# Simulation model middle ear

The simulation model of the human middle ear is a mathematical model based on the Finite Element Method (FEM). With the model’s help, information on the functioning of the middle ear can be obtained in detail and depicted visually. Further, the model is used to simulate reconstruction methods, replacement materials, prostheses and implantable hearing systems for the middle ear on the computer and to optimize them through variations. The experiments on temporal bone preparations that have been necessary to date are to be replaced with this method, while simultaneously improving middle ear reconstruction.

## Middle ear anatomy

The middle ear connects the inner ear with the auditory canal. It encompasses the eardrumand the three auditory ossicles(ossicles), hammer, anvil and stapes. The eardrum absorbs the sound conducted through the air coming from the auditory canal, the ossicles transfer the oscillations to the stapes footplate, where they are transmitted to the inner ear fluid (perilymph). The conversion of fluid oscillations into an electrical signal, needed for the acoustic nerve occurs by the hair sensory cells in the inner ear.

The fundamental function of the inner ear is the impedance adjustment between the air and the inner ear fluid. This is essentially achieved by the area ratio between the eardrum and the stapes footplate. Without the middle ear, hearing perception would be approximately 30-40 dB worse, which would translate to loud colloquial speech then only being perceived as whispering.

## Model structure

The simulation model was devised with the help of the Finite Element Method (FEM) (program package ANSYS). The eardrum is described as a multi-layered, thin, double-curved shell with orthotropic viscoelastic material properties. The ossicles are each represented by a rigid framework with a mass point element in the center of gravity in which all inertial properties are concentrated. The hammer-anvil articulation and the anvil stirrup joint are represented as a homogeneous isotropic viscoelastic material with 20 knot volume elements. The ligaments are rotationally symmetrical beams with isotropically elastic material behaviour.

The volume of the auditory canal is depicted as a compressible, lossless fluid and is connected to the eardrum via a fluid-structure coupling. At the entrance to the auditory canal, a boundary condition of type 3 (matched impedance) is realized. The air volume of the tympanic cavity is not taken into account (influence < 5 dB). The inner ear is approximated by a single-mass-spring-damper system. The geometry of the model correlates to an average middle ear. The material parameters of the model were adjusted by comparison with experimental studies on specimens.

## Model simulation for middle ear physiology

The function of the middle ear is essentially assessed using transfer functions (TF). The most commonly used TF accounts for the normal displacement or velocity of the stapes footplate to the sound pressure at the entrance of the auditory canal or in front of the eardrum. In doing so, it is assumed that the movement of the stapes footplate in the normal direction is the essential component for the sound transmission to the inner ear fluid. The amplitude frequency response of the TF is shown with a logarithmic or dB scale, as this offers the best comparison with the audiological examination results. From a medical therapeutic point of view, the speech frequency range, being approx. 100-6000 Hz, as well as sound pressure levels up to max. 100 dB are of special interest.

The left diagram shows that the TF of the simulation model lies within the range of the transfer function of normal middle ears. When comparing the middle ear transfer function (METF) with the experimental data, it should be noted that these mean values represent many different middle ears. The resonance characteristic of the middle ear is lost with this averaging, since e.g. the first resonance of the middle ear lies individually between 800-1000 Hz.

When solely regarding one METF it slightly suggests that there is only one form of movement in the middle ear. The animations of the oscillations of the middle ear structures at different frequencies clearly show, however, that the movement patterns are frequency-dependent. This is particularly evident in the eardrum.

Displacement field at 500 Hz

Displacement field at 4300 Hz

## Model simulation for middle ear reconstruction

### Evaluation for middle ear reconstruction with passive prostheses

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A typical application scenario for an FEM middle ear model is the evaluation of prostheses with joint or joint-like elements. During ossicular reconstruction using prostheses between the eardrum/hammer handle and stapes, the equalising function of the joints of the intact ossicular chain is lost.

An optimal replacement would be a prosthesis, which overall length changes by approximately 0.5 mm when a static force of up to 5mN is applied. This could compensate for changes in distance between the prostheses’ coupling points in the middle ear arising from scar traction, static pressure fluctuations occurring during disturbed middle ear pressure equalization and anatomic variations of the middle ear. A self-evident idea would be a prosthesis with an integrated spring-element (scheme see left picture).

However, calculations using a simplified model of such a “spring-prosthesis” show that spring elements that ensure a sufficient length change during installation and static pressure changes generate a worse METF.

The diagram on the left shows the amplitude frequency response of the middle ear transfer function (METF) for the reconstruction with prostheses of different elasticity (total stiffness between 9.4 and 833 N/m) relative to the TF of the intact middle ear. Furthermore, to compare the prostheses, the first natural frequency (bending vibration of the ring) is also stated. The numerical results show that all prostheses that provide an acceptable transmission behaviour of the middle ear (max. 10 dB deviation from the intact middle ear) are very stiff and therefore do not allow length adjustment. If the prosthesis is designed to be so flexible that 0.5 mm length changes are possible at 5 mN, then this leads to significant losses in the transmission behaviour of the middle ear.

### Optimal coupling points for implantable hearing aid actuators

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Implantable hearing aids (HA) are developed as an alternative to conventional hearing aids. A common feature of all implantable hearing aids is an actuator, which transmits an amplified signal directly onto the ossicles (excluding bone implants). This eliminates the need to close the auditory canal with an otherwise common sound converter and allows greater amplification at high frequencies. From the medical-therapeutic perspective, it is important to know which actuator types at which possible coupling points (and directions) produce the best results. Using model calculations, it is easily possible to examine the various coupling points (see scheme) and directions for the different possible actuators in the middle ear.

The diagram to the left shows the amplitude frequency response of the stirrup footplate displacement for different coupling points. The result of the best coupling point (footplate 0°-direction) forms the reference (0 dB line). All other results are displayed in relation to this. One can recognise that rather functional problems are to be expected when coupling to the anvil body. Although this point is the easiest to access during the surgical approach to the middle ear via the mastoid, it may provide the worst functional results. In certain coupling directions, it is possible that the oscillation patterns of the ossicles can be stimulated in which there is hardly any effective displacement of the stapes footplate. This case is can be seen in the diagram with the coupling to the anvil in 0° direction at approximately 1200 Hz (notch in amplitude frequency response).

- Bornitz M, Hardtke H.-J., Zahnert T.
*Evaluation of implantable actuators by means of a middle ear simulation model.*Hear Res, Feb, 2010. Vol. 263 , pp. 145-151. - Bornitz M, Lasurashvili N, Hardtke H.-J., Zahnert T.
*Evaluation of Laser Vibrometry as diagnostic utility by means of a simulation model of the middle ear.*In Middle Ear Mechanics in Research and Otology, 2007, pp. 222-229. World Scientific Publishing. - Bornitz M, Zahnert T, Hüttenbrink K.-B.
*Design considerations for length variable prostheses - Finite Element model simulations.*In Middle Ear Mechanics in Research and Otology, July, 2004. , pp. 153-160. World Scientific Publishing. - Schmidt R, Fleischer M, Bornitz M, Gärtner R, Baumgart J.
*FE-Modelle zur Hörforschung*. In ANSYS Conference Proceedings, 29. CADFEM Users' Meeting 2011. CADFEM GmbH.

Contact

Cooperation

The model was developed in cooperation with Prof. Rolf Schmidt from the Institute for Solid Mechanics (Professorship for Dynamics and Mechanism Technology).