Proceedings of Meetings on Acoustics

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1 Proceedings of Meetings on Acoustics Volume 19, ICA 213 Montreal Montreal, Canada 2-7 June 213 Engineering Acoustics Session 4pEAa: Sound Field Control in the Ear Canal 4pEAa6. A comparison of methods for estimating individual real-ear-to-couplerdifferences (RECDs) in hearing aid fitting Simon Köhler*, Tobias Sankowsky-Rothe, Matthias Blau and Alfred Stirnemann *Corresponding author's address: Institut für Hörtechnik und Audiologie, Jade Hochschule Wilhelmshaven/Oldenburg/Elsfleth, Ofener Str. 16/19, Oldenburg, 26121, Niedersachsen, Germany, simon.koehler@jade-hs.de The sound pressure at the ear drum is the reference quantity for almost all applications of sound delivery to the ear, especially in hearing aid fitting. Since hearing aids are typically calibrated using the so called 2cc-coupler, the link to the individual sound pressure at the ear drum is given by the real-ear-to-coupler-difference (RECD). Nowadays, averaged RECDs are used for hearing aid fitting, which do not account for inter-individual differences in ear canal acoustics. As a consequence, resulting coupling errors may reach 15 db for frequencies up to khz. Alternatively, there are methods for estimating individual RECDs, based on acoustic impedance measurements at the inner face of the ear mold. These methods differ in effort (e.g. the complexity of the ear canal model and fitting algorithm) and accuracy. By using an integrated ear canal microphone, individual RECD estimation could be feasible in future hearing aid fitting. In this research, six different methods to predict individual RECDs were compared using simulations as well as real ear measurements with and ear molds. As a result, it appeared that relatively simple cylindrical and conical ear canal models give the best compromise between effort and accuracy. Published by the Acoustical Society of America through the American Institute of Physics 213 Acoustical Society of America [DOI:.1121/ ] Received 22 Jan 213; published 2 Jun 213 Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 1

2 INTRODUCTION The sound pressure at the ear drum is the reference quantity for almost all applications of sound delivery to the ear, especially in hearing aid fitting. Since hearing aids are typically calibrated using the well-known 2cc-coupler, the link to the individual sound pressure at the ear drum is given by the real-ear-to-coupler-difference (RECD). The RECD depends on the properties of the outer and middle ear, and therefore, is individual for every subject. Since the direct measurement of the RECD in the immediate vicinity of the ear drum is rather complicated, averaged RECDs are typically used in hearing aid fitting. As a consequence, coupling errors occur and may reach 15 db for frequencies up to khz. Alternatively, there are methods for estimating individual RECDs, based on acoustic measurements at the inner face of the ear mold. By using an integrated ear canal microphone, such methods could be feasible in future hearing aid fitting. In this research, we concentrate on methods which are based on acoustic impedance measurements in the ear canal. To this end, we compare six different methods for predicting individual RECDs using simulations as well as real ear measurements with and ear molds. DESCRIPTION OF RECD PREDICTION METHODS By definition, the RECD describes the difference of the sound pressure levels measured at the ear drum and in the 2cc-coupler [1]. In this research, we consider the RECD to describe the complex-valued transfer function H RECD, given by the sound pressure at the ear drum divided by the sound pressure in the 2cc-coupler, H RECD = p dr. (1) p 2cc Considering the model framework shown in Fig. 1 and ignoring the leakage impedance Z leak for now, the sound pressure at the ear drum can be calculated according to [2], p dr 1 = qs. (2) v e 11 /Z s + e 12 /(Z dr Z s ) + e 21 + e 22 /Z dr v v q ec q s ( ) e11 e Z s p 12 ec Zec Z leak e 21 e 22 Z dr p dr FIGURE 1: Model framework of a hearing aid coupling. The drawing of the ear was adopted with kind permission from Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 2

3 The source impedance Z s is typically very high compared to the ear impedance. Thus, for Z s the term can be simplified to p dr 1 = qs (3) v e 21 + e 22 /Z dr v = Z trans,ec qs v. (4) Z trans,ec describes the transfer impedance of the ear canal and can be formulated either as a function of Z dr (see Eq. 3) or as a function of Z ec. The latter is given by Z trans,ec = p dr q ec = e 22 Z ec e 12. (5) The sound pressure in the 2cc-coupler can be calculated similarly from its transfer impedance, p 2cc v = Z trans,2cc qs v. (6) Hence, the RECD can be estimated from the ratio of the two transfer impedances, H RECD = Z trans,ec Z trans,2cc. (7) Considering an additional leakage impedance Z leak in parallel to the ear canal, but as part of the input impedance Z ec, the resulting transfer impedance extends to Z ec Z trans,ec = e 22 Z ec e 12 + e 12. (8) Z leak The third term containing e 12 and Z leak is usually about 2 db smaller than the other components. Thus, this term can be neglected and the calculation of Z trans,ec is identical to Eq. 5. It should be noted, however, that now the leakage impedance is included in Z ec and Z trans,ec, respectively. All following RECD prediction methods are based on estimating the individual transfer impedance Z trans,ec, which is given by the estimated ear canal parameters and either by the measured Z ec or the estimated Z dr. For calculcating the corresponding RECD, a theoretical two-port model of the 2cc-coupler is used according to [3]. The six different methods are described briefly in the following sections. Lossless Tube Ear Canal Model (M1) The first method M1 estimates the ear canal parameters using a lossless tube ear canal model. The twoport transfer matrix of such a model is given by ( cos(kl) E = j 1 Z w sin(kl) ) jz w sin(kl) cos(kl) with Z w = ϱc S, (9) where k represents the wave number, l the length of the ear canal model, Z w the wave impedance, ϱ the air density, c the speed of sound and S the cross sectional area in the ear canal. The length of the ear canal model is estimated from the λ/4 resonance of the measured ear canal input impedance. For the calculation of Z w a diameter of 7.5 mm is assumed, which corresponds to the ear canal diameter of the IEC 711 Ear Simulator. Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 3

4 Lossless Cone Ear Canal Model (M2) Method M2 uses a lossless cone for modeling the ear canal. parameters are given by The corresponding two-port e 12 = j d dr ϱc sin(kl), () d ec S dr e 22 = d ( ec cos(kl) + 1 d ) ec sin(kl). (11) d dr d dr kl The length of the ear canal model is again estimated from the λ/4 resonance of the measured ear canal input impedance. For the outer and inner diameter values of d ec = 9mm and d dr = 6mm were chosen. These values were determined experimentally and tend to give good results in RECD prediction without systematic over- or underestimation. Half T-Section Ear Canal Model (M3) Method M3 models the ear canal using a half T-Section element consisting of an acoustic mass L, an acoustic resistance R and an acoustic compliance C, acting as a series resonant circuit. With e 22 = 1, the calculation of the estimated transfer impedance is simplified to Ẑ trans,ec = Z ec (R + jωl). (12) The acoustic mass of a tube segment with length l and cross sectional area S is given by L = ϱ l S. (13) The length of the model is again estimated from the λ/4 resonance of the measured input impedance. As in M1, a diameter of 7.5 mm was choosen. The resistance of this series resonant circuit can be estimated from the absolute bandwidth B of the λ/4 dip, R = 2π L B. (14) Ear Canal Model from Reflectance (M4) Method M4 estimates the ear canal parameters using an optimized variant of the reflectance phase method [2, 4, 5]. Briefly, an ear canal model consisting of 32 lossy circular tube segments of equal length, but varying radius, is adapted to the reflectance measured at the inner face of the ear mold. Since the ear drum behaves nearly rigidly at high frequencies, the corresponding cost function M = khz f =3 khz ( arg { Rec,measured (f ) } arg { R ec,model (f ) }) 2 Rec,measured (f ) (15) considers only frequencies above 3 khz, and therefore, only information which is mainly influenced by the shape of the ear canal. Both the measured and modeled reflectance are computed with respect to the wave impedance of a tube with 7 mm diameter, R ec = Z ec Z w. (16) Z ec + Z w For the calculation of Z ec,model an averaged ear drum model according to [6] is used and partly modified at low frequencies, considering the individual leakage impedance acting in parallel to the ear drum impedance. In contrast to all other methods, the final estimate of Z trans,ec is computed from Z dr, see Eq. 3. Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 4

5 Eight-Parameter Ear Canal Model (M5/M6) In the last two methods, the measured input impedance is fitted to a model which represents both the ear canal and middle ear. The general model structure is shown in Fig. 2. The ear drum impedance is represented by the five-parameter middle ear model according to [7]. In order to model the ear canal, the first variant M5 uses the half T-Section model. In the second variant M6, the ear canal is represented by a lossless tube model, characterized by length and diameter, in combination with a single resistance. Altogether, both models depend on eight parameters each. For the nonlinear fitting process, the complex-valued and frequency-dependent cost function ( Zec,measured (f i ) Z ec,model (x, f i ) ) M(x, f i ) = Zec,model (x, f i ) is used, where x represents the set of eight parameters. The cost function is computed on a logarithmic frequency scale from Hz to 8 khz. In order to make the fit more robust in the presence of leakage, the cost function is weighted with 1/ below 3 Hz and with 1/3 between 3 Hz and 5 Hz. Using MatLab s lsqnonlin function (Optimization Toolbox, the nonlinear least squares problem min M(x) 2 x 2 = min ( M(x, f1 ) 2 + M(x, f 2 ) M(x, f n ) 2) (18) x is solved. Since M(x) is still complex-valued, the sum of both the squared real and imaginary part is minimized. Finally, only the ear canal model is used for estimating the transfer impedance from Z ec. (17) L 3 R 3 L 2 L 1 R 1 R 3 L 2 L 1 R 1 C 3 C 2 C 1 ( ) e11 e 12 e 21 e 22 C 2 C 1 FIGURE 2: Model framework of methods M5 (left) and M6 (right). In M5 the ear canal is represented by a half T-Section model, while M6 uses a lossless tube model im combination with a resistance R 3. RECD PREDICTION APPLIED TO SIMULATED DATA In this section, the six prediction methods are analyzed with the help of simulated hearing aid couplings. The general model structure of the simulations corresponds to Fig. 1. The source was modeled using a two-port model of a Sonion E5D hearing aid receiver, based on a SPICE model of the manufacturer, in series with a short tube of 5 mm in length, 1 mm in diameter and modeled as suggested in [3]. The dimensions of the tube correspond to a typical ITC 1 hearing aid device. In order to model the ear canal, 15 different radius functions from [8] were used. As suggested in [9], the inner 4 mm of the simulated ear canals were modeled as a small volume in parallel to the ear drum impedance. The length of the models was limited to an approximated position between the first and second bend of the ear canal and ranged from 11.6 to 15.7 mm. The ear canals were terminated by an average ear drum model proposed in [6]. Furthermore, no leakage or venting was considered. For each simulated hearing aid coupling, the simulated input impedance Z ec was used to predict the corresponding RECD. Subsequently, the predicted RECDs were compared to the simulated RECDs. Fig. 3 shows the resulting prediction errors for all six methods. It appears that 1 in the canal Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 5

6 M4 and M6 achieve the best performance with absolute errors below 1 db for frequencies up to 6 khz. At higher frequencies the absolute error increases, but remains within the ±5 db range with only a few exceptions. The error of M1 and M2 exhibits more variance above 2 khz, but still remains inside the ±5 db range in almost all cases. M3 tends to overestimate the RECD between 3 and 7 khz. Above 7 khz, both M3 and M5 result in absolute errors of up to 2 db. Apparently, these two methods cannot model the ear canal sufficiently, since the half T-Section model creates only one single resonance. Predicted re. simulated RECD in db M1 M and.9 quantiles 1k k 1k k 1k k FIGURE 3: RECD prediction errors of the simulated data for all six methods. Black lines indicate the.1 and.9 quantiles, gray shaded areas represent the range of ±5dB. M2 M M3 M6 In ear canal impedance measurements, one common error is an inaccurate estimate of the λ/4 resonance. To investigate the effect of such measurement errors on RECD prediction, we modified the length of the ear canal models by ±4mm to create a shifted λ/4 resonance. At the same time we rescaled the cross sectional area of the models to maintain a constant ear canal volume. RECD prediction based on the input impedance of the modified ear canal models was performed. Afterwards, the predicted RECDs were compared to the simulated RECDs of the non modified ear canal models. The corresponding prediction errors can be seen in Fig. 4. At frequencies above 6 khz, an overestimated ear canal length tends to results in a higher RECD prediction compared to the originally predicted RECD and vice versa. At lower frequencies, the prediction error is nearly unaffected. Predicted re. simulated RECD in db M1 M Original EC length EC length + 4mm EC length 4mm 1k k 1k k 1k k FIGURE 4: RECD prediction errors of the simulated data with modified ear canal lengths, averaged in bark bands. Error bars represent standard deviations. M2 M M3 M6 Next, we analyzed the performance for extra small and large ear canal volumes. To this end, we doubled and halved the volume of the ear canal models by rescaling the cross sectional areas, without shifting the λ/4 resonance. The resulting prediction errors are shown in Fig. 5. For M4 to M6 the ear canal volume has nearly no effect on the prediction error. Since M1 to M3 assume a constant ear canal diameter, the corresponding errors increase for small and large ear canal Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 6

7 models at high frequencies. Thus, these methods are expected to perform worse for extreme ear canal sizes in practice. Predicted re. simulated RECD in db M1 M Original EC volume Half EC volume Double EC volume 1k k 1k k 1k k FIGURE 5: RECD prediction errors of the simulated data with modified ear canal volumes, averaged in bark bands. Error bars represent standard deviations. M2 M M3 M6 RECD PREDICTION APPLIED TO REAL EAR MEASUREMENTS In this section, the performance of the six RECD prediction methods is evaluated using real ear measurements which were originally used in [4, 5]. This data contains measurements of p dr and Z ec for 2 ears with ear molds and for 28 ears with vented ear molds. Unfortunately, no 2cc-coupler measurements, and therefore, no RECDs are included in the data. But since several measurements were performed with the receiver coupled to rigidly terminated tubes of different length (for source model calibration), we used these as a coupler-reference instead. The two largest tubes, both 4.8 mm in diameter, had a length of 52.5 mm and 12.5 mm. The corresponding volumes were.95cm 3 and.23cm 3, respectively. In general, for comparing measured and estimated RECDs, the choice of the reference measurement (e.g. in the 2cc-coupler) is not crucial, as long as the impedance of the reference system is small compared to the source impedance. Therefore, at low frequencies we used the larger tube as a coupler-reference due to its smaller input impedance. At high frequencies above 2 khz, the impedance of the larger tube is no longer small, due to its resonances. Thus, we used the smaller tube at high frequencies instead. In Figure 6, the RECD prediction errors of all methods are shown for and ear molds separately. First of all, it can be seen that below 5 Hz the prediction errors are considerably high for all methods. Since the transfer impedance equals the input impedance at low frequencies, these errors are probably not caused by the prediction methods themselves. Potential reasons are the poor signal-to-noise-ratio at low frequencies, especially for vented ear molds, and the difference of leakage between the measurements of Z ec and p dr. In the mid-frequency range, all methods perform similarly. However, M4 exhibits slightly more variance for ear molds. At high frequencies above 6 khz, methods M3 and M5 perform worst, which was already expected from the simulation results. To give a more comprehensible overview of the prediction performance, the mean absolute error of each method was calculated in different frequency bands by averaging the absolute dbvalues of the prediction errors along a logarithmic halftone spaced frequency scale. The results are given in Tab. 1. It can be seen that methods M1, M2 and M6 give the best performance with mean absolute errors ranging from 2. db to 2.6 db between 2 khz and 5 khz. For lower and higher frequencies, the mean absolute error is still smaller than 4 db. Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 7

8 Predicted re. measured RECD in db Predicted re. measured RECD in db M M k k 1k k 1k k M4 M5 M k k 1k k 1k k FIGURE 6: RECD prediction errors of all six methods, displayed for and ear molds separately. For frequencies below 2 khz, marked by the black dashed line, the RECDs were calculated with respect to the larger tube and for frequencies above with respect to the smaller tube. Black solid lines indicate the.1 and.9 quantiles, gray shaded areas represent the range of ±5dB M3 TABLE 1: Mean absolute error of all six methods for different frequency ranges. The values were calculated by averaging the absolute db-values of the prediction errors along a logarithmic halftone spaced frequency scale. Method Hz to 2 khz 2 khz to 5 khz 5 khz to 7 khz M1 3.3 db 3.6 db 2. db 2.4 db 3.4 db 3.2 db M2 3.3 db 3.6 db 2.1 db 2.6 db 3.1 db 3.2 db M3 3.4 db 3.7 db 2.4 db 2.8 db 4.8 db 4.4 db M4 6. db 3.2 db 5.3 db 2.6 db 4.6 db 3. db M5 3.4 db 3.3 db 2.3 db 2.6 db 4. db 4.6 db M6 3.3 db 3.9 db 2.1 db 2.5 db 3.2 db 2.9 db DISCUSSION The results of the RECD prediction on real ear measurements revealed methods M1, M2 and M6 to perform best in the frequency range from Hz to 7 khz. Considering the complexity of the different methods, M1 and M2 give the best compromise between effort and accuracy, since M6 is based on a rather complex nonlinear fitting process. Comparing the different approaches of estimating the ear canal transfer impedance, the methods can be divided into two groups. M4 estimates a complex ear canal model and calculates the transfer impedance using an averaged ear drum model, while the other methods calculate the transfer impedance from the measured input impedance using a rather simple ear canal estimate. In the latter case, the individuality Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 8

9 is given by the ear drum impedance, which is contained in the estimated transfer impedance. In this research and in the frequency range considered, the second approach performs better. Furthermore, this approach is of advantage because the leakage impedance is contained in the ear canal input impedance, and thus, does not need to be estimated separately. CONCLUSION Six different methods for predicting individual RECDs, based on acoustic impedance measurements at the inner face of the ear mold, were compared to each other. Simulations showed that all methods are affected similarly by an inaccurate estimate of the ear canal length. Furthermore, when dealing with extra small and large ear canals, the methods which do not estimate an individual ear canal diameter are affected negatively. The evaluation on real ear measurements showed that relatively simple cylindrical and conical ear canal models yield the best compromise between effort and accuracy. ACKNOWLEDGMENTS This research was partly funded by Phonak AG Stäfa (Switzerland) and by Deutsche Forschungsgemeinschaft (DFG research unit FOR 1732 Individualized Hearing Acoustics). REFERENCES [1] H. Dillon, Hearing aids (Boomerang Press, Turramurra) (21). [2] M. Blau, T. Sankowsky, P. Roeske, H. Mojallal, M. Teschner, and C. Thiele, Prediction of the sound pressure at the ear drum in occluded human cadaver ears, Acta Acustica united with Acustica 96, (2). [3] D. H. Keefe, Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions, The Journal of the Acoustical Society of America 75, (1984). [4] T. Sankowsky-Rothe, M. Blau, E. Rasumow, H. Mojallal, M. Teschner, and C. Thiele, Prediction of the sound pressure at the ear drum in occluded human ears, Acta Acustica united with Acustica 97, (211). [5] T. Sankowsky-Rothe, M. Blau, H. Mojallal, M. Teschner, and C. Thiele, Prediction of the sound pressure at the ear drum for fittings, in Proceedings of the Acoustics 212 Nantes Conference, (212). [6] H. Hudde and A. Engel, Measuring and Modeling Basic Properties of the Human Middle Ear and Ear Canal. Part III: Eardrum Impedances, Transfer Functions and Model Calculations, Acta Acustica united with Acustica 84, (1998). [7] A. Stirnemann, Impedanzmessungen und Netzwerkmodell zur Ermittlung der Übertragungseigenschaften des Mittelohres, dissertation, ETH Zürich (198). [8] M. R. Stinson and B. W. Lawton, Specification of the geometry of the human ear canal for the prediction of sound-pressure level distribution, The Journal of the Acoustical Society of America 85, (1989). [9] H. Hudde, A. Engel, and A. Lodwig, Methods for estimating the sound pressure at the eardrum, The Journal of the Acoustical Society of America 6, (1999). Proceedings of Meetings on Acoustics, Vol. 19, 396 (213) Page 9