Improving the Performance of Hearing Aids Using AcousticSimulation

Mads Jakob Herring JensenWidex A/SNy Vestergaardsvej 25, DK-3500 Denmark, mjj@widex.dk

Abstract: In modern hearing aids, the per-formance of directional microphone systems isdependent on both the acoustics around thehearing aid and on the specific signal process-ing algorithms. The sound pressure at the mi-crophone inlets depends on microphone loca-tion in the hearing-aid shell, the inlet shape,and on the placement of the hearing aid on thehead of the user.

In the present work, the directional charac-teristics of a specific hearing aid is modeled infree field as well as placed on a head. The nu-merical results are also compared to measureddata for validation. The acoustic equations areimplemented using the general PDE formula-tion capabilities of Comsol [1]. The model en-ables systematic studies of both the free-fielddirectional characteristics and the true (realworld) characteristics of the hearing aid on ahead. The results may be applied in the earlydesign phase of new hearing aids. Further-more, it may be used for optimizing the per-formance of directional noise reduction algo-rithms for specific hearing-aid geometries.

Keywords: Acoustics, hearing aid, PML

1 Introduction

Finite element (FE) modeling, in Comsol, isused for many aspects when designing a hear-ing aid (HA). This may be when (1) analyz-ing feedback mechanism (mechanical and/oracoustic), e.g., see Ref. [7], (2) characterizingthe acoustic properties of new elements for usein a lumped parameter model, (3) studyingthe properties of microphones and/or receivers(miniature loudspeakers), e.g., see Ref. [6], or(4) when characterizing the acoustic interac-tion of the HA with incoming sound waves (infree field or when placed on a head). Thispaper is restricted to the latter and is con-cerned with aspects of the directional system(as mentioned in the abstract). The governing

equations, boundary conditions, and compu-tational domains are firstly introduced. Sec-ondly, we model the head related transfer func-tions of the KEMAR and compare to exper-iments. This serves as a test of the model.Thirdly, we shortly discuss what a directionalsystem is. Then, the case of a HA in free fieldis presented. In the sixth section we study thecase of a HA placed on a KEMAR head. Fi-nally, conclusions are given.

ΩΩ Ω

Ω Ω ∂Ω

∂ΩFigure 1: Sketch of the computational domain

including boundary and domain labels.

2 System and GoverningEquations

In the present work we study the acousticsaround a rigid object. This is either a hearingaid, a KEMAR manikin head, or a hearing aidplaced on a KEMAR. A sketch of the system isgiven in Fig. 1, where the label ”geom” repre-sents an arbitrary solid geometry. Around thegeometry we have the computational domain(light blue) consisting of an acoustic domain∂Ωll and ∂Ωtvf, and a perfectly matched layer(PML) domain ∂Ωpml (dark blue) to model the

Excerpt from the Proceedings of the COMSOL Conference 2009 Milan

open boundary.The geometry of the hearing aid and the

KEMAR is complex. In order for them to beimported into Comsol they have been cut inhalf, as illustrated by the dotted line in Fig. 1.This prevents confusion between ”inside” and”outside” when importing the geometry. Thetwo halves of the system are coupled on ∂Ωid

using an identity pair condition. Moreover,the PML is also coupled to the computationaldomain using an identity pair condition. Inthis way different meshes may be used in thedifferent domains.

The acoustic domain is further divided intotwo areas, a lossless domain Ωll and a lossy do-main Ωtvf where thermal and viscous losses areaccounted for. In the lossless domain we solvethe classical Helmholtz equation

∇2P + k2P = 0, (1)

where P is the acoustic pressure, k = ω/c thewave number, c the speed of sound, and ωthe angular frequency. In the lossy domain wesolve for the pressure p, velocity u = (u, v, w),and temperature T . The lossy acoustics areonly applied in regions where dimensions arecomparable to the viscous boundary layer,e.g., in microphone inlets on a hearing aid(they are 1 mm in diameter). Details of thethermo-viscous acoustic equations and of thePML are found in Refs. [7, 2, 3, 8].

On the solid surface of the hearing aid andthe KEMAR head we have used sound hardwalls

n · ∇P = 0, (2)

where n is the outward normal to the sur-face. The lossless and lossy acoustics are cou-pled by specifying continuity of normal stressand deformation using a weak constraint. Thegoverning equations (acoustics and PML) andboundary conditions are implemented in weakform using the general PDE formulation inComsol. Finally, because we are also inter-ested in the acoustic pressure in the far fielda Helmholtz-Kirchhoff (H-K) convolution inte-gral element has been defined on the boundary∂ΩHK. In this regards it is nice to have the ge-ometries defined in an assembly as the surfacenormals then are well defined. The element isdefined in the fem structure as:

el.elem=’elkernel’;

el.g=’1’;

el.name=’Pff’;

el.kernel=’helmholtz3D’;

el.iorder=’10’;

el.k=num2str(k);

el.symflags=’0’,’0’,’0’;

src.ind=bnd_el;

src.srcn=’-nx’,’-ny’,’-nz’;

src.srcu=’P’;

src.srcnux=’-nx*Px-ny*Py-nz*Pz’;

el.geomdim1=,,src;

fem.elem=el;

3 Head related transfer functionsof KEMAR manikin

The FE model is firstly tested on a knownsystem where measurements are readily ac-cessible. The head related transfer functions(HRTFs) of the KEMAR manikin are modeledand compared to experimental measurements.The HRTF describes how a given sound waveinput is filtered by the diffraction and reflec-tion properties of the head, pinna, and torso,before the sound reaches the eardrum. Theboundary mesh on the KEMAR manikin headis depicted in Fig. 2. The HRTF H is thetransfer function from a source/point in spaceto the eardrum

H = H(x, f) = 20 log(|P (x, f)/Ped(f)|), (3)

where Ped is the pressure at the eardrum, andx is the given point in space.

Figure 2: Boundary mesh on the KEMARmanikin.

In order to computationally efficiently de-termine the HRTFs we use the reciprocityprinciple [5, 4]. This means that we inter-change the source at x with the eardrum (mea-surement point). In doing so we get the HRTFfor all points in space for a given frequencyin one run. To get the HRTF values outsidethe computational domain (radius > 50 cm)

we apply the H-K convolution integral. Mea-surements and model results are compared inFig. 3. The HRTFs are depicted for x in thehorizontal plane that goes through the cen-ter point between the ears. From the graphswe see good agreement between measurementsand model. In the next sections the directionalpatterns of hearing aids are studied.

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Figure 3: HRTFs of the KEMAR manikin in the horizontal plane with center between the ears. At adistance of 100 cm measurements are given as circles and model results as a blue solid line. The red solid

line represents the HRTF at a distance of 20 cm. Front is towards −90o.

4 Directional patterns of hearingaids

Most modern hearing aids (HAs) have two mi-crophones, which enables spatial filtering ofsounds. The simplest linear combination ofthe front (f) and back (b) microphone signalsis the omnidirectional (omni) Ho and figure-

eight or bidirectional (bidir) Hb spatial re-sponse,

Ho = Ho(x, ω) = Pf + Pb (4)Hb = Hb(x, ω) = Pf − Pb (5)

where P is the pressure at the microphone.In the following we will study these two sim-ple spatial responses. In actual HAs complex

adaptive signal processing algorithms combinethe two signals in order to filter out, e.g., spa-tially localized noise sources. In order to op-timize the directional algorithms it is impor-tant to study variations in the shape of theresponse H. This shape is dependent on thegeometry of the HA, on head shape, and onthe placement of the HA on the ear. Direc-tional patterns are often only measured in oneplane, whereas, a FE simulation yields the full3D spatial response. Moreover, it is possible,with a FE model, to simulate the response ofnew HA geometries which still only exist asCAD figures on the computers of the mechan-ical designers.

5 Hearing aid in free field

Standard benchmark measurements on HAsinclude the directional response in free field,when isolated from other interfering objects(geometries). The geometry of the HA usedhere is given in Fig. 4.

Figure 4: Geometry of the Widex Inteo IN-mhearing aid including the microphone inlets.

The omni and bidir spatial response at5000 Hz of the HA is depicted in Fig. 5.The model results are compared to experimen-tal measurements and show good agreement.These results are also obtained using the reci-procity principle, i.e., numerically the micro-phone membranes are the sources of the sound.

In certain cases the design of the HA micro-phone system, e.g., inlet shape, require detailsof the pressure in the near field for a given in-cident wave. Here reciprocity is not applicablebut it is necessary to solve the exact problem.This may be done by utilizing the linearity ofthe governing equations [9]. Splitting the pres-sure into an incoming (i) and a scattered (s)

wave it applies that

P = Ps + Pi = Ps + exp(k · x) (6)

where, in this case, the incident wave is a planewave with direction k. The dependent variableto solve for is then Ps. Note that we operatein the Fourier frequency domain. An exampleof the pressure field around the HA is given inFig. 6 for a plane wave incident from the front.

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Figure 5: Omni (red) and bidir (blue) response ofthe HA at f = 5000 Hz. Circle markers representmeasurements and the solid line the FE results.

Figure 6: Sound pressure distribution around theHA for f = 5000 Hz. A plane wave is incident

from the front (along the x-axis).

6 Hearing aid on KEMAR manikin

When the HA is placed on a head the charac-teristic free-field directional patterns are dis-torted. To illustrate this effect, the directionalpatterns for the HA placed on the KEMARhead are modeled. An example of the CADgeometry is shown in Fig. 7. The calculatedomni and bidir characteristics are plotted for

two frequencies in Fig. 8 and compared to theideal free-field case. The curves are obviouslydistorted, compared to the free-field case, butwe note that they maintain their character-istic shapes. In the omni case we see thehead shadow effect as a decrease in Ho for thedirections coming from the head side (−60o

to 60o, the shadow side). However, in thebidir case, where the two microphone signalsare subtracted, it seems that a source to theshadow side of the head is better heard forregions next to the notch. The two notchesin the bidir characteristic are preserved eventhough they are either distorted or less pro-nounced. Generally, the figure-eight shape isskewed and rotated when the HA is placed onthe head. For sounds coming from the front

(−90o) we see that there are no changes com-pared to the ideal free-field case.

Figure 7: CAD drawing of the hearing aid placedon the KEMAR manikin head.

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Figure 8: Comparison of the free-field (solid blue line) and the on-the-head (red line with dots) directionalcharacteristics for the HA at a distance of 200 cm. The HA is located on the right ear (±180o) and front is

towards −90o.

7 Conclusion

This study has served as a validation of theComsol finite-element (FE) model used for de-termining characteristic directional patterns ofhearing aids. We have seen good agreementbetween model results and measurements inthe case of free-field measurements and whenstudying HRTFs of the KEMAR head. Fi-nally, we have used the FE model to investi-gate the case when the hearing aid is placedon a head. Here the directional patterns getdistorted due to head and ear. The model en-ables us to study the sound field around thehearing aid both locally and in the far field.In this way, we may characterize the hearingaid geometry (including microphone inlets) interms of directional patterns. Hence, the FEtool allows for early characterization of the di-rectional response of new hearing aid geome-tries, based on the CAD drawings of the hear-ing aids. We may also study proximity effectsof the directional patterns or even optimize thehearing aid geometry and microphone inlets.Knowledge of the real ”distorted” directionalpatterns may be used for optimizing the per-formance of the directional noise reduction al-gorithms.

References

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