. The forward triangle formula for calculation of the cardiac output. The indicator-dilution technique. Am. J. Cardiol., 12: 119, 1963. THE AMERICANJOURNAL OF CARDIOLOGY
Computers for Calculation of Cardiac Output N. F., BARBER, H. D., HOLMLUND,B. A. and MERRIMAN,J. E. A cardiac output computer for the rapid analysis of indicator-dilution curves. Digest of the 1961 International Conf. of Med. Electronics, p. 179, 1961. 9. HARA, H. H. and BELVILLE, J. W. On-line computation of cardiac output from dye-dilution curves. Circulation Res., 12: 379, 1963.
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IO. BENCHIMOL,A., Lx, Y. B., LEOLER, J. F. and DIMOND, E. G. Rapidly repeated determinations of the cardiac output with the indicator-dilution technic. Am. J. Cardiol., 13: 790, 1964. Il. BENCHIMOL, A., Lx, Y. B., DIUOND, E. G., VOTH, R. B. and ROLAND, A. S. Effect of heart rate, exercise and nitroglycerin on the cardiac dynamics in complete heart block. Circulation, 28: 510, 1963.