INTRODUCTION

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THE ACOUSTIC-REFLECTIONS TECHNIQUE has been applied to the lower airways (19) and to the glottic region (3, 24-26) for measurements of the cross-sectional area as a function of distance and for examination of the vocal tract with regard to speech reconstruction (27). The technique has been applied to the nasal cavity (13) and is increasingly used in clinical studies of the nasal cavity (10-12). The acoustic-reflections method for use in the nasal cavity [acoustic rhinometry (AR)] has been validated by comparison with computerized tomography (CT) and magnetic resonance (MR) scannings of subjects and by comparison with known dimensions of nasal casts (4, 13, 14). The results agree reasonably well except in the posterior part of the nasal cavity, where AR compared with MR overestimates the areas. This difference may partly be explained by a contribution from the maxillary sinus volume to the acoustically measured area-distance curve for the posterior part of the nasal cavity, whereas influences from the contralateral side seem to be of minor importance in the nasal cavity (15). Sound losses other than those to the sinuses may be present. Studies in the lower airways indicate that nonrigidity of the tissue may affect the measured area-distance function (7, 22), but the influence of sound loss caused by nonrigidity of the nasal mucosa, viscous loss, and losses caused by complex geometry in the nasal cavity has not been examined in detail. The accuracy of the acoustic reflections technique is also affected by the frequency bandwidth of the acoustic pulse and of the electric filter used, including the characteristics of the microphone. These factors and the sampling frequency during the measurements determine the resolution. Fredberg (7) has given indications that He-O₂ breathing increases the accuracy of the technique when applied to the lower airways, but He-O₂ breathing has not so far been examined for the nasal cavity. The present study investigated four important aspects concerning the accuracy of the acoustic reflections technique used in the nasal cavity: 1) sound losses in the nasal cavity, with special regard to nonrigidity of the nasal mucosa and the complex geometry of the cross-sectional area; 2) the accuracy in relation to the bandwidth of the acoustic signal, sampling frequency, and low-pass filtering; 3) the influence on the results of the use of 80% He-20% O₂ vs. air; and 4) the influence of the relationship of the surface to cross-sectional area.

	METHODS

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Subjects. Six subjects were included. MR scannings were performed on four of them. The scannings were carried out after decongestion of the nasal cavity to assure stable conditions. Decongestion was accomplished by two sprays of 640 µg of xylometazoline in each nostril. Precise total nasal cavity models in plastic were made for four of the subjects (8 nasal cavities) by stereolithography (see Stereolithography). The influence of He-O₂ was examined in four subjects, and rigidity of the mucosa was measured in one subject by using laser vibrometry. The study was approved by the local ethics committee.

AR. The AR technique has been described in detail before (13) and is based on the principle that an audible sound pulse propagating in a tube is reflected by local changes in acoustic impedance. Thereby, it is possible to estimate the cross-sectional area of the nasal cavity as a function of the distance from the nostril. The equipment (GJ Electronik, Skanderborg, Denmark) used for these measurements consists of a sound-pulse generator (a spark source); a microphone (Field Effect Transistor microphone, diameter 6 mm, range 20 kHz) with amplifier and low-pass filters with variable cutoff frequencies; a wave tube on which the sound source, the microphone, and a nosepiece are mounted; and a computer for data acquisition and analysis. The signals were sampled by an analog-to-digital board (CIO Junior 330, Computer Boards) that had a sampling frequency up to 330 kHz. For some of the measurements (complex geometric examination) an acoustic rhinometer based on pseudorandom acoustic signals (SR-Electronics, Lynge, Denmark) was used.

He-O₂ examination. The area-distance functions were measured in four casts previously described (15) and in four subjects (8 decongested cavities) by using air and He-O₂ (80% He-20% O₂). The He-O₂ was let into the sound tube of the AR equipment. Gas was sampled from the nasal cavity, and the nitrogen concentration was measured to assure complete exchange of air with He-O₂. For air, the signal was low-pass filtered, with cutoff at 10 kHz (sampling frequency, 50 kHz), and for He-O₂ at 19 kHz (sampling frequency, 100 kHz) because the speed of sound is 1.9 times higher in He-O₂. Fast Fourier transform (FFT) analysis showed a reasonable energy content of the incident pulse (6-dB decrease in amplitude for the unfiltered signal up to 22 kHz).

MR imaging. MR scans were performed by using a 1.5-Tesla Philips Gyroscan S15HP scanner. Slice thickness was 3.5 mm and equivalent to the distance between the data points in the acoustic measurements when sampled at 50 kHz. Anterior coronal scannings perpendicular to the nasal floor, starting at the tip of the nose and ending at the posterior wall of the epipharynx, were made in each subject (14). The cross-sectional areas and surface of each nasal cavity were determined by use of a special computer program after delineation of the boundary between air and mucosa was marked by hand with the use of a "mouse" attached to the computer (14, 15).

Accuracy of acoustic measurements in step models and circular nose-equivalent models. To evaluate the accuracy of the equipment, we constructed a model made of plastic, with rigid walls and stepwise increasing areas. The data of the obtained acoustic area-distance function were fitted to the mathematical function (1) describing the step change where d is the ordinate base value, a is the step change, b and c are constants, and x is the distance from x₀. We defined the rise distance as the difference between the abscissa values to 10 and 90% of the step response (100% = 2 cm²). The rise distance of the acoustic response to a step change was determined from the formula above and was plotted as a function of the low-pass filtering frequency.

Stereolithography. Although stereolithography modeling has been described before (15), it will be summarized here. The MR data for the subjects are transferred to a three-dimensional "solid" computer-aided design model and interpolated (by Mimics 1.0 software) to slice thicknesses of 0.2 mm. The model was built or "grown" in a bath with liquid plastic that solidified when exposed to ultraviolet light. A thin ultraviolet laser beam was guided by a computer over the surface of the liquid, which solidified to a thickness of 0.2 mm wherever it was exposed [SLA equipment (stereolithography); Danish Technological Institute, Aarhus]. Building up of the model started by "copying" its lowest layer in the surface of the liquid. When the first layer was solidified, it was submerged in the liquid and washed over with a new thin layer of liquid plastic, and the next layers were successively hardened until the model was finished.

Laser vibrometry of the nasal mucosa. The acoustic properties of the nasal mucosa of one male subject were examined by laser vibrometry. With his head supported by a vacuum pillow, the subject was lying on an operating table. Measurements were done without decongestion of the nasal mucosa. In the vibrometer (29), a beam splitter divides the laser beam into a measuring beam and a reference beam, one of which is frequency shifted by 40 MHz in a Bragg cell. The measuring beam was focused 1.5 cm from the nostril on the anterior part of the nasal septum which was most easily measured. The reflected light was recorded by the optical system and mixed with the reference beam. The resulting beat frequency is 40 MHz plus the Doppler shift in frequency proportional to the velocity of the movement of the mucosa surface. The mucosa was vibrated by a sound-chirp stimulus generated by a FFT signal analyzer (Hewlett-Packard model 3262 A) that was also used for computing the sound pressure and velocity spectra. The chirp (a brief pure tone that was linearly swept from 0.1 to 1 kHz) had a duration of 40 ms. It was amplified and delivered by a 6-in. speaker through a horn connected to the nose. The sound pressure in the nasal cavity was measured by a probe microphone (Brüel & Kjaer model 4170; probe length 6 cm, external diameter 1.25 mm) positioned a few millimeters from the laser beam focus site. The outputs from the microphone and the laser vibrometer, representing the sound pressure on and the velocity of the mucosa, were recorded by the FFT analyzer and were low-pass filtered at 5 kHz for antialiasing. In the analyzer, the transfer function (the specific acoustic admittance; i.e., velocity/sound pressure) between the two channels was calculated and was then graphically recorded.

Simulation. A simulation program to examine the effect of changes in the setup parameters of the equipment was made in MATLAB (MATLAB 4.0/w, Math Works). The flowchart of the simulation program is shown in Fig. 1. Three inputs are used in the model to simulate the effect of different combinations of the two setup parameters: low-pass filtering frequency and sampling frequency. The first input is the impulse response of the measurement system, including the characteristics of the sound source, the tube, and the microphone. In practice, this impulse response is calculated from the reflection of the incident pulse from a high-impedance termination of the measuring tube (closed tube). (This impulse response thus represents the reflected pulse in the calibration situation.) A similar impulse response is used as the second input. This impulse response is used to examine a given cavity in the measuring situation (to "add" the system characteristics of the equipment to the theoretical cavity-impulse response). The two impulse responses have been used to bring the simulation as close to reality as possible. The third input in the model is the theoretical area-distance function, which is to be modified by the equipment. The calculation of the impulse response, as it would be measured by the equipment, is done by solving the direct problem.

View larger version (18K): [in this window] [in a new window]   Fig. 1.   Flowchart for simulation of measurement errors (see METHODS and Fig. 5). AD function, analog-to-digital function.

	RESULTS

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He-O₂. The measurements made in He-O₂ vs. air showed no significant difference in the results, either in the nasal cavity cast or in the subjects. Figure 2A shows the results in one side of a cast for air and He-O₂, and Fig. 2B shows the 95% confidence interval for all eight cavities in subjects. As can be seen in Fig. 2B, there is no statistically significant difference between air and He-O₂.

View larger version (18K): [in this window] [in a new window]   Fig. 2.   A: effect of measurement in He-O2 (+) compared with air () in 1 nasal cavity (cast). B: mean difference (gray line) and 95% confidence intervals between air and He-O2 in 8 cavities (4 subjects; see text).

Measurements of nasal cavities and identical stereolithographic models with hard surfaces. The area-distance curves from the eight nasal cavities of the stereolithographic models were compared with the data from the measurements of the subjects. If there were no losses associated with wall motion and the models and the subjects had identical geometries, one would not expect any difference between the models and the subjects. Figure 3 shows the mean difference between the models and the subjects and the 95% confidence interval. The areas are 10-20% larger in the subjects than in the rigid models. A part of this difference is caused by the fact that the nosepiece used in this setup is inserted into the nostril and probably widens the anterior part of the vestibule slightly. This was not the case for the models. In the models, the nostril may in fact be the narrowest section. This made it difficult to align the curve from the models and the subjects, but only minor changes were observed with position differences of 1-2 data points (3.5-7 mm). The acoustic measurements of the subjects were made in relation to the scans and compared with acoustic measurements of the models when they were first made. This delay between the measurements, however, is probably of little or no importance. Even with these reservations, the influence of nonrigidity of the wall as measured in these experiments still seems to be <20%.

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Sound loss caused by nonrigidity. Solid line with : mean differences between acoustic area-distance curves obtained from nasal cavities and corresponding models. Gray lines, 95% confidence intervals.

Accuracy of acoustic measurements in step models and circular nose-equivalent models. An increase in circumference-to-area ratio did not have any significant effect on the acoustic area-distance function in a tube model (Fig. 4A), and the same area-distance function was found in a nasal cavity model with complex geometry and a circular model with the same cross-sectional areas for the first 5 cm (Fig. 4B). The measurements of the step cavity (Fig. 5A) show that the sampling frequency influences the ability of the equipment to reproduce a step (low-pass filter cutoff frequency fixed at 10 kHz). Figure 5B shows the measured rise distances (from the fit to the equation described earlier) as a function of low-pass cutoff frequencies (the markers depict the measured values; sampling frequency is 50 kHz). It is seen that the rise distance is inversely proportional to the cutoff frequency. The effect of the sampling rate was tested in the same way by using two different cutoff frequencies of 10 and 20 kHz (not shown). The results indicated that the rise distance is not affected by the sampling frequency if the frequency is more than approximately four times the low-pass filtering frequency. With the use of the simulation program described above and in Fig. 1, a plot was made of the rise distance in a step cavity (step of 1 cm²) as function of low-pass cutoff frequency at different sampling rates. The results of the simulations (Fig. 5C) are in agreement with the experimental results. The upper limit of the low-pass filtering frequency in the simulation is affected by the characteristics of the microphone as indicated by the closeness of curves sampled at >50 kHz. In accordance with the experimentally determined rise distances above, the simulated rise distance is inversely proportional to the low-pass cutoff frequency and is not affected by the sampling frequency if it is >3-5 times the low-pass filtering frequency.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   A: solid line, acoustic area-distance measurement for model with constant area and increasing circumference. Dashed line, circumference of model. B: acoustic area-distance curves from nasal-cavity model () and circular model (+) with same cross sections.

View larger version (20K): [in this window] [in a new window]   Fig. 5.   A: influence of sampling frequency on rise distance (see METHODS).  and solid line, 20 kHz; + and solid line, 100 kHz. Low-pass cutoff frequency is fixed at 10 kHz. B: measured rise distance as function of low-pass cutoff frequency. +, Measured values. C: simulated rise distance as function of low-pass cutoff frequency at sampling frequencies of 25, 50, 100, and 200 kHz.

Laser vibrometry of the nasal mucosa. Computation of the coherence function allowed us to discriminate between noise and signals causally related to the signals sent to the loudspeaker. In the frequency range of 100-1,000 Hz, both the sound pressure and the vibration velocity had reasonable coherence values (values >0.9 for the whole spectrum). From the amplitude and phase of the vibration velocity and the sound pressure, the specific acoustic admittance of the mucosa was calculated.

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View larger version (18K): [in this window] [in a new window]   Fig. 6.   Results of laser-vibrometry measurements (0 dB is equivalent to 8.0 µm · s1 · Pa1). A: amplitude vs. frequency. At 190 Hz, an amplitude maximum is seen. B: phase angle vs. frequency. At 190 Hz, phase angle is 0. C: circuit of a nasal airway wall analog (see text). vg, Voltage generator; R, resistor; L, inductor; C, capacitor.

View larger version (23K): [in this window] [in a new window]   Fig. 7.   A: PSPICE circuit with Laplace generator G model of a 7-cm- long homogeneous segment (see text). EMULT, multiplier. B: area-distance functions of segments with 0, zero loss; 1, loss equivalent to frequency-dependent loss measured by laser-vibrometry; 2, loss 100 × frequency-dependent loss measured by laser vibrometry; 3, frequency-independent loss 100 × maximum loss measured at 190 Hz by laser vibrometry.

	DISCUSSION

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Area-distance functions inferred from acoustic reflections in the nasal cavity seem to be valuable in clinical examination and research, although the same basic problems are present as in measurements in the lower airway, namely, whether the basic assumptions for use of the technique are fulfilled. For measurements in the nasal cavity, considerations regarding the assumptions may be especially important because of the complex geometry in comparison with the trachea and the larger bronchi. The assumptions for the acoustic reflections technique (20) are negligible sound loss, rigid airway walls, symmetrical branching, and one-dimensional (planar) wave propagation.

A high correlation has been described between the area-distance function obtained by AR and the area-distance function obtained by MR scannings (14) in vivo, although some deviations were seen especially in the posterior part of the nasal cavity. The paranasal sinuses may have influenced the result here because of sound loss/passage through the ostium to the sinuses (15). For the trachea, a very high correlation between acoustic measurements and X-ray measurements has been found (5, 6, 17, 19), although overestimation of the areas has been seen in a rigid model as well as in vivo. A large narrowing in the anterior part of the nasal cavity as well as in the trachea may cause errors in the acoustic area-distance function behind the constrictions. Measurements of a tracheal model have shown that constrictions with an area <1.0 cm² could induce errors (2). For the nasal cavity, areas down to 0.35 cm² did not interfere with the measurement (13). Both the difference between the rigid-wall model and the living tissue and the errors caused by a constriction represent violation of the assumption of no energy losses.

It has been suggested that the use of He-O₂ may improve the spatial resolution for two reasons: first, by increasing bandwidth before cross modes start to appear, and, second, by minimizing the part of the frequency band where wall motion may affect the results (7). Fredberg et al. (9) found that the area-distance curve of the tracheobronchial airways changed in He-O₂ compared with air in one subject with a unique configuration of the area-distance function at the carina. The other five subjects who were measured with He-O₂ only did not have this configuration at the carina. Furthermore, it has been questioned whether the content of high frequencies in the signal that was used was sufficient, and this may introduce errors in the results. Later studies, using two microphones in the nasal cavity (23) and the same equipment in the lower airways, tested with and without He-O₂ (22), indicate that high-pass filtering (excluding influence of wall motion at low frequencies) may be important, at least in the lower airways.

Use of He-O₂ does not per se increase the resolution, because this is determined by the wave length at the low-pass cutoff frequency. This can be increased during He-O₂ before cross modes start to appear, but the minimum wave length for cross modes to appear is the same for He-O₂ as in air. This means that there is no theoretical advantage of He-O₂ with respect to cross modes. In the present study, the model investigations in the rigid models did not reveal any significant difference between air and He-O₂; neither did the measurements in the subject.

Losses caused by noncircular geometry (a large circumference-to-area ratio) may also interfere with the results (viscous loss). Validation by CT scanning of a cadaver and of an infant cast (4, 13) showed high correlation between acoustic measurements and the X-ray measurements. Shrinkage of the tissue in the preserved cadaver head (13) may have induced a more open, circular, and less-complex geometry than occurs in vivo. In fact, the size of the areas of the cadaver head were considerably larger than in vivo measurements of subjects. Furthermore, preservation may induce a change in rigidity of the tissue. This may make the results not completely valid for the in vivo situation. Also, in the present study, the complex geometry (large circumference-to-area ratio) had no influence on the results. In the circular vs. the subject model, small differences were present, especially in the posterior part of the model caused by the direction of the scanning and the sound path or determination of the complex area at the middle turbinate. Other differences caused by the production process may also be present.

Measurements in the nose show approximately the same variation (5-10%) (11) as measurements in the trachea described by Brooks et al. (2). The variation and the absolute accuracy of the area-distance function is partly dependent on the algorithm chosen for solving the inverse problem and accuracy decreases with distance. The Ware-Aki algorithm seems to be one of the best (24). The frequency bandwidth in the incident wave and in the reflected wave is also important for accuracy. Bandwidth narrowing may increase the rise distance and thereby induce smoothing of the area-distance curve and reduce the magnitude of changes in areas behind a constriction. Bandwidth is also limited by the assumption of one-dimensional wave propagation, thereby limiting the accuracy of the acoustic technique (7, 16). The maximal frequency that can be used before cross modes appear is dependent on the internal dimension of the object (f_max = c/2D) where f is frequency, c is the speed of sound, and D is the largest internal diameter of the object (20). The spatial resolution is proportional to the maximal frequency in the sound spectrum (16, 24). It is possible that cross modes first start at a higher frequency than f_max= c/2D because of the slitlike nature of the nasal geometry and the damping of the cross modes, which is much higher than that of the planar mode. The different conditions for influence from cross modes have not been examined in this study. We found that increase in the sampling frequency (the spatial resolution) >3-5 × the low-pass filtering frequency did not further improve the accuracy of the area measurements. The present study has not addressed the influence of the resolution of the FFT analysis and the Hunt algorithm on the accuracy. Simulations indicate that adjustments in these calculations may further improve the accuracy.

A constriction may induce significant viscous losses and reduce the magnitude of the recovered signal (28). This has not been analyzed in the present study. Two of the major loss components in the trachea are 1) internal loss primarily of viscous nature and 2) loss caused by wall motion. In one study, the sound loss in the wave tube was 9 and 30-50% for the total system (wave tube and trachea) (20). Loss caused by wall motion may affect both the distance measurement and the area estimation, because impedance and area are not well measured in nonrigid systems (19). The loss caused by nonrigidity of the wall in the airways is diminished because of smooth bendings of the airways and the fact that the wave travels parallel to the wall, inducing a phase shift of nearly 180° in the reflected wave from the wall. This phase shift reduces the sound intensity and energy transfer in the boundary layer between air and tissue.

Direct measurements of nonrigidity of the wall, expressed as the wall admittance of the nasal mucosa, have not been made before, but measurements on the cheek revealed that the tissue behaves relatively rigidly at frequencies >120 Hz (21). For the trachea, wall motion can be expected at <100 Hz, whereas the dynamic compliance is decreasing considerably in the frequency range from 100 to 1,000 Hz (9). In the present study, we found that nonrigidity of the mucosa did not have a major effect on the acoustic area-distance function. Using the vibration measurements, the model and the assumption that the mechanical counterparts of L, C, and R are mass, compliance, and mechanical resistance per area unit of the tissue, one finds, in "daily life" units, a mass of 3.4 g/cm² and a compliance of 2.1 mm/atm. The values of these parameters should be viewed with caution, because several assumptions have to be made; e.g., that the measurement of the admittance of the mucosa in a single point is representative for the total mucosa and that the applied electromechanical model is valid for the mucosa. The measurement of the acoustic admittance was done in the anterior part of the septum, which has cavernous tissue similar to the inferior turbinate at the lateral wall. We measured in a nondecongested state, because nonrigidity is suspected to be greater than in the decongested state. Furthermore, measurement was done with a nosepiece inserted, similar to the means of measurement for area-distance that partly holds the outer part of the nose in a fixed position. The effect seems to be <10-20% in comparisons between subjects and rigid models and is insignificant compared with mucosa admittance measurements.

In conclusion, sound loss in the nasal cavity caused by noncircular geometry and wall motion is not a major source of error for the acoustic area-distance function. Low-pass filtering limits the resolution, and no advantages were found by using He-O₂ instead of air. The sampling frequency should be approximately four times the low-pass-filtering frequency caused by the microphone itself or added filters.