Sebastian Ihrle

Nonlinear stiffness characteristics of the annular ligament

The annular ligament provides a compliant connection of the stapes to the oval window. To estimate the stiffness characteristics of the annular ligament, human temporal bone measurements were conducted. A force was applied sequentially at several points on the stapes footplate leading to different patterns of displacement with different amounts of translational and rotational components. The spatial displacement of the stapes footplate was measured using a laser vibrometer. The experiments were performed on several stapes with dissected chain and the force was increased stepwise, resulting in load-deflection curves for each force application point. The annular ligament exhibited a progressive stiffening characteristic in combination with an inhomogeneous stiffness distribution. When a centric force, orientated in the lateral direction, was applied to the stapes footplate, the stapes head moved laterally and in the posterior-inferior direction. Based on the load-deflection curves, a mechanical model of the annular ligament was derived. The mathematical representation of the compliance of the annular ligament results in a stiffness matrix with a nonlinear dependence on stapes displacement. This description of the nonlinear stiffness allows simulations of the sound transfer behavior of the middle ear for different preloads.

Nonlinear modelling of the middle ear as an elastic multibody system - Applying model order reduction to acousto-structural coupled systems

In this study, modelling of the human hearing is considered. Due to the nonlinearity of the middle ear, the sound transfer changes as the equilibrium position of the middle ear structure varies. For the description of the middle ear a nonlinear elastic multibody system is derived. The tympanic membrane and the air in the ear canal as well as in the tympanic cavity are considered as elastic bodies. They are first modelled using the finite element method. The large number of degrees of freedom makes a following reduction step of the acousto-structural finite element model inevitable. The second-order structure of the system matrices is preserved by applying reduction techniques based on Petrov-Galerkin projection. The nonlinearity of the tympanic membrane is included following the approach of parametric model order reduction by matrix interpolation assuming that the nonlinearity can be represented by the relative pressure between the ear canal and the tympanic cavity. Finally the static and dynamic behaviour of the simulation model is reviewed for different static pressure loads of the middle ear.

In-plane motions of the stapes in human ears

The piston-like (translation normal to the footplate) and rocking-like (rotation along the long and short axes of the footplate) are generally accepted as motion components of the human stapes. It has been of issue whether in-plane motions, i.e., transversal movements of the footplate in the oval window, are comparable to these motion components. In order to quantify the in-plane motions the motion at nine points on the medial footplate was measured in five temporal bones with the cochlea drained using a three-dimensional (3D) laser Doppler vibrometer. It was found that the stapes shows in-plane movements up to 19.1 ± 8.7% of the piston-like motion. By considering possible methodological errors, i.e., the effects of the applied reflective glass beads and of alignment of the 3D laser Doppler system, such value was reduced to be about 7.4 ± 3.1%. Further, the in-plane motions became minimal (≈ 4.2 ± 1.4% of the piston-like motion) in another plane, which was anatomically within the footplate. That plane was shifted to the lateral direction by 118 μm, which was near the middle of the footplate, and rotated by 4.7° with respect to the medial footplate plane.

Sound wave propagation on the human skull surface with bone conduction stimulation

Background Bone conduction (BC) is an alternative to air conduction to stimulate the inner ear. In general, the stimulation for BC occurs on a specific location directly on the skull bone or through the skin covering the skull bone. The stimulation propagates to the ipsilateral and contralateral cochlea, mainly via the skull bone and possibly via other skull contents. This study aims to investigate the wave propagation on the surface of the skull bone during BC stimulation at the forehead and at ipsilateral mastoid. Methods Measurements were performed in five human cadaveric whole heads. The electro‐magnetic transducer from a BCHA (bone conducting hearing aid), a Baha® Cordelle II transducer in particular, was attached to a percutaneously implanted screw or positioned with a 5‐Newton steel headband at the mastoid and forehead. The Baha transducer was driven directly with single tone signals in the frequency range of 0.25–8 kHz, while skull bone vibrations were measured at multiple points on the skull using a scanning laser Doppler vibrometer (SLDV) system and a 3D LDV system. The 3D velocity components, defined by the 3D LDV measurement coordinate system, have been transformed into tangent (in‐plane) and normal (out‐of‐plane) components in a local intrinsic coordinate system at each measurement point, which is based on the cadaver heads shape, estimated by the spatial locations of all measurement points. Results Rigid‐body‐like motion was dominant at low frequencies below 1 kHz, and clear transverse traveling waves were observed at high frequencies above 2 kHz for both measurement systems. The surface waves propagation speeds were approximately 450 m/s at 8 kHz, corresponding trans‐cranial time interval of 0.4 ms. The 3D velocity measurements confirmed the complex space and frequency dependent response of the cadaver heads indicated by the 1D data from the SLDV system. Comparison between the tangent and normal motion components, extracted by transforming the 3D velocity components into a local coordinate system, indicates that the normal component, with spatially varying phase, is dominant above 2 kHz, consistent with local bending vibration modes and traveling surface waves. Conclusion Both SLDV and 3D LDV data indicate that sound transmission in the skull bone causes rigid‐body‐like motion at low frequencies whereas transverse deformations and travelling waves were observed above 2 kHz, with propagation speeds of approximately of 450 m/s at 8 kHz.

A FUZZY MODEL UPDATING TECHNIQUE MOTIVATED BY BAYESIAN INFERENCE

In this paper, the problem of structural uncertainty of models in the field of model updating is discussed. It is shown that stochastic methods are not appropriate to quantify this type of uncertainty, because of its epistemic nature and different properties. In this context, the fuzzy Bayesian estimation is introduced, which enables the analysis of structural uncertainty by means of fuzzy arithmetic. In this framework, uncertain parameters of the model are estimated and represented by fuzzy numbers. The estimates are based on measured reference outputs and prior information about the parameters in form of a sparse sample of observations or expert knowledge. For this purpose, a methodology for the combination of the information of the reference data and the prior information is proposed. The additional information of the prior is beneficial, as the accuracy of the estimated parameters is increased.

Biomechanics of the incudo-malleolar-joint - Experimental investigations for quasi-static loads.

Under large quasi-static loads, the incudo-malleolar joint (IMJ), connecting the malleus and the incus, is highly mobile. It can be classified as a mechanical filter decoupling large quasi-static motions while transferring small dynamic excitations. This is presumed to be due to the complex geometry of the joint inducing a spatial decoupling between the malleus and incus under large quasi-static loads. Spatial Laser Doppler Vibrometer (LDV) displacement measurements on isolated malleus-incus-complexes (MICs) were performed. With the malleus firmly attached to a probe holder, the incus was excited by applying quasi-static forces at different points. For each force application point the resulting displacement was measured subsequently at different points on the incus. The location of the force application point and the LDV measurement points were calculated in a post-processing step combining the position of the LDV points with geometric data of the MIC. The rigid body motion of the incus was then calculated from the multiple displacement measurements for each force application point. The contact regions of the articular surfaces for different load configurations were calculated by applying the reconstructed motion to the geometry model of the MIC and calculate the minimal distance of the articular surfaces. The reconstructed motion has a complex spatial characteristic and varies for different force application points. The motion changed with increasing load caused by the kinematic guidance of the articular surfaces of the joint. The IMJ permits a relative large rotation around the anterior-posterior axis through the joint when a force is applied at the lenticularis in lateral direction before impeding the motion. This is part of the decoupling of the malleus motion from the incus motion in case of large quasi-static loads.

PRELIMINARY STUDY TO INVESTIGATE THE EFFECT OF PISTON-LIKE AND ROCKING MOTIONS OF THE STAPES FOOTPLATE ON THE BASILAR MEMBRANE VIBRATION

The inner ear or cochlea is a bone structure of spiral shape and is composed of mainly two conical chambers which are filled with fluid and separated by a soft membrane, the basilar membrane. In case of a healthy ear, the closed hydraulic system is excited through the vibration of the stapes. According to present hearing theory, this leads to pressure waves in the cochlear fluid which in turn results in the characteristic vibration behavior of the basilar membrane. Related to the sound frequency, hair cells in certain areas of the basilar membrane are stimulated and cause hearing nerve stimulation. As reported in literature, the stapedial motion is mainly piston-like for low frequencies, whereas for higher frequencies rocking motions increasingly occur. Since purely rocking motions of the stapes footplate generate no net fluid displacement, several researches doubt that these motion components can lead to basilar membrane vibration and thus to hearing impression. Therefore, in this study a Finite Element model with simplified geometry of the human cochlea is developed using Eulerian-based acoustic elements to model the inner ear fluid. First the vibrations of the basilar membrane are calculated for a purely piston-like excitation mode. Then, these results are compared with the basilar membrane vibration pattern evoked by purely rocking motion around the short axis of the stapes footplate.