19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 27 THE SOUND FIELD IN AN EAR CANAL OCCLUDED BY A HEARING AID PACS: 43.66.Ts, 43.64.Ha, 43.38.Kb, 43.2.Mv Stinson, Michael R.; Daigle, Gilles A. Institute for Microstructural Sciences, National Research Council, Ottawa, Ontario K1A R6, Canada; mike.stinson@nrc-cnrc.gc.ca ABSTRACT The spatial variations of sound pressure inside the human ear canal are being investigated experimentally and theoretically. The three-dimensional interior sound field is calculated using a boundary element method (BEM) that accounts for the geometry of the ear canal and the acoustical boundary conditions presented by the eardrum and the hearing aid. Benchmark tests with real ear canal geometries demonstrate that the BEM approach predicts the same longitudinal variations as the analytic Webster horn equation, but the BEM approach also reveals transverse variations that the horn equation cannot. A simple model ear canal has been investigated experimentally. The canal was cylindrical, 7.5 mm diameter, and terminated with a Zwislocki coupler to represent absorption by the human middle ear; the outer end of the canal was driven by a test hearing aid fixture. The sound field inside the canal was measured using a specially-designed.2 mm o.d. probe microphone. Large transverse variations of sound pressure level, as much as 25 db at 8 khz, were found across the inner face of the hearing aid, particularly near the receiver and vent ports. The results are consistent with numerical calculations. Currently, this research is being extended to life-size ear canal replicas. INTRODUCTION The performance of hearing aids is dependent on the acoustical properties of the human ear canal. Our research is aimed at understanding these properties, experimentally and numerically, and their implications for feedback reduction and control of the acoustical input at the eardrum. At low frequencies, the ear canal can be treated simply as a compliant volume, but, as frequency increases, there will be longitudinal standing waves, increased dependence on the geometry of the ear canal [1], and transverse effects [2]. Ryan et al. [3] have been suggested that a second inner microphone in a hearing aid could be used to reduce the occlusion effect a detailed knowledge of the sound pressure variations in the vicinity of the inner face of the hearing aid would be needed. NUMERICAL APPROACH Previous work [1] has shown that a pseudo-one-dimensional approach can be applied to compute sound fields in ear canals, accounting for the curvature of the canal and the varying cross-sectional area along its length. This modified horn equation approach treats the sound pressure as being constant within transverse slices normal to a curved central axis. For an ear canal occluded by a hearing aid, though, large variations of pressure through transverse slices near the inner face of the hearing aid are anticipated [4]. A modelling approach that computes the full three-dimensional sound field is required. In our modelling, we are applying the boundary element method (BEM), making use of the SYSNOISE computational bundle. An example [5] of a BEM calculation is shown in Fig. 1. The geometry is based on a human ear canal. A uniform velocity excitation was assumed across the entrance plane (toward the bottom of the figure) at a frequency of 9 khz and, for this example, the eardrum (toward the top) assumed rigid. The colour plot shows the sound pressure over the mesh elements that define the surface of the ear canal. A longitudinal standing wave pattern, with alternating maxima and minima of sound pressure, is observed that follows the canal centre axis. The model mesh contains approximately 2 triangular elements, each 1 mm on a side; this resolution permits reliable BEM calculations up to frequencies of 2 khz, if desired.
Figure 1.-Numerical calculation of the sound field in a human ear canal, for a uniform velocity excitation across the canal entrance. The sound pressure at interior points within the canal can also be obtained with the BEM method. In particular, the sound pressure along the centre axis of the canal may be calculated. In Fig. 2, this longitudinal pressure distribution is shown (solid curve) for the same ear canal as in Fig. 1 but with the mesh elements representing the eardrum assigned an acoustical admittance, to provide acoustical absorption at this position. The alternating maxima and minima are apparent, as frequency increases, but the depth of the minima is limited by the absorption. For the same ear canal system, the modified horn equation was also used to calculate the longitudinal pressure distribution. This is shown by the dashed curves in Fig. 2. The agreement with the BEM calculation is very good. The one-dimensional horn equation approach is simpler and may be applied in many cases. However, for cases where transverse variations of sound pressure might arise, the BEM approach is necessary and available for use. Sound pressure magnitude (Pa) 6 4 2 15 5 8 6 (a) 2 khz 1-D horn equation 3-D BEM calculation (b) 6 khz (c) 15 khz Figure 2.-The sound pressure distribution along the length of an ear canal, calculated using two different approaches. 2 4 2 5 1 15 2 25 3 35 Position s (mm) 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID
SOUND PRESSURE MEASUREMENTS Measurements are performed on model ear canals of various geometries and complexities. For some of these canals, very large variations of sound pressure can occur over small distances, e.g., 1 or 2 mm. To determine these variations with accuracy, the measurement probe must be considerably smaller than the 1.2 mm of a typical microphone probe. We have developed a microprobe with an outside diameter of.2 mm [6]. It has a flat (within 5 db) frequency response and a sensitivity of about 2µV/Pa. A photograph of the microprobe is shown in Fig. 3. Figure 3.-The microprobe used for measurement inside models of the ear canal, indicated by the arrow. It has a diameter of 2µm, much smaller than the ½-in. microphone and 1.2 mm probe tube also shown. For measurement of sound pressure inside a model canal, the microprobe is inserted through small access holes drilled through the wall of the canal. The microprobe length of 5 mm limits the depth of insertion, and access from multiple directions is sometimes necessary to get adequate coverage. MODEL CANAL AND HEARING AID TEST FIXTURE The sketch in Fig. 4(a) shows the system being considered. A hearing aid occludes the ear canal. It has an external microphone, a receiver that emits sound into the ear canal, and circuitry in between that will not be considered here. A vent is generally required to reduce the occlusion effect. We have also included an inner microphone which has been suggested as a means for reducing the occlusion effect [3]. In an initial series of measurements, we wanted to assess the magnitude of transverse variations in sound pressure. A simple model canal, straight and with uniform circular cross section was chosen. Panel (b) in Fig. 4 shows this model canal. (a) (b) mic. vent receiver inner mic. eardrum test fixture receiver vent inner mic. microprobe holes middle canal model canal Zwislocki coupler Etymotic mic. Figure 4.-Sketch of (a) ear canal occluded by a hearing aid and (b) the model ear canal and hearing aid test fixture 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 3
The Zwislocki coupler introduces an acoustic impedance that is comparable to that of the human auditory system. The impedance of both the coupler and the terminating microphone were determined in subsidiary experiments and used as input for the numerical calculations. A test fixture represents the hearing aid. It is a stainless steel plug that fits smoothly into the model canal; it contains receiver, vent and inner microphone, arranged in a triangle configuration. The impedance presented by the vent was calculated [4]. Holes on the side of the model canal provide access for the microprobe. The sound pressure distribution in this model canal is shown in Fig. 5, for frequencies of 2, 4 and 8 khz. The symbols correspond to measurements, the curves to BEM calculations. 11 (a) large vent, 2 Hz 11 (a) large vent, 2 Hz 15 15 5 5-5 2 4 6 8 1 12 14 16 18-5 -4-3 -2-1 1 2 3 4 Longitudinal position z (mm) Transverse position t r, across receiver (mm) 11 15 (b) 4 Hz 11 15 (b) 4 Hz 95 95 9 15 9 15 5, center z axis, through microphone, through vent, through receiver lumped-element model 5, z =.15 mm, z =.7 mm, z = 1.7 mm, z = 2.7 mm -5 2 4 6 8 1 12 14 16 18 Longitudinal position z (mm) -5-4 -3-2 -1 1 2 3 4 Transverse position t r, across receiver (mm) 9 (c) 8 Hz 95 9 (c) 8 Hz 8 7 5-5 - -15-2 2 4 6 8 1 12 14 16 18 Longitudinal position z (mm) 85 8 75 5-5 - -4-3 -2-1 1 2 3 4 Transverse position t r, across receiver (mm) Figure 5.-Sound pressure distribution in the model canal. The panels on the left show the longitudinal variations, the panels on the right show variations in sound pressure along transverse trajectories. 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 4
For the longitudinal case, we present results along four parallel lines, one being the centre axis of the canal, the others passing through the receiver, vent and inner microphone. At distances of 4 mm or more from the hearing aid test fixture, all results are essentially the same and show a one-dimensional standing wave pattern. The dotted curve on the plots is calculated using the modified horn equation approach, treating the various impedances as lumped elements. This simple calculation agrees with measurements and BEM calculations away from the hearing aid, except for 8 khz for which the vent (2.2 mm diameter) has a resonance and hence low impedance. Near the hearing aid, though, the sets of results are quite different for different transverse positions, showing large differences. The transverse variations are examined more explicitly in the panels on the right side of Fig. 5, showing SPL along transverse paths normal to the centre axis and across the receiver position. For each frequency, the four sets of results correspond to paths that are.15 mm,.7 mm, 1.7 mm and 2.7 mm away from the face of the hearing aid test fixture. The transverse variations are significant, as much as 4 db at 2 khz, 15 db at 4 khz, and 2 db at 8 khz for the path closest to the test fixture. REPLICA EAR CANALS Our current research aims to extend the previous measurements to realistic life-size ear canal geometries. Replica ear canals have been constructed, based on previous determinations of ear canal geometry [7], using a SLA technique. The design file for one such replica is shown in Fig. 6. Once the replica canal has been fabricated, small holes are drilled through the 1 mm thick wall to provide access for the microprobe. The hearing aid test fixture used in the model canal experiments plugs in to the entrance of the canal. Figure 6.-Ear canal replica, meshed for SLA fabrication and numerical calculation. For calculation of the interior sound field, the replica mesh elements that comprise the inner canal surface are used, along with a detailed meshing of the inner face of the hearing aid test fixture. A sample calculation for one replica ear canal is shown in Fig. 7, showing the sound pressure on the canal wall as a colour plot for a frequency of 8 khz. The mesh elements corresponding to the receiver port have been given a constant velocity, the elements comprising the vent and inner microphone have been assigned appropriate specific impedances, and a rigid eardrum has been assumed. Along most of the ear canal, the sound field is approximately longitudinal, following the curvature of the centre axis. Near the entrance, at the inner face of the occluding hearing aid, there are large transverse effects. Higher sound pressures (red) are evident for and 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 5
near the elements that represent the receiver port, and (at this frequency) lower sound pressures (blue) are evident near the elements representing the vent. Figure 7.-Computed sound field on ear canal wall in replica #3, with the inner face of the hearing aid test fixture (downward, in this view) forming the canal entrance. CONCLUSIONS The sound field in the human ear canal has been shown, experimentally and numerically, to be quite complex, particularly at higher frequencies. Longitudinal standing wave patterns along most of the canal are evident above 2 khz. These can be described using a one-dimensional modified horn equation. In the vicinity of the inner face of an occluding hearing aid, large transverse variations arise, as much as 2 db variation across the face of the hearing aid. The use of a.2 mm microprobe was critical in resolving these variations. Computationally, it is necessary to use a technique such as the boundary element method to obtain the full threedimensional sound field. These spatial sound pressure variations are important to the understanding of the acoustical input delivered to the eardrum and the mechanism of acoustic feedback in hearing aids. If a second inner microphone can be used for the reduction of the occlusion effect [3], the large variations of SPL in the vicinity of the hearing aid inner face will need to be accommodated. References: [1] S. M. Khanna, M. R. Stinson: Specification of the acoustical input to the ear at high frequencies. Journal of the Acoustical Society of America 77 (1985) 577 589 [2] M. D. Burkhard, R. M. Sachs: Sound pressure in insert earphone couplers and real ears. Journal of Speech and Hearing Research 2 (1977) 799-87 [3] J. G. Ryan, B. Rule, S. W. Armstrong: Reducing the occlusion effect with active noise control. Journal of the Acoustical Society of America 119 (26) 3385 [4] M. R. Stinson, G. A. Daigle: Transverse pressure distributions in a simple model ear canal occluded by a hearing aid test fixture. Accepted for Journal of the Acoustical Society of America 121 (27) [5] M. R. Stinson, G. A. Daigle: Comparison of an analytic horn equation approach and a boundary element method for the calculation of sound fields in the human ear canal. Journal of the Acoustical Society of America 118 (25) 245-2411 [6] G. A. Daigle, M. R. Stinson: Design and performance of a microprobe attachment for a ½-in. microphone. Journal of the Acoustical Society of America 12 (26) 186-191 [7] M. R. Stinson, B. W. Lawton: Specifications of the geometry of the human ear canal for the prediction of soundpressure level distribution. Journal of the Acoustical Society of America 85 (1989) 2492-253 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 6