c©2014-TU Ilmenau

AN EAR-PINNA ACOUSTIC ANALYSIS COUPLED WITH AN EAR-CANALEMULATOR 711

E. Bances1, T. Schmidt2, T. Helbig1 , H. Witte1

1 Department of Biomechatronics, Ilmenau University of Technology. Germany

2 Department of Otolaryngology, University Hospital Jena. Germany

ABSTRACT

Simulations of the pressure on the pinna are sig-nificant contributions to the continuous improvementof hearing aids devices, i.e. they help to improve thereception of sound coming from different directions.Other interesting results are those that arise from anal-yses of the ear canal, leading to the implementation ofear-canal emulators, which mirror the acoustic behav-ior of the human ear. Analyses of the distribution ofinstantaneous pressure in the pinna and the ear canalallows better understanding, how the human auditorysystem behaves under sounds from various directions.In the present work, we present an ear pinna model cou-pled with an ear canal emulator, to understand how thepressure is distributed in the model covering the humanhearing range of 20Hz-20Khz. Comsol Multiphysics4.3 and its acoustic module in the frequency domainwere used to analyze two different cases: when thesound source comes from the lateral plane of the pinnaand when it comes from the dorsal plane.In each casethe eardrum sound perception (pressure distribution) atdifferent frequencies was studied.

Index Terms— Acoustic, Ear Canal, Pinna Simu-lation, Emulator 711 coupler, Comsol-Acoustic.

1. INTRODUCTION

Several studies based on finite element method / vol-ume methods are used to analyze auditory system inhuman being. Hudde [2009] e.g. used a box enclosingthe pinna to elucidate the characteristics of the ear canalsound field, and to identify the limits of unidimensionalapproaches using fundamental modes. Takemoto [2010]studied the reflection and diffraction by head and pinnain order to locate the sound source in three dimensionalspace. Moreover, he developed an acoustic simulatorbased on finite-difference time-domain (FDTD) methodthat can visualize temporal changes in the acoustic field(pressure distribution) and particle velocity. This sim-ulation proved to have an accuracy similar to the re-sults taken with a microphone, used to measure in par-

allel the sound pressure changes at a certain point in thespace. Additionally, Makoto [2010] analyzed the sur-face pressure on the pinna, Head-related transfer func-tion (HRTF) in the time and the frequency domainsusing numerical simulation boundary element method(BEM). His results demonstrate the extent to whichpart of pinna contributes to a production of HRTF spec-tral notches and peaks depending of the source eleva-tion. Other studies are focussed on the evaluation andtesting of ear canal emulator, Comsol [2012] simulatedthe thermoacoustics behavior of the standard coupler711 and its losses using finite elements. The coupler isthe device for measuring the acoustic output of soundsources with a calibrated microphone defined by thestandard IEC 60318-4.

This model describes the pressure wave propaga-tion in an ear-pinna. It refers to an artificial human headcalled Neumann KU80 [1]. The ear-pinna is coupledwith an ear-canal emulator regarding the internationalstandard specifications IEC 60318-4.

In this simulation an ear-pinna box of cubic shapeis considered, which approximates the free space, pro-viding an absorbing volume and using the walls of thebox as external sound sources from different directions.

The simulation of the complete model was done inComsol Mutiphysics 4.3 and the frequency simulationrange covers 20Hz to 20Khz,the human hearing range.

The purpose in this simulation is to show how isthe pressure distribution along the pinna surface andwithin the ear canal,as well as analyze and take conclu-sion about the behavior or the human hearing system.

2. MODEL DEFINITION

The human ear-pinna model is based on the artificialhead KU80 made by Georg Neumann & Co in 1975[1]. The ear-pinna is covered by a cube used to approx-imate free-field conditions and to implement externalsound fields in the walls. The cube side dimension isa = 80mm, which have been adapted to the shape ofthe head around the pinna. On the other hand, an earcanal emulator (coupler 711) is a commercial device

URN (Paper): urn:nbn:de:gbv:ilm1-2014iwk-159:6 58th ILMENAU SCIENTIFIC COLLOQUIUM Technische Universität Ilmenau, 08 – 12 September 2014

URN: urn:nbn:de:gbv:ilm1-2014iwk:3

based on a standards conditions and intended for mea-surement of hearing aids earphones, and in our casecoupled to the pinna. Finally the complete model wasdesign using Solidworks 3D-Cad software. Consecu-tively, all the parts were assembled and the model wasimported by Comsol multiphysics, to apply finite ele-ment method as is shown in the Figure 2.

As mentioned above, an external sound field actingonto the cube walls is activated by Comsol tools, thisfields come from different directions as the Figure 1shows.

Fig. 1: Ear pinna simulation box

2.1. Geometry

The dimension of the right ear pinna model has the nor-mal characteristic of an adult man, the scanned modelis a replica of the human ear made by Georg NeumannGmbH. Furthermore, the Coupler 711 model based onthe international standard IEC 60318−4 [2] was added,this device measures the acoustic output of sound sourceswith a calibrated microphone, the shape is describedas a cylinder of length L = 12, 5mm and diameterD = 7.5mm and two side volume as rings attachedto the cylinder via slender slits of hight h1 = 69µmand h2 = 170µm. A complete description on the ge-ometry and parameter values could be consulted in thereferences [2] and [3].

The parameters considered in this simulation aregiven in the Table 1. All of them respond to the physi-cal characteristics about the entire model. Furthermore,the simulation considers normal environment param-eters, such as the temperature 20◦C (293.15◦K), thereference pressure for air is 20 [µPa] and the speed ofsound air c = 343[m/s].

Name Value DescriptionmuB0 0[Pa.s] Bulk viscosityTref 20[degC] Reference temperaturesimp 1.6e6[N.s/(m3)] Impedance of skinpref 20e-6[Pa] Reference pressurepin 1[Pa] Pressureedimp 9.4[N.s/m3] Impedance eardrumCmic 0.62e−13[m5/N] Microphone complianceLmic 710[Kg/m4] Microphone massRmic 119e6[N.s/m5] Microphone resistance

Table 1: Simulation parameters

Fig. 2: Pinna & coupler

3. SIMULATION METHOD

The entire model was imported using the CAD import-module LiveLinkTM for Solidworks R© allowing to makeany necessary modification in comsol. The model solvesthe problem in the frequency domain using the time-harmonic Pressure Acoustic interface of Comsol (acpr).

The frequency domain, or time-harmonic formula-tion, uses the inhomogeneous Helmholtz equation:

∇(−1

ρ(∇p− qd))−

ω2.p

ρ.c2= Qm (1)

where:

Keq = (ωc )2 : Waves number

ρ : Density

ω : Angular frequency

c : Speed sound

p : Acoustic pressure

qd : Dipole source [ Nm3 ]

Qm : Monopole source [ 1s2 ]

The Frequency domain interface is designed for theanalysis of various types of pressure acoustics prob-lems in the frequency domain, in our simulation theair is as a transport medium of the sound wave. Themodel describes the pressure-wave propagation in earpinna coupled to the emulator generic 711.

3.1. Boundary Conditions

3.1.1. Sound Hard Boundary (wall)

At the solid boundaries, which are the outer of the earpinna and the ear canal emulator, the interface adds acondition for a sound hard boundary or wall, which isa boundary at which the normal component of the ac-celeration is zero and its specified mathematically by:

∇(−n.1ρ(∇p− qd)) = 0 (2)

3.1.2. Plane wave radiation

This radiation condition allows an outgoing plane waveto leave the modeling domain with minimal reflections,when the angle of incidence is near to normal. In thefirst analysis we used a lateral plane, the ear receivesthe sound wave directly, besides in the second simula-tion the source is in the dorsal plane, the pinna receivesthe wave from the back. The Incident Pressure Field(IRF) for both simulations is of the planar type withthe value of 1[Pa].

3.2. Impedance

The impedance is a generalization of the sound-hardand sound-soft boundary conditions. In this particularmodel, the main impedance taken was the skin impedance,this particular value varies depending on the sample.Furthermore, the air impedance and the microphoneimpedance were added to the model and are specifiedmathematically by:

∇(−n.1ρ(∇p− qd)) = −p.(

iω

Zi) (3)

Zi is the acoustic input impedance of the exter-nal domain and it has the unit of a specific acousticimpedance. From a physical point of view, the acousticinput impedance is the ratio between the local pressureand local normal particle velocity. Z = p

νThe Impedance boundary condition is a good ap-

proximation for a local reaction on the surface, wherethe normal velocity at any point depends only on thepressure at that exact point.

In this model we considered difference impedancesvalues and were taken from different literatures [4], [5].

Skin impedance : 1.6e6[ kgs.m2 ]

Air impedance : 411.6[ kgs.m2 ]

The microphone model Brel & Kjar 4192 has animpedance corresponding to the mechanical propertiesgiven by:

Zmic =1

iωCmic+Rmic + iωLmic (4)

4. RESULTS

The data presented below is the result from two simu-lations. The first one shows the sound pressure distri-bution on the pinna and the coupler 711 within a fre-quency range of (20Hz-20KHz). The external soundsource represented by the box walls, vibrates at dif-ferent frequencies approximating the sound incidencefrom different directions. This means in the first simu-lation the sound source comes from the lateral side, andin the second one from the dorsal side. Each wall is ac-tivated independently in order to achieve best analyses.

The simulation was made using the acoustic mod-ule by Comsol, the pressure analysis in the frequencydomain is governing by the equation of Helmholtz ( 1)and in this particular case, la simulation considers nor-mal environment parameters (see above). The excit-ing sound pressure amplitude is 1[Pa] in each wall.Moreover, other important parameters were considerednamely skin impedance of the pinna, the microphoneand air impedance.

The goal of these simulations was to analyse the be-havior and the sound pressure distribution through thepinna and the ear canal (coupler), considering a deeperunderstanding of characteristic sound field. Further-more is shown the pressure distribution on the micro-phone surface of the coupler, to simulate the eardrumreaction. Finally, the second simulation shows similardata except that the sound pressure source comes fromthe dorsal.

4.1. Lateral Sound Source

The lateral exciting sound source with 1 [Pa] of ampli-tude vibrates at different frequencies, the sound waveapproaches the ear. In the Figure 3, could we takean idea how the sound wave propagation and veloc-ity direction of the particles (red arrows) considerablychange due to the frequencies changes before and afterthe impact with the ear. Indeed, these affects provokedifferent results while the frequency increases (Figure5).

Fig. 3: Sound wave propagation

The average pressure in the pinna at lower frequen-cies, shows an almost constant distribution along themodel such as Figure 4 displays within the model.As shown below, at low frequencies the distribution ofpressure on the pinna is less than 1 Pa. Nevertheless,as the frequency increases the pressure effect within thecoupler undergoes considerable changes, in particularin the cavities of the pinna such as the Tragus or theConcha, besides the eardrum (microphone).

(a) 120 Hz

(b) 5020 Hz

(c) 10020 Hz

(d) 19720 Hz

Fig. 4: Acoustic Pressure Distribution- Lateral Source

Figure 6 shows a cut plane through the middleof the pinna and ear canal. Thus better can be ob-served how the pressure is distributed, moreover thevelocity in different directions where the wave makes

contact with the surface. The pressure in the pinnaalong the frequencies range is quite uniform, oscillat-ing between -0.6 to 0.6 Pa. Furthermore, the pressurein the eardrum (coupler microphone) presents severalchanges oscillating between -19 to 13 Pa, as the Fig-ure 7 shows. Regarding high frequencies, the pressureinside the coupler and the eardrum intensifies and thevelocity is randomly dispersed.

(a) Low frequency

(b) High frequency

Fig. 5: Sound Pressure Level

The figure 6 also displays how the sound wave im-pact on the surface and inside the ear canal.

(a) 120 Hz (b) 5020 Hz

(c)10020 Hz (d)19720 Hz

Fig. 6: Sound pressure distribution and velocity -Lateral Source

(a) Eardrum average pressure

(b) Pinna average Pressure

Fig. 7: Average Pressure Distribution - Lateral Source

4.2. Dorsal Sound Source

In this simulation, the sound incidence plane providesthe wave behind the pinna. The average pressure in thepinna surface has no significant changes compared with

the previous data, at low frequency (<4 KHZ), wherethe pressure ranges from -0.4 to +0.4 Pa, however athigher frequencies (>10kHz), the pressure varies from-0.2 to +0.2 Pa as shown in Figure 8 (b). Regard-ing surface pressure of the microphone, at medium andhigh frequencies changes are significant, due the soundwave impact is not directly into the ear canal (Figure 8(a)).

(a) Eardrum average pressure

(b)Pinna average Pressure

Fig. 8: Average Pressure Distribution - Dorsal Source

4.3. 711 Microphone - eardrum analysis

The pressure distribution level in the microphone of theemulator 711 representing the eardrum using the refer-ence sound pressure in air (pref = 20µPa (rms)) iscalculated by:

Lp = 20 log

(PrmsPref

)[dB] (5)

The results shown below are further evidence of thedifference in pressure distribution due to the directionof the emitted wave (Figure 9).

Fig. 9: Eardrum pressure level - Lateral Source

In dorsal analysis, doing a similar analysis with themicrophone (eardrum), the instantaneous pressure dis-tribution and the sound pressure level decreased con-siderably (Figure 10).

Fig. 10: Eardrum pressure level - Dorsal Source

5. CONCLUSIONS

This study served to simulate the pressure changes onthe ear pinna surface coupled to the ear canal emula-tor, using finite element method. The free field condi-tions was represented by a box surrounding the pinnaand used to implement external sound field from twodirections activated independently, with the advantageof getting a better analysis of the sound pressure andthe effects on the surfaces. To develop an optimal re-sults,the acoustic module of COMSOL Multiphysicswas used to analyze the pressure acoustics problemsin the frequency domain.

In the first approach an external sound field fromthe lateral side was used. The pinna received the wavesound directly, however the average of the pressure onthe surface does not present significant changes alongthe frequency range. Regarding to the values reached

within the ear canal emulator (coupler), the correspond-ing pressure variation in the eardrum reaches values upto 18 [Pa].

On the other hand, when the external sound fieldcomes from the dorsal side, the variation range on thepinna surface does not vary significantly with regardto the previous results, except at high frequencies (>15[kHz]) where the pressure tends to reach the valueof pressure 0 [Pa]. The same phenomena is presentedin within the ear canal, the eardrum pressure at highfrequencies oscillates around 0 [Pa] showing a con-siderable difference compared to the previous analysis,where the pressure at the same frequencies reached val-ues up to 8 [Pa].

The sound velocities in isosurfaces always point inthe direction of propagation. Here the isosurfaces ofpressure magnitude and phase and the wave fronts co-incide. The phase isosurfaces almost exclusively de-pend on the shape of the ear canal and not on frequency.

In this paper, the inuence of the source on the soundeld in the pinna and ear canal is only investigated forexternal sound sources. The goal is to elucidate thecharacteristics of ear canal sound elds and to identifythe limits of unidimensional approaches using finite el-ements. Hence, a deeper understanding of the charac-teristics of ear canal represented by a standard emulatorcoupler 711, can be useful in some applications, wherethe sound sources inuences has high signicance in theform of the eld. These sources can be positioned far orclose to the pinna or in the case of different types ofhearing aids they can act at the entrance or even withinthe ear canal.

6. REFERENCES

[1] H. W. R. Krer, G. Flege, “Artificial head forthe electroacoustic recording of three dimensionalsound field,” Georg Neuman & Co, Audio Export,Tech. Rep., 1975.

[2] Eletroacoustics - Simulator of human Head andear. Part 4: Occluded-ear simulator for measure-ment of earphones coupled to the ear by meansof ear inserts, International Standard IEC 60318-4 Std., 2010.

[3] C. M. 4.4, “Generic 711 coupler: An occluded earcanal simulator,” Acoustic, 2013.

[4] B. . Kjaer, Microphone Handbook: For the Falconrange Microphone products, 1995.

[5] R. B. Northrop, Noninvasive Instrumentation andMeasurement in Medical Diagnosis, M. R. Neu-man, Ed. CRC Press, 2002.