Jyhn C. Wood’ and Daniel T. Barry2 Deportment of Pediatrics, Yale University

’Department of Physicol Medicine and Rehabilitation, University of Michigan Medico1 School

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Time- Frequency Ana lysis of the First Heart Sound

obert Hooke, famous for his work with R material elasticity, was the first to attrib- ute diagnostic potential to cardiac ausculta- tion, “I have been able to hear very plainly the beating of a Man’s Heart ... Who knows, I say, but that it may be possible to discover the Motions of the h e m a l Parts of Bod- ies ... by the sound they make, that one may discover the Works performed in the several Offices and Shops of a Man’s Body, and thereby discover what Instrument or Engine is out of order [I].” With the advent of Laennec’s stethoscope, cardiac auscultation became a fundamental clinical tool and re- mains so today. However quantitative phonocardiography, despite its potential for noninvasive cardiac diagnosis, has lagged behind. The lack of standards in nomencla- ture, recording transducers, and recording locations have slowed progress; as has poor understanding of heart sound mechanisms and the inherent complexity of phono- cardiographic signals. Signal processing ad- vances, particularly in nonstationary signal analysis, have recently aided the latter two problems. The contributions of these tech- niques to the analysis of the first heart sound are the subject of this review.

The first heart sound occurs during the isovolumic contraction period, when left ventricular pressure is rising rapidly (Fig. 1). Four valvular events punctuate the first heart sound, mitral valve closure, tricuspid valve closure, pulmonic valve opening and aortic valve opening, generally in that order. Echocardiography demonstrates the coincidence of first heart sound high frequency components and atrioventricu- lar valve closure; however, the nature of these vibrations is unknown. In fact, valve collision itself is noiseless; vibrations be- gin as the valve movements are abruptly arrested [3, 41. To explain this phenome- non, Rushmer [ 5 ] proposed that the valves act indirectly by rapidly decelerating the left ventricular blood mass, thereby initi- ating vibrations of the entire “cardiohemic system”. Furthermore, he argued that any event that produced sudden accelerations or decelerations of the blood mass creates vibrations. The general framework of the cardiohemic theory is attractive because it provides intuitive explanations for both valvular sounds (S 1 , S2) and non-valvular sounds (S3 and S4).

However, within the cardiohemic the-

ory there has been considerable disagree- ment as to the relative importance of the myocardium and the valves in generating the ensuing vibrations. Some have argued for a valvular resonance model, with spring-mass oscillations of the left ven- tricular blood mass and the mitral valve [6]. According to this hypothesis, first heart frequency is proportional to the stiff- ness and tension of the valve and inversely related the valvular area; the increase in first heart sound frequency observed with porcine mitral valve xenograft calcifica- tion supports this hypothesis [6].

Alternatively, proponents of a myocar- dial resonance argue that valve closure initi- ates resonant myocardial vibrations [7] . Indeed, direct measurements of myocardial resonant frequency in-vitro are consistent with first heart sound frequency spectra [8]. The frequency of vibration of these models is determined primarily by myocardial ten- sion and stiffness, as well by as chamber geometry. Clinically, the decrease in first heart sound frequency seen with myocardial infarction and cardiomyopathy has been suggested as a manifestation of decreased myocardial stiffness [7].

Both valvular and myocardial models predict first heart sound frequencies pro- portional to left ventricular pressure. Since left ventricular pressure rises rap- idly throughout first heart sound genera- tion, both models predict a frequency that rises with time. This response is analogous to a sound that a guitar string would make if it was plucked and then progressively tightened. Additional nonstationarities arise from the discrete loading perturba- tions produced by valvular activity. Con- sequently, standard frequency analysis techniques that assume signal stationarity, such as the Fourier transform or autore-

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1. Schematic illustrating first heart sound relationship to events of the car- diac cycle.

IEEE ENGINEERING IN MEDICINE AND BIOLOGY 0739-51 75/95/$4.0001995 Morth/Aprill995

gressive techniques, have had limited suc- cess in unravelling the complex mechanisms of first heart sound generation.

Approaches Toward Time-Frequency Analysis of Heart Sounds

The concept that heart sounds are non- stationary signals has been recognized since at least the 1950s [ 1,9]. The earliest phonocardiographic time-frequenc y spec- tra exploited a heterodyning bandpass fil- ter device called the sound spectrograph. Initially, the spectrograph density plots were difficult to interpret, but Winer, et a1 [ I O ] in 1965 introduced more favorable contour-type representations. Clinically, the sound spectrograph found use as an adjunct for prosthetic valve malfunction [ 1 1 - 131. Unfortunately, the sound spectro- graph was expensive, cumbersome to use, and not commonly available. In addition, spectrographic filters have a ringing/reso- lution tradeoff, analogous to time-band- width tradeoff encountered in short time Fourier transform analysis. That is, good frequency resolution demands narrow- band filters; but decreasing filter band- width prolongs filter impulse response, yielding poor temporal resolution.

Despite the spectrograph’s long his- tory in phonocardiography, short-time methods such as the spectrogram were applied only relatively recently. Suobank, et al., [ 131 performed the first heart sound spectrograms in an in-vitro aortic valve flow chamber to characterize the spectral “signatures” of two prosthetic aortic valve types as well as their responses to adherent foreign materials. One appeal of short time Fourier transforms (STFT) and spectro- grams is their intuitive generalization of linear system theory to nonstationary sys- tems. Using a model of heart sound gen- eratiodpropagation (Fig. 2), Durand, et al., [ 141 have used the STFT to construct a time-varying transfer function and a co- herence function relating intracardiac and extrathoracic vibrations. According to their model, intracardiac pressure fluctua- tions (phonocardiograms) excite a time- varying transfer function consisting of the cardiac structures and thoracic tissue; ex- ternally recorded heart sounds represent filtered intracardiac sounds contaminated by white Gaussian noise. If the cross- STFT between the intracardiac and exter- nally recorded heart sounds is known, the time-varying cardiothoractic transfer function and coherence can be estimated. Since the spectrogram is positive semi- definite, the cross-coherence function pro- d u c e s a va lue be tween 0 a n d I , corresponding to the transfer function re- liability at a given frequency. The strengths of this approach are its intuitive nature and the ease with which linear sys- tem tools can be used for hypothesis test-

ing. Using this technique, Durand investi- gated the effects of neuromuscular block- ade, thoracotomy, PR interval, and inotropy on the spectra, transfer function, and coherence in chronic dog models, finding predictable changes in heart sound spectral gain without changes in spectral contour.

Jamous, et al., also used this approach to derive the optimal duration spectrogram window for first heart sound analysis [ 151.

They reasoned that a properly tailored spectrogram window would yield mini- mum smoothing jointly in time and fre- quency. Smoothing, like averaging, increases coherence between input and output. Hence the optimal duration win- dow should produce the minimum mean coherence between input and output. Fig- ure 3 demonstrates the mean and maxi- m u m c o h e r e n c e s as a func t ion of spectrogram length; the minimum mean

2. Durand model of heart sound generation. Intracardiac vibrations, x(t) excite a time-varying linear transfer function to yield thoracic vibrations, v(t). White Gauss- ian noise signals, m(t) and n(t), contaminate observations of both intracardiac and thoracic recordings. (Redrawn from Durand, et al., [14] with permission from Medi- cal & Biological Engineering & Computing).

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coherence occurs somewhere between 16 and 32 ms. Many investigators have em- ployed window durations equal to the iso- volumic contraction period (60-90 ms) [6][7][14]. These data suggest, however, that shorter windows are more appropriate for the underlying signal dynamics.

The primary limitation of the Durand model is that it assumes that the intra- cardiac phonocardiogram is a system ex- citation when, in fact, it is an output of a highly complex contractile process. The coupled vibrations of the myocardium, valves and intraventricular blood mass cannot be realistically described by a ra- tional transfer function, even if time-vary- ing. Furthermore, since intracardiac sounds are pressure fluctuations, and tho- racic sounds are shear waves secondarily transduced to pressure fluctuations, one is actually comparing apples to oranges. In that regard, epicardial vibrations may be considered a more appropriate repre- sentation of the “input” to the thoracic transfer function. Despite these physical considerations, the high coherence be- tween the intracardiac and epicardial re- cordings implies that the model has significant predictive capability, as long as the underlying vibrating system com- plexity is appreciated.

In addition to the STFT, other investi- gators have used short time parametric methods. Iwata [16], likening heart mur- murs to speech, attempted to classify high frequency phonocardiograms using linear predictive coding. Because of their auto- correlation-extension property, short-time parametric techniques can use much shorter windows than the STFT without unduly compromising frequency resolu- tion. Furthermore, parametric techniques have fewer degrees of freedom, making them suitable for parametric or neural net- work classification schemes. However, parametric models are sensitive to poor model-fit and signal nonstationarity. Al- though nonstationary parametric tech- niques have been developed, such as the zero-tracking techniques used by Akay, et al., [17], to track the evolution of epi- cardial artery resonances during diastole, such methods can not be expected to char- acterize accurately the rapid frequency dynamics of the first or second sound.

Recently, wavelet time-frequency analysis has generated considerable inter- est in the signal processing literature. Sim- plistically, wavelets can be viewed as frequency-varying short-time Fourier transforms, i.e., longer window durations are used for lower frequencies such that an equal number of cycles is sampled at each frequency. Potentially, then, wavelets should allow excellent temporal resolu- tion of high frequency components while simultaneously providing good frequency

146

resolution of low-frequency components, ideal for broad-spectrum signals such as speech. However, applications to phono- cardiography have been few, and are not strikingly different from previous spectro- gram and spectrograph results [ 181. This finding is not surprising, considering that heart sound frequency spectra have rela- tively narrow bandwidth. Thus, the ana- lyzing wavelet (filter) varies little, producing a time-frequency spectrum comparable to a fixed window spectro- gram.

All short-time techniques suffer from a time and frequency resolution tradeoff, i.e., decreasing window size improves temporal resolution at the expense of poorer frequency resolution, while in- creasing window size produces the con- verse situation. The Wigner distribution, and its many related transforms, achieve temporal resolution by using the signal itself as the convolving window function in a manner analogous to the matched-fil- ter [ 191. The reversal-correlator operation yields good time-resolution, independent of convolving window length, while the long window duration simultaneously al- lows accurate frequency estimation. High resolution, however, has its cost; interac- tions between different time-frequency energy concentrations, or cross-terms, can obscure the “true” signal dynamics. Con- sequently, time-frequency transforms that sacrifice some signal resolution for de- creased cross-term sensitivity, while re- taining the psuedo-density properties of the Wigner Distribution, are very popular for biomedical signal processing, includ- ing heart sound analysis [20-211. The Choi-Williams distribution, the binomial distribution, reduced interference distri- butions (RID), and the Bessel distribution are a few examples of this class of trans-

To demonstrate the superior resolution of RID-type transforms over previous methods, Fig. 4 compares canine epi- cardial first heart sound time-frequency transforms calculated using a digital- simulation of McKusick’s sound spectro- graph, a 33 ms window spectrogram (Hanning window), and a binomial time- frequency spectrum [24]. Although simi- lar time-frequency dynamics are seen in each representation, the binomial time- frequency transform provides much greater detail. The most prominent feature is a rising frequency component that be- gins at the ECG R-wave. Also apparent are two impulse-like components, one at 40 ms and another at 80 ms. In addition, a sinusoidal or slowly rising frequency component is seen at around 45 Hz.

forms [20-231.

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Applications

Prosthetic and Bioprosthetic Valve Studies

Heart sound frequency analysis has fo- cused upon noninvasive diagnosis of pros- t h e t i c a n d b i o p r o s t h e t i c v a l v e dysfunction. Because of space limitations, only the contributions of time-varying fre- quency analysis will be discussed; a com- prehensive review and bibliography may be found in [25]. Prosthetic and biopros- thetic valves present different physiologi- cal and signal processing challenges.

Morth/April 1995

Prosthetic valves, because they are con- structed of plastic and metal, have long life expectancies, are thrombogenic (often re- quiring lifelong systemic anticoagula- tion), and produce loud clicks that contain higher frequencies than native valves. Fre- quency analysis has focused upon the de- tection of wear or breakage and the detection of valve thrombus. Early ball- type valves often developed ball-variance (imprecise ball/orifice seating) at unpre- dictable intervals following replacement. Using the sound spectrograph, Hylen, et al., [ 1 11 was able to document decreased aortic opening sound frequency in patients with Starr-Edwards aortic prostheses hav- ing ball variance (Fig 7). Similar results were seen by Gordon, et al., [ 121 who also were able to successfully distinguish inno- cent paravalvular leak from intrinsic val- vular dysfunction.

Both of these studies utilized the in- stantaneous peak frequency, which de- pends considerably upon recording system passband. Some authors have ar- gued that instantaneous bandwidth meas- ures have higher sensitivity and specificity as well as less recording system depend- ence [26]. Suobank, et al., [13] used spec- trograms and an in-vitro flow tank to characterize the acoustic signatures of the Starr-Edwards 2400, and Smeloff aortic prostheses and the responses to simulated valvular thrombosis. Through joint in- spection of the time and time-frequency domains, they identified multiple unique, reproducible, opening and closing signal components corresponding to mechanical interactions of the valve assembly. Appli- cation of a small amount of silicone gel,

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6. Figure 2 compares the first heart sound acceleration (high pass filtered at 30 Hz) recorded from the left ventricular wall with unfiltered LVP”, and LVP” high pass filtered at 30 and 100 Hz. ECG lead 11, mitral valve closure, and aortic valve opening pro- vide a timing reference (Reprinted from Wood, et al., [27] with permission from IEEE).

Marth/April1995 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 141

producing only an 8% reduction of oc- cluder motion, markedly decreased the signal bandwidth in both valves. In this in-vitro model, the frequency spectra monotonically decreased and peak fre- quency was unchanged.

Bioprosthetic valves may be constructed many ways, but the most common supply source is glutaraldehyde-fixed porcine aor- tic valves. Bioprosthetic valves have the advantage that they are not thrombogenic, however, they are prone to calcification and their life expectancy is only 5-7 years [6]. Calcification increases heart sound fre- quency; diagnosis through parametric and nonparametric techniques using stationary techniques alone have been fairly success- ful. Whether non-stationary techniques will improve sensitivity and specificity remains an open question.

Genesis Mechanisms While mitral valve closure is funda-

mental to heart sound generation, it occurs significantly later than the onset of first heart sound epicardial vibrations, suggest- ing a nonvalvular contribution to the first heart sound. Figure 6 demonstrates epi- cardial acceleration recordings from 15 locations across the canine left ventricle and intracardiac phonocardiograms (at high pass filter settings of 30 and 100 Hz), contrasted with mitral closure and aortic valve opening [27]. In all recordings, one to one and a half oscillations occur prior to mitral valve closure. Mitral valve clo- sure coincides with a burst of high fre- quencies in the intracardiac recordings (ICPlOO), while aortic valve opening pro- duced no changes in either filtered or un- filtered recordings. Figure 7 demonstrates the time-frequency spectra from the intra- cardiac and epicardial recording sites. There are many common features. The most striking is a single rising frequency that begins prior to mitral valve closure and two impulse-like components. The first impulse coincides with mitral valve closure while the second one precedes aortic valve opening. Since tricuspid valve closure is a possible candidate for the sec- ond impulse-like component, tricuspid valve imaging was attempted in these ex- periments but was unsuccessful.

The complex mode shape observed in Fig. 6 suggests that the first heart sound may be dominated by propagating tran- sients rather than resonant vibrations. Since resonance is a global phenomenon, a focal perturbation in myocardial me- chanical properties should produce global frequency changes. Consider a tuning fork that has one tine magically turned from steel to lead; both tines will vibrate at the same new (lower) frequency despite hav- ing drastically different material proper- ties. To simulate this phenomenon, canine

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Time Point 8. First heart sound median frequency changes with ischemia recorded from the is- chemic (LCX) and nonischemic (LAD) zones. Data reflect mean changes from base- line; error bars are standard error of the mean. Statistics performed using Wilcoxin signed-rank test from each time point to baseline. Baseline variability indicated by shaded background which represents one standard error of the mean for baseline values (reprinted from Wood, et al., [28] with permission of the Journal of Applied Physiology).

epicardial acceleration was recorded si- multaneously from the watershed distri- butions of the left-coronary circumflex (LCX) and left anterior descending (LAD) arteries, prior to and following occlusion of the LCX [28]. Figure 8 demonstrates

the median frequency changes in the is- chemic zone (LCX) and the nonischemic zone (LAD) at 5 , 15, 30 minutes, 1 hour, and 2 hours following coronary occlusion. The first heart sound frequency in the nonischemic zone was unchanged at all

148 IEEE ENGINEERING IN MEDICINE AND BIOLOGY March/April1995

timepoints. In contrast, ischemic zone me- dian frequency was significantly elevated for the occlusion duration. This result was surprising, not only because it violated resonance assumptions, but because is- chemia was expected to decrease (not in-

crease) the first heart sound frequency in the ischemic zone.

The first heart sound time-frequency spectra provide some insight; a repre- sentative experiment is shown in Fig. 9. At baseline, both zones exhibited similar dy-

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namics consisting of rising frequencies and impulses. Following coronary occlu- sion, there is preferential suppression of the early low frequency oscillations (the first cycle or cycle and one half following ventricular excitation) leading to an appar- ent frequency increase in that interval. In addition, impulse-like components have become much more prominent, particu- larly in the ischemic zone. This increased prominence does not arise solely from at- tenuation of other components, since first heart sound power did not decrease in either zone following occlusion.

This impression was further supported by statistics derived from a Radon-Bino- mial transform. Figure 10 shows the maxi- mum of the Radon-Binomial transform with respect to rotation angle (normalized to signal power) for the nonischemic zone and the ischemic zone at each of the time points. This statistic measures the concen- tration of power in the time-frequency plane oriented at a particular angle. At baseline, the two zones have a similar distribution; power is concentrated at 0, 72, and 90 degrees, corresponding to im- pulses, slowly rising frequency compo- n e n t s , a n d s t a t i o n a r y s i n u s o i d s , respectively. Following 5 a minute occlu- sion, there is a marked suppression of rising frequency and sinusoidal compo- nents in both zones and a marked increase in impulse-like components in the is- chemic zone. After two hours of occlu- sion, rising-frequency and stationary components had rebounded to supranor- mal levels in the non-ischemic zone but were still suppressed in the ischemic zone. Impulse-like components were more prominent in both zones after two hours of occlusion. These data support the qualita- tive changes observed in the time-fre- quency spectra; i.e., ischemia does attenuate the early-rising frequency com- ponents as well as the low frequency sta- tionary components while accentuating one or both of the impulse-like compo- nents. Our hypothesis is that the accelera- tion of myocardial contraction produces the early rising frequency and stationary components; by impairing contraction, is- chemia attenuates these components. The transient decline, followed by a rebound in the nonischemic zone may reflect an initial mechanical disadvantage as the ventricle dilates with subsequent compen- sation. The reason for the increased im- pulse prominence in the ischemic zone is unclear, but may result from increased effective myocardial stiffness in the is- chemic zone. Although lacking contractile function, ischemic myocardium is para- doxically stiffer than normal myocardium because it has higher wall stress (same pressure, thinner wall, greater radius of curvature) and because it is operating on

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10. (Top panels) Nonischemic and ischemi.: zone average orientation density (maximum of the Radon-Binomial transform with respect to angle) for all timepoints. (Middle pan- els) Comparison of orientation density at baseline and five minutes of coronary occlu- sion. The shaded areas indicate the interanimal average orientation concentration one standard deviation of the mean. (Lower panels) Similar comparison of orientation den- sity at baseline and two hours of coronary occlusion (reprinted from Wood, et al., [28] with permission of the Journal of Applied Physiology).

the steep portion of an exponential stress- strain curve, while healthy myocardium approximates Hookean mechanics.

Discussion Modern nonstationary analysis tech-

niques are an essential tool for studying the first heart sound because this sound is a complicated, multicomponent, and non- stationary signal. Although many tech- niques are available, reduced interference distributions or comparable transforms of- fer the best compromise between resolu- tion and cross-term artifact. With the greater detail provided by the high resolu- tion time-frequency transforms, however, comes the task of objectively identifying and quantifying individual components within the time-frequency plane. When the components are oriented horizontally or vertically in this plane, they may be easily recognized and quantitated by pro- jecting the plane onto the time or fre- quency axis (corresponding to the signal instantaneous power and power spectrum respectively) [ 191. This process may be

generalized to axes of any orientation through Radon transformation of time- frequency spectra. The maximum of this representation with respect to angle pro- vides an insightful index into the orienta- t ion of s igna l p o w e r wi th in the time-frequency plane. While the Radon- Wigner transform has many interesting signal processing properties other than its pattern classification capabilities, they will not be discussed here; the interested reader may see [29, 301.

However, parametric and nonparamet- ric power spectral analysis techniques are still important. Studies from canine epi- cardium suggest that the first heart sound consists of superimposed propagating me- chanical transients, rather than a dominant myocardial or valvular resonant fre- quency [27, 281. In fact, while epicardial frequency dynamics have prominent chirp-like components, the frequency dy- namics observed on the intact human tho- rax are dominated by quasi-stationary components and impulses; few rising or falling frequencies are observed [3 11.

Consequently, in some situations properly windowed power spectral techniques may provide superior frequency estimation of heart sound subcomponents than joint time-frequency techniques. However, in these cases, joint time-frequency tech- niques are extremely helpful in tailoring the power spectral window orientation, shift, and duration.

Conclusions Quantitative phonocardiography has

been limited by many factors, nonstandard nomenclature and recording techniques, complicated mechanoacoustic generation, propagation and coupling, and inherent heart sound nonstationarity. New nonsta- tionary signal processing techniques pro- v i d e a p o w e r f u l too l f o r phonocardiography, particularly in regard to the first heart sound. Recent work sup- ports the concept that the first heart sound is composed of valve-initiated myocardial traveling waves superimposed upon the acceleration of myocardial contraction. Clinically, nonstationary signal analysis has been most frequently applied toward the study of mechanical prosthetic valves. However, a better understanding of first heart sound mechanics may facilitate the diagnosis of myocardial and native-valve pathology. Given the inherent system complexity, an interdisciplinary approach incorporating physicians, mechanical en- gineers, seismologists, and electrical engi- neers is imperative.

Acknowledgment This work has been supported by a

Grant-in-aid from the American Heart As- sociation of Michigan, Lathrup Village, Michigan, and in part by NS01701 from the National Institute of Communication Disorders and Stroke, and HL34691 from the National Heart, Lung, and Blood Insti- tute of the NIH, Bethesda, Maryland, as well as BSC-9000257 from the National Science Foundation; stipend support from the NIH Medical Scientist Training Pro- gram, and the University of Michigan Medical School, Department of Pediatrics is acknowledged as well. The authors are also grateful to Dr. William J. Williams for his advice and the use of the University of Michigan Signal Processing Laboratory facilities.

John C. Wood may be reached at the Department of Pediatrics, Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06520.

Duniel T. Burry may be reached at the Astronaut Office, Mail Code CB, NASA- Johnson Space Center, Houston, TX, 77058.

150 IEEE ENGINEERING IN MEDICINE AN0 BIOLOGY Marth/April 1995

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19. Wood JC, Barry DT: Analysis of multicom- ponent, nonstationary biological signals. Med & Life Sciences in Eng (in press). 20. Cohen L: Time frequency distributions, a review. Proc IEEE, 77:41-981, 1989. 21. Choi HI, Williams WJ: Improved time-fre- quency representation of multicomponent signals using exponential kernels. IEEE Trans Acoust Speech and Sig Proc 37:862-871, 1989. 22. Jeong J, Williams WJ: Kernel design for

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reduced interference distributions, IEEE Trans Acoust Speech and Sig Proc, 40: 402-412. 23. Guo 2, Durand LG, Lee HC: The time-fre- quency distributions of nonstationary signals based on a Bessel kernel. IEEE Trans Acoust Speech and Signal Proc, 42: 1700- 1707, 1994. 24. Wood JC, Buda AJ, and Barry DT: Time- frequency transforms: A new approach to first heart sound frequency analysis. IEEE Trans in Bio Eng, 38:728-739, 1992. 25. Durand LG: Evaluation of prosthetic heart valve functions by signal processing of heart valve sounds. J Med & Life Sciences Eng, (in press). 26. Kagawa Y, Sat0 N, Nitta S, Saji, Tanaka K, Shibota Y, Honuchi T: Real-time sound spec- troanalytic for diagnosis of malfunctioning pros- thetic valves. J Thor & Cardio Surg, 79:671-679, 1980. 27. Wood JC, Lim ML, Buda AJ, and Barry DT: Spatial variation of first heart sound fre- quency dynamics across the canine left ventricle. Proc of the IEEE SOC Eng Med & Biol 13:2099- 2100, 1991. 28. Wood JC, Festen MP, Lim MJ, Buda AJ, Barry DT: Differential effects of myocardial is- chemia on regional first heart sound frequency. J Appl Physiol, 36( 1):291-302, 1994. 29. Wood JC, Barry DT: Radon transformation of time-frequency distributions for analysis of multicomponent signals. IEEE Trans Acoust, Speech, & Sig Proc, Vol34(1 I), 1994. 30. Wood JC, Barry DT: Tomographic time-fre- quency analysis and its application toward time- varying filtering and adaptive kernel design for multicomponent linear-FM signals. IEEE Trans Acoust, Speech, & Sig Proc, 34:2094-2105, 1994. 3 1. Wood JC, Barry DT: The variation of first heart sound frequency dynamics across the human chest wall. Comput & Eng in Med & Biol, July, 1994.

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