Mechanical Aspects of the Round Window Stimulation

Available online at www.sciencedirect.com

ScienceDirect Procedia IUTAM 24 (2017) 15 – 29

IUTAM Symposium on Advances in Biomechanics of Hearing

Mechanical aspects of the round window stimulation Christoph Heckeler∗, Albrecht Eiber Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany

Abstract During the last years, the round window (RW) has become a well established application position for active middle ear implants 1 . The coupling condition between actuator and round window membrane (RWM) is the critical point regarding the lasting function of the reconstruction. A preload force is needed to maintain sound transmission dealing with an unilateral contact. In this work, the RW stimulation is examined from the mechanical point of view. Based on laboratory experiments and computational simulations, the effects of parameter variations on the dynamical behaviour of the reconstructed ear are revealed in sensitivity analyses and case studies. Force-displacement measurements are carried out in order to capture the nonlinear stiffening and the relaxation behaviour of the RWM. Its characteristics are quantifed by mechanical parameters based on visco-elastic models 2 . A simplified mechanical multibody model is used to simulate the transfer of sound in the natural ear. Hereby, the transmission ratio between oval window and RW has to be taken into account. In case of otosclerosis, stiffening of the annular ring leads to alterations in the transfer behaviour. A hearing loss is observed mainly in the low frequency range, whereas increased hearing sensation may occur in the higher frequency range. With free floating actuators, vibration is transmitted via the actuator housing. The working principle is based on the inertia effect of an internal seismic mass. As an example, the Floating Mass Transducer (FMT) is presented, which is acting as a force transducer. In the not implanted case, the actuator exhibits freqency dependent spatial motions. For assessing the dynamics of the reconstructed ear, the natural structure and the actuator have to be considered as a whole. Based on a multibody model, various influences are investigated by means of virtual experiments, e.g. the preload force, the actuator suspension and the intermediate layer in the contact area. The preload force leads to stiffening of the natural system due to its nonlinear behaviour. As a consequence, resonances are shifted to higher frequencies and low frequency amplitudes are reduced. With increasing preload force, the dynamic force amplitude transmittable without lift-off in the contact area is increased. The corresponding maximum level of equivalent sound pressure is determined by the mechanical properties of the natural structure, but not by not the actuator. The suspension of the actuator housing should be designed to be as compliant as possible in order to maintain the mobility of the actuator during stimulation and to preserve the preload force during large quasistatic deformations of the RWM. Increased motion transfer is observed in the higher frequency range in case of additional damping in the intermediate layer. c2017 by Elsevier B.V. 2017Published The Authors. Published © by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of IUTAM Symposium on Advances in Biomechanics of Hearing. Peer-review under responsibility of organizing committee of IUTAM Symposium on Advances in Biomechanics of Hearing

Keywords: Active Middle Ear Implants; Floating Mass Transducer; Round Window Membrane; Round Window Excitation; Ear Modelling;

∗

Corresponding author. Tel.: +49-711-685-66414 ; fax: +49-711-685-66400. E-mail address: [email protected]

2210-9838 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of IUTAM Symposium on Advances in Biomechanics of Hearing doi:10.1016/j.piutam.2017.08.039

16

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

1. Introduction Dealing with a hearing loss, the most common technical device is the conventional hearing aid, where the sound is amplified by means of a loudspeaker placed in the outer ear canal. However, in some cases it may be refused by patients due to aesthetic reasons, the sound quality may not be satisfactory, e.g. due to distortions or feedback, or the amplification may just not be sufficient 3 . A surgical procedure may then be a better or even the only alternative to improve hearing. Active middle ear implants (AMEI) are mechanical transducers that are surgically inserted into the human hearing organ. Their task is to transfer forces and motions to the natural ear structure, e.g. to the ossicular chain or the round window membrane (RWM). An overview on AMEI is given e.g. by Beutner and H¨uttenbrink 4 . As an example of a free-floating actuator, the reconstruction with an Floating-Mass Transducer (FMT) at the round window (RW) is examined here. During the last years, the RW as a possible application point of AMEI has come more and more into focus of ear surgeons and prosthesis designers. The first implantation of a FMT at the RW was reported by Colletti et al. 1 , nowadays this reconstruction has become well established. Attempts with the DACS-actuator (Direct Acoustic Cochlea Stimulation) have been reported by Maier et al. 5 . Motivated by the ongoing development of new application techniques, the present paper deals with the RW stimulation of the human ear from the mechanical point of view. The aim is to analyze the dynamical behaviour of a reconstruction having special regard to the coupling area and the suspension design. Besides laboratory experiments, computational simulations are carried out based on mechanical models of the human ear and the actuators. In these virtual experiments, parameters such as the static preload force, the suspension characteristics and the intermediate layer in the contact area are varied and their influence on the performance of the reconstruction are studied. Although the applied models are very simplified representations of reality, they can be used to describe effects of interest including e.g. the nonlinear visco-elastic behaviour of the round-window membrane. 2. Unilateral actuator coupling An unilateral coupling exists, when two surfaces are pressed against each other without additional fixation e.g. by glueing or clipping, which is the case in the contact area beteen an AMEI and the driven natural structure. The coupling behaves stiff for pushing forces, but compliant for pulling forces. In an idealized consideration neglecting e.g. adhesion effects, the contact force is Fc > 0 .

(1)

In order to prevent lift-off during harmonic excitation with an angular frequency ω, a static preload force Fp is necessary in the contact area. With the dynamic part Fdyn , the contact force reads Fc = Fp + Fˆ dyn sin(ωt) , 

(2)

Fdyn

and the condition for permanent contact and undistorted force transmission regarding Eq. 1 is Fp > Fˆ dyn .

(3)

Hence, the preload force Fp is a most critical parameter for the performance and function of a mechanical reconstruction at the RW. The ammount of Fp is dependent on the given infeed of the AMEI against the driven structure on the one hand side. On the other hand, it is depending on the mechanical properties, in particular the stiffness, of the driven system and of its equilibrium position. Alterations in the equilibrium position may be caused e.g. by static pressure changes at the ear drum or in the cerebral fluid and by creeping effects of preloaded soft tissues. Due to the nonlinear force-deflection behaviour of the ligaments and membranes, their stiffness is depending on the actual pretension Fp . As a consequence, the dynamical behaviour respective the transfer function from the actuator to the inner ear excitation is depending on Fp Due to creeping effects in the visco-elastic soft tissues, a given Fp is reducing in a long term time range and consequently is changing the transfer behaviour. In the following, fundamental influences of several parameters on the transfer behaviour are studied based on numerical simulations.

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

3. Mechanical properties of the round window membrane In the following, the mechanical properties of a natural RWM shall be investigated. Its visco-elastic behaviour shall be quantified in terms of parameter values of mechanical models, which will be used for numerical simulations presented in the later stage of this paper. 3.1. Measurement setup The presented measurents were carried out in cooperation with the Hannover Medical School on fresh temporal bones preserved in thiomersal solution. The middle ear structures and the inner ear were removed, so that only the RWM enclosed by a bony ring remained after preparation. Force was captured by a one-dimensional load cell (Kyowa LVS100GA) mounted on a positioning unit consisting of two manually driven micro stages (Physik Instruments M126, M105) for positioning the indenter and one electrically driven micro stage (Physik Instruments M126) for automatic loading of the RWM. The load-cell indenter (Renishaw) was ball-shaped and had the diameter of 1 mm. With a measurement amplifier, the resistance change of the strain-gauge-based load cell was transferred into a voltage signal. The compliance of the load cell was excluded from the measured displacement data by measuring the displacement directly on the backside of the indenter with an 1D LDV (Polytec OFV 3001, OFV 303). All signals were low-pass filtered at 25 Hz in a postprocessing procedure using the software Matlab. The measurement setup is sketched in Fig. 1 (b). The temporal bones were clamped in a custom-made fixation device rigidly mounted on the experiment desk. They were adjusted in such a way, that the RWM was oriented normal to the direction of loading. Through a hole in the front plate of the fixation device, the load-cell indenter was approached from the lateral side onto the center of the RWM. The contact situation was inspected visually with a microscope camera (dnt Digi Micro 1.3). Figure 1 (a) shows a photograph of the arrangement. The measurement procedure was made up from several steps of increasing loads. Each step consisted of applying the defined displacement increment Δyp = 20 μm to the load cell, and by holding this position for 30 seconds. The displacement increment Δyrw captured at the indenter was slightly smaller due to the inner compliance of the load cell. The mean velocity of driving was approx. 50 μm/s, the sampling rate of data recording was 100 Hz.

(a) Clamping device with temporal bone, the load-cell indenter is in contact with the RWM 6 .

(b) Schematic sketch of the measurement setup.

Fig. 1: Force-displacement measurements on a natural RWM. In order to get comparable and reproducible measurement results, the initial position of the indenter was defined at a force threshold of 0.5 mN. At this force value, the muccosa layer on the surface of the RWM was estimated to be completely compressed, so that the connective tissue of the RWM dominates the force-displacement behaviour. 3.2. Force-displacement measurement on the RWM In Fig. 2 (a) the displacement-time curve of the penetration measured on the load-cell indenter is shown. The measurement procedure comprises six measurement steps reaching a maximum displacement of yrw ≈ 115 μm. In

17

18

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

Fig. 2 (b), the force-time curve is shown. Within each step, relaxation can be observed. Figure 2 (c) shows the forcedisplacement curve. Over all steps a nonlinear behaviour can be observed. The courses of the force values before and after relaxation are interpolated as dashed lines Frw,max and Frw,min .

(a) Displacement yrw vs. time.

(b) Force Frw vs. time.

(c) Force-displacement curve.

Fig. 2: Force-displacement measurement on the RWM. . 3.3. Parameters of visco-elasticity Mechanical parameters of visco-elasticity shall be estimated by comparing the measured relaxation curves of each load step to the relaxation curve of the spring-damper combination depicted on the left-hand side of Fig. 3 (a). The lower branch consists of a series connection of a spring and a damper known as Maxwell model, the upper branch is a parallel connection of another spring. This arrangement is commonly used in biomechanics of hearing 7,8 and is referred to as Kelvin model in the following 2 . For a more simplified description, linear behaviour is assumed within a single load step. The differential equation of the Kelvin model is given by F+

  c1 d2 ˙ y˙ . F = c1 y + d2 1 + c2 c2

(4)

If at time tst the displacement step ⎧ ⎪ ⎨0 y(t) = ⎪ ⎩y st

for t < tst for t ≥ tst ,

(5)

is imposed, the relaxation curve is found to be ⎧ ⎪ 0 ⎪ ⎪ ⎨

t − t  F(t) = ⎪ st ⎪ ⎪ ⎩ c1 + c2 exp yst τ

for t < tst for t ≥ tst .

(6)

with the time constant τ=

d2 . c2

(7)

Values of mechanical parameters can be derived from the course of the measured relaxation curve, as schematically illustrated in Fig. 3 (b).

19

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

(a) Kelvin model (left-hand side) and Voigt model (right hand side) as simplified model applicable for harmonical excitation in certain frequency intervals.

(b) Relaxation curve of the Kelvin model.

Fig. 3: Spring-damper models for approximating the visco-elastic properties of the RWM in terms of mechanical parameters. Each load step is compared seperately to the relaxation curve of the Kelvin model. Forces and displacements are thereby taken as relative values to the previous load step. In contrary to the theoretical model, there are no displacement steps possible in the experiment. The stiffness values c1 and c2 are therefore slightly underestimated. Furthermore, the relaxation process of each load step is not completely finished after the hold time of 30 seconds. The stiffness values c1 are therefore slightly overestimated. In Tab. 1, the parameter values of the Kelvin model are given for all load steps. The time constant τ represents the duration of the short time relaxation and is in the range of several tenths of a second. In Fig. 4, the values of the stiffness and damping parameters are plotted over the displacement yrw . The nonlinear progressive courses of c1 and c2 are approximated by polynomials of third order and are given as dashed lines. The damping parameter d2 also tends to increase with displacement yrw . The derived parameter values are applicable only for the present configuration of loading, which is the centric contact by a ball-shaped indenter (diameter 1 mm). However, they may be approximately adapted to other configuartions based on the theoretical deformation profile of a circular plate 9 . In case of pressure loading of the RWM, e.g. during physiological hearing excitation, the effective RWM stiffness related to volume displacement is increased roughly by factor 12. Table 1: Parameter values of the Kelvin model and time constant τ for six load steps. Load step

1

2

3

4

5

6

c1 c2 d2 τ

21 N/m 48 N/m 41 Ns/m 0.85 s

28 N/m 77 N/m 55 Ns/m 0.72 s

51 N/m 109 N/m 51 Ns/m 0.47 s

63 N/m 166 N/m 82 Ns/m 0.5 s

93 N/m 241 N/m 112 Ns/m 0.46 s

118 N/m 348 N/m 134 Ns/m 0.39 s

(a) Stiffness parameters c1 and c2 .

(b) Damping parameter d2 .

Fig. 4: Stiffness and damping parameter values derived from the Kelvin model for six load steps on the RWM.

20

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

Based on Eq. 4, the transfer function of the Kelvin model reads Gkel ( jω) =

c22 d2 F(ω) c22 c1 + d22 ω2 (c1 + c2 ) + j ω = . x(ω) c22 + d22 ω2 c22 + d22 ω2   cres

(8)

dres

Looking at the parameters cres and dres for very low and very high frequencies, lim cres ( jω) = c1 ,

ω→0

lim dres ( jω) = d2

ω→0

lim cres ( jω) = c1 + c2 ,

ω→∞

lim dres ( jω) = 0

ω→∞

(9) (10)

it seems feasible to approximate the Kelvin model for certain frequency ranges by a parallel connection of a spring and a damper as depicted on the right hand side of Fig. 3 (a). This structure also referred to as Voigt model is commonly used e.g. in multibody system models and its transfer function reads Gres ( jω) = cres + jωdres .

(11)

The limit values for ω → 0 in Eq. 9 are applicable in case of quasistatic loading. As the transition range between the two limit cases has been found below 10 Hz for the given parameter sets, the limit values for ω → ∞ in Eq. 10 are applied here for harmonic excitation at physiological frequencies. However, the Kelvin model itself is only a rough estimation of the visco-elastic behaviour of the countinous RWM. Higher vibration modes, for example, cannot be described with the given combination of discrete spring and damper elements. 4. Simplified mechanical model of the human ear Regarding the spatial dynamics of the human middle ear, e.g. Koike et al. 10 and Eiber 11 have presented elaborate Finite Element and multibody models. The fluid-structure interactions in the human cochlea have been simulated in detail e.g. by Gan et al. 12 and Kim et al. 13 . In this work, relationships between causes and effects shall be revealed under well defined conditions rather than giving a most realistic depiction of a specific situation. For this, a strongly simplified mechanical model of the human hearing organ is applied. The middle ear ossicles are modelled as rigid bodies carrying out unidirectional motion, malleus and incus are described as a single body. The elastic structures of the middle ear are described as massless spring-damper elements. The cochlea fluid is simplified as constant mass by estimating the fluid column vibrating between the oval and the RW at approx. 1000 Hz. The RWM is modelled as a spring-damper combination based on the measurement results presented in section 3. Between the areas of the oval window Aow and the RW Arw , the ratio Aow ih = >1 (12) Arw occurs acting as a hydraulic transmission. In the simplified model it is expressed in terms of a kinematic constraint between the RW motion ycf and the stapes motion ys , ycf = ih ys .

(13)

The model structure is illustrated in Fig. 5 (a), the parameter values are given in Tab. 2. 4.1. Forward stimulation For the forward stimulation, the displacements ymi and ys are used as generalized coordinates. Regarding Eq. 12 the parameter values of the cochlea have to be multiplied by the factor i2h . Based on the normal stapes motion ys,n at harmonic pressure excitation with 60 dB SPL at the ear drum, the stapes motion ys , e.g. in case of a reconstructed ear, is transformed into the equivalent sound pressure level   ys Leq [dB] = 60 dB + 20 log10 . (14) ys,n In Fig. 5 (b) the normal stapes motion ys,n is shown. The stapes amplitude at 60 dB SPL remains in the corridor derived from the ASTM Standard (American Society for Testing and Materials) up to approx. 4 kHz.

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

Table 2: Parameter values for the simplified model of the human ear. mmi = 18 · 10−6 kg ms = 3.4 · 10−6 kg mcf = 66 · 10−6 kg ctm = 300 N/m dtm = 0.1 Ns/m cis = 4000 N/m dis = 0.05 Ns/m car = 1000 N/m dar = 0.3 Ns/m crw = 828 N/m drw = 1 · 10−6 Ns/m

Mass off malleus-incus complex Mass of stapes Mass of cochlea fluid Stiffness of tympanic membrane Damping of tympanic membrane Stiffness of incudo-stapedial joint Damping of incudo-stapedial joint Stiffness of annular ring Damping of annular ring Stiffness of RWM Damping of RWM

(a) Model structure with hydraulic transmission ih . The harmonic pressure excitation at the ear drum is modelled by an equivalent excitation force Fec acting on the malleus-incus complex. The mechanical parameters are defined in Tab. 2.

(b) Simulated transfer behaviour in case of the normal ear and in case of otosclerosis at the the oval window (stiffness car increased by factor 100). Harmonic sound pressure excitation at the ear drum with 60 dB SPL.

Fig. 5: Simplified mechanical model of the human ear.

5. Free-floating actuators The working principle of free-floating actuators is based on the inertia effect. An actuated seismic mass inside evokes a reaction force acting on the actuator housing. As the actuator housing acts as the driving structure, it should remain in contact to the driven structure. Furthermore, the actuator housing should remain mobile in the implanted configuration. Here, the influences of preload forces, suspension design and intermediate layers in the contact area on the performance of the reconstruction are of main interest. In the following, the FMT depicted in Fig. 6 is used as an example. It has a length of 2.3 mm and a mean diameter of 1.8 mm. Its overall mass is approx. 25 mg.

21

22

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

(a) Microscopic photograph 14 .

(b) Schematic sketch 15,14 .

Fig. 6: Floating Mass Transducer (FMT) by MED-EL as an example of a free-floating actuator. The FMT is part of the hearing system Vibrant Soundbridge. 5.1. Spatial motion of the FMT In a laboratory experiment, the actuator was hung at its cable, the cable length was lk = 50 mm. Harmonical excitation between 12.5 Hz and 10 kHz was applied using a linear chirp signal with a block length of 80 ms. At nine different measurement points on the housing surface, spatial translations were captured with a 3D LDV (Polytec CLV 3000). The sampling freqeuncy was 25.6 kHz, all signals were low-pass filtered at 10 kHz and averaged over 100 measurement blocks. The measurement setup is shown schematically in Fig 7 (a). In the work of Strenger 16 , a similar measurement setup with an 1D LDV was used. With the cable acting as a coupling element in the mechanical sense, the actuator housing has six degrees of freedom as a rigid body. Its translations and rotations sketched in Fig. 7 (b) are collected in the vector of the generalized coordinates u = [xh yh zh αh βh γh ]T ,

(15)

whereas yh is in the desired working direction. The rigid body motion of the actuator housing is reconstructed from the measured point motions in the following way. In the inertial system, the position vector ri of the ith measurement point reads ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢⎢⎢ 1 −γh βh ⎥⎥⎥ ⎢⎢⎢ xi ⎥⎥⎥ ⎢⎢⎢ xO ⎥⎥⎥ ⎢⎢⎢ xi ⎥⎥⎥ ⎢⎢⎢⎢yi ⎥⎥⎥⎥ = ⎢⎢⎢⎢ γh 1 −αh ⎥⎥⎥⎥ · ⎢⎢⎢⎢y ⎥⎥⎥⎥ + ⎢⎢⎢⎢yO ⎥⎥⎥⎥ . ⎢⎣ ⎥⎦ ⎥⎦ ⎢⎣ i ⎥⎦ ⎢⎣ ⎥⎦ ⎢⎣ zi −βh αh 1 zi zO     ri

ri

S

(16)

rO

The matrix S is the linearized rotation matrix, the position vector r i = const. refers to the ith measurement point in the body-fixed reference frame O , and the position vector rO indicates the position of O in the inertial system. In the initial position, the vector ri,0 reads ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢⎢⎢ xi ⎥⎥⎥ ⎢⎢⎢ xO ,0 ⎥⎥⎥ ⎢⎢⎢ xi,0 ⎥⎥⎥ ⎢⎢⎢⎢yi,0 ⎥⎥⎥⎥ = ⎢⎢⎢⎢y ⎥⎥⎥⎥ + ⎢⎢⎢⎢yO ,0 ⎥⎥⎥⎥ , ⎢⎣ i ⎥⎦ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ zi,0 zi zO ,0    ri

ri,0

(17)

rO ,0

and the spatial motion at the ith measurement point with respect to the initial position is ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎢⎢⎢ xh ⎥⎥⎥ ⎢⎢⎢ xi − xi,0 ⎥⎥⎥ ⎢⎢⎢ 0 −γh βh ⎥⎥⎥ ⎢⎢⎢ xi ⎥⎥⎥ ⎢ ⎥ ⎥⎥⎥ ⎢⎢⎢ ⎢⎢⎢ ⎥⎥⎥ ⎢⎢⎢  ⎥⎥⎥ ⎢⎢⎣ yi − yi,0 ⎥⎥⎦ = ⎢⎢⎣ γh 0 −αh ⎥⎥⎦ · ⎢⎢⎣yi ⎥⎥⎦ + ⎢⎢⎢⎢⎣yh ⎥⎥⎥⎥⎦ .  zh zi − zi,0 −βh αh 0 zi     ui

S−E

ri

uO

(18)

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

(a) Schematical sketch of the measurement setup.

(b) Generalized coordinates for the rigid-body motion of the FMT housing (line of sight in direction of the laser beam).

Fig. 7: Measurement of the spatial motion of the not implanted FMT. The sought generalized coordinates u are found in the vector uO and in the matrix S − E. With the chosen n = 9 measurement points, the overdetermined linear equation system ⎡ ⎤ ⎡ ⎤ ⎢⎢⎢u1 ⎥⎥⎥ ⎢⎢⎢T1 ⎥⎥⎥ ⎡ ⎤ ⎢⎢⎢u ⎥⎥⎥ ⎢⎢⎢T ⎥⎥⎥ ⎢⎢⎢1 0 0 0 zi yi ⎥⎥⎥ ⎢⎢⎢ 2 ⎥⎥⎥ ⎢⎢⎢ 2 ⎥⎥⎥ ⎢⎢⎢  ⎥ with Ti = ⎢⎢0 1 0 −zi 0 xi ⎥⎥⎥⎥ (19) ⎢⎢⎢ .. ⎥⎥⎥ = ⎢⎢⎢ .. ⎥⎥⎥ · u ⎣ ⎦ ⎢⎢⎢ . ⎥⎥⎥ ⎢⎢⎢ . ⎥⎥⎥   0 0 1 y −x 0 ⎣ ⎦ ⎣ ⎦ i i un Tn leads to a least-square averaging of the vector u. A similar procedure was applied e.g. by Lauxmann 17 in order to derive quasistatic spatial motions of the stapes. In Fig. 8 (a) the transfer functions from excitation voltage to spatial translation of the actuator housing are shown. Besides the desired axial translation yh , pronounced out-of-plane translations occur. In distinct frequency intervals they even show higher amplitudes than the axial motion, as can be observed for the zh -compnent around 200 Hz and for the xh -compnent around 800 Hz. The rotations shown in Fig. 8 (b) remains small over the whole frequency range.

(a) Spatial translation.

(b) Spatial rotation.

Fig. 8: Spatial motion of the FMT housing. Rigid body motion reconstructed from spatial point translations on the housing surface. There are unavoidable imperfections in the manufacturing and assembly of the actuator leading e.g. to excentric centers of gravity. Also the excitation force may not be acting precisely in the desired working direction. The frequency-dependent cable dynamics may have an effect on the housing motion as well 16 . Pronounced out-of-plane motions may lead to inefficient stimulation and to undesired effects, e.g. hammering agains the skull. Hence, spatial motion behaviour is an important criterium regarding placement, orientation and guidance of the FMT during a surgical procedure. 5.2. Mechanical parameters of the FMT In order to simulate the axial motion of a not implanted free-floating actuator, a two-mass oscillator is used as simplified actuator model as depicted in Fig. 9 (a), a similar model is used e.g. by Strenger 16 . The stiffness and

23

24

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

(a) Simplified model of a free-floating actuator. The mechanical parameters are defined in Tab. 3.

(b) Measured and simulated actuator transfer functions from the internal excitation force Fe to the displacement yh of the housing for two different cable lengths.

Fig. 9: Influence of the suspension on the axial transfer behaviour of the not implanted FMT. damping parameters given in Tab. 3 were estimated from the translation yh of the actuator housing during free vibration and during chirp excitation using the measurement setup described above. The transducer constant is an estimation of how the excitation voltage is transformed into the excitation force Fe . In Fig. 9 (b), a comparison of the measured and simulated actuator transfer funcion Gact ( jω) =

yh Fe

(20)

from excitation force Fe to displacement yh in desired working direction of the housing is shown for the cable length lc = 50 mm. The resonances are found at f1 = 3.4 Hz and f2 = 1530 Hz. Table 3: Model parameters for the FMT, cable length 50 mm. Mass of housing Seismic mass Inner stiffness Inner damping Transducer constant

mh = 16 · 10−6 kg msm = 6 · 10−6 kg ci = 400 N/m di = 8.4 · 10−6 Ns/m kUF = 2.2 · 10−3 N/V

The dynamical behaviour of the FMT is determined by the mechanical properties of its elements. In terms of the simplified actuator model, those are its masses, stiffnesses and dampings. The properties of the actuator parts are given by the constructive design. However, the properties of the suspension are affected by the actual configuration, e.g. in a laboratory experiment. Simulations showed that variation in the suspension stiffness up to approx. csu = 100 N/m primarily affect the resonance frequency f1 . Only above approx. csu = 1500 N/m the change in f2 becomes dominant. For a cable length of lc = 50 mm, the stiffness and damping parameters of the suspension were estimated in the range of csu = 0.01 N/m and dsu = 4 · 10−6 Ns/m. Regarding other cable lengths, the stiffness csu can be roughly estimated from linear beam theory by the relation csu ∼

1 . lc3

(21)

The simulated transfer function in case of the reduced cable length lc = 5 mm is also shown in Fig 9 (b). It becomes clear that the properties of the suspension must be taken into acount when stating the dynamic properties of a freefloating actuator. However, a change in the resonance frequency f2 is negligible for a realistic change in cable length, as was also stated by Strenger 16 .

25

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

Modelling the cable as a discrete, massless spring-damper element is a rough simplification of reality suitable for short cables. Especially in case of long cables, there is expected an influence of the cable dynamics on the housing motion.

6. Round window stimulation with a free-floating actuator In the first step of the simulation, the equilibrium position of the simplified human-ear model is numerically evaluated for different preload forces Fv acting at the RW. For that, the nonlinear force-displacement characteristic of the RWM is derived from the measurement results presented in section 3 regarding the limit case ω → 0. The nonlinear properties of the annular ligament are adapted from measurements presented by Lauxmann 17 . During excitation with a free-floating actuator, the reconstructed ear carries out only small displacements around its equilibrium position in contrast to large quasistatic displacements due to preloading. Thus, for simulating the RW excitation in the second step, the nonlinear model is linearized about the preloaded equlibrium positions. As a result, distinct sets of parameter values valid for actual preload forces are available. The linearized model of the reconstructed ear with the generalized displacements ycf and y˜ mi =

1 ymi ih

(22)

is sketched in Fig. 10. The corresponding generalized parameters tagged with a tilde symbol have been divided by i2h . The stiffness values of the RWM are derived from the limit case ω → ∞ of section 3. The stiffness values of the annular ring are adapted from Lauxmann 17 in a similar way. The intermediate layer is modelled as a spring-damper combination. For the free-floating actuator the parameter values of the FMT from section 5 are used. The stiffness values crw of the RWM are derived from the measurement results in section 3 regarding the limit case ω → ∞. The stiffness values c˜ ar of the annular ring are adapted in a similar way. For the free-floating actuator the parameter values of the FMT from section 5 are used. The intermediate layer between the actuator and RWM is modelled as a spring-damper combination.

Fig. 10: Simplified mechanical model of the reconstructed ear, harmonic excitation with a free-floating actuator at the RW. The mechanical parameters are defined in Tabs. 2 and 3.

6.1. Detection of lift-off in the contact area In the simulation, the unilateral contact between actuator and RWM is regarded in the following way. The transfer function G F ( jω) =

Fdyn Fe

(23)

26

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

between the internal actuator excitation force Fe and the dynamic portion Fdyn of the contact force is calculated for the case of bilateral contact. The maximum admissible actuator excitation force Fe,ad without lift-off in the contact area at a given static peload force Fp is Fe,ad =

Fp . |G F |

With the transfer functions Gact given in Eq. 20 and ycf ys Gio,rev ( jω) = = ih yh yh

(24)

(25)

from the motion yh of the actuator housing to the stapes motion ys , the limit curve of the maximum possible equivalent sound pressure level without lift-off can be calculated based on Eq. 14 as  ⎞ ⎛ ⎜⎜⎜ Fe,ad GactGio,rev  ⎟⎟⎟ ⎟⎟⎠ dB . Leq,max = 60 dB + 20 log10 ⎜⎜⎝ (26) ys,n     Rewriting the numerator Fe,ad GactGio,rev  = Fp ys /Fdyn  it turns out that the lift-off limit Leq,max at a given preload force Fp is determined by the properties of the natural ear represented by the transfer function from the dynamic force component Fdyn at the RWM to the stapes motion ys . However, the achievable sound pressure level at a certain excitation force Fe depends on the mechanical properties of the actuator. In the following, numerical experiments related to the hearing stimulation with an FMT at the RW are carried out. 6.2. Influence of the preload force In Fig. 11 (a), the lift-off limit Leq,max is shown for six different preload forces between 1 mN and 50 mN. The curves are altered in a nonlinear way due to the nonlinear characteristics of the natural ear structure. In certain frequency ranges, the lift-off limit may even be reduced with increasing preload force, as can be observed for 20 mN and 50 mN between 800 Hz and 1000 Hz. A considerable equivalent sound pressure level is achieved already with moderate preload forces around 1 mN. However, the choice of an appropriate preload force depends on multiple criteria, e.g. the equivalent sound pressure level necessary to compensate hearing loss, the frequency interval of hearing loss, the maximum actuator excitation force and mechanical properties of the natural ear structures, which are individually different and are not known a priori. Generally, an optimal value for the preload force can hardly be stated. For the following investigations of transfer behaviour it is assumed, that the excitation level remains below the liftoff limit. For analysing the influence of the preload force on the tranfer behaviour, the intermediate layer is defined to be rigid, i.e. cil → ∞, and it is yg = ycf . As suspension stiffness, the value csu = 10 N/m derived in section 5 for the cable length of 5 mm is used here. In Fig. 11 (b), the transfer function |Gact | is shown for different preload forces. For comparison, the curve of the not implanted FMT is plotted as dashed line. There occur three resonance peaks in the transfer function |Gact |. The first resonance frequency is determined mainly by the cumulated mobile mass of the reconstructed ear as well as the suspensions of natural structure and actuator against the skull. Due to nonlinear progressive stiffnesses of the annular ring and the RWM, the resonance is increased under preload from approx. 530 Hz at 1 mN to approx. 1140 Hz at 50 mN. However, for the not implanted actuator the first resonance is observed at approx. 100 Hz. Quantitative findings related to the dynamics of the not implanted actuator cannot be transferred to the implanted case, as the dynamic behaviour of the reconstruction is strongly effected by the mechanical properties of the driven natural structure. As a characteristic of the function principle of free-floating actuators based on the inertia effect, all curves approach zero amplitude for low excitation frequencies. Thus, the higher the preload force, the higher excitation forces are necessary in the low frequency range. Due to dynamic effects there is a contrary behaviour observable in the high frequency range above approx. 1 kHz. The second resonance frequency is related to the second resonance of the actuator, where the seismic mass is in antiphase to the housing. It is found at a slightly lower frequency compared to the not implanted actuator, as the cumulated mass of the natural structure is attached. As the internal stiffness ci of the actuator is not affected by a change in preload force, the resonance remains almost constantly around 1.4 kHz. The third resonance frequency is hardly visible as a slight shoulder at approx. 2.5 kHz. Here, the malleus-incus complex is vibrating against the rest of the structure, determined by the stiffness c˜ is of the incudo-stapedial joint.

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

(a) Maximum possible sound pressure level at different preload forces Fp .

(b) Transfer function |Gact | at different preload forces Fp .

Fig. 11: Influence of the preload force Fp .

6.3. Influence of the suspension stiffness One crucial issue during the surgical procedure is the actuator suspension towards the skull. In the following virtual experiments, the influence of the suspension stiffness csu in the implanted configuration is analysed with regard to preload forces and harmonical excitation. Once again, the intermediate layer is defined to be rigid for simplification. In Fig. 12 (a) the ransfer function |Gact | of the FMT is shown for five different stiffness values Fsus between 10 N/m and 50 kN/m, the preload force is 10 mN in all cases. The increase in suspension stiffness from 10 N/m to 100 N/m has no significant effect on the course of the transfer function, as these stiffness values are low compared to the other stiffness values of the system. At csu = 1000 N/m, mainly the first resonance frequency is increased, at csu = 10 kN/m both. An increased suspension stiffness reduces the vibration amplidues in the low frequency range as a static effect. However, as an dynamic effect hearing excitation may be increased in the high frequency range, as can be observed between 800 Hz and 1.3 kHz for csu = 1000 N/m and between 1.5 kHz and 4 kHz for csu = 10 kN/m. In order to apply a preload force on the actuator housing, the suspension towards the skull is designed as some kind of pretensioned spring. Due to quasistatic deformation changes of the RWM, its quasistatic deformation state is not constant. Figure 12 (b) shows schematically the linear force-displacement curves of a stiff and a compliant spring. The preload force Fp is set by initially compressing the suspension spring by s0,s respective s0,c . In case of a variation Δs in spring length, e.g. due to a deformation change of the RWM, the stiff spring shows a high variation ΔFv,s in force, which may lead to a zero preload force and lift-off in the worst case. With a compliant spring there occurs only a small variation ΔFv,c , and the free-floating atuator is able to compensate quasistatic deformation changes of the RWM.

(a) Transfer function |Gact | for different suspension stiffnesses csu .

(b) Influence of the suspension stiffness on the preload force at a variation in deformation.

Fig. 12: Influences of the suspension stiffness csu .

27

28

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

6.4. Influence of damping in the intermediate layer A visco-elastic intermediate layer between actuator and RWM has to be taken into account when e.g. natural or artificial tissue is placed in the contact area or when the actuator has compliant elements attached, as it was pointed out e.g. by Mlynski et al. 18 . In the following, the influence of damping in the intermediate layer is investigated. For all simulations, the stiffness value cil = 100 N/m is used. In general, the term damping is associated with energy dissipation and disadvantageous effects regarding e.g. the performance of a hearing reconstruction. However, the effect of a damping element on the dynamic behaviour is dependent on its position in the system 19 . Figure 13 (a) shows the transfer function |Gact | (referring to the displacement yh of the actuator housing) for different values dil of damping in the intermediate layer. In Fig. 13 (b), the transfer function |GactGio,rev | (referring to the stapes displacement ys of the actuator housing) from excitation force Fe to stapes motion ys is shown. Regarding the motion of the actuator housing in Fig. 13 (a), the increase of damping results in a decrease of resonance amplitudes. Looking at the stapes motion in Fig. 13 (b), amplitudes are increasing with increasing damping for excitation frequencies above approx. 450 Hz. With respect to the stapes motion the actuator excitation is acting as a base excitation. The higher the frequency is, the higher is the portion of the velocity dependent damping in force transmission via the intermediate layer. Thus, in presence of a intermediate layer damping has an advantageous effect on the performance in contrast e.g. to damping in the suspension towards the skull.

(a) Transfer function |Gact | referring to the displacement yh of the actuator housing.

(b) Transfer function |GactGio,rev | referring to the stapes displacement ys .

Fig. 13: Influences of the damping dil in the intermediate layer. There have been reported experimental results e.g. by Salcher et al. and Gostian et al. 20,21 , where higher stapes amplitudes were observed when using an intermediate layer, e.g. consisting of Tutopatch. Related to the presented simulation results this may be due to a geometric effect, which is not conisdered here. Covering the RWM with interface material leads to an extensive contact area. Therefore, the volume displacement may be increased compared to direct contact e.g with a ball-shaped indenter.

7. Conclusions A most crucial point for the durable and reliable function of a hearing reconstruction with an AMEI is the coupling between natural structure and actuator. As the coupling is unilateral, a preload force is needed in the contact area in order to transfer forces without lift-off during excitation. The design of the actuator suspension towards the skull is of great importance for maintaining the preload force under quasistatic deformation changes of the RWM. The mechanical behaviour of the natural ear structures depends on multiple influences, as has been revealed for the RWM in force-deflection measurements and parameter estimations based on a Kelvin model. Stiffness and damping parameters are determined by the load configuration, e.g. load by a concentrated single force or distributed pressure. The frequency of excitation plays an important role regarding the visco-elastic characteristics of the RWM. Due to the hydraulic transmission ratio between oval window and RW, the location of excitation, e.g. at the ear drum (forward) or at the RWM (backward), effects the mechanical impact of the natural structures.

Christoph Heckeler and Albrecht Eiber / Procedia IUTAM 24 (2017) 15 – 29

The function of free-floating actuators is based on the inertia effect. Due to the purely dynamical working principle, force amplitudes approach zero for low frequencies. The FMT carries out pronounced spatial motions which may lead to undesired hammering effects in the implanted configuration. Special attention has to be given to the orientation and guidance of the actuator. The FMT is a force actuator. Hence, the mechanical properties of the actuator and the natural structure have to be considered as an entire system when assessing the dynamics of the reconstructed ear. The maximum equivalent sound pressure level achievable at a certain preload force without lift-off is determined by the mechanical properties of the driven natural structure. For preload forces in the range of 1 mN, the lift-off limit is found around 110 dB SPL. High preloading leads to nonlinear stiffening of the natural structure. Resonances are shifted to higher frequencies and amplitudes are reduced in the low frequency range. The suspension of the FMT housing towards the skull should be compliant in order to maintain mobility. Moreover, a compliant suspension is advisable in order to preserve the preload force under quasistatic deformation variations of the RWM. In presence of a visco-elastic intermediate layer between the actuator and the driven structure, damping has an advantageous effect on the transfer of motion via the contact area. Acknowledgements The authors want to thank Hannes Maier for his kind cooperation in performing temporal-bone measurements. References 1. Colletti, V., Soli, S., Carner, M., Colletti, L.. Treatment of mixed hearing losses via implantation of a vibratory transducer on the round window. International Journal of Audiology 2006;45:600–608. 2. Roylance, D.. Mechanics of Materials. New York: John Wiley & Sons; 1996. 3. Luers, K.B.. Implantierbare H¨orger¨ate. HNO 2011;59:980–987. J., Beutner, D., H¨uttenbrink, URL: http://dx.doi.org/10.1007/s00106-011-2402-0. 4. Beutner, D., H¨uttenbrink, K.B.. Active and passive implants. Laryngo-Rhino-Otologie 2009;88:32–47. 5. Maier, H., Salcher, R., Schwab, B., Lenarz, T.. The effect of static force on round window stimulation with the direct acoustic cochlea stimulator. Hearing Research 2013;301:115–124. doi:10.1016/j.heares.2012.12.010. 6. Gonz´alez Garcia, V.. Test setup for measuring the force-deflection characteristics of soft tissues. Master thesis DIPL-MSC-198; Institut f¨ur Technische und Numerische Mechanik, Universit¨at Stuttgart; 2013. 7. Aernouts, J., Dirckx, J.. Static versus dynamic gerbil tympanic membrane elasticity: Derivation of the complex modulus. Biomechanics and Modeling in Mechanobiology 2012;11(6):829–840. doi:10.1007/s10237-011-0355-6. 8. Zhang, X., Gan, R.Z.. Finite element modeling of energy absorbance in normal and disordered human ears. Hearing Research 2013; 301:146–155. doi:http://dx.doi.org/10.1016/j.heares.2012.12.005. 9. Wolmir, A.S.. Biegsame Platten und Schalen. Berlin: VEB Verlag f¨ur Bauwesen; 1962. 10. Koike, T., Wada, H., Kobayashi, T.. Modeling of the human middle ear using the finite-element method. Acoustical Society of America 2002;111(3):1306–1317. doi:10.1121/1.1451073. 11. Eiber, A.. On the simulation of human hearing. International Journal for Computational Vision and Biomechanics 2009;2(2):157–169. 12. Gan, R.Z., Reeves, B.P., Wang, X.. Modeling of sound transmission from ear canal to cochlea. Annals of Biomedical Engineering 2007; 35(12):2180–2195. doi:10.1007/s10439-007-9366-y. 13. Kim, N., Homma, K., Puria, S.. Inertial bone conduction: Symmetric and anti-symmetric components. Journal of the Association for Research in Otolaryngology 2011;12(3):261–279. 14. Wahl, P.. Zur Ankopplung eines Schwingungserregers an das runde Fenster der Cochlea. Student thesis STUD-382; Institut f¨ur Technische und Numerische Mechanik, Universit¨at Stuttgart; 2012. 15. Ball, G.R., Pombo, A.C., Julian, C.A., Jaeger, E.M., Dietz, T.G., Katz, B.H.. Dual coil floating mass transducers, US–patent No. 6676592 B2. 2004. 16. Strenger, G.. Laservibrometrische Schwingungsmessungen am Floating Mass Transducer des teilimplantierbaren Mittelohrh¨orger¨ates Vibrant Soundbridge. Ph.D. thesis; Julius-Maximilians-Universit¨at W¨urzburg; 2009. 17. Lauxmann, M., Eiber, A., Haag, F., Ihrle, S.. Nonlinear stiffness characteristics of the annular ligament. The Journal of the Acoustical Society of America 2014;136(4):1756–1767. URL: http://scitation.aip.org/content/asa/journal/jasa/136/4/10.1121/1.4895696. doi:http://dx.doi.org/10.1121/1.4895696. 18. Mlynski, R., Nguyen, T., Plontke, S., Ko, S.. Presentation of floating mass transducer and vibroplasty couplers on ct and cone beam ct. European Archives of Oto-Rhino-Laryngology 2014;271:665–672. 19. Magnus, K., M¨uller, H.. Grundlagen der Technischen Mechanik. Stuttgart: Teubner; 1990. 20. Salcher, R., Schwab, B., Lenarz, T., Maier, H.. Round window stimulation with the floating mass transducer at constant pretension. Hearing Research 2014;314:1–9. 21. Gostian, A., Pazen, D., Ortmann, M., Luers, J., Anagiotos, A., H¨uttenbrink, K., et al. Impact of coupling techniques of an active middle ear device to the round window membrane for the backward stimulation of the cochlea. Otology & Neurotology 2015;36(1):111–117.

29