IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 38. NO I I , NOVEMBER 1991

Noninvasive Estimation of Cardiac Output Walter Welkowitz, Fellow, IEEE, Qing Cui, Yun Qi, and John B. Kostis

Abstract--A noninvasive method of measuring cardiac output is described. The method uses adaptive aorta models in conjunction with femoral and carotid pulse contour waveform measurements to calculate aortic flow. Results are presented from measurements on dogs using internal pressure recordings made with fluid-filled catheters and compared with electromagnetic flow measurements taken in the ascending aorta. Preliminary results using external pulse measurements on patients are also presented and compared with thermal dilution measurements.

INTRODUCTION useful cardiovascular measurement which can be made is of cardiac output since it is a direct measure of blood flow to the systemic circulation and therefore a measure of the transport of oxygen and nutrients to the cells. Since most presently used techniques are invasive [ 11, [2] the development of a reliable noninvasive method is important. A simple-to-use noninvasive instrument to estimate cardiac output could be applied to all patients, in or out of hospitals, and could therefore be a primary measurement in cardiovascular examinations. Thus, there have been extensive efforts for many years to develop reliable noninvasive techniques for such a measurement. Cope [3] developed a set of equations utilizing pressure measurements and the Windkessel theory to calculate stroke volume. Guier [4] developed improved equations using mean vascular resistance, aortic and venous pressure, and cycle intervals. Starmer er al. [SI evaluated the pulse contour methods for computing stroke volumes from central aortic pressure and concluded that, while many of them were satisfactory for normal subjects with regular heart rates, they had limited usefulness when there were disorders. In order to eliminate problems encountered with a single pressure measurement, McDonald [6] used two pressure measurements in the aorta 3-5 cm apart. These data were incorporated into the Wormersley equation [7] to calculate aortic flow and stroke volume. This approach still had problems with the nonuniform geometric and elastic properties of the aorta. To overcome these problems Muthukrishnan er al. [8] used a parameter optimization technique to compute aortic input impedance in a manner derived from Strano et al. [9] based upon the aorta

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Manuscript received March 2, 1990; revised March 22, 1991. W. Welkowitz, Q. Cui, and Y. Qi are with the Department of Biomedical Engineering, Rutgers University, Piscataway, NJ 08855. J . B. Kostis is with the Department of Medicine, Robert Wood Johnson Medical School-UMDNJ, Piscataway, NJ 08855. IEEE Log Number 9103282.

model described by Welkowitz and Fich [lo]. While agreement with direct flowmeter measurements was good, this two-pressure method was invasive. Min er al. [ I I ] extended this technique using two simultaneous noninvasive pulse contour measurements acquired with two piezoresistive pulse transducers combined with an ultrasonic measurement of aortic diameter. In addition to these pressure and pulse techniques there has been much effort to solve the problem by using doppler ultrasound [ 121 and bioimpedance [ 131. This paper describes work which is an extension of the techniques of Muthukrishnan [8] and Min et al. [ 111 and has lead to the development of a cardiac output instrument which shows promise in preliminary measurements. METHODS Two methods are being used, both based upon the model of Welkowitz and Fich [IO]. In this model the aorta with its geometric taper and nonuniform elasticity is described by a hybrid network (Fig. l ) consisting of distributed segments analogous to the elasticity, area, viscosity, and viscoelasticity of the physiological system and a lumped inertance of the blood in the aorta. In this model [ 101 the massless distributed portions of the systems have equations

_ -ap ax

=

R,,Q

where P is pressure at any location Q is flow at any location C, is the hydraulic capacitance per unit length R,, is the hydraulic resistance per unit length. The taper is assumed to be exponential. If the origin is taken at the distal end, then the inside radius of the aorta is given by

(3) where k is the taper coefficient. Since the modulus of elasticity of the vessel wall has been shown to increase as one moves distally from the heart it is assumed that

E,,? E@) = r,,(4 where E(x) is the modulus of elasticity.

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Fig. 1. A schematic of the aorta based upon the nonuniform hybrid model of a tapered aorta with a lumped inertance.

(12)

Hence, the hydraulic capacitance is

. (y cosh yl1, - k sinh y l n ) where h,, is the vessel wall thickness. The lumped inertance is given by

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where

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for this nonuniform hybrid model (Fig. 1). Watts [ 141, [ 151 has shown that the input impedance to the aorta as a function of frequency is given by

A third-order lumped circuit equivalent to 2, can be synthesized from the general form

where p

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is the blood density is the length of aorta between measurement points is the average cross-sectional area of the aorta over that length.

The pressure transfer function for the hybrid system shown in Fig. 1 is then given in the following equations in terms of the Laplace transform operator.

Y

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Z , ( j w ) = K , jw(-w'

+ j K 2 w + w: +jK3w + w;)'

(16)

The first method describes the aorta as an equivalent lumpled circuit as shown in Fig. 2, based upon the analysis by Watts. This circuit is simulated in a PC-AT type computer using the SPICE circuit analysis program [ 161. Simultaneous pulse contour waveforms are obtained noninvasively using piezoelectric transducers placed over the carotid artery and the femoral artery. The carotid pulse waveform is fed into the circuit as the input. The circuit output waveform as well as the femoral pulse waveform are displayed on the computer screen. The circuit parameters are adjusted from the computer keyboard until the "best" match of these two waveforms is obtained by visual inspection. The input current of the model circuit is then the aortic flow and it too is displayed on the computer screen. Fig. 3 is a flow chart of the computer program to carry out these procedures. Since the pulse contour measurements are not calibrated in pressure units, an external systolic/diastolic arm cuff measurement is used to calibrate the carotid pulse waveform input. The femoral waveform calibration relative to the carotid can be obtained from the transfer function calculations obtained using (7)-(13). An inverse transform can be used to ob-

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IEEE TRANSAC TIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 11, NOVEMBER 1991

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tain the time function from (7) and the resultant amplitude values. The second method uses the hybrid model directly [ 101. From the two-pulse contour measurements and the external calibration, a measured transfer function is calculated by carrying out a Fourier analysis of each waveform and then dividing the resultant terms (term by term) to obtain amplitude and phase as a function of frequency. The parameters of the hybrid model are varied automatically until the transfer function in phase and amplitude of the model is optimally matched to the measured transfer function. When that occurs the computer calculates the input flow using the input carotid pressure and the model input impedance of (15). Fig. 4 is a flow chart of this procedure. Fig. 5 shows a comparison of phase and amplitude of the transfer function of the model optimally adjusted versus the transfer function obtained from a dog using intemal measurements of carotid and femoral pressures taken with fluid filled catheters [ 151. The pulse waveform transfer function and the pressure transfer function are assumed to be equal. This has been confirmed by some re-

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cent studies on twelve patients taken at NYU Medical Center. A comparison of the results obtained from internal and extemal measurements shows a correlation of 0.90.

EXPERIMENTAL PROCEDURES Two series of experiments were carried out to evaluate the methods described and the performance of the computer programs. The first of these experiments was carried out on three dogs using internal pressure measurements

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Fig. 6. Block diagram of system hardware

obtained via fluid filled catheters placed in the carotid and femoral arteries. Aortic flow for comparison purposes was obtained with an electromagnetic flowmeter placed around the ascending aorta. Data were recorded on a multichannel instrument recorder and then played into the computer through an A I D converter. A block diagram of this system is shown in Fig. 6. The second series of measurements was carried out on three patients using Electronics for Medicine external pulse transducers and preamplifiers, and a multichannel instrument recorder. The pulse transducers were placed over the carotid and femoral arteries and the distance between transducers was measured. Systolic and diastolic pressures were obtained using an arm cuff sphygmomanometer. The data were entered into the computer through the A I D converter. Patient data for comparison were obtained using a thermal dilution procedure with an Electronics for Medicine thermal dilution computer with an accuracy of approximately 10%. A "blind" procedure was followed so that the thermal dilution results were not disclosed until the other calculations were completed.

RESULTS

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Fig. 8 . Aortic flow waveform match, dog 1 experiment, circuit method. --- circuit.

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Fig. 9. Aortic flow waveform match, dog 1 experiment, transfer function method. Phase shift is due to electronic circuit time delays. --- transfer function.

As indicated, the first experiments were carried out on

dogs with internal pressure measurements in order to avoid errors produced by inside to outside transfer functions. Clearly some error is possible due to catheter produced phase shifts. This is minimized since lesser weighting is given to phase shift matches than to amplitude matches. Using the circuit analog approach, a typical femoral pressure waveform matchup obtained comparing the circuit output and the actual pressure measurement is shown in Fig. 7. Using this approach, the comparison between the analog flow in the circuit and the electromagnetic flowmeter measurement is shown in Fig. 8. From these curves it was possible to calculate stroke volume and mean flow. The error as compared to the thermal dilution technique when using the analog circuit technique is less than 2 % in mean flow. A comparison of flow measurements on the

same dog using the transfer function approach is shown in Fig. 9. The phase shift in the figure is caused by an electronic circuit time delay. The error in mean flow in this case was about 4% when compared to the thermal dilution technique. The results obtained from three dogs using both methods are summarized in Table I. A second study was carried out on three patients using external measurements. The femoral matchup from one of the these patients using the circuit analog approach is shown in Fig. 10. The analog aortic flow derived from this approach is shown in Fig. 11. Using an average of three thermal dilution flow measurements taken on this patient as a standard, the cardiac output calculatied from the aortic flow waveform is within the accuracy of the thermal dilution technique. The transfer function tech-

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 11, NOVEMBER 1991

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TABLE 1 TABLE 11 A COMPARISON OF MEASUREMENTS ON DOGS USING A N ELECTROMAGNETIC A COMPARISON OF MEASUREMENTS ON PATIENTS USING THE METHODS FLOWMETER BASEDUPONTHE TECHNIQUES DESCRIBED FOR STROKE WITH THERMAL DILUTION MEASUREMENTS DESCRIBED VOLUME AND CARDIAC OUTPUT Meas. Circuit Transfer Patient # sv Flow SV Flow Dog Method # (calc) (meas) HR (meas) (calc) 4.3 4.4 I/m 4.6 I 4.2 4.8 4.9 I I 14.7 ml. transfer 153 bpm 2.2 I/m 4.3 2.3 4.8 4.8 I I 16.4 174 16.9 2.9 4.8 2.9 circuit 4.5 1 I74 16.9 2.9 circuit 16.9 2.9 I 4.5 4.6 1 4. I 4.6 1 2. I 14.9 2 transfer 2.0 4.4 4.7 av . 140 2 14.4 2.0 circuit 14.5 2.0 2 circuit I25 14.3 15.0 1.9 I .8 5.5 4.4 4.7 2 5.2 4.6 2 5.3 3 transfer 12.4 I .8 I .9 5.2 4.4 4.6 2 3 I49 10.8 11.1 1.6 I.7 circuit 6.2 4.5 4.6 2 3 13.0 1.8 circuit I46 12.5 I .9 5.5 4.4 2 4.5 5.2 2 5.3 4.6 av. ~

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nique is also within this accuracy. Table I1 is a summary of patient results from the three patients with results calculated from six different cardiac complexes from each patient data record. In addition, the three or four thermal dilution measurements taken on each patient are also shown. The agreement with thermal dilution measurements is good. Discussio~

The adaptive model technique of analysis that has been described, when coupled to simultaneous pulse contour measurements obtained externally above the carotid and femoral arteries, yields a good estimation of cardiac output as well as providing aortic flow waveforms on a beatto-beat basis. Clearly, the accuracy of the technique is

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highly dependent on obtaining good pulse measurements with pulse transducers that can be easily affixed to the patient. Improvements in this area are still under investigation. Since the external pulse measurements are only relative, further investigations of the calibration and zero setting techniques are warranted to supplement the use of the external arm cuff blood pressure measurements. In order to reliably extend this method to routine clinical use a number of areas clearly need extensive investigation. It should be recognized that the flow estimated from an aorta model transfer function essentially excludes flow to the head, neck, and coronary arteries. It thus should be consistently somewhat lower than the total cardiac output. This question will be explored more fully in further patient studies and appropriate calibration adjustments investigated. It should be noted in this regard that the standard cardiac output measurement techniques presently most used clinically (Fick, thermal dilution) are not highly accurate and migh mask the problems described when used as comparison standards. The results presented in this paper, however, clearly warrant studies with large patient bases in order to effectively validate the procedure. ACKNOWLEDGMENT The authors wish to thank Dr. E. Glassman and his group at NYU Medical Center for help in obtaining the internal versus external measurements.

REFERENCES [ l ] D. R. Richardson, Basic Circulatory Physiology. Boston, MA: Little, Brown, 1976. [2] E. K . Daily and J . Mersch. "Thermodilution cardiac output using room and ice temperature injectate: Comparison with the Fick method," Heurr Lung, vol. 16, p. 294, 1987.

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131 F. W. Cope, “Elastic reservoir theories of human circulation with applications to clinical medicine and to computer analysis of the circulation.” Adi: Med. B i d . f h . ~ .vol. , IO. pp. 277-355, 1965. [4] W. H. Guier, “A Method for determining cardiac stroke volume from arterial pressure that is especially applicable to ectopic beats,” John Hopkins Univ. App. PhFs. Lab. Tech. Memo.. TG-I 134. pp. 1-70. 1970. 151 C. F. Starmer, P. A. McHale. F. R. Cobb. and 0. C. Greenfield. “Evaluation of several methods for computing stroke volume from central aortic pressure.’’ Circ. Ri,.s.. vol. 33. pp. 139-148. 1973. London: Edward Amold. 161 . . D. A. McDonald, Blood Flow in Arteries. 1960. 171 J. R. Womersley. “The mathematical analysis of the arterial circulation in a state of oscillatory motion.” WADC Tech. Rep. WADCTR56-614, 1957. 181 S. Muthukrishnan. D.Jaron. E. N. Cooper, and K. E. Karlson, “Determination of blood flow from pressure measurement: Preliminary results.” in f r o c . 3rd Nciv Eng. B i o m g . Conf.. 1975. pp. 322-333. I91 J. J. Strano, W. Welkowitz, and S. Fich, “Measurement and ultilization of in vivo blood pressure transfer functions of dog and chicken aortas,” IEEE Trans. Biomed. Eng. BME, vol. 19, pp. 261-271, 1972. applied to the determination of aorta parameters.” hit. J . Eng. Sei, vol. IO. pp. 1081-1091. 1972. B. G. Min. W. Welkowitz. and J. B. Kostis. “Noninvasive cardiac output estimation based upon a mathematical model of the aorta: Comparison with thermo- dilution method in 13 patients.” in F “ c . 6th New Eng. Bioeng. Cunj.., 1978, pp. 15-19. W. Welkowitz and S. Deutsch, Bionirdicul Instrunients: Throry crnd Design. New York, Academic, 1976. W. G. Kubicek. R. P. Patterson. and D. A. Witsoe. “Impedance cardiography as a noninvasive method of monitoring cardiac function and other parameters of the cardiovascular system.” Ann. NY Acud. Sei.. vol. 170. p. 724, 1970. R. N. Watts, “A mathematical model for studying the mechanical properties of the impaired left ventricle.” Ph.D. dissertation. Rutgers Univ. New Brunswick. NJ 1974. W Welkowitz, Engineering Hemorlynumicst Applicutiori t o Curdiuc Assist device.^, 2nd ed. New York. NYU. 1987. MicroSim Corporation, PSPICE-An Electrical Circuit Simulation, IYXU.

Walter Welkowitz, (S’46-A.49-M.55-SM.74F’76) was born in Brooklyn. NY, on August 3. 1926. He received the B.S. degree in electrical engineering from Cooper Union. New York, NY. In 1948. and the M.S. and Ph.D. degrees from the University of Illinois. Urbana. in 1949 and 1954. respectively. He was a Research Associate at Columbia University. New York, NY, from 1954 to 1955. He joined Gulton Industries. Inc., in 1955, and worked in various phases of medical Instrumentation until 1964. He thien joined Rutgers University. New Brunswick. NJ. where he is currently Professor and Chairman of the Department of

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Biomedical Engineering. Adjunct Professor in the Department of Surgery (Biomedical Engineering) and Graduate Director of the Program in Biomedical Engineering. Dr. Welkowitz is a member of Tau Beta Pi. Eta Kappa Nu, Phi Kappa Phi. Sigma X I , the American Heart Association. the New York Academy of Sciences, and the American Society of Anifical Internal Organs. He received the IEEE Centennial Medal in 1984.

Qing Cui received the B.S. degree in electrical engineering from Tianjin University, Tianjin, China, in 1982. From 1982 to 1985 he joined the Faculty of Electrical Engineering at Tianjin University, Tianjin, China, as a Research Associate and lecturer, where his work involved applications of microcomputer in DC-motor control. He was a member of Chinese Association for the Industrial Automation. In 1985 he came to the U.S. as a visiting scholar in Rutgers University. He became a gineering, Piscataway, NJ, in 1986, where his research interests have centered around Cardiovascular Hemodynamics.

Yun Qi was born in Hangzhou, China, in 1963. He received the B.S. degree in biomedical engineering from Zhejiang University. China. in 1986. He joined the Department of Animal Research at Zhejiang Medical Research Institute. Zhqjiang. China. in 1986 as a Research Associate. where his work involved external radio-power implant transmission. He has been studying and working for Ph.D. degree in biomedical engineering since 1986 where his research interests include cadiovasular hemodynamics and Chinese medicine systems.

John B. Kostis was born in Greece. He received the M.D. degree in 1960 at the University of Salonica. Greece. He is now Professor of Medicine and Pharmacology and Chairman of the Department of Medicine at the University of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School. He is involved in several large multicenter NIH clinical trials and has published extensively in the areas of clinical cardiology and hypertension, cardiovascular pharmacology, and biomedical engineering. He is the John. G. Detwiler Professor of CardiolOgY.