An acoustic model of the respiratory tract - Semantic Scholar

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 48, NO. 5, MAY 2001

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An Acoustic Model of the Respiratory Tract Paul Harper, Steven S. Kraman, Hans Pasterkamp, and George R. Wodicka*, Senior Member, IEEE

Abstract—With the emerging use of tracheal sound analysis to detect and monitor respiratory tract changes such as those found in asthma and obstructive sleep apnea, there is a need to link the attributes of these easily measured sounds first to the underlying anatomy, and then to specific pathophysiology. To begin this process, we have developed a model of the acoustic properties of the entire respiratory tract (supraglottal plus subglottal airways) over the frequency range of tracheal sound measurements, 100 to 3000 Hz. The respiratory tract is represented by a transmission line acoustical analogy with varying cross sectional area, yielding walls, and dichotomous branching in the subglottal component. The model predicts the location in frequency of the natural acoustic resonances of components or the entire tract. Individually, the supra and subglottal portions of the model predict well the distinct locations of the spectral peaks (formants) from speech sounds such as /a/ as measured at the mouth and the trachea, respectively, in healthy subjects. When combining the supraglottic and subglottic portions to form a complete tract model, the predicted peak locations compare favorably with those of tracheal sounds measured during normal breathing. This modeling effort provides the first insights into the complex relationships between the spectral peaks of tracheal sounds and the underlying anatomy of the respiratory tract. Index Terms—Acoustic modeling, breathing sounds, respiratory sounds, respiratory tract.

I. INTRODUCTION A. Tracheal Sound Analysis

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INCE 1816 [1] the stethoscope has been used effectively by physicians to listen to respiratory sounds for clinical diagnosis. Recently, transducers such as microphones have allowed for the collection of more accurate acoustical data over a wider range of frequencies. Characteristic patterns in the data, thus recorded have been associated with conditions affecting airway patency such as asthma, obstructive sleep apnea, infections, airway edema, malformations and tumors [1]–[9]. One common location for recording breathing sounds is on the neck at the suprasternal notch over the extrathoracic trachea, with the sounds recorded referred to as tracheal sounds. These sounds are relatively large in amplitude and have a wider range of frequencies than sounds recorded at the chest wall, and also have a close relation to the tracheal airflow [10]. The spectra Manuscript received August 30, 1999; revised January 13, 2001. Asterisk indicates corresponding author. P. Harper is with the School of Electrical and Computer Engineering, and Department of Biomedical Engineering, Purdue University, West Lafayette, IN 47907–1285 USA. S. S. Kraman is with the VA Medical Center and University of Kentucky, Lexington, KY 40506 USA. H. Pasterkamp is with the Department of Pediatrics and Child Health, University of Manitoba, Winnipeg, MB R3A1S1, Canada. *G. R. Wodicka is with the School of Electrical and Computer Engineering, and Department of Biomedical Engineering, Purdue University, West Lafayette, IN 47907–1285 USA (e-mail: [email protected]). Publisher Item Identifier S 0018-9294(01)03393-6.

of these tracheal sounds have been characterized as broad frequency noise with discernible spectral peaks ranging between 80 Hz to more than 1500 Hz with a “cut-off”-like frequency of around 800 Hz [11]. Pasterkamp et al. [6] suggested that subjects with obstructive sleep apnea (OSA—a cessation of breathing caused by an obstruction of the air passages during sleep) might not be able to properly dilate their pharynx while lying down during inspiration even while they are awake. Tracheal sounds were recorded from seven patients with OSA and eight control subjects in both sitting and supine positions. The researchers noted a larger than normal increase in tracheal sound amplitude when subjects with OSA changed their posture from sitting to supine. This finding suggested that even while awake there was a narrowing of the pharynx in a supine position that presumably resulted in an increase in airflow turbulence and hence, an increase in respiratory sound levels in the trachea. Also, in the OSA patients and the control subjects, there were shifts in some of the spectral peak locations that were associated with the change in posture. Yonemaru et al. [9] analyzed tracheal sounds recorded from patients with tracheal stenosis (a narrowing of the trachea). They studied five normal women and 13 women with tracheal stenosis and recorded tracheal sounds with a microphone placed on the right side of the neck at the level of the thyroid cartilage. It was demonstrated that in patients with tracheal stenosis there was a significant increase in both the peak spectral power at about 1 kHz and the spectral power in a bandwidth from 600 to 1300 Hz over that measured for the normal women. In another study, it was shown that the spectral profile of tracheal sounds correlates with body height. Sanchez et al. [12] recorded the tracheal sounds of 21 healthy children and 24 healthy adults. They found that there were spectral differences between children and adults and suggested that these differences are likely a function of differences in the upper and central airway dimensions—the smaller dimensions for children being associated with more turbulent airflow (louder sounds) and higher natural resonance frequencies. They also concluded that similar acoustical measurements might be of value when studying abnormalities in the upper and central airways. B. Acoustic Modeling of the Respiratory Tract These findings suggest that there is a potential for these easily-measured tracheal sounds to be used in clinical practice for the diagnosis and monitoring of various respiratory conditions. For such potential clinical applications to be most useful, the relationships between the attributes of these sounds and the underlying anatomy, and ultimately pathophysiology, need to be determined. As a first step in this process, this manuscript describes the development of an acoustic model of

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the respiratory tract that is based on its anatomy and allows for the prediction of its natural acoustic resonances. We view this effort as a necessary first step toward gaining insights into the anatomical–acoustical relationships between measurements and measurable spectral peak locations. This first step should provide a foundation for more complex modeling approaches that will account for flow-induced sound generation in various pathologies that interact with the acoustic resonance properties of the respiratory tract. The model predicts the locations of spectral peaks that could be measured under various circumstances and is analogous to the electrical transmission line approach used to describe signals on distributed circuits such as coaxial lines. For many years, researchers have used this approach to better understand the acoustical processes within the vocal tract during speech [13], [14]. Other investigators have used it to determine the acoustical transmission and reflection properties of the branching structures within the thorax [15]–[20]. Our goal is to both integrate and expand upon these efforts to develop a comprehensive acoustic model of the complete respiratory tract that begins to link tracheal sound spectral features with the underlying anatomy. First, the supraglottal (vocal tract) portion of the respiratory tract was modeled based upon previous and well-described approaches employed in speech research and the predicted natural resonances compared to measurements of speech made at the mouth. Then, the acoustic properties of the branching subglottal portion of the respiratory tract were simulated and the predicted location in frequency of natural resonances compared to measurements of speech made over the extrathoracic trachea, and with other previous studies. The supra and subglottal portions of the model were then coupled through an open glottis and the predicted resonance locations compared to the spectral peak locations estimated from tracheal sounds measured in healthy adults during normal breathing. All measurements were approved by either the Committee on the Use of Human Subjects in Research at Purdue University or at the University of Manitoba as appropriate dependent upon the geographic location of the study component.

II. ACOUSTIC TRANSMISSION LINE MODELING FUNDAMENTALS The transmission line approach has been used to model the vocal tract in speech research for many years [13], [14], but in order to apply it to the respiratory tract consideration must be given to the frequency range of interest. As long as the wavelength of the highest frequency of interest is considerably greater than the largest cross sectional dimension of the (typically) tube-like structure to be modeled, only plane waves will propagate and the system can be approximated by a one-dimensional (1-D) wave equation. For lossless, rigid cylindrical tubes, the so-called “cuton” frequency for the first nonplanar , where propagation mode is given by is the speed of sound and is the radius of the tube [21]. If one assumes that the respiratory tract is lossless and rigid, using 35 400 cm/s as the speed of sound in moist air and a conservative 2.0 cm as the maximum radius through the respiratory tract, then this yields a prediction that plane waves

Fig. 1. Lumped acoustic circuit element representation of a lossy tube section with rigid walls in T network form. L ; R ; C , and G are defined in Table I.

would propagate for all sonic frequencies below roughly 5000 Hz. If the tube is viewed as uniform short sections by cuts perpendicular to the direction of sound wave propagation, and these sections are much smaller than the shortest wavelength of interest, then the acoustic properties of each section can be accurately represented by a arrangement composed of lumped circuit elements. Such a -section of a hard-walled, lossy tube is shown in Fig. 1. The accuracy of this approach can be improved by increasing the number of segments used to represent a length of tract. The maximum section length used is typically less than 1/8th the shortest wavelength of interest [13]. Since the maximum frequency recorded in any of our tracheal sound measurements was 3000 Hz, we used this as the upper frequency limit in our simulations, and this resulted in a maximum model segment length of 1.5 cm. An impedance-type analogy [14], [22] is used in this modeling where the voltage drop across an electrical element corresponds to the acoustic pressure drop across an acoustical element. This pressure drop is relative to the atmospheric pressure and has the dimensions of force per unit area. The electrical current through an element corresponds to the volume velocity or speed at which a volume of fluid moves in response to an applied pressure. It has the dimensions of volume per time. The acoustical impedance, again analogous to the electrical impedance, can be defined as the ratio of the acoustical pressure to the volume velocity. For a medium to support wave propagation, it must exhibit inertia and elasticity, and it also typically dissipates energy. In an acoustical propagation through a fluid medium, these three attributes correspond to acoustic inertance, compliance, and resistance, respectively. results primarily from viscous The acoustic resistance or thermal losses at the boundaries and thermal losses during arises expansions and compressions, and the conductance from heat conduction on the walls of the tube. The compliance is associated with the ability of the fluid medium to exwith the mass of pand and compress, and the inertance the medium. The equations used to estimate the parameters for the transmission line segment corresponding to a lossy, smooth, hard-walled tube are provided in Table I; and the physical properties employed are provided in Table II [14], [23]. A. Unique Respiratory Tract Properties The wall tissue found in the respiratory tract yields in response to applied acoustic pressure; consequently, the rigidwalled assumption is, in general, not valid. Nonrigid walls that are homogeneous in composition along their length can at low frequencies be modeled accurately using a series combination of


HARPER et al.: AN ACOUSTIC MODEL OF THE RESPIRATORY TRACT

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TABLE I LUMPED PARAMETERS FOR A LOSSY RIGID-WALLED TRANSMISSION LINE SEGMENT [13], [14], [26]

TABLE III NONRIGID WALL, LUMPED PARAMETERS FOR A SEGMENT LENGTH l [14], [25], [26], [36]

OF

TABLE IV DEFAULT WALL PARAMETER VALUES FOR RESPIRATORY TRACT [20], [26]

tube radius [cm]; segment length [cm]; radian density of median [g/cm ]; shear viscosity frequency; cross-sectional area [cm ]; speed of sound [dyne s/cm ]; ratio of specific heats; heat conduction ceofficient [cm/s]; specific heat at constant pressure [cal/g- C]. [cal/cm-s- C]; and

TABLE II PHYSICAL PROPERTIES OF AIR [14], [26]

These definitions are used for both the soft tissue and the cartilage, where the value in the subscript is either an (soft tissue) tube raor a (cartilage) throughout any given definition. radian frequency; segment length [cm]; and dius [cm]; wall thickness [cm] The tissue properties are: denshear viscosity [dyne s/cm]; sity [g/cm ]; and elasticity [dyne/cm ]. The tissue-specific values for , , are defined in Table IV and

a resistance , inertance , and compliance [24], [25] added to the rigid-walled, -section. For walls that exhibit a degree of spatial inhomogeneity along their length, for example the tracheal wall consisting of soft tissue interspersed with cartilage rings, each tissue type can be represented by its own series combination of resistance, inertance, and compliance (see Tables III and IV) in a manner depicted in Fig. 2. One approach that has been taken to model the heterogeneous composition of the subglottal airways is to specify the fraction of cartilage each , based upon its anatomical locaairway length contains tion, and then to adjust the wall circuit parameters for a segment by this parameter [26], [27]

(1) In the above equations, the circuit parameters with the subscript (e.g., , ) are calculated for the total segment length using the corresponding default tissue parameters. These total segment values are then scaled that according to the fractional value of the tissue type is appropriate for that segment. When the subglottal airways are modeled, the transmission line segments are assembled into a tree-like branching network similar to the structure of the airways. Using terminology from graph theory [28], we adopted the following conventions: a

Fig. 2. Lumped acoustic circuit element representation of a tube section with yielding walls. L ; L , R ; R , C , and C are defined by (1) and Table III for the subglottal system or (2) for the vocal tract.

branch is a subglottal airway segment connecting two nodes; a node is the root or a point of intersection of two or more branches; and the depth of a node is determined by counting the number of branches from the root node. The depth of a branch (or airway segment) is determined by the depth of its parent node. In our case, for the subglottal airways, the glottis represents the root node. The trachea is the branch with depth zero, and the right and left main bronchi are branches with a depth of one. Using this convention, Table V lists the airway parameters for a uniformly branching subglottal network with a depth up to ten [26]. This depth was used since at the relatively low frequencies of interest, the more numerous and smaller airways at subsequent depths in total yield a very large total cross-sectional area that primarily acts as an open-tube termination after a depth of roughly ten. Also, symmetric branching was assumed to reduce the computational complexity of the


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TABLE V AIRWAY SEGMENT PARAMETERS FOR THE SUBGLOTTAL AIRWAYS BEGINNING WITH THE TRACHEA (DEPTH 0). AFTER HORSFIELD [37], HABIB [36], AND MANSFIELD [26]

approach, noting that asymmetries have been shown to have an increasingly important effect with increasing frequency [17]. For the series of simulations described, a single volume velocity source was placed between two -segments and used as the model excitation. This source was positioned to excite the inherent resonance properties of the tract and should not be considered an attempt to accurately model the spatially distributed sources that actually occur within the respiratory tract during breathing. Also, since standing waves are generated with nodes and antinodes, the simulated measurement location was selected to avoid nulls in acoustic pressure that might not reveal all of the resonance locations over the bandwidth of interest. III. VOCAL TRACT MODELING AND MEASUREMENTS The vocal tract of a human subject with mouth open can be roughly described as a 17-cm-long nonuniform tube that is open at its proximal end and nearly closed at its distal end due to the vocal folds. If one assumes that the soft palate blocks off the nasal tract and, therefore, the effects of the paranasal sinus cavity resonances, and that the walls are rigid and the crosssectional area is uniform, then one realizes a simplistic lossless open-closed tube model of the supraglottal respiratory tract that exhibits odd quarter-wave harmonic resonances according to the classic equation [29]

where is the tube length and 0, 1, 2, . These resonance frequencies are presented and compared to those predicted by the transmission line simulation of this case, in Table VI, noting an expected similarity between the two. For the next simulation, the vocal tract walls were considered to be nonrigid using the previously described approach. This yielding behavior was implemented via a single series acoustic wall impedance using the wall parameters given by Flanagan [14]

(2)

TABLE VI SUMMARY OF FIRST THREE QUARTER-WAVE ODD HARMONIC RESONANCES PREDICTED FOR A LOSSLESS, RIGID WALLED, 17-cm-LONG VOCAL TRACT AND THE CORRESPONDING PREDICTED RESONANCES FROM THE TRANSMISSION LINE MODEL

Fig. 3. Predicted spectrum of the response of the vocal tract with yielding walls and Russian /a/ cross-sectional profile. The output is taken 3.0 cm above the glottis in response to a normalized volume velocity input 1.5 cm above the glottis.

where is the radius in centimeters of the current vocal tract segment, and is the length of the segment. For frequencies above 100 Hz, the tissue shows evidence of only resistive and mass reactive components. The addition of this impedance resulted in only a slight drop in the amplitude of the resonance peak near 500 Hz owing primarily to the losses associated with the wall motion for each segment, with little change in the odd quarter-wave harmonic behavior of the overall model. In the final simulation of the vocal tract that was performed, a radiation impedance (i.e., the acoustic effect of the air outside the mouth on the acoustic properties within the respiratory tract) was added at the mouth [14], and the radius of the vocal tract was varied over its length according to a vocal tract area profile determined by Fant [13] for the Russian vowel sound /a/ with the resulting spectral predictions shown in Fig. 3. These predictions are compared with an earlier simulation performed by Portnoff [30] (using the same area profile yet treating the subglottal system as a single lumped impedance) in Table VII, along with the measured formants from Fant’s subject and the results of our own experiment described below. We estimated the supraglottal resonances that occurred in four healthy male subjects while making the vowel sound /a/. A microphone (Sony K120) was placed one inch from each subject’s mouth, and the voiced sound was recorded with a Sony model TCD-D7 DAT recorder. The recordings were then sampled at 11 kHz with a 16-bit resolution, and to better isolate the resonance frequencies, a formant extraction was performed using linear predictive coding (LPC) analysis [31]. For each formant, the average was calculated across the four subjects. When comparing the results of our simulation against the other simulation and measurements, it was assumed that while



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TABLE VII SUMMARY OF PREDICTED (VIA TRANSMISSION LINE MODEL AND PORTNOFF’S MODEL [30]) AND MEASURED FORMANTS (VIA OUR SUBJECT MEASUREMENTS AND FANT’S [13]) FOR THE VOCAL TRACT (IN Hz)

Fig. 4. Predicted spectrum of the response of the subglottal airways modeled to a depth of ten. The output is taken 3 cm below the glottis in response to a normalized volume velocity source 1.5 cm below the glottis.

the /a/ sound was being produced the glottal opening was effectively closed [32], and hence, the experimental situation closely matched the model of the vocal tract with the mouth open, the /a/ vocal tract profile, and the glottal opening closed. Our simulation’s formants were within 10% of Portnoff’s simulation, within 6% of the means of the formants for our measurements, and within 10% of the formants for Fant’s subject (Table VII). Both Portnoff’s simulation and our simulation used the same vocal tract profile: the one measured by Fant. When we compared the results of the simulations with the formants for Fant’s subject, our results were closer than Portnoff’s in two out of three of the formants measured. Thus, the transmission line model of the vocal tract with yielding walls and a variable cross-sectional area profile predicted well the locations of resonances in the measured /a/ sound. With this as a foundation, modeling of the subglottal portion of the respiratory tract was undertaken using this general approach. IV. SUBGLOTTAL MODELING AND MEASUREMENTS As with the model of the vocal tract, the glottis was assumed to be closed for the simulations of the subglottal system, and the respiratory tract walls were considered to be yielding. In addition, as previously described, the terminal branches of the subglottal airways at a depth of ten were considered to have their distal ends open due to the large total cross-sectional area that these numerous airways represent [33]. Even for a simulation with a depth of one (i.e., only including the trachea and main stem bronchi), the resonances deviated from a quarter-wave, odd harmonic pattern that would be expected for a simple closed/open tube, primarily due to wall motion. The first resonance (648 Hz), if assumed to be consistent with the closed/open tube model, matches a tube about 10% shorter than the one modeled (tracheal length of 10 cm and main bronchi length of 5 cm). The second resonance (1759 Hz), assuming this is three times the first to be consistent with the open/closed tube model, is also about 10% lower than expected. As the depth (i.e., number of airways) being modeled was increased with subsequent simulations, the resonance peaks continued to shift downward in frequency relative to a simple closed/open tube model. At a depth of ten, a stable spectral pattern was reached (Fig. 4) with the first spectral peak at 569 Hz and the second at 1360 Hz, which are clearly not harmonically related. This modeling procedure highlighted the fact that the acoustic behavior of the branching and yielding subglottal air-

TABLE VIII SUMMARY OF PREDICTED (VIA TRANSMISSION LINE MODEL AND ISHIZAKA’S MODEL [16]) AND MEASURED RESONANCES (VIA OUR SUBJECT MEASUREMENTS) FOR THE SUBGLOTTAL RESPIRATORY TRACT (IN Hz)

ways deviate significantly from that of a uniform and rigid tube that is closed at its proximal end and open distally. To compare these predicted resonance frequencies to actual subglottal measurements, acoustic recordings were made in four healthy, male subjects while each voiced the /a/ sound. Measurements were performed using a contact sensor (PPG #201, Technion, Haifa, Israel) attached to the suprasternal notch (overlying the extrathoracic trachea) using double sided tape. As before, the data were digitized at 11 kHz and formant extractions were performed. The formants were then grouped across the four subjects and the averages determined. The results are summarized in Table VIII, along with our predictions and those from Ishizaka’s model (scaled for western anatomy) of the total subglottal impedance calculated just below the glottis [16]. When comparing the results of our simulation against the other simulation and measurements, the resonances were within 8% of Ishizakas predictions, and within 12% of the means of the resonances for our measurements. Thus, through the inclusion of the effects of airway branching and yielding walls, the simulated subglottal system allows for reasonably accurate modeling of its acoustic properties in terms of the locations in frequency of its natural resonances. V. RESPIRATORY TRACT MODELING AND MEASUREMENTS The transmission line models of the supraglottal and subglottal portions of the respiratory tract were then coupled to create a model of the entire respiratory tract, where the degree of coupling was determined by the size of the glottal opening. Initially, to better assess the effects of the coupling alone, both the supraglottal and subglottal airways were represented as single


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TABLE IX SUMMARY OF PREDICTED (VIA TRANSMISSION LINE MODEL) AND MEASURED RESONANCES FOR ENTIRE RESPIRATORY TRACT (IN Hz)

Fig. 5. Predicted spectrum of the response of the entire respiratory tract as measured 1.5 cm below the glottis due to a normalized volume velocity source located 6.0 cm above the glottis.

uniform and rigid tubes. This allowed us to validate the transmission line model using the simple standing wave tube models with appropriate boundary conditions. With the glottis closed, the supraglottal and subglottal tubes both showed the expected quarter wave, odd harmonic pattern (for an open/closed tube). As the glottal opening widened, the resonance peaks in both sections shifted. Finally, when the glottis was fully open, the half wave, integer harmonic pattern characteristic of a single open/open tube with the length equal to the sum of the supra and subglottal lengths resulted. Next, the previously described supraglottal and subglottal models were coupled via the glottal opening. The supraglottal portion of the model used the same vocal tract wall parameters and area profile as in the previous vocal tract modeling, and similarly the subglottal portion used subglottal wall parameters and a branching network to a depth of ten as previously described. For coupling, the glottis was assumed to be open with a cross-sectional area of 1.6 cm [34]. The volume velocity source was located 6.0 cm above the glottis where adequate coupling for all the measured resonances was obtained, and the pressure output was 1.5 cm below the glottis at a point where there were no apparent nulls near the resonances. The predicted spectral characteristics of the respiratory tract are shown Fig. 5, noting the relatively large number of spectral peaks in the simulation bandwidth as compared to either the subglottal or supraglottal simulations, and no clearly discernible harmonic behavior. This more complex spectral behavior is the result of many factors acting in concert, including a variable vocal tract cross-sectional area profile, yielding walls, and subglottal airway branching. To compare these predicted resonance frequencies for the complete respiratory tract to those observed in tracheal sound measurements, four healthy males were studied. Each had a contact sensor (PPG #201, Technion, Haifa, Israel) attached to his suprasternal notch using double sided tape and were instructed to breathe quietly while their tracheal sounds were digitally recorded. It was assumed that during quiet breathing the glottal opening would approach its maximum size and that this would, therefore, correspond to the previously described simulation conditions of the respiratory tract. The analysis was performed on sounds measured during expiration since the turbulence-generated sound sources are believed to be more centrally

located during this phase as compared to inspiration [35]. The spectral peak locations were estimated, and for each resonance, the average resonance location across subjects was determined (the fifth resonance was not discernible for two of the subjects). Table IX includes these average resonance values along with the locations of the first five resonance peaks from the simulation as previously shown in Fig. 5. When the predictions of the simulation were compared to the measurements, it was found that the first five simulation resonances (going from low- to high-frequency) were within 11%, 4%, 10%, 2%, and 7% respectively of the average measured values. This similarity once again highlights the predictive capability of such a model in terms of the locations of the natural resonances of the system, noting that the model is relatively complex taking into account such factors as yielding walls and branching and using nominal parameter values based on the anatomy of an adult male. VI. SUMMARY The primary objective of this initial modeling and experimental effort was to construct a model that begins to link the underlying anatomy of the respiratory tract and its natural acoustic resonances to the spectral peaks found in tracheal sounds. To achieve this goal, we performed simulations using models that ranged from simple tubes to more complex branching geometries, and compared the predicted resonances to existing data and/or the results of targeted experiments in our laboratory. In general, the simulations compared favorably with the experimental results, indicating that links between even the relatively complex anatomical components and the locations of spectral peaks in measured tracheal sounds can be made. Through the approach of beginning with simple acoustic models and progressing toward more anatomically detailed ones, it became clear that the incorporation of yielding wall behavior, longitudinally varying cross-sectional area profiles, and subglottal branching is necessary in order to accurately predict the locations of spectral peaks in tracheal sounds. Thus, the acoustic characteristics of the intact respiratory tract deviate significantly from those of a uniform and rigid tube open both at the mouth on one end and to the large air volume reservoir of the lungs at the other. While respiratory tract length is a key parameter from an acoustic perspective, the heterogeneous anatomy of the tract yields acoustic behavior that is predictably complex in the frequency range of tracheal sounds, thereby making it difficult to relate specific spectral peak locations to individual anatomical structures. Rather, these easily measured sounds reflect the interaction of a variety of anatomical



components that together give rise to highly complex acoustic behavior and sound patterns. The model assumes 1-D acoustic wave propagation, airway geometries with second-order wall dynamics derived from previous measurements on adult males, and an estimated vocal tract profile for /a/ sound generation. This acoustic representation of the average respiratory tract anatomy predicts the location of spectral peaks in vocal tract, subglottal, and complete respiratory tract acoustic measurements with disparate sound sources such as the speech sound /a/ and breath sounds. These findings stress the composite importance of anatomical parameters such as overall tract length, depth of subglottal branching, vocal tract profile, and wall properties on spectral peak location while de-emphasizing the impact of specific source location and type. However, it is likely that such sources play a key role in the determination of the overall spectral features and amplitude of such easily-measured sounds.

ACKNOWLEDGMENT The authors would like to thank K. N. Stevens for providing many helpful insights and suggestions during the investigations and preparation of this manuscript.

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Paul Harper received the B.S. degree in physics and M.S. degree in electrical engineering from the University of Massachusetts, Amherst, in 1971 and 1977, respectively. After working in industry in the areas of software design, automatic testing and human factors, he received the Ph.D. degree in electrical engineering from Purdue University, West Lafayette, IN, in 2000. His research interests are in acoustic modeling of the respiratory tract and the general area of biomedical acoustics. Dr. Harper is an IGERT fellow.


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Steven S. Kraman was born in Chicago, IL and grew up in Brooklyn, NY. He received the M.D. degree from the University of Puerto Rico, San Juan, P.R., in 1973 and did his residency in internal medicine and fellowship in pulmonary medicine at the Brookdale Hospital and Queens General Medical Centers, New York, NY. He currently holds the rank of Professor of Medicine at the University of Kentucky College of Medicine and is Chief of Staff of the VA Medical Center in Lexington, KY. He. has conducted and published research in various aspects of respiratory acoustics since 1980 with particular interest in the production and transmission of normal lung and tracheal sounds.

Hans Pasterkamp received the M.D. degree from the Medical University Lübeck, Lübeck, Germany, in 1976 and certifications as a pediatrician from the College of Physicians, Schleswig-Holstein, Holstein, Germany and from the Royal College of Physicians and Surgeons of Canada, Ottawa, ON, in 1984 and 1987, respectively. He is currently Professor and Head of the Section of Respirology at the Department of Pediatrics and Child Health, University of Manitoba, Winnipeg, Canada. His research interests are in respiratory acoustics, asthma and sleep medicine.

George R. Wodicka (S’79–M’89–SM’95) received the B.E.S. degree in biomedical engineering from the Johns Hopkins University, Baltimore, MD, in 1982, the S.M. degree in electrical engineering and computer science and the Ph.D. degree in medical engineering, from the Massachusetts Institute of Technology, Cambridge, MA, in 1985 and 1989, respectively. He is currently Professor and Head of Biomedical Engineering and Professor of Electrical and Computer Engineering at Purdue University, West Lafayette, IN. His research interests are in biomedical acoustics, acoustical modeling, and signal processing. Dr. Wodicka is a member of the Administrative Committee of the IEEE Engineering in Medicine and Biology Society, a recipient of a National Science Foundation Young Investigator Award, a fellow of the American Institute for Medical and Biological Engineering, and a Guggenheim Fellow.
