Journal of Mechanics in Medicine and Biology Electronic of an article published as Journal of Mechanics in Vol. 5, No. 3version (2005) 415–428 Vol.5, N.3, 2005, Publishing pp.415-428, DOI: 10.1142/S0219519405001552 c World
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SMOOTHED-PSEUDO WIGNER–VILLE DISTRIBUTION OF NORMAL AND AORTIC STENOSIS HEART SOUNDS

ABDELGHANI DJEBBARI∗ and F. BEREKSI-REGUIG Laboratory of Biomedical Engineering Faculty of Engineering Sciences University Abou Bekr Belka¨ıd B. P. 119, Tlemcen, Algeria ∗a [email protected], a [email protected] * [email protected] Accepted 19 January 2005 In this paper, we are interested in the acquisition and the time-frequency analysis of the Phonocardiogram (PCG) signal. The interactive software “PCG Recorder” we implemented in MATLAB, drives the sound card of a personal computer for acquisition purposes. Normal and abnormal heart sounds were acquired with 16 bits resolution and at high sampling frequencies; the value 2 kHz was selected as sampling rate to avoid spectral aliasing. For each patient, additional information like the age, the gender, the weight as well as the auscultation area can be introduced within the saved data file. The aortic, the tricuspid, the mitral and the pulmonic areas are considered for the acquisition task. The Smoothed-Pseudo Wigner–Ville Distribution (SPWVD) yield adequate Time-Frequency Representations (TFRs) of such non-stationary signal as heart sounds. Moreover, by taking into account the corresponding auscultation area for each obtained TFR, we adopt exclusion reasoning to attribute each burst to its origins within the myocardium. Furthermore, the alternating functioning of heart valves and cavities in systole and diastole was characterized in the time and frequency domains. Aortic stenosis heart sounds were involved in our study in a view to confirm their pathological nature towards the normal heart sounds findings. Indeed, the weakened S1 and S2 heart sounds and the strong systolic ejection murmur which dominates the overall systole, confirm our hypotheses. Thus, modulations laws relating to the systolic ejection of blood through the stenosed orifice were characterized by means of the reliable SPWVD approach. A third heart sound (S3) which is an indicator of the presence of systolic dysfunction and the elevated filling pressure for aortic stenosis lesion was also characterized. Keywords: Normal heart sounds; aortic stenosis; Wigner Distribution (WD); cross-terms; Smoothed-Pseudo Wigner–Ville Distribution (SPWVD).

1. Introduction The human heart is constituted of two non-connected parts functioning in synchrony. Each part is composed of an atrium and a ventricle and is parenthetically called a heart.1–3 Thus, in the left and the right hearts, the atrium and the ventricle are connected through the atrioventricular valves, namely the mitral and the tricuspid valves. Each part receives the blood throughout its atrium, hence ejecting this same blood by a ventricular contraction. The heart ejects blood to the lungs 415

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through the pulmonary artery, by means of the pulmonic valve and towards all peripheral tissues through the aorta by means of the aortic valve. When the aortic heart valve is closed, it allows the left ventricle to be filled from the left atrium, which is connected to the lungs. At its opening, the aortic orifice allows this same blood to leave the left ventricle towards peripherals organs through the aorta. In the same way, the closing of the pulmonic heart valve allows the filling of the right ventricle from the right atrium, through the opened tricuspid orifice. This oxygenlow content blood coming from the peripheral organs is being ejected to the lungs through the pulmonic orifice when it opens again. The human heart activity is basically articulated around its two functioning modes, namely, the contraction (systole) and the relaxation (diastole) of the cardiac periods. The boundaries of each cardiac period are marked by the changing of the heart valves that are involved, whereas the blood flow circulation and the heart valves function generate heart sounds. Deterioration of the cardiac valves affects the nature of the generated sounds by adding stenotic, regurgitant and musical murmurs. Hence, the generated heart sounds and murmurs constituting the Phonocardiogram (PCG) signal are correlated with the intracardiac movements of structures and blood.4 However, these sonic vibrations are also affected by the heart–thorax system.5,6 The human ear cannot perceive accurately the temporal and spectral characteristics of the heart sounds and murmurs, because of their very short durations and their low frequency harmonics.7 Additionally, the PCG signal restrains both modulation laws caused by blood turbulences into the myocardium and splitted sounds components.4 For a normal subject, four heart sounds can be recorded denoted S1, S2, S3 and S4.2,7–10 The first heart sound (S1) contains halting snaps of the mitral and tricuspid heart valves opening sounds of aortic and pulmonic valves, and sounds related to blood flow circulation within cavities of the myocardium.4 This signal is a multicomponent non-stationary heart sound dominated by quasi-stationary and impulselike components,11 and dominating frequencies between 91 and 179 Hz.12 This sound indicates the beginning of the ventricular systole phase and is mainly due to the closure of atrioventricular valves.4 It was shown by Wood et al.13,14 that the first heart sound (S1) when recorded on the epicardium, contains a rapidly rising frequency component during early systole, which was correlated with the rising left ventricular pressure. Moreover, the first heart sound S1 favor impulse-like components. The second heart sound (S2) appears at the beginning of the ventricular diastole, generated by the closure of aortic and pulmonic valves and the opening of mitral and tricuspid ones, and can reach a frequency of 200 Hz for normal subjects.7 For a normal subject, the third and the fourth heart sounds (S3 and S4) cannot be recorded because of their low intensity.4 These heart sounds are of great clinical importance. They are generated by the mechanical impact between blood and ventricular muscular tissues and are good indicators of cardiac failure and ventricular dysfunction.15,16 Ishikawa et al. reported that a clearly audible fourth heart sound (S4) highlights the risk of adverse cardiac events.17

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As concluded by Durand et al. in their work carried out on dogs,5,6,18 the heart– thorax system affects recording of intracardiac heart sounds which are attenuated within the thoracic PCG. Transmitted through thoracic tissues, the S1’s rising frequency component is affected by magnitude attenuation or phase shift. They also reported that heart sounds are mainly generated by broadband components and the recorded PCG changes by changing the auscultation area with advantage of valvular or non-valvular components. Heart sounds are of great clinical importance, but their origins are not yet well known. The more persuading theory is that recently proposed by Durand et al.,4 which gathered both the valvular and the hemorehological theories. This approach consists of correlating heart sounds to vibrations due to the cardiac valves functioning, as well as blood circulation in heart vessels and cavities. This new approach stipulates that before arriving to the thorax surface, heart sounds have crossed different tissues; and have been affected by the anatomical structure of the overall heart–thorax system.5 This concept highlights the relationship between cardiac structures, their vibrations modes, and surrounding tissues to the resulting thoracic Phonocardiogram (PCG). From the pathological heart sounds that we recorded within the Teaching Hospital of Tlemcen (Algeria), we selected an aortic stenosis case as a sample to be analyzed. Most of the patients presenting such heart troubles are affected by several valvular pathologies rather than a unique dysfunction and physicians’ interpretation may be supported by digital signal processing techniques to avoid erroneous diagnosis. In order to adequately interpret cardiac activity, heart sounds we recorded from the aortic, the pulmonic, the mitral and the tricuspid auscultation areas have been analyzed by means of high resolution time-frequency approaches to yield the instant and the spectral bandwidth of each cardiac event. For this, the Smoothed-Pseudo Wigner–Ville Distribution (SPWVD)19 was used.

2. Data Acquisition Monitoring heart sounds is increasingly taking advantage of computerized systems to allow more reliability towards medical diagnosis. For instance, Guo et al. developed a virtual instrument20 allowing the acquisition and the analysis of the PCG signal. This instrument requires a data acquisition board and a bio-signal preamplifier, that is used with a Personal Computer (PC) driven by LabVIEW software. Tavel et al. developed a hand-held visualization system of the PCG signal,21 which allows for a quick auscultation with a limited graphical resolution. Unfortunately, this system has limited graphical performance, mainly in the perception of highfrequency murmurs. The PCG acquisition system we proposed22 when compared to previously cited systems, constitutes a more vulgarized and practical acquisition tool for the medical staff. Indeed, our acquisition system conceived around a PC, requires no external

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acquisition board. Through an ordinary stethoscope head, heart sounds are captured through a microphone and conveyed to the PC-sound card which performs the sampling process at higher resolution. In the “cardiology Ward” of the “Teaching Hospital of Tlemcen” (Algeria), our new PCG acquisition system allowed the collection of diversified pathological heart sounds for both genders aged between 17 to 84 years. 2.1. Hardware Materials involved in the PCG acquisition system we developed, consisted of a stethoscope head, a microphone and an audio cable allowing connection to the PC’s soundcard, as illustrated in Fig. 1. Heart sounds are captured by a microphone mounted on an ordinary stethoscope head and carried to the analog input of the PC’s soundcard through an ordinary audio cable. 2.2. Software The acquisition process is driven by using the software developed by us the script we proposed22 written in MATLAB 6.5 (R13). The “PCG Recorder” and the Graphical User Interface (GUI), reassemble functionalities of the “Data Acquisition Toolbox Version 2.2 (R13)”, and allows acquiring the analog input of the PC’s soundcard. This interactive GUI is vulgarized to be easily manipulated by medical staff (Fig. 2). Within the “PCG recorder” software, the PCG signal can be recorded as a 16 bits data file. The sampling frequency and the acquisition interval are beforehand set by the user, as depicted in Fig. 2. Additional information are appended to the heading of the data file, namely the age, gender and the weight of the patient, as well as the auscultation area which can be set to one of the following: aortic, tricuspid, mitral, or pulmonic areas. When the duration is not beforehand settled, that is, the duration field in the “PCG Recorder” GUI is left empty, then the acquisition can be started up, and turned off at the desired time.

Fig. 1. Descriptive diagram of the PCG acquisition system.

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Fig. 2. PCG recorder interface.

3. Time-Frequency PCG Signal Analysis Wood et al.13,14 found that the first heart sounds in normal patients are basically composed of rising frequency components over the time-frequency plane. Furthermore, as argued by Boashash,23 the Wigner–Ville Distribution (WVD) can adequately represent linear chirps. Therefore, WVDs and its improved versions should yield high resolution TFRs. 3.1. Wigner Distribution (WD) The Wigner Distribution (WD) can be expressed as follows19,24 :
 τ  −j2πf τ  τ WVD s (t, f ) = s∗ t − e dτ s t+ 2 2 τ

(1)

or alternatively as     ζ ζ S∗ f + e−j2πζt S f − dζ. 2 2 ζ


WVD s (t, f ) =

(2)

The asterisk denotes the complex conjugate and the S(f ) represent the spectrum of the analyzed signal s(t). The Wigner Distribution (WD)19,24 is a bilinear distribution that the kernel is equal to 1. This TFR is endowed by several desirable mathematical properties. Indeed, the auto-WD is always real-valued (Eq. (3)), preserves time shift (Eq. (4)) and frequency shift (Eq. (5)), satisfies time marginal (Eq. (6)) and frequency marginal (Eq. (7)). Moreover, the instantaneous frequency (Eq. (8)) and the group delay (Eq. (9)) can be evaluated using first–order moments of the WD. Also, the

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WD is satisfying the time-frequency scaling property (Eq. (10)) and also time and frequency support. As quoted by Hlawatsch and Boudreaux–Bartels,24 the WD is privileged by its concentration in time and in frequency within the time-frequency plane, which is not ensured by spectrogram and scalogram approaches. However, and according to the quadratic superposition principle,24 the main drawback of the WD is its substantial cross-terms which considerably affect the resulting TFR. These interesting properties can be expressed as follows;24 WD ∗s (t, f ) = WD(t, f )

(3)

WD s˜(t, f ) = WD s (t − t0 , f ) for s˜(t) = s(t − t0 ) WD s˜(t, f ) = WD(t, f − f0 )


f

for s˜(t) = s(t) e

j2πf0 t

WD s (t, f )df = |s(t)|2

(4) (5) (6)




WD s (t, f )dt = |S(f )|2


tn WD s (t, f )dtdf = tn |s(t)|2 dt t f t


n f WD s (t, f )dtdf = f n |S(f )|2 df t f f   f WD s˜(t, f ) = WD s at, a

(7)

t

(8) (9) for s˜(t) =

 |a| s(at) with a
= 0.

(10)

However, the main drawback of this approach is its quadratic nature, which introduces cross-terms in the resulting TFR of multicomponent signals. Boashash and Black25 concluded that the use of the analytic signal, instead of the original signal, avoids aliasing within the WD and reduces cross-terms over the timefrequency plane. Nevertheless, interferences between the auto-components of the analyzed signal should be reduced by improved approaches.

3.2. Smoothed-Pseudo Wigner–Ville Distribution (SPWVD) Ville26 constructed distributions from characteristic functions also considered as an expectation value. Classical variables used in these functions yield ambiguity in the derivation of the WD and allow many operator correspondences.27 The Wigner–Ville Distribution (WVD), which is the expected value of the WD of a non-stationary random process,24 is suitable towards the analysis of PCG signals. The spectrogram can be viewed as a smoothed WD which the kernel is the WD of the sliding window,24 as follows:

w WD w (t − t, f  − f )WD s (t , f  )dt df  , (11) SPEC s (t, f ) = t


f


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where w(t) is the sliding window of the Short-Time Fourier Transform (STFT),28 and s(t) denotes the analyzed signal. The spectrogram is a convolution between WD of the sliding window w(t) and the WD of the analyzed signal. The kernel WD(−t, −f ) of the spectrogram is a smoothing function which is limited in spread by the uncertainty principle. Therefore, appreciable cross-terms attenuation cannot avoid the worse time-frequency concentration.24 Indeed, a short window leads to good time localization at the cost of poorer frequency resolution and vice-versa. Owing to the inherent trade-off between time localization and frequency resolution19,24 in the STFT, the Smoothed-Pseudo Wigner–Ville Distribution (SPWVD)24 can be considered as an alternative time-frequency distribution, and can be expressed as follows:

(t, f ) = g(t − t )H(f − f  )WD s (t , f  )dt df  , (12) SPWVD g,H s t


f


where g(t) and H(f ) are the time and the frequency smoothing functions respectively. The SPWVD is basically characterized by its separable smoothing kernel g(t)H(f ), which allow independent adjustment of temporal and frequency resolutions. For instance, for a zero temporal resolution, i.e., g(t) = δ(t), there is no time smoothing with the resulting SPWVD. The resulting time-frequency distribution is known as the Pseudo-WVD (PWVD). The great difference between the classical spectrogram and the SPWVD is that the trade-off between time and frequency resolutions is now replaced by a compromise between the joint time-frequency resolution and the level of the interference terms. The more we smooth, the poorer is the resolution in both time and frequency and vice-versa. 4. Results and Discussion 4.1. Normal heart sounds Using the acquisition system described above, normal and abnormal heart sounds are recorded with appropriate settings; e.g., the sampling frequency which is selected to 2 kHz to avoid spectral aliasing. PCG signals are recorded from four auscultation areas upon the chest wall namely from the aortic, the tricuspid, the mitral and the pulmonic auscultation areas. At the isovolumic ventricular contraction, the closure of the mitral and the tricuspid heart valves constitute the main origins of the first heart sound (S1).4 Indeed, as illustrated in Fig. 3, the S1 heart sound recorded from the aortic auscultation area is more attenuated than other auscultation areas. This is due to the remoteness of the stethoscope head from its originating heart valves (mitral and tricuspid). Thus, at the mitral auscultation area, the first heart sound (S1) which is stronger at its beginning should be the mitral valve contribution (M1). From the aortic auscultation area, the aortic heart valve closure contributes strongly to the second heart sound (S2).

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Fig. 3. PCG signal of a normal subject recorded upon (a) aortic, (b) tricuspid, (c) mitral and (d) pulmonic auscultation area (one cardiac cycle).

The following TFRs are illustrated as bidimensional images, represented by gray tone changing from white (lower values) to black color (higher values). As illustrated in Fig. 4, the smoothing carried out by the SPWVD is obviously well characterizing heart sounds in the time-frequency plane. Thus, the SPWVD is suitable for the analysis if such non-stationary signal which still baffles the medical staff about its components origins. We should notice that the position of the acquiring stethoscope over the chest wall of the patient between mitral, tricuspid, aortic and pulmonic auscultation areas is achieving a certain filtering of the acquired PCG signal, carried out by the heart–thorax system hypothesized by Durand et al.6 Therefore, timefrequency bursts upon the obtained results could be related to the closer valves and cavities within the myocardium. The acquisition carried out from the aortic auscultation area, as illustrated by Fig. 4(a) allows us to attribute the burst localized below 50 Hz to the aortic valve within the S1 heart sound spectral content. Thus, the snapping of the atrioventricular heart valves (mitral and tricuspid) could be filtered by the heart–thorax system as quoted by Durand et al.4 As depicted by Fig. 4(b), for the tricuspid auscultation area, the relatively strong burst localized at the vicinity of 60 Hz could be related to the mitral valve activity. The tarnished second heart sound S2 is slightly marking frequencies below 50 Hz. As shown in Fig. 4(b), only the tricuspid auscultation area allows S1 and S2 heart sounds to be recorded with comparative amplitudes. Moreover, the shape of the clearly delimited bursts in Fig. 4 confirms modulation laws hypothesis towards heart sounds content also quoted by Wood et al.14 Thus, the first and the second heart sounds, S1 and S2, are mainly generated by blood flow circulation within the heart cavities and also of atrioventricular valves snapping. Thus, the spectral activity in the S1 heart sound in Fig. 4(a) concerns the aortic valve opening. Spectral bursts of each TFR upon Fig. 4 are summarized within

SPWVD of Normal and Aortic Stenosis Heart Sounds

(a)

(b)

(c)

(d)

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Fig. 4. SPWVDs of normal PCG signals (Fig. 3): (a) aortic, (b) tricuspid, (c) mitral and (d) pulmonic auscultation areas.

Table 1 shown below. Indeed, we remark that spectral contents of S1 and S2 are alternating between each chest wall auscultation area. For instance, the 25 Hz component appears in the S1 heart sound when acquired from the four auscultation areas, and is absent at the pulmonic area. Thus, this spectral component could be the effect of the tricuspid heart valve snapping. The finding we should emphasize is the obvious alternating aspect of the frequency regions occupied by the normal S1 and S2 heart sounds. Indeed, alternating cardiac activities are highlighted by the same gray tone color within Table 1. The S1 and S2 heart sounds occupy the same regions within the time-frequency plane but with changed intensities for auscultation area within the same cardiac cavities. We should point out the fact that the heart valves are sharing cardiac cavities within the myocardium affects considerably the generated frequencies. Thus, within the right ventricle, the pulmonic and the tricuspid valves interactively vibrate, yielding this frequency alternating sounds, and vice versa for the aortic and the mitral valves which share the left ventricle. Indeed, we reexamine Table 1 by highlighting the shared frequencies between tricuspid and pulmonic valves, as well as between the

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A. Djebbari & F. Bereksi-Reguig Table 1. S1 and S2 heart sounds spectral content with regard to auscultations areas. S1

S2

Aortic

M 25 Hz

Pulmonic

From 20 to 70 Hz M 40 Hz

Mitral

M 25 Hz S 50 Hz M 90 Hz

VW 25 Hz

S 25 Hz M 60 Hz S 120 Hz

M 40 Hz M 70 Hz S 100 Hz

Tricuspid

S 25 Hz M 90 Hz M 120 Hz —

S: strong M: medium W: weak VW: very weak —: absence

mitral and the aortic valves. Hence, we can affirm such suspicion since the 40 Hz component is present only in the pulmonic and the tricuspid auscultation areas. Concerning the mitral and the aortic valves, we can evidently see that both the 25 Hz and the 90 Hz spectral components are present. The 25 Hz should represent the aortic heart valve closing and is also strongly present at the S2 heart sound, when acquiring from the aortic area.

4.2. Aortic stenosis heart sounds Within the “Cardiology Ward” of the “Teaching Hospital of Tlemcen” (Algeria), a variety of pathological subjects are examined by experienced cardiologists. Pathological heart sounds are then recorded from the four auscultations areas as quoted in Sec. 2 and saved as data files for further digital signal processing. The analysis of aortic stenosis heart sounds, mainly characterized by a systolic ejection murmur and a reduced or absent second heart sound are involved in the analysis for comparison purposes. Hence, additional murmurs and changes upon heart sounds within the PCG signal can well be characterized in the time-frequency plane. From the auscultation areas indicated in Fig. 5, four PCG signals of a patient affected by aortic stenosis are recorded. As illustrated in Fig. 6 and as quoted by Portaluppi et al.,29 for patients affected by the aortic stenosis pathology, the aortic and the pulmonic components in the S2 heart sound are comparably tarnished when compared with that of the S1 heart sound. Indeed, the second heart sound S2 is attenuated in comparison with the S1 heart sound. Moreover, the entire systolic phase of aortic stenosis PCG signals is affected by a strong diamond-shaped murmur in comparison with the S1 and S2

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Fig. 5. PCG signal of abnormal subject (aortic stenosis), (a) aortic, (b) tricuspid, (c) mitral and (d) pulmonic auscultation area (one cardiac cycle).

(a)

(b)

(c)

(d)

Fig. 6. SPWVDs of abnormal PCG signal of Fig. 5 (aortic stenosis): (a) aortic, (b) tricuspid, (c) mitral and (d) pulmonic auscultation areas.

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heart sounds. This murmur is correlated with the turbulent blood flow around the aortic orifice. However, the S1 and S2 heart sounds can be well perceived at the mitral and the tricuspid auscultation areas. Similar to the normal case, only the tricuspid auscultation area allows us to record strongest S1 and S2 heart sounds (Fig. 6, Table 1), but at displaced frequencies. Indeed, the first heart sound S1 can be localized below 60 Hz when recorded from the tricuspid auscultation area, and still weaker for other recordings. On the other hand, for the same auscultation area, weaker second heart sound S2 can be perceived at frequencies lower than 60 Hz. Indeed, as shown in Fig. 6(b), the first heart sound S1 contains two separated bursts at 20 and 50 Hz. Furthermore, the second heart sound S2 loses its high frequency content and conserves a burst around 30 Hz. This should be the consequence of the stricture of the aortic valve and to the intracardiac pressure due to regurgitated blood. The attenuation of S1 and S2 heart sounds is confirmed to be one of the main characteristics of aortic stenosis lesion. Moreover, the systolic ejection of blood through the stenosed aortic orifice begets a systolic murmur clearly delimited in the time-frequency plane. Indeed, this murmur conserves its energy for all auscultation areas in different shapes and at displaced frequencies. However, the systolic murmur within the aortic stenosis PCG signal is mainly characterized by two frequency modulation laws, at 150 Hz and 180 Hz, respectively appearing in different shapes for every auscultation area upon the chest. Another burst appearing between 0.6 sec. and 0.8 sec. in the time domain and lower than 20 Hz for the frequency domain [Fig. 6(b)], within the time-frequency plane could be a third heart sound S3. The third heart sound is uncommon for patients with aortic stenosis disease, usually indicating the presence of systolic dysfunction and elevated filling pressure.30,31 Therefore, the ability of the SPWVD to indicate its presence upon the time-frequency plane is of great clinical importance. 5. Conclusion The acquisition system we developed proves its effectiveness through tests achieved in the “Cardiology Ward” of the “Teaching Hospital of Tlemcen” (Algeria). Hence, phonocardiograms of several pathologies were examined by experimented cardiologists and collected data were processed by advanced TFR. Indeed, the SPWVD provides high time and frequency resolution within the time-frequency plane. Clinical interests are valorized by taking into account acquisition from the following auscultation areas; aortic, tricuspid, mitral and pulmonic. This leads to a more pragmatic interpretation capability of the obtained result by attributing each spectral activity to its originating cardiac valve or cavity, rather than by using only one auscultation area. The time-frequency analysis performed by means of the SPWVD upon normal and aortic stenosis heart sounds, allowed us to retrieve the specificity of each case. For normal heart sounds, an alternating functioning of heart valves is unraveled. Indeed, the frequency content of the S1 and S2 heart sounds throughout the PCG signal alters with regard to valves sharing the same cardiac cavity. This

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frequency alternating aspect of normal heart sounds cannot be detected for aortic stenosis heart sounds, owing to the weakness of S1 and S2 heart sounds towards the strong systolic ejection murmur. However, modulations laws around 150 and 180 Hz related to the stricture of the aortic orifice are well characterized. Moreover, the tricuspid auscultation area has been considered as the region upon the chest most capable of retrieving S1 and S2 heart sounds with comparable intensities. Indeed, aortic stenosis heart sounds when acquired from this auscultation area, contain S1 and S2 heart sounds of similar shapes to the normal case, but at lower frequencies. The acquisition and analysis system we have developed, allows physicians to overcome the human hearing limitation by means of time-frequency characterization of heart sounds. Acknowledgment The authors would like to thank Dr. Meziane Tani, Doctor of Medicine, Departmental Manager of the Cardiology Service in the “Teaching Hospital of Tlemcen”, and the Assistant Lecturer in the Faculty of Medicine (University Abou Bekr Belka¨ıd) in Tlemcen, for all the facilities that he placed in our disposal, for the accomplishment of the data acquisition task. References 1. Abdelghani D, Analyse Temporelle, Spectrale et Spectro-Temporelle du Signal Phonocardiogramme, Magister Thesis, Department of Electronics, Faculty of Engineering Sciences, University Abou Bekr Belka¨ıd, Tlemcen, Algeria, 1999. 2. Hamladji RM, Pr´ecis de s´emiologie, Office des Publications Universitaires, 1996. 3. Thomas D, Cardiologie, Ellipses AUPELF/UREF, 1994. 4. Durand LG, Pibarot P, Digital signal processing of the phonocardiogram: Review of the most recent advancements, Crit Rev Biomed Eng 23(3–4):163–219, 1995. 5. Durand LG, Guardo R, A model of the heart–thorax system, IEEE Eng Med Biol Soc 29–41, 1982. 6. Durand LG, Genest Jr J, Guardo R, Modeling of the transfer function of the heart– thorax system in dogs, IEEE T Bio-med Eng 592–601, 1985. 7. Leatham A, Auscultation of the Heart and Phonocardiography, Churchill Livingstone, London, UK, 1975. 8. Luisada A, The Sounds of the Normal Heart, WH Green, St Louis, 1972. 9. Abrahams J, Current concepts of the genesis of heart sounds. II. Third and fourth sounds, JAMA 239:2029–2030, 1978. 10. Holldack K, Ghal K, Auscultation et Percussion: Inspection et Palpation, Vigot, 1995. 11. Wood JC, Barry DT, Quantification of first heart sound frequency dynamics across the human chest wall, Med Biol Eng Comput 32(4):S71–S78, 1994. 12. Iwata A, Ishii N, Suzumara N, Algorithm for detecting the first and second heart sounds by spectral tracking, Med Biol Eng Comput 18:19–26, 1980. 13. Wood JC, Barry DT, Time-frequency analysis of the first heart sound, IEEE Eng Med Biol 14(2):144–151, 1995. 14. Wood JC, Buda AJ, Barry DT, Time-frequency transforms: A new approach to first heart sound frequency dynamics, IEEE T Bio-med Eng 39(7):730–740, 1992.

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15. Drazner MH, Rame JE, Dries DL, Third heart sound and elevated jugular venous pressure as markers of the subsequent development of heart failure in patients with asymptomatic left ventricular dysfunction, Am J Med 114(6):431–437, 2003. 16. Perloff JK, Importance of elevated jugular venous pressure and a third heart sound in asymptomatic left ventricular dysfunction, Am J Med 114(6):499–500, 2003. 17. Ishikawa M, Sakata K, Maki A, Mizuno H, Ishikawa K, Prognostic significance of a clearly audible fourth heart sound detected a month after an acute myocardial infarction, Am J Cardiol 80(5):619–621, 1997. 18. Durand LG, Langlois YE, Lanthier T, Chiarella R, Coppens P, Carioto S, BertrandBradley S, Spectral analysis and acoustic transmission of mitral and aortic valve closure sounds in dogs. Part 1. Modelling the heart/thorax acoustic system, Med Biol Eng Comput 28(4):269–277, 1990. 19. Cohen L, Time-frequency distributions — a review, Proc IEEE 77(7):941–981, 1989. 20. Guo Z, Moulder C, Zou Y, Loew M, Durand LG, A virtual instrument for acquisition and analysis of the phonocardiogram and its internet-based application, Telemed J E Health 7(4):333–339, 2001. 21. Tavel ME, Brown DD, Shander D, Enhanced auscultation with a new graphic display system, Arch Intern Med 154(8):893–898, 1994. 22. Abdelghani D, Fethi BR, Tani M, Acquisition and time-frequency analysis of the phonocardiogram signal, Conf´erence Internationale sur les Syst`emes de T´el´ecommunications, d’Electronique M´edicale et d’Automatique (CISTEMA 2003), Tlemcen, Algeria, 2003. 23. Boashash B, Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications, Proc IEEE 80(4):540–568, 1992. 24. Hlawatsch F, Boudreaux-Bartels GF, Linear and quadratic time-frequency signal representations, IEEE Signal Proc Mag 9(2):21–67, 1992. 25. Boashash B, Black PJ, An efficient real-time implementation of the Wigner-Ville Distribution, IEEE T Acoust Speech 35:1611–1618, 1987. 26. Ville J, Th´eorie et applications de la notion de signal analytique, Cables et Transmission 2A:61–74, 1948. 27. Cohen L, Generalized phase-scape distribution functions, J Math Phys 7:781–786, 1966. 28. Nawab SN, Quartieri TF, Short-time Fourier transform, in Lim JS and Oppenheim AV (eds.), Advanced Topics in Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1988. 29. Portaluppi F, Vadlamudi LS, Atluri VL, Knighten V, Luisada AA, The pulmonary component of the second heart sound in acquired aortic stenosis, Jpn Heart J 22(4):527–536, 1981. 30. Mehta NJ, Khan IA, Third heart sound: Genesis and clinical importance, Int J Cardiol 97(2):183–186, 2004. 31. Folland ED, Kriegel BJ, Henderson WG, Hammermeister KE, Sethi GK, Implications of third heart sounds in patients with valvular heart disease. The Veterans Affairs Cooperative Study on Valvular Heart Disease, New Engl J Med 327(7):458–462, 1992.