Spectral analysis of arterial sounds: A noninvasive method of studying arterial disease

Spectral analysis of arterial sounds: a noninvasive method of studying arterial disease* Ramesh Gupta J. Wayne Miller Ajit P. Yoganathan

Firdaus E. Udwadia Wil l iam H. Corcoran California Institute of Technology, Pasadena, Calif. 91125, USA

Bang M. Kim Bioengineering Section, College of Physicians & Surgeons, Columbia University, New York, USA

Abstract--A partially obstructed latex tube was used to mode/a stenosed artery. The frequency spectrum contains peaks corresponding to the resonant frequencies of the tube. Resonant peaks were also observed in the spectra of the Korotkoff sounds from the brachial artery. The resonant peaks are related to the geometry and elasticity of the artery and the surrounding tissue. Some useful diagnostic information about the state of the arteries is therefore likely to be obtained from the spectra/analysis of arterial sounds,

Keywords--Arterial disease, Spectral analysis, Turbulence, Korotkoff sounds, Noninvasive diagnosis

1 Introduction

ATHEROSCLEROSIS is a leading cause of death in the United States of America (Statistical Abstract of USA, 1969). It is estimated that nearly half of all deaths are caused by disease of the heart and other blood vessels. Various techniques have been developed over the years to assess the state of the arteries. Most of the diagnostic and investigative methods available today are invasive in nature. For example, catheter angiography is a very reliable method for determining the location and severity of arterial narrowing caused by atherosclerotic disease. How- ever, this method is invasive in nature, requires expensive equipment, and involves pain and radia- tion hazards to the patient.

The need for a simple and noninvasive diagnostic method has been long recognised. Inexpensive, simple and noninvasive methods should be developed tomonitor the state of arteries. One of the noninvasive techniques which is currently undergoing development and clinical evaluation uses ultrasonic waves (JoYNER and REID, 1963; STRANDNESS et al., 1967). Reflection of ultrasonic waves from blood vessels could be quantitatively interpreted in order to obtain clinically important parameters such as the vessel diameter and the blood velocity. This research group and others are trying to obtain information about the state of arteries from an analysis of arterial sounds (LEEs and DEWEY, 1970; FREDBERG et al., 1970; KIM and CORCORAN, 1974).

Auscultation is not a new science, and it has long been recognised that vascular sounds provide some

"First received 1st July and in final form 30th October 1974

very important bits of diagnostic information to physicians. Modern phonocardiography has come a long way since 1819 when a crude stethoscope was designed by La~nnec. Even today, however, very little of the information available in a phonocardiogram recording is utilised. Only sketchy references are available in the literature where the various vascular sounds have been subjected to a quantitative analysis. In general clinical practice, the analysis of a phonocardiogram recording is limited to pattern recognition only.

Recently, FREDBERG et al. (1970) and LEES and DEWEY (1970) have suggested that significant diagnostic information about a stenosed artery can be obtained by a quantitative analysis of the flow turbulence downstream from the stenosis. The pressure fluctuations associated with turbulent flow induce stresses in the blood vessel, and the resulting vibrations result in the production of arterial sounds. In their analysis, FREDBERG et al. (1970) and LEES and DEWEY (1970) neglect any interaction between the turbulent flow and the elastic wall of the artery. It is assumed that the spectrum of sound is the same as that of turbulent flow, and that an analysis of the sound spectrum should yield information about the state of the artery.

For the analysis of arterial sounds to be used as a practical diagnostic tool, it is essential that basic studies be made on blood turbulence in arteries, interaction of turbulence with the elastic wall of the artery, and transmission of the resulting sound through the tissue. As a first step towards this goal, KIM and CORCORAN (1974) investigated the turbulence spectra distal to simulated stenoses.

700 Medical and Biological Engineering September 1975

Here we report our studies on the interaction of turbulence with the elastic wall and the generation of sound. We have used partially obstructed latex tubes as model experiments and have analysed the Korotkoff sounds from the brachial artery of humans. Unlike the turbulence spectrum, the sound spectrum contains resonant peaks. The resonant peaks are related to the geometry and elasticity of the artery and the surrounding tissue. Some useful diagnostic information about the state of the arteries is therefore likely to be obtained from the spectral analysis of arterial sounds.

2 Model studies with latex tubes

Blood flow in arteries and the generation of arterial sounds is a complex phenomenon, and modelling is a difficult task. The flow is unsteady, the fluid is a suspension, and the wall of the artery is nonhomogeneous, nonisotropic, and viscoelastic in nature (BER6EL, 1961). Also the transmission function of the surrounding tissue, the irregular geometry of the stenosis, arterial tapering, and arterial branch- ing should be taken into account. Obviously, the incorporation of all the above factors in a simulated model is a very difficult mission. In our preliminary investigation, we used a highly simplified model. Later in this paper, we present the analysis of Korot- koff sounds which are emitted from the human brachial artery in vivo.

Our simulated model consisted of steady-state flow of water in a latex tube (length = 381 mm (15in), inside d i a m e t e r = 9 . 5 m m (~-in)). The experimental setup was similar to the one described by KIM and CORCORAN (1974) in their study of turbulence distal to stenoses. Turbulence and sound were generated by a stenosis that was simulated by the insertion of a Lucite cylinder, of length 25.4 mm (1 in), diameter 9.5 mm (~-in), and with an orifice diameter of 3.2 mm (~ in), halfway down the latex tube. Auxiliary parts of the experimental system were a constant-head tank, a flow valve, a rota- meter, and a manometer to read pressure inside the latex tube.

A contact type microphone (Hewlett Packard 21050 A) was used to obtain the sound signal. The signal was amplified and recorded on an f.m. tape recorder (Lockheed 417). This recorder had a flat frequency response in the frequency range 0--2000 Hz and a signal-to-noise ratio of 40 dB.

2.1 Data processing

The sound spectra for various experiments were obtained by processing the sound signals on the digital-data-analysis system which was developed at the Jet Propulsion Laboratory for induced-random- environment tests (CHAPMAN and SOTOMAYOR, 1972). The basic hardware for the system consists of a Fourier processor (Time-Data 100), a miniature computer (Honeywell 316), and an interface con-

troller that couples the computer to the Fourier processor.

The playback signal from the tape recorder was preconditioned by using 25 Hz highpass and 500 Hz lowpass filters. The analysis time for each experiment was 30 s. Using a digitisation rate of 1000 s-1, the Fourier processor obtained a Fourier transformation for 0.1 second. A mean spectrum for the 30 s time span was obtained by averaging 300 such spectra. This average power spectrum for the frequency range 25-500 Hz with a frequency resolution of 5 Hz was obtained in a graphical form at the computer output.

2.2 Experimental results and analysis

Sound spectra were determined for different flow rates at various distances downstream from the orifice.

Fig. 1 shows a typical sound spectrum between the frequency range 25-250Hz measured 25 .4mm (1 in) downstream from the orifice for a latex tube of wall thickness 0.4 mm ( ~ in). The Reynolds number was 1600, and the pressure difference between the inside and outside of the tube was 10 torr. The spectrum has dominant resonant peaks at 120 Hz and 205 Hz. These peaks in the sound spectrum are introduced because of the coupling of turbulent flow with the flexible wall of the tube. Note that only the sound spectrum contains these peaks. The turbulence spectrum distal to stenosis determined by KaM and CORCORAN (1974) lacks any such peaks.

The effect of pressure difference across the wall of

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Fig. 1 S o u n d spect rum for la tex- tube m o d e l Wal l thickness - - 0 . 4 m m (~�89 in) ; Reynolds numbe r - - 1600

Medical and Biological Engineering September 1975 701

the latex tube was investigated. Fig. 2 shows the location of the resonant peaks for different pressure differences. The resonance frequencies of the latex tube increase with increasing pressure difference.

In Fig. 2, the sound measurements were made 25.4 mm (1 in) downstream from the orifice. How- ever, no significant change in the nature of the sound spectrum was observed when the microphone was moved up to 76.2 mm (3 in) downstream from the orifice. No measurements were made beyond a distance of 76-2 mm. Because there was, however, a gradual transition from turbulent to laminar flow at larger distances, a disappearance of the resonant peaks in the sound spectrum was expected.

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Fig. 2 Effect of static-pressure difference across the tube wall on the resonant peak frequencies

Experiments with a Reynolds number of 2000 in a tube with a wall thickness of 0.4 mm ( ~ in) yielded the same results as experiments with a Reynolds number of 1600, except that in some experiments with Reynolds number of 2000, more than two resonant peaks were observed. This observation is not surprising. With a higher flow rate, the turbulence spectrum has a high intensity even at a frequency corresponding to the third resonant peak, and the tube can vibrate at this frequency.

Some experiments were conducted with latex tubes of wall thickness greater than 0.4 mm (~- in) . The resonant peaks were not as dominant as in experiments with a wall thickness of 0.4 mm.

The experimental results can be explained on the basis of the work of FUNG et aL (1957) and WEYERS (1959) on the vibration of thin cylindrical shells. FUNG et al. (1957)studied the resonance of thin cylindrical shells which were excited by a sinusoidal sound

wave. WEYERS (1959), with the aim of understanding noise inside an aircraft, studied the noise produced by turbulent flow in a flexible tube. A cylindrical shell can vibrate in a great variety of ways, and the theory of vibration is rather complicated. Under the assumption that the cylinder is 'freely supported' in such a fashion that the ends remain circular and there is no restraint on the axial and tangential dis- placement at the ends, the frequency equation given by WEYERS (1959) is

- (l 2 + ~ ) 2 + ~ ( I - ~

Pd22 pdl2 (I) • (t~ + ~)~ + ~ + 2e~

where

d = diameter of cylinder E = Young's modulus f = natural frequency of oscillation l = 1, 2, 3, - - , = number of circumferential waves

in cylinder L = length of cylinder m = 1, 3, 5 , - - , = number of axial halfwaves in

cylinder p = static pressure difference across cylinder wall t = thickness of cylinder wall p = wall density 2 = nondimensional parameter = mnd/2L a = Poisson's ratio The above variables are in units such that each term in eqn. 1 is dimensionless.

The first two terms on the right-hand side of eqn. 1 describe the influence of stretching and the influence of bending of the shell, respectively. The third and the fourth terms describe the contribution of the axial stress and the hoop stress to the natural frequency f.

Eqn. 1 is derived for the vibration of a cylindrical shell of length L that is 'freely supported' at the ends. In our model experiments, turbulence and vibration existed only downstream from the stenosis located halfway down the length of the tube. Also, because the latex tube was not freely supported, eqn. 1 holds only qualitatively for our experiments. Nevertheless, eqn. 1 is important because it predicts the existence of resonant frequencies in the sound spectrum and shows that these resonant frequencies are related to the geometry and elasticity of the wall.

3 Korotkoff sounds

The Korotkoff sounds are heard from the brachial artery when it is subjected to an external occlusive pressure between the systolic and the diastolic level. The auscultatory technique based on the phenomenon of Korotkoff sounds is a standard clinical method for the indirect measurement of blood pres-


sure. A pneumatic cuff is wrapped around the upper arm and is inflated to a pressure above the systolic level. When the cuff pressure is gradually reduced, characteristic tapping sounds can be heard with the help of a stethoscope placed on the brachial artery at the elbow. These tapping sounds, called the Korotkoff sounds, appear when the cuff pressure equals the systolic pressure. When the cuff pressure is further reduced, the Korotkoff sounds become louder, then muffled, and finally disappear at the diastolic pressure level.

The basic mechanism by which the Korotkoff sounds are produced is not clearly understood. Although many hypotheses have been put forward to explain the genesis of Korotkoff sounds (ANLIKER and RAMAN,. 1966; ERLANGER, 1916; ERSKINE, 1957; RODBARD and SAIKI, 1953), it is generally believed that these sounds are the result of arterial vibrations induced by turbulence and eddies (CHUNGCHAROEN, 1964; LANGE et aL, 1956; LANGE and HECrtT, 1958; Mus[cK, 1957). We obtained the frequency spectra of Korotkoff sounds to determine whether the spectra contain any resonant frequencies similar to the resonant frequencies of the model experiments.

3.1 Clinical method and instrumentation

A standard clinical cuff placed around the upper arms of a series of young, healthy males was inflated to the appropriat~pressures. In the early experiments, the microphone was held in the antecubital fossa by means of an elastic strap. Later we found it more convenient to hold the microphone against the brachial artery by mounting the microphone on a telescopic mechanical arm with ball-and-socket joints. In our preliminary experiments, the instrumentation and procedure for the acquisition and analysis of Korotkoff sounds were similar to those for the model experiments with latex tubes. Analysis of the 30 s-data segments containing approximately 35 Korotkoff sounds revealed a rapidly decreasing amplitude of the power spectrum with frequency, and a worsening signal/noise ratio with increasing frequency.

To improve the signal/noise ratio, the following steps were taken. A highpass amplifier (Hewlett Packard heart sound amplifier 8813 A) was inserted between the microphone and the f.m. tape recorder. This amplifier has a slope of 12 dB/octave over the frequency range of interest, i.e., for every doubling of frequency, the signal amplitude coming out of the amplifier increases by a factor of four. The signal/ noise ratio was further improved by conducting the experiments in a sound-proof room. In addition, the method for analysis of the data was also improved as described below.

3.2 Data analysis

In the data-analysis system described previously, a Fourier transformation was obtained by analysing

the data for a continuous time span of 30 s. This method is ideal for the model experiments which use a steady-state flow. Korotkoff sounds, however, are transitory in nature. The 30 s time span contains the Korotkoff sounds at periodic intervals so that the Korotkoff sounds are separated by time periods which contain no sound signal but only background noise. Therefore, to improve the overall signal/noise ratio for analysis of the data, it was necessary to ignore the time periods of the noise signal that occurred between the Korotkoff sounds.

Using an analogue-digital convertor, the playback signal of 30 s duration was digitised (at a digitisation rate of 2000 s- 1), and a digital tape was generated. The digitised data were plotted on graph

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Fig. 3 A typical Korotkoff sound after 12 dB/octave filtering

paper using the Calcomp plotter facilities of the Cal- tech computer centre. Fig. 3 shows a typical Korot- koff sound as it appears at periodic intervals in the plotted time function. Recall that the Korotkoff sound of Fig. 3 has undergone a 12 dB/octave filtering prior to recording.

A frequency spectrum for the 0.2 s interval that contains the Korotkoff sound was obtained by using the fast-Fourier-transform algorithm developed by COOL~Y and TuKEv (1965). Finally, a mean power spectrum was obtained by averaging the spectra of 30 Korotkoff sounds. This average spectrum was corrected for 12 dB/octave filtering, and the resulting spectrum with a frequency resolution of 1.95 Hz was plotted in a graphical form.

3.3 Results

The Korotkoff sounds flom three young and


healthy males were analysed for various cuff pressures between the systolic and the diastolic levels.

It was found that the Korotkoff sounds contain a small peak in their spectra. Fig. 4 is the spectrum of the Korotkoff sound from one of the subjects. The subject under investigation had a blood pressure of 120/70 torr. A cuff pressure of 90 torr was used in the experiment of Fig. 4. The spectrum has a small peak at a frequency of 84 Hz. The spectra from the same subject for cuff pressures of 70 and 80 torr contain similar peaks. No peak was observed, however, for cuff pressures of 100 tort and above. The spectra of the other two subjects exhibited small peaks at frequencies of 71 Hz and 73 Hz.

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Fig. 4 Power spectrum of the Korotkoff sound

Peaks were reproducible for experiments at different times. The peak in the spectrum is not introduced because of some extraneous noise or the noise from the measuring and recording instruments. Results of experiments conducted in two different soundproof laboratories in two different buildings were identical. The background noise was also subjected to spectral analysis. Here the periods of noise signal that occurred between consecutive Korotkoff sounds in the 30 s segment of data were analysed. The noise spectrum was not found to have a peak at a frequency corresponding to the peak in the spectrum of the Korotkoff sound. Also, at the frequency corresponding to the peak, the signal intensity was greater than the noise intensity by a factor of over 100.

There are only a few studies reported in the literature on the spectral analysis of arterial sounds. None of these studies, however, reports the existence of a peak in the spectrum. We believe that the pre- vious studies have failed to notice any peak in the

spectrum because of the approximate way in which the power spectra were obtained. For example, FREDBERG et al. (1970) Obtained a frequency spectrum by sweeping the signal with a narrow-band- frequency filter. This technique displays a difficulty in averaging, and hence the frequency spectra reported by FREDBERG et al. contain error bars denot- ing estimated uncertainties. Any small peak in the spectrum will be eclipsed by these error bars. WARE and ANDERSON (1966) in their analysis of Korotkoff sounds, digitised the signal using a Gerber curve follower. Their computation method, however, provided the energy densities at 10Hz and at harmonics of 10 Hz. A small peak is very likely to be omitted with a frequency resolution of 10 Hz. The spectra presented by WARE and ANDERSON (1966) do contain some wide peaks. These peaks, however, seem to be artefacts and have been ignored by WARE and ANDERSON (1966). The data-analysis procedure used in the present work has a high statistical accuracy and should detect any small peaks in the spectrum.

4 Conclusions

Small resonant peaks have been detected in the frequency spectra of Korotkoff sounds. A compari- son between the Korotkoff sounds and experiments in the latex tube strongly suggests that the peak in the spectrum of the Korotkoff s6und is introduced as a result of resonance in the artery. The observations support the hypothesis that the Korotkoff sounds are produced by the vibration of the arterial wall induced by the pressure fluctuations associated with turbulent flow.

Latex tubes have large peaks in their spectra compared with the peaks that exist in the spectra of Korotkoff sounds. This difference can be attributed to the attenuation of Korotkoff sounds by the tissue. The role of tissue in signal attenuation and modifica- tion needs to be investigated.

The resonant peaks in the spectra are related to the geometry and elasticity of the vessel. Because of the complex nature of blood flow and the fact that the surrounding tissue modifies the arterial sounds, it is very difficult to compute directly the geometry and elasticity of the artery from a measurement of the peak frequency. The basic concept of the study can be used, however, in monitoring the state of the arteries. If a record is kept of the peak frequencies of the arteries of the extremities, then a change in the peak frequencies will signify a change in the state of the arteries. This methodology would be simple, inexpensive, and noninvasive in nature. Of course, the technique will need more investigation, and it must be validated against currently known clinical techniques before it can be used.

Work reported here is also useful in the study of the cause of poststenotic dilation. FOREMAN and HUTCHISON (1970) studied the vibration of the


arterial wall in vitro and postulated that poststenotic weakening and dilation results f rom high strains produced at resonance. The present study indicates the existence of resonant frequencies in arteries in vivo.

Acknowledgment--This research was supported by the Donald E. Baxter Foundation, and the support is grate- fully acknowledged.

References

ANLIKER, M. and RAMAN, K. R. (1966) Korotkoff sounds at diastole--a phenomenon of dynamic instability of fluid-filled shells. Int. J. Solid Structures 2, 467.

BERGEL, D. H. (1961) The static elastic properties of the arterial wall. J. Physiol. 156, 445.

BERGEL, D. H. (1961) The dynamic elastic properties of the arterial wall. ibid. 156, 458.

CHAPMAN, C. P. and SOTOMAYOR: B. R. (1972) Off-line data analysis and data reduction from digitally con- trolled random test signals, Proc. Inst. Env. SoL, Mt. Prospect, Ill., p. 120.

CtItrNaCHAROEN, D. (1964) Genesis of Korotkoff sounds. Am. J. PhysioL 207, 190.

COOLEY, J. W. and TurEv, J. W, (1965) An algorithm for the machine calculation of complex Fourier series. Math. o f Comput. 19, 297.

ERLANGER, J. (1916) Studies in blood pressure estimation by indirect methods. Pt. I I - -The mechanism of the compression sounds of Korotkoff. Am. J. Physiol. 40, 82.

ERSKINE, M. J. (1957) Blood pressure sounds and their meanings. Springfield.

FOREMAN, J. E. K. and HurcmsoN, K. J. (1970) Arterial wall vibration distal to stenoses in isolated arteries of dog and man, Circulation Res. 26, 583.

FREDBERG, J. J., LEES, R. S. and DEWEY, C. F., JUN. (1970) How to listen to arteries (or how your doctor would hear if he were a fluid dynamicist). AIAA 8th Aerospace Sciences Meeting, New York, USA.

FUNG, Y. C., SECHLER, E. E. and KAPLAN, A. (1957) On the vibration of thin cylindrical shells under internal pressure. J. Aero. Sci. 24, 650.

JOYNER, C. R., JUN. and REID, J. M. (1963) Application of ultrasound in cardiology and cardiovascular physiology. Progr. Cardiovasc. Dis. 5, 482.

KIM, B. M. and CORCORAN, W. H. (1974) Experimental measurements of turbulence spectra distal to stenoses, J. of Biomechanics 7, 335.

LANGE, R. L., CARLISLE, R. P. and HECHT, H. H. (1956) Observations on vascular sounds; the 'pistol shot' sound and the Korotkoff sound. Circulation 13, 873.

LANGE, R. L. and HECHT, H. H. (1958) Genesis of pistol-shot and Korotkoff sounds, ibid. 18, 975.

LEES, R. S. and DEWEY, C. F., JUN. (1970) Phono- angiography: a new noninvasive diagnostic method of studying arterail disease. Proe. Nat. Acad. o f Sci. 67, 935.

McKuslcK, V. A. (1957) Symposium on cardiovascular sound./--Mechanisms. Circulation 16, 270.

RODBARD, S. and SAIKI, H. (1953) Flow through col- lapsible tubes. Am. Heart J. 46, 715.

Statistical Abstract of the United States (1969) US Bureau of the Census, Washington, DC, 90th edition, p. 58.

STRANDNESS, D. E., JUN., SCmJLTZ, R. D., SUMNER, D. S. and RUSHMER, R.. F. (1967) Ultrasonic flow detection. A useful technique in the evaluation of peripheral disease. Am. J. Surg. 113, 311.

WARE, R. W. and ANDERSON, W. L. (1966) Spectral analysis of Korotkoff sounds. IEEE Trans. BME-13, 170.

WEYERS, P. F. R. (1959) Vibration and near field sound of thin-walled cylinders caused by internal turbulent flow. NASA Technical Note D-430.

Analyse spectrale des sons artdriels: methode noninvasive d'6tude des maladies art6rielles

Sommaire---On a utilis6 un tube de latex obtur6 partiellement pour modeler une art~re st6nos6e et on a d6termin6 le spectre de fr6quences du son engendr6 par turbulence dans le tube module. Le spectre contient des crates correspondant aux fr6quences de r6sonance du tube. Des crates de r6sonance ont 6t6 6galement observ6es darts le spectre des sons de Korotkoff provenant de l'art~re brachiale. Ces pointes de rgsonance sont li6es b. la configuration et h l'61asticit6 de l'art~re et des tissus environnants. C'est pourquoi l'analyse spectrale des sons art6riels est susceptible de fournir des renseignements diagnostiques utiles sur l'6tat des art~res.

Spektralanalyse von Arterienger~iuschen: ein inoffensives Verfahren zur Untersuchung von Arterienkrankheiten

Zusammenfasstmg--Eine teilweise behinderte Latexrt~hre wurde als Modell fiir eine verengte Arterie verwendet. Das Frequenzspektrum wurde aus T6nen festgelegt, die durch Wirbelstrom in der Modellrfhre erzeugt wurden. Das Spektrum enth~ilt Spitzen, die den Resonanzfrequenzen der ROhre entsprechen. Die Resonanzspitzen wurden ebenfalls in den Spektren yon Korotkoffschen Gerauschen der Armarterie beobachtet. Die Resonanzspitzen stehen in Bezug zur Form und Elastizit~it der Arterie und zum umgebenden Gewebe. Man kann daher wahrescheinlich durch die Spektralanalyse der Arterienger~iusche ni~tzliche diagnostische Angaben tiber den Zustand der Arterien erhalten.


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Spectral analysis of arterial sounds: A noninvasive method of studying arterial disease