Michael Lauxmann

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.

Contribution of complex stapes motion to cochlea activation.

Classic theories of hearing have considered only a translational component (piston-like component) of the stapes motion as being the effective stimulus for cochlear activation and thus the sensation of hearing. Our previous study (Huber et al., 2008) qualitatively showed that rotational components around the long and short axes of the footplate (rocking-like components) lead to cochlear activation as well. In this study, the contribution of the piston-like and rocking-like components of the stapes motion to cochlea activation was quantitatively investigated with measurements in live guinea pigs and a related mathematical description. The isolated stapes in anesthetized guinea pigs was stimulated by a three-axis piezoelectric actuator, and 3-D motions of the stapes and compound action potential (CAP) of the cochlea were measured simultaneously. The measured values were used to fit a hypothesis of the CAP as a linear combination of the logarithms of the piston-like and rocking-like components. Both the piston-like and rocking-like components activate cochlear responses when they exceed certain thresholds. These thresholds as well as the relation between CAP and intensity of the motion component were different for piston-like and rocking-like components. The threshold was found to be higher and the sensitivity lower for the rocking-like component than the corresponding values for the piston-like component. The influence of the rocking-like component was secondary in cases of piston-dominant motions of the stapes although it may become significant for low amplitudes of the piston-like component.

Errors in measurement of three-dimensional motions of the stapes using a Laser Doppler Vibrometer system

Previous studies have suggested complex modes of physiological stapes motions based upon various measurements. The goal of this study was to analyze the detailed errors in measurement of the complex stapes motions using laser Doppler vibrometer (LDV) systems, which are highly sensitive to the stimulation intensity and the exact angulations of the stapes. Stapes motions were measured with acoustic stimuli as well as mechanical stimuli using a custom-made three-axis piezoelectric actuator, and errors in the motion components were analyzed. The ratio of error in each motion component was reduced by increasing the magnitude of the stimuli, but the improvement was limited when the motion component was small relative to other components. This problem was solved with an improved reflectivity on the measurement surface. Errors in estimating the position of the stapes also caused errors on the coordinates of the measurement points and the laser beam direction relative to the stapes footplate, thus producing errors in the 3-D motion components. This effect was small when the position error of the stapes footplate did not exceed 5 degrees.

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.

Experimental study on admissible forces at the incudomalleolar joint.

Hypothesis The forces that cause rupture of the incudomalleolar joint during the fixation of stapedial prostheses can be determined by means of load-deflection measurements at the long process of the incus. As in other tissues, 3 ranges of forces can be defined: micro rupture, rupture, and short-term maximum. Background A crucial step in stapes surgery is the attachment of the stapedial prosthesis to the long process of the incus. It is unknown which forces occur during the crimping process that increase the risk of damage to the incudomalleolar joint or incus luxation. The goal of this study was to assess the admissible range of forces at the long process of the incus that would be tolerable before damaging the structures and to compare them with the forces occurring during surgery. Methods Load-deflection curves in the lateral-medial and anterior-posterior direction were measured in 9 freshly frozen or fresh temporal bones. The force was measured with a load cell, and displacement was taken from the encoder information of the electrically driven translation stage on which the load cell was mounted. The long process of the incus was coupled to the load cell via a customized needle. We also monitored with video recordings for visual confirmation of findings. Results The rupture force at which the middle ear was found to be severely injured was 894 (724–1018) mN in the anterior-posterior direction and 695 (574–771) mN in the lateral-medial direction. Micro-ruptures occurred at forces around 568 (469–686) mN in the anterior-posterior direction and in the lateral-medial direction at 406 (254–514) mN. Short-term maximum forces of 1,321 (1,051–1,533) mN were measured in the anterior-posterior direction and 939 (726–1,132) mN in the lateral-medial direction. Conclusion Rupture forces of the incudomalleolar joint could be defined with high accuracy. These results were used to calculate risks of incus luxation or subluxation during stapes surgery. Compared with the use of clip and SMA prostheses, the risk of damage from a crimping procedure is significantly higher.

Spatial Motion in Natural and Reconstructed Middle Ears and the Impact on Sound Transfer

During sound transmission the elements of the middle ear carry out frequency dependent motions in all three spatial directions. Particularly the stapes exhibits a piston and rocking motion and recent studies show that rocking also has an impact on hearing. Here the spatial motions of natural and reconstructed ears are considered on the basis of experiments and numerical simulations based on Multibody System (MBS) approach and Finite Element Method (FEM). In case of a passive reconstruction with a PORP the stapes carries out pronounced rocking motions as well as the piston driven by the natural incus in classical stapedotomy. In the active, electromagnetic middle ear implant Phonak Ingenia, a piston prosthesis is driven by the actuator. Due to anatomical restrictions, the axes of the actuator and the prosthesis are not in line and thus a rocking motion of the prosthesis occurs. Compared to passive reconstructions and the natural ear, this rocking is about in the same range of magnitude. In particular, the ...