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Assessment of cardiovascular function in patients undergoing coronary artery bypass grafting
J THoRAc CARDIOVASC SURG 1988;96:400-7
Assessment of cardiovascular function in patients undergoing coronary artery bypass grafting Blood pressure and flow in the ascending aorta were measured in 16 patients undergoing coronary artery bypass grafting. The analog records were digitized and the data used to compute total hemodynamic power and aortic input impedance, wbich may be cOMidered to be direct indices of cardiac performance and the state of the cardiovascular system. Varioos indirect indices were alcio computed from the same data and statistically compared with the two direct indices. The results showed that it is necessary to measure both pressure and flow to achieve statistically significant correlatiom, and that none of the indirect indices was capable of describing either cardiac performance or the state of the cardiovascular system comprehenshely, or unambiguously, in these patients.
Gordon Wright, BA, MSc, PhD, RMN, FRSA: Staffordshire, Eng/and. John S. T. Sum Ping, MB, ChB, FFARCS, FMGEMS,b Colin S. Campbell, BSc, FRCS(CTh),C and Michael A. Tobias, MB, ChB, FFARCS,b Manchester, Eng/and
During coronary artery bypass operations, the total hemodynamic state of the patient is usually assessed on the basis of a variety of measurements of cardiovascular and respiratory function as well as an assessment of physical signs. Cardiovascular measurements form an essential part of this assessment and are usually based on continuous monitoring of the electrocardiogram, blood pressure in a peripheral artery, and left and right atrial pressures. Sometimes, cardiac output is measured intermittently by an indicator-dilution technique. Otherwise, it is obliquely assumed that cardiac output will be maximized by optimizing the left atrial pressure through an unquantified Starling relationship and by pharmacologic control of the systemic afterload. This empirical approach contrasts sharply with the more rigorous approach adopted in engineering. Here, the terms power and impedance are used to describe the performance and load of mechanical and electrical systems. When appropriately expanded in the frequency domain, these From the W. E. Dunn Unit of Cardiology, Department of Biological Sciences,' University of Keele, Staffordshire, England, and the Departments of Anaesthesia" and Thoracic Surgery,' Wythenshawe Hospital, Manchester, England Supported by a project grant from the British Heart Foundation. Received for publication Aug. 7, 1987. Accepted for publication Feb. 20, 1988. Address for reprints: Gordon Wright, BA, MSc, Senior Research Fellow, W. E. Dunn Unit of Cardiology, Department of Biological Sciences, University of Keele, Staffordshire ST5 5BG, England.
400
Pressure (mmHg)
10:[ 30 20
Flow (Lmln-1)
10 0 -10
Fig. 1. Blood pressure and flow in ascending aorta in patient with coronary artery disease. Mean pressure was 70 mm Hg and cardiac output was 4.969 L . min-I.
terms describe the system comprehensively and unambiguously. However, they are seldom used in routine medicine or surgery. There appear to be two principal reasons for this anomaly. First, for the most general application, hemodynamic power and input impedance must be computed from measurements of left ventricular or aortic blood pressure and flow, but clinical
Volume 96 Number 3
Cardiovascular function during bypass grafting
September 1988
40 1
Table I. Hemodynamic data in patients undergoing coronary artery bypass graft operations Age (yr)
Body weight (kg)
(sec:'}
Mean
Systolic
Diastolic
L . min:'
rnl . kgr'min:'
16
64 40 53 55 49 41 48 57 47 56 62 58 57 68 56 35
73.4 110.0 50.6 99.5 67.0 81.2 70.3 62.9 64.9 78.0 71.0 91.0 72.6 61.0 90.0 46.3
1.35 1.60 1.63 1.18 1.50 1.38 1.60 1.67 1.82 0.97 1.40 1.45 1.07 2.05 1.27 1.45
83.5 84.5 74.6 81.0 91.5 103.3 70.2 68.3 53.3 76.3 77.0 89.7 77.3 65.0 81.0 77.7
100.6 95.1 83.4 100.1 96.7 113.5 84.6 75.8 56.8 102.6 88.4 105.5 93.9 71.7 109.2 86.0
68.7 74.9 67.0 64.4 88.9 96.0 61.2 63.2 51.0 58.3 64.5 75.7 63.7 62.6 59.5 70.2
5.290 4.201 3.965 8.344 7.494 4.969 2.143 6.598 1.747 5.096 3.354 4.442 4.494 3.237 4.086 6.600
72.1 38.2 78.4 83.9 111.8 61.2 30.5 104.9 26.9 65.3 47.2 48.8 61.9 53.1 45.4 142.5
Mean SEM
53 2
74.4 4.2
1.46 0.26
78.4 11.5
91.5 14.9
68.1 11.3
4.754 0.453
67.0 7.8
Patient No.
I 2 3 4 5 6 7 8 9 10
II 12 13 14
IS
Heart rate
Aortic pressures (rnrn Hg)
Cardiac output
SEM. Standard error of the mean.
priorities usually prohibit the acquismon of the flow data. Second, the computational procedures are complex and it is not yet known whether the additional technical and intellectual effort is worthwhile, the traditional monitoring techniques being associated with long clinical experience. Cardiac operations offer a unique opportunity to interrogate these reasons by permitting access to the ascending aorta. We have taken advantage of this opportunity to measure blood pressure and flow in the ascending aorta and then used these measurements to compute hemodynamic power and aortic input impedance. The results are statistically compared with some of the indirect indices of cardiovascular function commonly used by physicians, anesthetists, and surgeons, and some that are not, to determine whether any of these indices are a satisfactory alternative to computing power and impedance.
Materials and methods With informed consent and ethical committee approval, blood pressure and flow in the ascending aorta were recorded in 16 patients shortly after sternotomy during coronary artery bypass graft procedures at Wythenshawe Hospital, Manchester. The patients were premedicated with lorazepam (40 ug kg"), fentanyl (1.0 J.tg. kg:'), and droperidol (100 J.tg . kg:"); anesthesia was induced with fentanyl (10 J.tg . kg'") and droperidol (100 J.tg . kg') and maintained with a 1: 1 mixture of oxygen and nitrous oxide supplemented by further half doses of fentanyl every 30 to 60 minutes. Pancuronium (0.1 mg . kg:') was used for muscle relaxation >
and a further half dose of fentanyl was given immediately before the chest was opened by a mid-sternal incision. This anesthetic technique was chosen because we have found that it provides stable cardiovascular function. Aortic blood pressure was recorded by means of a 30 em long 5F catheter with one end hole and six side holes. The catheter was placed in the ascending aorta with the end hole pointing away from the aortic valve. It was connected to a Statham P23D strain-gauge transducer (Spectramed Co., Cardiovascular Division, Oxnard, Calif.) coupled to a Hewlett-Packard HP7754B amplifier (Hewlett-Packard Company, Medical Products Group, Andover, Mass.). Blood flow in the ascending aorta was measured by placing a Buckberghandle aortic flow probe around the aorta and coupling this to a Gould-Statham SP2204 electromagnetic flowmeter. The size of the flow probe was chosen to be a tight, but noncompressive, fit during diastole. Both pressure and flow recording equipment were statistically and dynamically calibrated. The amplitude of the pressure system was flat to 15 Hz and +1.43% Hz:" from 15 to 50 Hz. The phase lag was 0 to 17 Hz and 0.45 Hz " from 17 to 50 Hz. The amplitude of the flow recording system was flat to 22 Hz and damped by 2.17% Hz-l from 22 to 50 Hz (3 dB down at 34 Hz). The flow phase lag was 5.4 Hz:" up to 50 Hz and was proportional. These measurement errors were corrected as part of the analytical procedure as previously described. 1 Definitions of the hemodynamic power and impedance parameters and the mathematical equations that formed the basis for the computer programs can be found in standard texts.i' Briefly, with respect to this study, blood pressure and flow in the ascending aorta were recorded on magnetic tape, digitized, and subjected to Fourier analysis to derive total hemodynamic power as the independent sums of three equations-potential plus kinetic power, pulsatile plus nonpu1satile power, and cospectral (in-phase) plus quadrature (out-of-phase) power. In each case, the power 0
0
40 2 Wright et al.
The Journal of Thoracic and Cardiovascular Surgery
Table II. A typical analysis of pressure and flow waveforms in the human ascending aorta
NUMBER OF SAMPLES PER BEAT= 114 119 121 115 115 116 AV= 116 COEFFICIENT OF VARIATION = 0.13913% TIME PRESSURE FLOW POWER EEP (Js- 1 ) (ms) (mmHg) (Lmin- 1) (mmHg) 71.6 -0.350 -0.055 o 71.6 25 78.0 3.645 75.7 0.626 50 99.0 17.320 3.771 90.7 105.6 20.131 4.678 98.5 75 100 104.4 19.691 4.521 101.2 125 98.9 15.794 3.471 101.3 150 97.8 9.821 2. 113 100.9 175 94.3 5.209 1.080 100.5 100.3 200 90.4 0.958 0.190 225 87.0 -2.413 100.5 -0.462 250 100.9 87.4 -2.347 -0.451 275 101.0 87.3 -0.949 -0.183 101.1 300 85.4 -0.200 -0.037 101.1 -0.062 325 83.6 -0.339 350 101 • 1 -0.022 81.5 -0.122 375 0.014 101.2 80.2 0.081 400 -0.001 101.2 79.3 -0.005 77.8 -0.179 -0.031 101.3 425 450 77.5 -0.179 -0.031 101.4 475 76.7 0.361 0.061 101.3 500 74.9 0.079 0.013 101.2 525 73.4 -0.320 -0.052 101. 3 550 71.6 -0.982 -0.155 101 .4 575 70.3 -0.542 -0.084 101.6 MEAN VALUES HEART RATE PRESSURE FLOW 1 POW!i~ STROK!i1WORK (Lmin-) (.rs ) (mmHg) (Js ) (beats/min) 85.3 3.702 0.695 0.480 103.0 PRESSURE FLOW POWER AMPLITUDE PHASE AMPLITU~E PHASE COSPIf
Volume 96 Number 3 September 1988
component was obtained as the product of pressure and flow, whereas aortic input impedance was obtained as the quotient of pressure and flow. Unlike peripheral vascular resistance, which iscalculated as thequotient of mean pressure and mean flow, impedance is a complex parameter that incorporates inertance andcompliance as well as resistance andisfrequency dependent. The computer analyses were each performed on a single pulse derived as the average of six consecutive pulses and the data were tested for variance and coherence. A coefficient of variation among the durations of the six pulses of less than 0.025 anda coherence greater than 0.9 for all harmonics up to and including the fifth were required for acceptance. All indices, both direct and indirect, were calculated from the single averaged pulse. Results The patient data are listed in Table I, and representative blood pressure and flow records are shown in Fig. 1. A typical computer output is shown in Table II. Pulsatile power accounted for an average of 11.35% of total hemodynamic power.The best linear and nonlinear least squares fit relationships between total hemodynamic power and some other indices of cardiac performance are listed in Table III. The index of identification indicatesthe reliability of predicting total hemodynamic power from the other indices by the best least squares fit formula. A perfect fit has an index of identification of 1.0000and random scatter has an index of identification of 0.0000. The relationships were linear, power, hyperbolic, or exponential functions, and the two best nonlinear relationships are illustrated in Figs. 2 and 3. The correlation coefficient in Table III indicates the reliability of making the same prediction on the basis of the linear regression equation. Table IV shows the linear and nonlinear relationships between aortic input impedance and other indices of the state of the systemic load. By definition, the peripheral vascular resistance is equal to the mean term (zeroth harmonic) of the impedance spectrum, but peripheral vascular resistance is only weakly related to the pulsatile components of impedance derived as the average of impedancesin the frequency range 2 to 12 Hz, or to the reactive part of impedance as indicated by the phase lag of pressure behind flow for the fundamental harmonic of the impedance spectrum. This is illustrated in Fig. 4, and the weak relationship between systolic blood pressure and peripheral vascular resistance is shown in Fig. 5. Discussion Despite the apparent complexity of biochemical and mechanical events associated with cardiac muscle con-
Cardiovascular junction during bypass grafting
2000
403
••
1500
•
Tota I power
1000
(mJs- 1) 500
500
1000
1500
2000
Mean power (mJs-1 )
Fig. 2. Relationship between mean and total hemodynamic power in ascending aorta.
traction, the heart is essentially a transducer with the single function of converting the potential energy contained in adenosine triphosphate molecules into the mechanical energy that is required to perform internal and external work. Internal work is necessary to extend the series elastic elements in the walls of the ventricles.' External work is performed by the ventricles, slightly assisted by the atria and slightly impeded by the outflow valves. The external work of the left ventricle is to eject blood through the aortic valve against the complex vascular resistances, inertance, and compliance that together constitute the many vascular impedances. However, the ventricle "sees" only what is immediately beyond the aortic valve, and this is the aortic input impedance. Total hemodynamic power, as computed herein, describes the energy delivered into the ascending aorta each second to perform external work. Like impedance, it is a complex quantity composed of a mean component equal to the product of mean pressure and mean flow, and pulsatile components similarly derived as the frequency-dependent products of pressure and flow. The sum of the mean component and all significant harmonics is total power. Hemodynamic power may be viewed as the rate at which energy is transmitted downstream in the form of flowing blood and laterally into the tissues to stimulate metabolism by mechanical agitation and to promote the movement of tissue fluids and lymph.v" If this description of hemodynamic power is accepted, it follows that lateral energy transmission is dependent on the pulsatile properties of cardiac output, the inertance of blood flow, and the compliance of the major arteries. Therefore, neither cardiac performance nor cardiovascular state can be considered in isolation from the other,
The Journal of Thoracic and Cardiovascular Surgery
4 0 4 Wright et al.
2000
•
•
1500
Total power
•
1000
(mJs-l) 500
• 0
0
3
4
5
Cardiac output
6
8
9
(Lmin-1 )
Fig. 3. Relationship between cardiac output and total hemodynamic power in ascending aorta.
Table ill. Correlation and regression relationships of total hemodynamic power (w,) and other indices of cardiac performance in patients undergoing coronary artery bypass graft operations (n = 16) Index of cardiac performance W, (mJ . sec I) W m (mJ . sec')
CO (L . min-I) TIl (mm Hg . sec)
Fp
Coefficient ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r
= = = = = = = = = = = = = = = = = = = = = = = =
0.9968 0.9865 0.9429 0.9069 0.8779 0.6068 0.8304 0.8304 0.6790 0.6265 0.6766 0.4183 0.6665 0.4854 0.5391 0.5194 0.5363 0.5362 0.2579 0.0026 0.1933 0.1906 0.1727 0.0810
Least squares equation y = x/(0.9212 - 0.0001 x) y = 1.0927x + 33.029 y = 133.938x L25 y = 237.787 - 168.418 y = x/(0.0614 - 0.001 Ix) y = 35.932x - 34.86 y = 3.4316x - 270.032 y = 3.4316x - 270.032 y = x/(0.3858 - 0.0037x) y = 30.504x - 1437.227 y = x/(0.3765 - 0.0029x) y = 19.614x - 842.242 y = x/(0.3971 - 0.0033x) y = 24.665x - 1185.679 y = 1/(0.6276 - 0.0004x) y = 2.85x - 50.693 y= 17.39x - 883.299 y = 17.39x - 883.299 y = x/(0.0003x + 0.358) y = 1004.5 - 0.128x y = 159.427eOO128, y = 1O.543x - 427.6 Y = 1/(0.OOI5x - 0.0008) y = 1629.0 - 462.828x
W" Total hemodynamicpower;Wms mean hemodynamicpower;CO. cardiac output; TTl. tension-timeintegral = area under the systolicpart of the aortic bloodpressure curve"; F..... peak aortic blood flow; APmeans mean aortic blood pressure;AP"'. systolic aortic blood pressure; EEP. energy equivalent pressure": EEP = fPF dt . fF dt; dF /dtm~. maximum rate of increase of flow; EDP. end-diastolic pressure;dP /dt~. maximum rate of increaseof pressure;HR. heart rate; 10. index of identification; r, correlation coefficient.
nor can they be adequately described by mean values alone. It also follows that both pressure and flow are required for sensible interpretation of hemodynamic data. Power and impedance are descriptive terms. They
fully characterize the hemodynamic state viewed from the ascending aorta. They give no information about the factors responsible for the attainment of this state or their dependency on other factors, such as the atrial blood pressures or the oxygen content of the blood. As
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Cardiovascular function during bypass grafting
September 1988
405
Table IV. Correlation and regression relationships of aortic input impedance with other indices of cardiovascular state in patients undergoing coronary artery bypass graft surgery (n = 16) Index of cardiovascular state
R in (X10'kg . m- 4s- l ) PVR (X10'kg . m- 4s- 1 AP m "", (mm Hg) AP", (mm Hg) EDP (mm Hg)
Coefficient
ID r ID r ID r ID r
= 1.0000 = 1.0000 = 0.2162 = 0.1899 = 0.1969 = 0.1514 = 0.1428 = 0.1428
Least squares equation
y=x y=x Y= (113.87 Ix) + 0.0079 y = 3.0054 - 0.0193x Y= (l02.63/x) + 0.3372 Y= 2.717 - 0.Ql34x Y= 2.582 - 0.01624x Y= 2.582 - 0.01624x
Zo (X108kg . m- 4s- l ) EDP (mm Hg) AP m"", (mm Hg) AP", (mm Hg) PVR (X10'kg . m- 4s- l ) (rads) PVR (X10'kg . m- 4s- l )
ID = 0.6002 r = 0.3744 ID = 0.5937 r = 0.5517 ID = 0.5611 r=0.5166 ID = 0.2112 r = 0.2112
y = 1/(0.000063x - 0.00265) y = 0.2156 - 0.OO2x Y= (1.434/x) - 0.1054 Y= 0.277 - 0.0025x y = (l3.139/x) - 0.0663 y = 0.2529 - 0.00187x y = 0.0349x + 2.95 y = 0.0349x + 2.95
ID r ID r ID r ID r
y = (4.391/x) - 0.00187 Y= 0.0035 - 0.OOO14x y = 1.4159 - (37.931/x) y = 0.0069x + 0.3840 Y= 0.0045x + 0.5073 Y= 0.0045x + 0.5073 Y= 1.2712 - (22.81/x) Y= 0.0049x + 0.5919
<1>'1
AP m"", (mm Hg) AP", (mm Hg) EDP (mm Hg)
= 0.3207 = 0.1402 = 0.2747 = 0.2745 = 0.2020 = 0.2020 = 0.1580 = 0.1496
R•• Input resistance = peripheral vascular resistance; PVR. peripheral vascular resistance; AP m~. mean aortic blood pressure; AP",. systolic aortic blood pressure; EDP. end-diastolic pressure; Zo. characteristic impedance; <1>,,, phase lag of the fundamental harmonic of impedance; 10. index of identification; r. correlation coefficient.
calculated, hemodynamic power is to be considered as external to the heart and not confused with internal power, which is normally used to measure the efficiency of the heart in converting metabolic energy into mechanical work. Total hemodynamic power in the human ascending aorta was computed in patients undergoing cardiac catheterization by Nichols and associates' (1977) and by Gundel and colleagues' (1981). Aortic input impedance has been computed by several groups.':" Our results are similar in both respects, although the hemodynamic power data are below previouslypublished data (843 ± 404 m.l . sec:" [mean ± standard deviation] compared with 1120 ± 249 mJ . sec- t by Nichols and co-workers'), possibly because of the cardiodepressant effects of thoracotomy. Since total hemodynamic power and aortic input impedance comprehensively and unambiguously describe cardiovascular function as viewed in the ascending aorta, they may be considered to be the standards against which all indirectly derived indices must be compared. In this paper, we have attempted to
compare total hemodynamic power and aortic input impedance with some alternative indirect indices that have been considered to be related to these basic parameters. As predicted by the theory, none of the indirect parameters was perfectly correlated with total hemodynamic power. The most reliable index was mean power, which requires measurements of both pressure and flow. The linear and nonlinear correlations with coefficients close to 1.0000 imply that mean hemodynamic power can be used with confidence to predict total hemodynamic power in the ascending aorta under the conditions of coronary artery bypass graft operations. For this predictability to be achieved, the best least squares fit equations shown must be used. Proportionality is not implied, so that a fractional change in mean power would not indicate the same fractional change in total power. Furthermore, mean power is a rational value that is derived from mean pressure and mean flow alone, whereas total power is complex and can be dissected into its spectral components to provide a complete description of cardiac performance as seen at
The Journal of Thoracic and Cardiovascular Surgery
4 0 6 Wright et al.
• •
1·2
•••• • • •• •• •
1'0
•
0·8
Impedance phase lag
•
2'5
• •
•
Peripheral 1'5 vascular resista nce
0·8
(X10 8 kg m-4s- 1)1-Q
0·4
0'5
• • •
•
(r a ds )
OL.-_~-_--=---.---..---_
0·2
o
20
40
60
80
100
120
Systolic blood pressure (mmHg) O~-",":","":-
o
0·5
~
1'0
1'5
~
2'0
2'5
Peripheral vascular resistance (x 10 8kgm-4s-1 )
Fig. 4. Relationship between the resistive and reactive components of aortic input impedance.
the entrance to the systemic load. Below mean power, cardiac output achieved the highest correlation with total hemodynamic power, though even this fell below the 0.95 limit demanded for statistical significance. The use of parameters derived from pressure recordings alone, such as systolic blood pressure and the maximum rate of change of pressure, provided data that was unreliable and difficult to interpret in terms of cardiac performance or systemic load. Unlike the harmonics of the power spectrum, impedance harmonics cannot be summed to derive an interpretable total value. This is because the mean term defines the resistive component of the systemic load, whereas the higher frequency terms relate to reactance as well as resistance. Table IV suggests that the reactive state of the cardiovascular system, indicated by the characteristic impedance or the phase lag, cannot be accurately predicted from any of the indirect indices that we computed. Part of the data processing procedure was to correct inevitable frequency-dependent measurement errors. Failure to do so would lead to further weakening of the relationships between the compared parameters. Also, it is common practice to record pressure in peripheral arteries rather than in the ascending aorta. This adds a further complication, since the pressure wave is modulated as it travels through the arteries. Measurements of cardiovascular function form only part of the overall assessment of the hemodynamic state of patients undergoing coronary artery bypass grafting. The outstanding success of this operation is a testimony that serious misjudgments are rare. Nevertheless, it is
Fig. 5. Relationship between systolic blood pressure and peripheral vascular resistance.
legitimate to ask whether the traditional indirect indices of cardiovascular function provide an optimal, or even adequate, basis for clinical judgments. If the initial premise is accepted, that total hemodynamic power and aortic input impedance are to be considered as the basic, direct indices against which all others must be compared, then it appears that traditional indices are not optimal. Most of the indirect indices that we tested were weakly correlated with total hemodynamic power and aortic input impedance. Although mean power could be used to predict total power, both this and the corresponding term of the impedance spectrum, peripheral vascular resistance, are deficient in their omission of pulsatile components. Of the single parameter measurements, cardiac output provided the best, but still statistically inadequate, index of cardiac performance, but pressure records on their own provided only uninterpretable data.
REFERENCES I. Wright G, Sum Ping JST, Campbell CS, Tobias MA.
2. 3. 4.
5.
Computation of haemodynamic power and input impedance in the ascending aorta of patients undergoing open-heart surgery. Cardiovasc Res 1988;22:179-84. McDonald DA. Blood flow in arteries. London: Edward Arnold, 1974. Milnor WR. Hemodynamics. Baltimore: Williams & Wilkins, 1982. Levine HJ, Forwand SA, McIntyre KM, Schechter E. Effect of afterload on force-velocity relations and contractile element work in the intact dog heart. Circ Res 1966;18:729-44. Shepard RB, Kirklin JW. Relation of pulsatile flow to oxygen consumption and other variables during cardiopul-
Volume 96 Number 3 September 1988
monary bypass. J THoRAc CARDIOVASC SURG 1969; 58:694-702. 6. Parson RJ, McMaster PD. The effect of the pulse upon the formation and flow of lymph. J Exp Med 1938; 68:353-76. 7. Nichols WW, Conti CR, Walker WE, Milnor WR. Input impedance of the systemic circulation in man. Circ Res 1977;40:451-8. 8. Gundel W, Cherry G, Rajagopalan B, Tan L-P, Lee G, Schultz D. Aortic input impedance in man: acute response to vasodilator drugs. Circ Res 1981;63:1305-14.
Cardiovascular function during bypass grafting
40 7
9. Gabe IT, Karnell J, Porge IG, Rudewald B. The measurement of input impedance and apparent phase velocity in the human aorta. Acta Physiol Scand 1964;61:73-84. 10. Mills CJ, Gabe IT, Gault JH, et al. Pressure-flow relationships and vascular impedance in man. Cardiovasc Res 1970;4:405-17. II. Pepine JC, Nichols WW, Conti CR. Aortic input impedance in heart failure. Circulation 1978;58:460-5. 12. Murgo JP, WesterhofN, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure waveform. Circulation 1980;65:105-16.
Assessment of cardiovascular function in patients undergoing coronary artery bypass grafting Blood pressure and flow in the ascending aorta were measured in 16 patients undergoing coronary artery bypass grafting. The analog records were digitized and the data used to compute total hemodynamic power and aortic input impedance, wbich may be cOMidered to be direct indices of cardiac performance and the state of the cardiovascular system. Varioos indirect indices were alcio computed from the same data and statistically compared with the two direct indices. The results showed that it is necessary to measure both pressure and flow to achieve statistically significant correlatiom, and that none of the indirect indices was capable of describing either cardiac performance or the state of the cardiovascular system comprehenshely, or unambiguously, in these patients.
Gordon Wright, BA, MSc, PhD, RMN, FRSA: Staffordshire, Eng/and. John S. T. Sum Ping, MB, ChB, FFARCS, FMGEMS,b Colin S. Campbell, BSc, FRCS(CTh),C and Michael A. Tobias, MB, ChB, FFARCS,b Manchester, Eng/and
During coronary artery bypass operations, the total hemodynamic state of the patient is usually assessed on the basis of a variety of measurements of cardiovascular and respiratory function as well as an assessment of physical signs. Cardiovascular measurements form an essential part of this assessment and are usually based on continuous monitoring of the electrocardiogram, blood pressure in a peripheral artery, and left and right atrial pressures. Sometimes, cardiac output is measured intermittently by an indicator-dilution technique. Otherwise, it is obliquely assumed that cardiac output will be maximized by optimizing the left atrial pressure through an unquantified Starling relationship and by pharmacologic control of the systemic afterload. This empirical approach contrasts sharply with the more rigorous approach adopted in engineering. Here, the terms power and impedance are used to describe the performance and load of mechanical and electrical systems. When appropriately expanded in the frequency domain, these From the W. E. Dunn Unit of Cardiology, Department of Biological Sciences,' University of Keele, Staffordshire, England, and the Departments of Anaesthesia" and Thoracic Surgery,' Wythenshawe Hospital, Manchester, England Supported by a project grant from the British Heart Foundation. Received for publication Aug. 7, 1987. Accepted for publication Feb. 20, 1988. Address for reprints: Gordon Wright, BA, MSc, Senior Research Fellow, W. E. Dunn Unit of Cardiology, Department of Biological Sciences, University of Keele, Staffordshire ST5 5BG, England.
400
Pressure (mmHg)
10:[ 30 20
Flow (Lmln-1)
10 0 -10
Fig. 1. Blood pressure and flow in ascending aorta in patient with coronary artery disease. Mean pressure was 70 mm Hg and cardiac output was 4.969 L . min-I.
terms describe the system comprehensively and unambiguously. However, they are seldom used in routine medicine or surgery. There appear to be two principal reasons for this anomaly. First, for the most general application, hemodynamic power and input impedance must be computed from measurements of left ventricular or aortic blood pressure and flow, but clinical
Volume 96 Number 3
Cardiovascular function during bypass grafting
September 1988
40 1
Table I. Hemodynamic data in patients undergoing coronary artery bypass graft operations Age (yr)
Body weight (kg)
(sec:'}
Mean
Systolic
Diastolic
L . min:'
rnl . kgr'min:'
16
64 40 53 55 49 41 48 57 47 56 62 58 57 68 56 35
73.4 110.0 50.6 99.5 67.0 81.2 70.3 62.9 64.9 78.0 71.0 91.0 72.6 61.0 90.0 46.3
1.35 1.60 1.63 1.18 1.50 1.38 1.60 1.67 1.82 0.97 1.40 1.45 1.07 2.05 1.27 1.45
83.5 84.5 74.6 81.0 91.5 103.3 70.2 68.3 53.3 76.3 77.0 89.7 77.3 65.0 81.0 77.7
100.6 95.1 83.4 100.1 96.7 113.5 84.6 75.8 56.8 102.6 88.4 105.5 93.9 71.7 109.2 86.0
68.7 74.9 67.0 64.4 88.9 96.0 61.2 63.2 51.0 58.3 64.5 75.7 63.7 62.6 59.5 70.2
5.290 4.201 3.965 8.344 7.494 4.969 2.143 6.598 1.747 5.096 3.354 4.442 4.494 3.237 4.086 6.600
72.1 38.2 78.4 83.9 111.8 61.2 30.5 104.9 26.9 65.3 47.2 48.8 61.9 53.1 45.4 142.5
Mean SEM
53 2
74.4 4.2
1.46 0.26
78.4 11.5
91.5 14.9
68.1 11.3
4.754 0.453
67.0 7.8
Patient No.
I 2 3 4 5 6 7 8 9 10
II 12 13 14
IS
Heart rate
Aortic pressures (rnrn Hg)
Cardiac output
SEM. Standard error of the mean.
priorities usually prohibit the acquismon of the flow data. Second, the computational procedures are complex and it is not yet known whether the additional technical and intellectual effort is worthwhile, the traditional monitoring techniques being associated with long clinical experience. Cardiac operations offer a unique opportunity to interrogate these reasons by permitting access to the ascending aorta. We have taken advantage of this opportunity to measure blood pressure and flow in the ascending aorta and then used these measurements to compute hemodynamic power and aortic input impedance. The results are statistically compared with some of the indirect indices of cardiovascular function commonly used by physicians, anesthetists, and surgeons, and some that are not, to determine whether any of these indices are a satisfactory alternative to computing power and impedance.
Materials and methods With informed consent and ethical committee approval, blood pressure and flow in the ascending aorta were recorded in 16 patients shortly after sternotomy during coronary artery bypass graft procedures at Wythenshawe Hospital, Manchester. The patients were premedicated with lorazepam (40 ug kg"), fentanyl (1.0 J.tg. kg:'), and droperidol (100 J.tg . kg:"); anesthesia was induced with fentanyl (10 J.tg . kg'") and droperidol (100 J.tg . kg') and maintained with a 1: 1 mixture of oxygen and nitrous oxide supplemented by further half doses of fentanyl every 30 to 60 minutes. Pancuronium (0.1 mg . kg:') was used for muscle relaxation >
and a further half dose of fentanyl was given immediately before the chest was opened by a mid-sternal incision. This anesthetic technique was chosen because we have found that it provides stable cardiovascular function. Aortic blood pressure was recorded by means of a 30 em long 5F catheter with one end hole and six side holes. The catheter was placed in the ascending aorta with the end hole pointing away from the aortic valve. It was connected to a Statham P23D strain-gauge transducer (Spectramed Co., Cardiovascular Division, Oxnard, Calif.) coupled to a Hewlett-Packard HP7754B amplifier (Hewlett-Packard Company, Medical Products Group, Andover, Mass.). Blood flow in the ascending aorta was measured by placing a Buckberghandle aortic flow probe around the aorta and coupling this to a Gould-Statham SP2204 electromagnetic flowmeter. The size of the flow probe was chosen to be a tight, but noncompressive, fit during diastole. Both pressure and flow recording equipment were statistically and dynamically calibrated. The amplitude of the pressure system was flat to 15 Hz and +1.43% Hz:" from 15 to 50 Hz. The phase lag was 0 to 17 Hz and 0.45 Hz " from 17 to 50 Hz. The amplitude of the flow recording system was flat to 22 Hz and damped by 2.17% Hz-l from 22 to 50 Hz (3 dB down at 34 Hz). The flow phase lag was 5.4 Hz:" up to 50 Hz and was proportional. These measurement errors were corrected as part of the analytical procedure as previously described. 1 Definitions of the hemodynamic power and impedance parameters and the mathematical equations that formed the basis for the computer programs can be found in standard texts.i' Briefly, with respect to this study, blood pressure and flow in the ascending aorta were recorded on magnetic tape, digitized, and subjected to Fourier analysis to derive total hemodynamic power as the independent sums of three equations-potential plus kinetic power, pulsatile plus nonpu1satile power, and cospectral (in-phase) plus quadrature (out-of-phase) power. In each case, the power 0
0
40 2 Wright et al.
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Table II. A typical analysis of pressure and flow waveforms in the human ascending aorta
NUMBER OF SAMPLES PER BEAT= 114 119 121 115 115 116 AV= 116 COEFFICIENT OF VARIATION = 0.13913% TIME PRESSURE FLOW POWER EEP (Js- 1 ) (ms) (mmHg) (Lmin- 1) (mmHg) 71.6 -0.350 -0.055 o 71.6 25 78.0 3.645 75.7 0.626 50 99.0 17.320 3.771 90.7 105.6 20.131 4.678 98.5 75 100 104.4 19.691 4.521 101.2 125 98.9 15.794 3.471 101.3 150 97.8 9.821 2. 113 100.9 175 94.3 5.209 1.080 100.5 100.3 200 90.4 0.958 0.190 225 87.0 -2.413 100.5 -0.462 250 100.9 87.4 -2.347 -0.451 275 101.0 87.3 -0.949 -0.183 101.1 300 85.4 -0.200 -0.037 101.1 -0.062 325 83.6 -0.339 350 101 • 1 -0.022 81.5 -0.122 375 0.014 101.2 80.2 0.081 400 -0.001 101.2 79.3 -0.005 77.8 -0.179 -0.031 101.3 425 450 77.5 -0.179 -0.031 101.4 475 76.7 0.361 0.061 101.3 500 74.9 0.079 0.013 101.2 525 73.4 -0.320 -0.052 101. 3 550 71.6 -0.982 -0.155 101 .4 575 70.3 -0.542 -0.084 101.6 MEAN VALUES HEART RATE PRESSURE FLOW 1 POW!i~ STROK!i1WORK (Lmin-) (.rs ) (mmHg) (Js ) (beats/min) 85.3 3.702 0.695 0.480 103.0 PRESSURE FLOW POWER AMPLITUDE PHASE AMPLITU~E PHASE COSPIf
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component was obtained as the product of pressure and flow, whereas aortic input impedance was obtained as the quotient of pressure and flow. Unlike peripheral vascular resistance, which iscalculated as thequotient of mean pressure and mean flow, impedance is a complex parameter that incorporates inertance andcompliance as well as resistance andisfrequency dependent. The computer analyses were each performed on a single pulse derived as the average of six consecutive pulses and the data were tested for variance and coherence. A coefficient of variation among the durations of the six pulses of less than 0.025 anda coherence greater than 0.9 for all harmonics up to and including the fifth were required for acceptance. All indices, both direct and indirect, were calculated from the single averaged pulse. Results The patient data are listed in Table I, and representative blood pressure and flow records are shown in Fig. 1. A typical computer output is shown in Table II. Pulsatile power accounted for an average of 11.35% of total hemodynamic power.The best linear and nonlinear least squares fit relationships between total hemodynamic power and some other indices of cardiac performance are listed in Table III. The index of identification indicatesthe reliability of predicting total hemodynamic power from the other indices by the best least squares fit formula. A perfect fit has an index of identification of 1.0000and random scatter has an index of identification of 0.0000. The relationships were linear, power, hyperbolic, or exponential functions, and the two best nonlinear relationships are illustrated in Figs. 2 and 3. The correlation coefficient in Table III indicates the reliability of making the same prediction on the basis of the linear regression equation. Table IV shows the linear and nonlinear relationships between aortic input impedance and other indices of the state of the systemic load. By definition, the peripheral vascular resistance is equal to the mean term (zeroth harmonic) of the impedance spectrum, but peripheral vascular resistance is only weakly related to the pulsatile components of impedance derived as the average of impedancesin the frequency range 2 to 12 Hz, or to the reactive part of impedance as indicated by the phase lag of pressure behind flow for the fundamental harmonic of the impedance spectrum. This is illustrated in Fig. 4, and the weak relationship between systolic blood pressure and peripheral vascular resistance is shown in Fig. 5. Discussion Despite the apparent complexity of biochemical and mechanical events associated with cardiac muscle con-
Cardiovascular junction during bypass grafting
2000
403
••
1500
•
Tota I power
1000
(mJs- 1) 500
500
1000
1500
2000
Mean power (mJs-1 )
Fig. 2. Relationship between mean and total hemodynamic power in ascending aorta.
traction, the heart is essentially a transducer with the single function of converting the potential energy contained in adenosine triphosphate molecules into the mechanical energy that is required to perform internal and external work. Internal work is necessary to extend the series elastic elements in the walls of the ventricles.' External work is performed by the ventricles, slightly assisted by the atria and slightly impeded by the outflow valves. The external work of the left ventricle is to eject blood through the aortic valve against the complex vascular resistances, inertance, and compliance that together constitute the many vascular impedances. However, the ventricle "sees" only what is immediately beyond the aortic valve, and this is the aortic input impedance. Total hemodynamic power, as computed herein, describes the energy delivered into the ascending aorta each second to perform external work. Like impedance, it is a complex quantity composed of a mean component equal to the product of mean pressure and mean flow, and pulsatile components similarly derived as the frequency-dependent products of pressure and flow. The sum of the mean component and all significant harmonics is total power. Hemodynamic power may be viewed as the rate at which energy is transmitted downstream in the form of flowing blood and laterally into the tissues to stimulate metabolism by mechanical agitation and to promote the movement of tissue fluids and lymph.v" If this description of hemodynamic power is accepted, it follows that lateral energy transmission is dependent on the pulsatile properties of cardiac output, the inertance of blood flow, and the compliance of the major arteries. Therefore, neither cardiac performance nor cardiovascular state can be considered in isolation from the other,
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2000
•
•
1500
Total power
•
1000
(mJs-l) 500
• 0
0
3
4
5
Cardiac output
6
8
9
(Lmin-1 )
Fig. 3. Relationship between cardiac output and total hemodynamic power in ascending aorta.
Table ill. Correlation and regression relationships of total hemodynamic power (w,) and other indices of cardiac performance in patients undergoing coronary artery bypass graft operations (n = 16) Index of cardiac performance W, (mJ . sec I) W m (mJ . sec')
CO (L . min-I) TIl (mm Hg . sec)
Fp
Coefficient ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r ID r
= = = = = = = = = = = = = = = = = = = = = = = =
0.9968 0.9865 0.9429 0.9069 0.8779 0.6068 0.8304 0.8304 0.6790 0.6265 0.6766 0.4183 0.6665 0.4854 0.5391 0.5194 0.5363 0.5362 0.2579 0.0026 0.1933 0.1906 0.1727 0.0810
Least squares equation y = x/(0.9212 - 0.0001 x) y = 1.0927x + 33.029 y = 133.938x L25 y = 237.787 - 168.418 y = x/(0.0614 - 0.001 Ix) y = 35.932x - 34.86 y = 3.4316x - 270.032 y = 3.4316x - 270.032 y = x/(0.3858 - 0.0037x) y = 30.504x - 1437.227 y = x/(0.3765 - 0.0029x) y = 19.614x - 842.242 y = x/(0.3971 - 0.0033x) y = 24.665x - 1185.679 y = 1/(0.6276 - 0.0004x) y = 2.85x - 50.693 y= 17.39x - 883.299 y = 17.39x - 883.299 y = x/(0.0003x + 0.358) y = 1004.5 - 0.128x y = 159.427eOO128, y = 1O.543x - 427.6 Y = 1/(0.OOI5x - 0.0008) y = 1629.0 - 462.828x
W" Total hemodynamicpower;Wms mean hemodynamicpower;CO. cardiac output; TTl. tension-timeintegral = area under the systolicpart of the aortic bloodpressure curve"; F..... peak aortic blood flow; APmeans mean aortic blood pressure;AP"'. systolic aortic blood pressure; EEP. energy equivalent pressure": EEP = fPF dt . fF dt; dF /dtm~. maximum rate of increase of flow; EDP. end-diastolic pressure;dP /dt~. maximum rate of increaseof pressure;HR. heart rate; 10. index of identification; r, correlation coefficient.
nor can they be adequately described by mean values alone. It also follows that both pressure and flow are required for sensible interpretation of hemodynamic data. Power and impedance are descriptive terms. They
fully characterize the hemodynamic state viewed from the ascending aorta. They give no information about the factors responsible for the attainment of this state or their dependency on other factors, such as the atrial blood pressures or the oxygen content of the blood. As
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Table IV. Correlation and regression relationships of aortic input impedance with other indices of cardiovascular state in patients undergoing coronary artery bypass graft surgery (n = 16) Index of cardiovascular state
R in (X10'kg . m- 4s- l ) PVR (X10'kg . m- 4s- 1 AP m "", (mm Hg) AP", (mm Hg) EDP (mm Hg)
Coefficient
ID r ID r ID r ID r
= 1.0000 = 1.0000 = 0.2162 = 0.1899 = 0.1969 = 0.1514 = 0.1428 = 0.1428
Least squares equation
y=x y=x Y= (113.87 Ix) + 0.0079 y = 3.0054 - 0.0193x Y= (l02.63/x) + 0.3372 Y= 2.717 - 0.Ql34x Y= 2.582 - 0.01624x Y= 2.582 - 0.01624x
Zo (X108kg . m- 4s- l ) EDP (mm Hg) AP m"", (mm Hg) AP", (mm Hg) PVR (X10'kg . m- 4s- l ) (rads) PVR (X10'kg . m- 4s- l )
ID = 0.6002 r = 0.3744 ID = 0.5937 r = 0.5517 ID = 0.5611 r=0.5166 ID = 0.2112 r = 0.2112
y = 1/(0.000063x - 0.00265) y = 0.2156 - 0.OO2x Y= (1.434/x) - 0.1054 Y= 0.277 - 0.0025x y = (l3.139/x) - 0.0663 y = 0.2529 - 0.00187x y = 0.0349x + 2.95 y = 0.0349x + 2.95
ID r ID r ID r ID r
y = (4.391/x) - 0.00187 Y= 0.0035 - 0.OOO14x y = 1.4159 - (37.931/x) y = 0.0069x + 0.3840 Y= 0.0045x + 0.5073 Y= 0.0045x + 0.5073 Y= 1.2712 - (22.81/x) Y= 0.0049x + 0.5919
<1>'1
AP m"", (mm Hg) AP", (mm Hg) EDP (mm Hg)
= 0.3207 = 0.1402 = 0.2747 = 0.2745 = 0.2020 = 0.2020 = 0.1580 = 0.1496
R•• Input resistance = peripheral vascular resistance; PVR. peripheral vascular resistance; AP m~. mean aortic blood pressure; AP",. systolic aortic blood pressure; EDP. end-diastolic pressure; Zo. characteristic impedance; <1>,,, phase lag of the fundamental harmonic of impedance; 10. index of identification; r. correlation coefficient.
calculated, hemodynamic power is to be considered as external to the heart and not confused with internal power, which is normally used to measure the efficiency of the heart in converting metabolic energy into mechanical work. Total hemodynamic power in the human ascending aorta was computed in patients undergoing cardiac catheterization by Nichols and associates' (1977) and by Gundel and colleagues' (1981). Aortic input impedance has been computed by several groups.':" Our results are similar in both respects, although the hemodynamic power data are below previouslypublished data (843 ± 404 m.l . sec:" [mean ± standard deviation] compared with 1120 ± 249 mJ . sec- t by Nichols and co-workers'), possibly because of the cardiodepressant effects of thoracotomy. Since total hemodynamic power and aortic input impedance comprehensively and unambiguously describe cardiovascular function as viewed in the ascending aorta, they may be considered to be the standards against which all indirectly derived indices must be compared. In this paper, we have attempted to
compare total hemodynamic power and aortic input impedance with some alternative indirect indices that have been considered to be related to these basic parameters. As predicted by the theory, none of the indirect parameters was perfectly correlated with total hemodynamic power. The most reliable index was mean power, which requires measurements of both pressure and flow. The linear and nonlinear correlations with coefficients close to 1.0000 imply that mean hemodynamic power can be used with confidence to predict total hemodynamic power in the ascending aorta under the conditions of coronary artery bypass graft operations. For this predictability to be achieved, the best least squares fit equations shown must be used. Proportionality is not implied, so that a fractional change in mean power would not indicate the same fractional change in total power. Furthermore, mean power is a rational value that is derived from mean pressure and mean flow alone, whereas total power is complex and can be dissected into its spectral components to provide a complete description of cardiac performance as seen at
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4 0 6 Wright et al.
• •
1·2
•••• • • •• •• •
1'0
•
0·8
Impedance phase lag
•
2'5
• •
•
Peripheral 1'5 vascular resista nce
0·8
(X10 8 kg m-4s- 1)1-Q
0·4
0'5
• • •
•
(r a ds )
OL.-_~-_--=---.---..---_
0·2
o
20
40
60
80
100
120
Systolic blood pressure (mmHg) O~-",":","":-
o
0·5
~
1'0
1'5
~
2'0
2'5
Peripheral vascular resistance (x 10 8kgm-4s-1 )
Fig. 4. Relationship between the resistive and reactive components of aortic input impedance.
the entrance to the systemic load. Below mean power, cardiac output achieved the highest correlation with total hemodynamic power, though even this fell below the 0.95 limit demanded for statistical significance. The use of parameters derived from pressure recordings alone, such as systolic blood pressure and the maximum rate of change of pressure, provided data that was unreliable and difficult to interpret in terms of cardiac performance or systemic load. Unlike the harmonics of the power spectrum, impedance harmonics cannot be summed to derive an interpretable total value. This is because the mean term defines the resistive component of the systemic load, whereas the higher frequency terms relate to reactance as well as resistance. Table IV suggests that the reactive state of the cardiovascular system, indicated by the characteristic impedance or the phase lag, cannot be accurately predicted from any of the indirect indices that we computed. Part of the data processing procedure was to correct inevitable frequency-dependent measurement errors. Failure to do so would lead to further weakening of the relationships between the compared parameters. Also, it is common practice to record pressure in peripheral arteries rather than in the ascending aorta. This adds a further complication, since the pressure wave is modulated as it travels through the arteries. Measurements of cardiovascular function form only part of the overall assessment of the hemodynamic state of patients undergoing coronary artery bypass grafting. The outstanding success of this operation is a testimony that serious misjudgments are rare. Nevertheless, it is
Fig. 5. Relationship between systolic blood pressure and peripheral vascular resistance.
legitimate to ask whether the traditional indirect indices of cardiovascular function provide an optimal, or even adequate, basis for clinical judgments. If the initial premise is accepted, that total hemodynamic power and aortic input impedance are to be considered as the basic, direct indices against which all others must be compared, then it appears that traditional indices are not optimal. Most of the indirect indices that we tested were weakly correlated with total hemodynamic power and aortic input impedance. Although mean power could be used to predict total power, both this and the corresponding term of the impedance spectrum, peripheral vascular resistance, are deficient in their omission of pulsatile components. Of the single parameter measurements, cardiac output provided the best, but still statistically inadequate, index of cardiac performance, but pressure records on their own provided only uninterpretable data.
REFERENCES I. Wright G, Sum Ping JST, Campbell CS, Tobias MA.
2. 3. 4.
5.
Computation of haemodynamic power and input impedance in the ascending aorta of patients undergoing open-heart surgery. Cardiovasc Res 1988;22:179-84. McDonald DA. Blood flow in arteries. London: Edward Arnold, 1974. Milnor WR. Hemodynamics. Baltimore: Williams & Wilkins, 1982. Levine HJ, Forwand SA, McIntyre KM, Schechter E. Effect of afterload on force-velocity relations and contractile element work in the intact dog heart. Circ Res 1966;18:729-44. Shepard RB, Kirklin JW. Relation of pulsatile flow to oxygen consumption and other variables during cardiopul-
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monary bypass. J THoRAc CARDIOVASC SURG 1969; 58:694-702. 6. Parson RJ, McMaster PD. The effect of the pulse upon the formation and flow of lymph. J Exp Med 1938; 68:353-76. 7. Nichols WW, Conti CR, Walker WE, Milnor WR. Input impedance of the systemic circulation in man. Circ Res 1977;40:451-8. 8. Gundel W, Cherry G, Rajagopalan B, Tan L-P, Lee G, Schultz D. Aortic input impedance in man: acute response to vasodilator drugs. Circ Res 1981;63:1305-14.
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9. Gabe IT, Karnell J, Porge IG, Rudewald B. The measurement of input impedance and apparent phase velocity in the human aorta. Acta Physiol Scand 1964;61:73-84. 10. Mills CJ, Gabe IT, Gault JH, et al. Pressure-flow relationships and vascular impedance in man. Cardiovasc Res 1970;4:405-17. II. Pepine JC, Nichols WW, Conti CR. Aortic input impedance in heart failure. Circulation 1978;58:460-5. 12. Murgo JP, WesterhofN, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure waveform. Circulation 1980;65:105-16.