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Sensing by Acoustic Biosignals

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Biomedical Signals and Sensors II

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

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Abstract

After the interface between physiologic mechanisms and the resultant biosignals has been examined (Volume I), the subsequent interface between acoustic biosignals and the associated sensing technology is discussed here. A large variety of acoustic biosignals—permanent biosignals—originates in the inner human body, including heart sounds, lung sounds, and snoring sounds. These biosignals arise in the course of the body’s vital functions and convey physiological data to an observer, disclosing cardiorespiratory pathologies and the state of health. The genesis of acoustic biosignals is considered from a strategic point of view. In particular, the introduced common frame of hybrid biosignals comprises both the biosignal formation path from the biosignal source at the physiological level to biosignal propagation in the body, and the biosignal sensing path from the biosignal transmission in the sensor applied on the body up to its conversion to an electric signal. Namely, vibrating structures in the body yield acoustic sounds which are subject to damping while propagating through the thoracic tissues towards the skin. Arrived at the skin, different body sounds interfere with each other and induce mechanical skin vibration which, in turn, is perceived by a body sound sensor and then converted into the electric signal. It is highly instructive from an engineering and clinical point of view how sounds originate and interact with biological tissues. Discussed phenomena teach a lot about the physics of sound (as engineering sciences), and, on the other hand, biology and physiology (as live sciences). Basic and application-related issues are covered in depth. In fact, these issues should remain strong because these stand the test of time and mine knowledge of great value. Obviously, the highly interdisciplinary nature of acoustic biosignals and biomedical sensors is a challenge. However, it is a rewarding challenge after it has been coped with in a strategic way, as offered here. The chapter is intended to have the presence to answer intriguing “Aha!” questions.

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Notes

  1. 1.

    The heart and blood together is comparable to a thin-walled and fluid-filled balloon which, when stimulated at any location, starts to vibrate as the whole and to emit sounds (Rangayyan 2002).

  2. 2.

    The asynchronous closure of atrioventricular valves can be attributed to several factors (Brooks et al. 1979). In particular, the left ventricle contracts slightly before the right ventricle, yielding an earlier closure of the mitral valve (Fig. 4.3). In addition, the mitral valve is more (nearly) closed when the contraction of the left ventricle begins than is the tricuspid valve when the contraction of the right ventricle begins; the asynchronous closure also greatly depends on the contraction and relaxation of both atria. The inspiration also delays the closure of the tricuspid valve because of increased venous return (see section “Normal Respiration” in Sect. 3.2.1.1), which enhances the splitting of the first heart sound (see section “Normal Respiration” in Sect. 3.2.1.2).

  3. 3.

    The significantly higher pressures on the left side of the heart cause the left-sided valves to shut harder and faster than the closure of the right-sided valves . Therefore, the majority of auscultated heart sounds originates from the left-sided valves; though this can not be generalised and depends strongly on the auscultation location (compare section “Normal Respiration” in Sect. 3.2.1.2).

  4. 4.

    A spectrogram provides information of how signal power (i.e., signal variance) is distributed as a function of frequency and time; compare Footnote 193 in Sect. 3. Likewise, the spectrogram shows how the power spectral density varies with time. As illustrated in Fig. 4.5b, the horizontal axis represents time t while the vertical axis frequency f. The dot color in the image (i.e., the third dimension) reflects the signal power in a logarithmic scale for a particular frequency and at a particular time instant, see the color bar to the right of Fig. 4.5b. The striped pattern of the spectrogram in the vertical direction results from the fact that the power spectral density was calculated for time intervals of 0.128 s duration with 50 % overlap, yielding a time resolution of 0.064 s (Fig. 4.5b) and a frequency resolution of about 1/0.128 s ≈ 7.8 Hz.

  5. 5.

    Streamlined flow or smooth laminar flow occurs when air tends to move in parallel layers as if adjacent layers would slide past one another without lateral mixing. In a tube, the air travelling at the same velocity will be symmetrically arranged around the tube axis, forming cylindrical lamina; the maximum velocity arises at the centre of the tube (Sect. 2.5.2.2). However, the laminar flow can be maintained when it is sufficiently slow or it happens on a sufficiently small scale. Otherwise, rough turbulent flow occurs with eddies leading to lateral mixing and not contributing to the volume flow rate. The onset of the turbulent flow is roughly determined through the tube’s geometry and the Reynolds number

    $$ R = \frac{ < u > \cdot 2r \cdot \rho }{\mu }. $$

    Here <u> is the average flow velocity of air—with its density ρ and its dynamic viscosity μ—through the tube with the radius r. In an approximation, the turbulent flow starts to develop with R > 2000.

    Interestingly, the pressure gradient scales linearly with the volume flow rate in the case of the laminar flow, as shown in (2.18). In contrast, the pressure gradient is approximately proportional to the square of the flow in the case of the turbulent flow. Because of the lateral mixing and vortices formed in the turbulent flow, extra energy is required (i.e., disproportionately higher pressure gradient) to maintain the increased movement of air that does not directly contribute to the net flow.

    Likewise, the air flow of low u is laminar and thus is silent. With increasing u (or r) turbulences start to occur causing vibrations of air and airway walls, which constitute sound sources . The arising sound is a noise-like signal with a relatively wide spectrum, whereas the particular frequency range of noise depends on the level of u.

  6. 6.

    In alveoli the velocity of the air flow is very low because of a very large total cross-sectional area of the airways. Consequently, the air flow is laminar and air turbulences are missing; compare Footnote 5.

  7. 7.

    A very short musical wheeze is also known as squawk . Squawks are a combination of wheezes and crackles; they are thought to occur from an explosive opening of airways and fluttering of unstable airway walls.

  8. 8.

    Epidemiological studies have shown that nearly 40 % of males and about 20 % of females are snorers (Saletu 2001). The prevalence of habitual snoring rises markedly after the age of 40, whereas more than 60 % of males and more than 40 % of females are snorers in this aged population (Beck et al. 1995).

  9. 9.

    In fact, the physics of sound formation in snoring is very similar to that in speech (Perez-Padilla et al. 1993). For instance,

    • voiced sounds are related to vibrations of vocal cords,

    • fricative sounds are related to the friction of turbulent air flow through a narrow orifice, and

    • explosive sounds are related to sudden release of pressure.

  10. 10.

    Snoring is favoured by physiological factors such as small pharyngeal area and increased pharyngeal floppiness, i.e., excessive change in pharyngeal area occurs in response to applied air pressure (Saletu and Saletu-Zyhlarz 2001; Brunt et al. 1997). In addition, the supine sleep posture (i.e., retroposition of the tongue), obesity (i.e., high body mass index BMI, Footnote 202 in Sect. 3), large neck circumference (Sergi et al. 1999), presence of space occupying masses which block airways (e.g., hypertrophy of the soft palate or uvula), or a pathological narrowing of the nasal airway facilitate (disadvantageously) the generation of snoring. Among social factors contributing to the occurrence of snoring, mental stress, tiredness, and alcohol intake can be mentioned. Interestingly, subjective factors as familiar home settings or less familiar sleep labs also seem to influence the severity of nocturnal snoring which, in fact, tends to be heavier while sleeping in a sleep lab (Series et al. 1993).

  11. 11.

    From the physiological point of view, the snoring, especially obstructive snoring , may be connected to increased morbidity, systemic hypertension, cerebrovascular disease, stroke, and even impaired cognitive functions (Saletu and Saletu-Zyhlarz 2001; Series et al. 1993; Wilson et al. 1999). In addition, obstructive and loud snoring is a major cause of disruption to other family members besides the snorer himself; it represents a disadvantageous social impact of snoring.

  12. 12.

    The narrowing of the pharyngeal airway (or even its partial and passive collapse) can be due to negative oropharyngeal pressure generated during inspiration , relaxation of the pharyngeal muscles, or even sleep-related fall in the tone of the upper airway muscles (Liistro et al. 1991). The pharyngeal muscle tone is reduced not only during sleep, but also under the influence of alcohol or drugs (Saletu and Saletu-Zyhlarz 2001).

  13. 13.

    The Bernoulli’s equation governs the behaviour of u and p in an ideal flow, which is deduced from the principle of the conservation of energy (Nichols and O’Rourke 2005). According to Fig. 4.12, the total energy, i.e., the sum of potential and kinetic energies, at a non-constricted site with p 1 and u 1 is equal to the total energy at a constricted site with p 2 and u 2, considering a single horizontal airway. It yields

    $$ p_{1} - p_{2} = \frac{1}{2} \cdot \rho \cdot \left( {\;u_{2}^{2} - u_{1}^{2}} \right)\, ,$$

    where ρ is the air density. The latter equation demonstrates that p 2 < p 1 if u 2 > u 1, i.e., p is decreased at the constricted site if a constant q A along the airway is given. In other words, the opening pressure at the constricted site is decreased, which promotes the airway collapsibility at its constriction even more.

  14. 14.

    It seems that the critically low cross-sectional area and critical limitation of the flow q A initiate the oscillation of airway walls (Liistro et al. 1991; Perez-Padilla et al. 1993). In general, the limitation of q A appears when u equals the velocity of propagating pressure pulse waves along the airway. Likewise, the oscillations occur more readily at a lower q A, provided that the compliance of the airway is high.

  15. 15.

    This theory is called “ flutter theory ” (Perez-Padilla et al. 1993); compare Footnote 16. That is, it explains the continuous form of snoring sounds in the time domain. These sounds arise in the course of oscillations of airway walls when the airflow is forced through a highly compliant airway and can interact with the elastic walls (Fig. 4.12a). The resulting oscillation frequency tends to decrease with increasing wall thickness and decreasing longitudinal tension in the walls, this tension being also affected by the activity of pharyngeal muscles.

  16. 16.

    This theory is called “ relaxation theory ” (Perez-Padilla et al. 1993); compare Footnote 15. That is, it explains the discontinuous form of explosive snoring sounds in the time domain, which are due to repetitive openings of local occlusions of the airway (Fig. 4.12b). The resulting oscillation frequency is relatively low because of large radial deflection of airway walls.

  17. 17.

    In general, spectral characteristics of emitted sounds result from both the source of sound and filtering properties (or resonant properties) of the airway (Perez-Padilla et al. 1993). For instance, the source properties change when a different segment starts to oscillate or the mechanical characteristics of the other oscillating segment are different. In analogy, the filtering properties change when geometric dimensions of the pharynx or mouth cavity vary over time (i.e., dimensions of resonating cavities in front of the source location, cavities acting as band-pass filters; compare Fig. 4.24), or dimensions of neighbouring apertures for the air escape vary over time. In fact, emitted sounds are determined by a product of the sound source (usually broadband source) and the filtering function (band-pass filters) of the airway.

  18. 18.

    Supraglottic pressure is the pressure drop along the upper airway above the epiglottis, see Fig. 4.10.

  19. 19.

    Interestingly, the largest and sharpest deflection of the sound wave coincides with the peak of the air flow, considering the complex-waveform snoring (Beck et al. 1995). It indicates the relevance of the air flow for the generation of snoring sounds, according to discussed mechanisms shown in Fig. 4.12.

  20. 20.

    The abbreviation dB SPL refers to a logarithmic measure of the sound pressure level relative to a reference pressure level (of 20 µPa), i.e., relative to the threshold of human hearing. For instance, a normal conversation yields about 60 dB SPL, whereas a pneumatic drill—in a distance of a few meters—yields 100 dB SPL.

    However, the human ear does not equally respond to all frequencies and it is highly sensitive to sounds in the frequency range of about 1–5 kHz; likewise, the ear is less sensitive to very low or very high frequencies of sounds. To accommodate this behaviour, sound meters use frequency filters which mimic this non-linear frequency response of the ear. In this context, the abbreviation dBA stays for a logarithmic measure of the sound pressure level employing the so-called A-weighting filter. This filter disproportionately attenuates very low frequencies, e.g., an attenuation of −30 dB is applied at 50 Hz while no attenuation (of 0 dB) is applied at 1 kHz.

  21. 21.

    Namely, obstructive snoring is considered as a primary symptom for sleep apnea (Brunt et al. 1997). However, the noisy respiration during sleep, as actually the snoring corresponds to, can not be used as a sole indicator of breathing abnormalities, such as sleep apnea (Wilson et al. 1999). Likewise, snoring lacks specificity for diagnosis of apneas.

  22. 22.

    Sound is provided by mechanical oscillations in an elastic medium, as illustrated in Fig. 4.19a for longitudinal waves . Under influence of a transient external force, composing particles of the medium (e.g., molecules in the air or tissue) are dislocated from their equilibrium (rest) position and are then left to their own devices. Inertial and elastic forces (restoring forces) are induced, which force these particles to move back, so that the particles start to swing around their equilibrium positions with a certain particle velocity in terms of mechanical oscillations. Consequently, as demonstrated in Fig. 4.19, the mechanical overpressure (positive sound pressure ) arises in the regions of increased medium density while the underpressure (negative sound pressure) arises in the regions of decreased density, as compared with the resting state of the medium without propagating sounds; compare Footnote 26. Please note that

    • the spatial wave of the sound pressure p(x) propagating in the direction x (Fig. 4.19b) is in-phase with the wave of the particle velocity u(x) in unlimited elastic medium (but not in the limited resonating cavity such as in Fig. 4.24), whereas

    • the corresponding wave of the particle deflection is dislocated by 90° with respect to p(x) or u(x).

    In fact, the particle velocity strongly differs from the sound propagation velocity (4.3). The particle velocity (4.6) is usually by many orders lower than the propagation velocity; e.g., 5 · 10−8 m/s versus 343 m/s in the air (Table 4.1) at the human auditory threshold at 1 kHz (Veit 1996). In addition, the particle velocity increases with increasing loudness (sound intensity) while the propagation velocity usually does not.

  23. 23.

    The influence of temperature and humidity on v—and thus also on λ (4.3)—should be discussed shortly from a physiological point of view. It is well known that v in the air tends to increase with increasing temperature , yielding an increase rate of about 0.6 m/s per degree Celsius. During inspiration the air at room temperature (usually < 37 °C) enters the respiratory airways, whereas during expiration the warmed up air at body temperature (≈ 37 °C) leaves the airways. Consequently, the level of v in the large airways decreases with inspiration by a few percent and correspondingly increases with expiration.

    Regarding the influence of humidity , it should be noted that the inspired air is saturated with water vapour (relative humidity of 100 %) as it flows over the wet and warm mucous membranes lining the respiratory airways (Sect. 2.6.2). The effective value of v is very slightly influenced by the air humidity, e.g., a change in the relative humidity from 50 % at inspiration to 100 % at expiration increases v by only about 0.5 % at 37 °C.

  24. 24.

    The value of v in the lung tissue depends strongly on the air content in the lung. Provided that the volumetric portion of the air is 75 % and the rest is tissue (Wodicka et al. 1989), the effective ρ and D of the composite mixture can be estimated as

    $$ \rho = 0.75 \cdot \rho_{\text{A}} + 0.25 \cdot \rho_{\text{T}} \approx 0.25 \cdot \rho_{\text{T}} $$

    and

    $$ D = 0.75 \cdot D_{\text{A}} + 0.25 \cdot D_{\text{T}} \approx 0.75 \cdot D_{\text{A}} $$

    where ρ A (= 1.2 kg/m3) and ρ T (= 1,040 kg/m3) are approximate densities of the air and tissue, respectively. In analogy, D A (= 7,083 GPa−1) and D T (= 0.43 GPa−1) are the corresponding compliances which are estimated using (4.4) with v (Table 4.1) and ρ as parameters. It can be observed that ρ A ≪ ρ T and D A ≫ D T. With the effective ρ and D from above equations, (4.4) yields v = 27 m/s fitting well the reported range of 23–60 m/s (Kompis et al. 2001).

    In fact, the above postulation of a homogenous mixture of gas and tissue assumes that the size of λ in the lung parenchyma is significantly larger than the alveolar size (diameter < 1 mm). In fact, this assumption is entirely met by body sounds in the frequency range up to 2 kHz (see section “Volume Effects” in Sect. 4.1.2.2).

  25. 25.

    The inverse square law applies for spherical waves (Sect. 6) when sounds are radiated in lossless media outward radially from a point source, as illustrated in Fig. 4.21. Since the original source power P is spread out over an area (= 4π · r 2) of a sphere, which increases in proportion to r 2 with the velocity v, the resulting sound intensity I at the distance r (passing through a unit area and facing directly the point source) is equal to

    $$ I = \frac{P}{{4\pi \cdot r^{2} }}\, , $$

    i.e., is inversely related to r 2. As demonstrated in Fig. 4.21, the level of I quadruples while p doubles when r is halved.

  26. 26.

    It should be stressed that the sound pressure p is an overpressure (and the corresponding underpressure ) related to the ambient atmospheric pressure; compare Fig. 4.19. Consequently, positive or negative p means pressure above or below the ambient pressure, respectively. In this context, Fig. 4.22 demonstrates the decay of this overpressure (or the decay of the underpressure), whereas Fig. 4.24 demonstrates periodic changes of the instantaneous sound pressure from values below the ambient pressure to that above the ambient pressure and vice versa.

  27. 27.

    Generally, different assumptions regarding the geometry-related damping factor, i.e., the factor 1/r from (4.7), can be found in literature. For instance, this factor was completely neglected in Wodicka et al. (1989), assuming plain wave conditions for the propagation of the intensity I in the lung parenchyma (I ∝ p 2, (4.5)). In contrast, authors in Kompis et al. (1998, 2001) assumed an even stronger damping factor 1/r 2 for the assessment of the spatial distribution of the effective p in the thorax.

  28. 28.

    Various experimental data confirm the dependence of the propagation pathway on the sound frequency and thus the dependence of v on the frequency. The authors in Pasterkamp et al. (1997b) demonstrate that low frequency sounds at 200 Hz are transmitted from the trachea to the chest wall with a phase delay of about 2.5 ms, whereas high frequency sounds at 800 Hz traverse a faster route with a phase delay of only 1.5 ms. For an assumed propagation distance of 20 cm, it would yield v ≈ 80 m/s for low frequency sounds and v ≈ 130 m/s for high frequency sounds.

    The hypothesis of parenchymal propagation of sounds at lower frequencies is also supported by the fact that the inhalation of a helium-oxygen mixture (80 % helium and 20 % oxygen) affects only weakly (i.e., reduces) the phase delay of the sound transmission from the trachea to the chest wall at lower frequencies, in comparison with the inhalation of air (Pasterkamp et al. 1997b). In contrast, this phase delay is significantly reduced at higher frequencies while inhaling the helium-oxygen mixture. In quantitative terms, a reduction by about 0.7 ms was observed at 800 Hz (i.e., from 1.5 ms for the air inhalation down to 0.8 ms for the gas mixture) with almost no reduction at 200 Hz (i.e., 2.5 ms for both the air and gas mixture). Since the helium-oxygen mixture shows higher value of v than the air, the discussed observation proves a predominantly airway-bound sound transmission of high frequency sounds in the thorax.

  29. 29.

    In fact, the standing wave within the resonating cavity is the sum of incident and reflected p waves which move in opposite directions (compare Footnote 170 in Sect. 2 and Sect. 6). However, the resulting standing wave oscillates only but does not propagate any more. For instance, at the closed end (hard sound-reflecting surface) the incident pressure wave p I = P I · cos(kx − ωt)—propagating in the x direction with the pressure amplitude P I, angular frequency ω (= 2π · f), and wavenumber k (= 2π/λ)—is reflected without phase change. The reflected pressure wave p R = P R · cos(kx + ωt) with the amplitude P R = P I = P interferes with p I; e.g., interferes constructively at the closed end; compare Footnote 161 in Sect. 2. The resulting standing wave p I + p R = 2P · cos(ωt) · cos(kx) extends along x—with the closed end located at x = 0—and pulsates with t. Along the cavity in the x direction,

    • constructive interference , i.e., amplitudes of the in-phase incident and reflected pressure waves add, and

    • destructive interference , i.e., amplitudes of the out-of-phase incident and reflected pressure waves subtract,

    occur. From a physical point of view, the pressure of air molecules reflecting off the closed end adds to that of air molecules approaching the closed end. In consequence, the total p doubles at the closed end, i.e., p I + p R = 2P at x = 0 and t = 0.

  30. 30.

    Homogenous materials tend to absorb the acoustic energy mainly because of the inner friction , i.e., because of local deformations and frictions within the propagation medium. In contrast, porous materials such as the lung parenchyma also absorb the acoustic energy in terms of the outer friction (Veit 1996), i.e., the friction between oscillating air particles in alveoli and semi-solid medium encircling alveoli.

  31. 31.

    To give an example, if only very low values of α F are considered (Table 4.1), the sound pressure p at 1 kHz would decrease by about 1 dB either after 11,000 km while sound travelling in water, or after 11 km while travelling in the air (compare the exponential term in (4.7)).

  32. 32.

    The compressibility of the propagation medium is higher at lower frequencies before the vibrational relaxation (i.e., f ≪ 1/(2π · τ)) in comparison with higher frequencies after the relaxation (f ≫ 1/(2π · τ)). Thus the relation v 0 < v applies; compare the influence of D on the size of v in (4.4) (Meyer and Neumann 1975).

  33. 33.

    In contrast, sea water shows a significantly higher α M because of two additional relaxation phenomena in it with one relaxation frequency above 1 kHz (ionic dissociation of boric acid H3BO3) and another one above 100 kHz (ionic dissociation of magnesium sulphate MgSO4). For instance, at the sound frequency 1 kHz and temperature 20 °C the sound attenuation in sea water totals about 0.06 dB/km or α M = 7 · 10−6 m−1.

  34. 34.

    For instance, the relaxation frequency of pure oxygen is only about 10 Hz yielding a large τ of about 16 ms.

  35. 35.

    Experimental data confirm the frequency dependence of the medium-related damping. For instance, authors in Erikson et al. (1974) report that α is approximately proportional to f, whereas individual tissues may yield a stronger frequency dependence up to f 2, e.g., hemoglobin has α proportional to f 1.3. Studies in Loudon and Murphy (1984), Hadjileontiadis and Panas (1997a) show that the intensity of vesicular lung sounds (Sect. 4.1.1.2) declines exponentially with increasing f, which implies the proportionality between α and f; compare (4.7) and Fig. 4.22.

  36. 36.

    In fact, high frequency sounds exhibit localising properties , which are very useful in diagnosis. High frequency sounds do not spread as widely or with the intensity that low frequency sounds spread across the thorax (Ertel et al. 1966b). It means that as soon as high frequency sounds (usually pathological sounds) are heard, the corresponding sound source (or the site of pathology) is already close to the current auscultation site. This offers physicians an ability to localise pathological breathing sounds to their point of origin.

  37. 37.

    Sound transmission through the thorax may be of high clinical value if altered transmission patterns correlate with pathology (Peng et al. 2014). For instance, changes in the lung structure due to the presence of pneumothorax—creating more barriers to the propagating acoustic waves—causes a drop in the intensity of the transmitted mechanical waves at high frequencies (above 100 Hz in humans (Peng et al. 2014)), which are subjected to relatively strong attenuation in tissue (see text). In contrast, sound waves at lower frequencies (below 100 Hz)—subjected to relatively low attenuation in tissue—can travel a longer distance (around the internal organs in the thorax) before these waves lose their energy. Consequently, structural changes of the internal organs may result in small effects on the propagation of these low frequency sounds.

    Authors in Peng et al. (2014) showed that the presence of pneumothorax had smaller effects on the sound transmission through the thorax at lower frequencies. Likewise, it seems that high frequency mechanical waves (as could be introduced at the anterior chest surface by an actuator) propagate directly (to the posterior chest surface where a sensor resides) through internal organs (lying between the actuator and sensor). Therefore, any change in the intrathoracic structure would affect the propagation of high frequencies through the thorax.

  38. 38.

    In this case, thermal losses arise because bubble compressions require greater work performed by the acoustic wave than the work performed by the air in bubbles during bubble expansions (Wodicka et al. 1989). The resulting energy difference is conducted into the lung tissue as heat. Interestingly, enlarged alveoli tend to increase thermal losses and thus to attenuate more strongly body sounds within the lungs in comparison with reduced alveoli (pre-compressed bubbles).

  39. 39.

    From an acoustical point of view, inhomogeneities or obstacles are given by media with different Z (4.6). That is, fluctuations of the medium density ρ or the varying propagation velocity v of sounds (when entering a different medium, (4.4)) constitute inhomogeneities for the sound wave.

  40. 40.

    Inhomogeneities on an even smaller scale such as cellular structures or protein aggregates are unimportant for the scattering of body sounds because the effective λ of sounds is already orders of magnitude larger than the dimensions of these inhomogeneities. However, such small structures are highly relevant for the optical scattering (Sect. 5.1).

  41. 41.

    In fact, every unobstructed point on the incident wavefront momentarily present in the opening (or slit) acts as a source of a secondary spherical wave . The superposition of all spherical waves determines the form of the resulting transmitted wavefront at any subsequent time behind the slit, i.e., the superposition determines the resulting diffraction pattern of the slit. Obviously, not only amplitudes but also relative phases of the individual spherical waves govern their interference pattern and thus the resulting transmitted wavefront beyond the opening. Namely,

    • in-phase superposition leads to constructive interference and thus to the maximum of the transmitted intensity at a certain observation point beyond the opening. In contrast,

    • out-of-phase superposition leads to destructive interference and thus to the null in the transmitted intensity at an observation point beyond the opening; for details see Sect. 6.

  42. 42.

    It is interesting to note that the boundary between the sound wave (i.e., compressions and rarefactions) and the sound shadow (i.e., died wave) always extends over a certain number of wavelengths because the mechanical sound wave can not die abruptly due to elastic interactions among adjacent molecules. This effectively determines the spatial extension of the diffraction, which is greater at large λ (or low sound frequency) and less at small λ (or high sound frequency). Likewise, a sound shadow behind an obstacle decreases in size with increasing λ.

  43. 43.

    For instance, if a trilayer is assumed with only one intermediate layer (with Z I) between the tissue (Z T) and the air (Z A), the resulting two reflection factors Γ M (of two reflecting surfaces) for sounds emanating from the body would amount to

    $$ \varGamma_{\text{M,1}} = \frac{{Z_{\text{I}} - Z_{\text{T}} }}{{Z_{\text{I}} + Z_{\text{T}} }}\quad {\text{and}}\quad \varGamma_{\text{M,2}} = \frac{{Z_{\text{A}} - Z_{\text{I}} }}{{Z_{\text{A}} + Z_{\text{I}} }}. $$

    Provided that Z A < Z I < Z T, the respective magnitudes of Γ M satisfy |Γ M,1| < |Γ A| and |Γ M,2| < |Γ A|, whereas Γ A of a simplified bilayer tissue-air is given by (4.15). Thus the trilayer shows lower reflection losses in comparison with the bilayer.

  44. 44.

    Willebrord Snellius (1580–1626) was a Dutch astronomer and mathematician after which Snell’s law was named. This law relates the degree of the wave bending to the physical properties of materials which surround the bending surface.

  45. 45.

    In fact, body sounds cause skin vibrations of three different waveform types: transverse waves (or shear waves), longitudinal waves (or compression waves, compare Fig. 4.19), and a combination of the two types (Ertel et al. 1971). The corresponding deflection amplitude of particles involved in the transmission of acoustic sounds, e.g., the deflection amplitude of air molecules while transmitting air sounds (Footnote 22), is proportional to the sound pressure level and inversely proportional to the sound frequency, medium density, and sound velocity (Giancoli 2006). To give a quantitative example, the deflection in air at 1 kHz is about 8 µm at the sound threshold of pain in humans and less than 0.1 nm (i.e., the approximate size of an atom) at the threshold of human hearing.

  46. 46.

    For the sake of completeness, it should be noted that there are other acoustical sensing devices, besides the chestpiece. For instance, piezoelectric sensors shaped as a flat diaphragm can also be used for direct skin attachment and the recording of body sounds.

  47. 47.

    The vibration amplitude of the skin—may be less than a few µm, compare Footnote 45—depends strongly on the method of sound recording. For instance, a massive chestpiece and a tight skin contact would impose a significant mechanical loading on the skin surface. Consequently, the resulting mechanical stress would rise in the skin beneath the chestpiece, which would significantly limit the mechanical deflection amplitude of the skin surface; compare with the influence of the pre-stressed skin on the acoustic transfer function of the chestpiece (Fig. 4.29 and Footnote 52).

  48. 48.

    Friedrich Wilhelm Bessel (1784–1846) was a German astronomer who systematically derived Bessel functions appearing in mathematical descriptions of many physical phenomena, such as the flow of heat or the propagation of electromagnetic waves.

  49. 49.

    Hermann von Helmholtz (1821–1894) was a German scientist and philosopher whose groundbreaking investigations occupied almost the whole field of science, including physiology, physics, electricity, and chemistry.

  50. 50.

    The function of Helmholtz resonator can be summarised as follows. A volume of the air in and near the neck—compare Fig. 4.28b—starts to vibrate in response to external excitation. For instance, pushing extra air down the neck into the cavity creates an overpressure in the cavity. After release of the external force, the air rushes out due to the springiness (or compressibility) of the air within the cavity. Shortly afterwards, the air pressure inside the cavity undershoots the equilibrium level (i.e., the atmospheric pressure, Footnote 26) because the air in the neck has mass and thus possesses momentum when it rushes out. A slight vacuum occurs in the cavity, which then sucks some air back into the cavity. It results in a (damped) oscillation of the air (in and near the neck) into and out of the cavity at a specific natural frequency, known as the resonance frequency f HR.

  51. 51.

    The quality factor represents the degree to which an oscillatory system is undamped. It is defined as the ratio of the resonance frequency (e.g., f HR from (4.18)) to the bandwidth Δf of the sound oscillation. Here the bandwidth Δf is determined as the difference of two frequencies (above f HR and below f HR) at which the acoustical power left (or dissipated) in the oscillatory system is one-half (or 3 dB less than) its maximum value at f HR, compare Fig. 4.29. The quality factor > 0.5 represents an underdamped system in which oscillations can arise in response to an external disturbance displacing the system from its equilibrium state. Otherwise, the factor < 0.5 represents an overdamped system and implies an exponential decay back to the equilibrium state in response to a temporal external disturbance. In other words, lossy materials have lower quality factor and make the response curve (transfer function) wider and lower; i.e., Δf increases while G decreases in Fig. 4.29.

  52. 52.

    The application pressure of the chestpiece on the skin is a relevant issue because the varying pressure alters sound filtering characteristics of the diaphragm (Fig. 4.28). In fact, the chestpiece must be used with the principles of a damped diaphragm in mind, namely,

    • the lightest possible application for the auscultation of low frequency sounds and

    • the firmest possible application for the auscultation of high frequency sounds .

    It is important to note here that increasing application pressure increases not only the pre-stress of the artificial diaphragm but also the mechanical stress of the skin region under the diaphragm, the skin encompassed by the rim of the bell. As a result, increased stress of the skin—or increased pre-stress of the natural diaphragm so formed (4.17)—contributes to the auscultation of high frequency sound components because the natural diaphragm oscillates concurrently with the artificial diaphragm .

  53. 53.

    From a diagnostic point of view, the effect of the attenuation of lower frequencies (< f 01, Fig. 4.29) by simply increasing the application pressure of the chestpiece on the chest wall is deliberately used by physicians (Hollins 1971; Ertel et al. 1966b; Abella et al. 1992); compare Footnote 52. That is, increased application pressure favours the detection of high frequency sounds (> f 01, Fig. 4.29) which usually indicate pathology (see section “Volume Effects” in Sect. 4.1.2.2) and possess localising properties (Footnote 36).

  54. 54.

    Masking of body sounds is important in two respects (Rappaport and Sprague 1941),

    • masking of a sound in the presence of other sounds and

    • masking of a sound following another sound of considerably large intensity .

    In the first case, as a sound mixture becomes more intense, the low pitched sound components (e.g., heart sounds ) start to dominate because the high pitched components (e.g., lung sounds ) are masked by peculiar characteristics of human hearing. In the second case, a preceding sound of a comparably great intensity tends to temporarily fatigue the ear, thereby masking a following low intensity sound.

  55. 55.

    Surprisingly, the original Laennec’s stethoscope (Fig. 1.9), i.e., a simple wooden cylinder , has been shown to amplify body sounds by about 18 dB at the sound frequency of 200 Hz, as noted in Ertel et al. (1966b), Hollins (1971). Surprisingly, this high amplification value is comparable with those of modern chestpieces, which makes it difficult to espouse an optimistic view of continuing acoustical improvement of the chestpiece over nearly two centuries (Sect. 1.2.1) aside from the convenience and aesthetic of the modern chestpiece (Fig. 4.31).

  56. 56.

    An air leak —if there is one in the chestpiece—behaves as a high-pass filter . In general, the larger is the air leak the more balanced are the sound pressures inside and outside of the chestpiece because of leaking air down the pressure gradient. While the frequency of sound gets lower, there is more time for the air to leak out or in, which equalises the latter pressures to a larger extent. As a result, the transmission of low frequency sounds deteriorates provided that an air leak is present. Conclusively, the air leak acts as a high-pass filter. It is interesting to note that some stethoscopes had even an adjustable leak valve, i.e., an adjustable high-pass filter. This valve was used to regulate the amount of (low frequency) heart sounds reaching the output of the stethoscope (Rappaport and Sprague 1941).

  57. 57.

    The capacitance C of the condenser microphone from Fig. 4.30b can be approximated as

    $$ C = \frac{\varepsilon \cdot A}{{x_{0} +\Delta x}}\, , $$

    where ε is the dielectric permittivity of the air between the plates, A the cross sectional area of the fixed plate, x 0 the distance between the plates, and Δx the change of this distance due to the sound pressure wave; compare Sect. 6. The above approximation holds only if the inequality Δx ≪ x 0 applies and Δx is constant over the entire A. It should be noted that the size of A is nearly equal to the cross sectional area of the flexible plate and that of the output channel, see Fig. 4.28a. For instance, if a harmonic oscillation of the flexible plate is assumed (Fig. 4.30a) in response to the sound pressure variation at the flexible plate then Δx = X · cos(ωt) with X as the amplitude of this oscillation.

  58. 58.

    The voltage u C across the capacitor which carries the electric charge Q is given by

    $$ u_{C} = \frac{Q}{C} = \frac{Q}{\varepsilon \cdot A} \cdot (x_{0} +\Delta x)\, ; $$

    compare Footnotes 33 in Sect. 2 and 57. For the sound frequencies

    $$ f \gg \frac{1}{2\pi \cdot R \cdot C}\, , $$

    the level of Q remains nearly constant. Here R denotes the resistance of the RC circuit within the signal amplifier operating the condenser microphone (Fig. 4.30b). In other words, if the time constant R · C is much larger than the oscillation period of the sound, i.e., the operating circuit is too inert to follow instantaneously the changes in the sound pressure, then the current dQ/dt through the capacitor is almost zero and Q changes are negligible. The latter condition is fulfilled for typical frequencies of body sounds, which yields that the voltage u C is a function of Δx only, to be more precise, Δu C is (approximately) linearly dependent on Δx.

  59. 59.

    For instance, human ears alter the performance of the whole stethoscope because earpieces of the stethoscope are terminated with the acoustical impedance of ears and, on the other hand, the latter impedance varies with the sound frequency. As a practical consequence, an artificial ear , i.e., a mechanical ear analog with the acoustics of human ears, should be incorporated into experimental systems for the assessment of the objective acoustic transfer functions of stethoscopes (Ertel et al. 1966a, b); compare Fig. 4.32.

  60. 60.

    It should be noted that the course of P L from Fig. 4.34b does not follow the individual heart sounds, i.e., the first or second heart sound, but rather the assembly of both heart sounds as a unit. This is because time intervals for P L estimation (of 256 ms duration, Fig. 4.34) are larger than individual durations of heart sounds (usually < 140 ms, Sect. 4.1.1.1). Consequently, the instantaneous level of P L is a sliding average over both heart sounds.

  61. 61.

    In general, the heart rate f C can be estimated from the time course of P L in different ways:

    • In the time domain , detection of peaks in P L (or, alternatively, zero crossings in P L) could be performed, whereas the difference between the corresponding neighbouring timestamps of peaks (or zero crossings) yields the instantaneous level of 1/f C; compare Figs. 5.31 and 5.33.

    • In the frequency domain , peaks in the power spectral density of P L could be detected, especially those peaks which reside at multiple frequencies. These multiple frequencies would most likely correspond to multiple harmonics of f C, i.e., f C, 2 · f C, … k · f C with k as the integer index. Since a time interval (window) of P L is used for the calculation of the power spectral density and thus the estimation of f C, this method yields only an average level of f C within this particular time interval (window). The corresponding examples are demonstrated in Figs. 4.34b and 4.35.

  62. 62.

    In analogy with Footnote 61, the respiratory rate f R can be estimated from the time course of P W in the time domain (by detecting peaks or zero crossings) and the frequency domain (by detecting multiple harmonics of f R).

  63. 63.

    There are numerous methods to detect sleep apneas by acoustical means. However, strong variability of snoring sounds—or, in general, variability of breathing sounds—within single subjects and even from one breath to another complicates matters (Sect. 4.1.1.3). In fact, apneas are characterised by

    • increased total intensity of breathing sounds which surround apneas because of deteriorated pharyngeal dynamics (Itasaka et al. 1999; Pasterkamp et al. 1997b). Thus, intensity thresholds and time interval measurements can be applied for apnea detection (Brunt et al. 1997). In addition, obstructive snoring shows increased amount of high frequency components (Sect. 4.1.1.3), so that

    • increased partial intensity of breathing sounds within a limited (specific) frequency range favours apnea detection (McCombe et al. 1995; Penzel et al. 1990; Rauscher et al. 1991; Verse et al. 2000).

    Usually, an overestimation of the number of apneas is reported, which were detected by acoustical means. The reliability of apnea detection typically increases with the apnea severity (or with the airway obstruction severity) and with respiratory disturbance index (Sect. 3.1.2). Provided that the waveform of P W serves as a basis for apnea detection—as illustrated in Fig. 4.36—adaptive and time-dependent power thresholds can be used. The resulting intervals in combination with time limits facilitate apnea detection (Kaniusas 2006).

  64. 64.

    The appearance of high frequencies in body sounds is a clear indication for approaching obstruction . For instance, as discussed in Kaniusas et al. (2005),

    • normal breathing shows a predominance of low frequency sound power according to P L′ > P M > P H,

    • normal snoring yields P L′ ≥ P M > P H, and

    • obstructive snoring shows a predominance of high frequency power corresponding to P L′ ≥ P H ≥ P M.

    Here P L′ is the signal power of the phonocardiogram in the extended low frequency range up to 300 Hz, P M the signal power in the medium frequency range 300–800 Hz, and P H the signal power in the high frequency range 800–2,000 Hz; see Sect. 4.1.1.3.

  65. 65.

    It should be noted that sound frequencies which lateralize best coincide well with sound frequencies which tend to be coupled from the airy respiratory airways into the semi-solid mediastinum (or into the lung parenchyma); compare with the frequency dependent propagation of body sounds in Fig. 4.23 and Section “Specific Issues” in Sect. 4.1.2.1. Thus, it can be expected that heterogeneous tissues contribute significantly to the asymmetric transmission of vesicular lung sounds at relatively low sound frequencies. At relatively high frequencies, the asymmetry of the sound transmission is weaker because sounds predominantly prefer airway-bound routes and their pathways are more direct, bypassing the damping effect of the asymmetric mediastinum.

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Kaniusas, E. (2015). Sensing by Acoustic Biosignals. In: Biomedical Signals and Sensors II. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45106-9_4

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