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Wave-like differential equations occur in many engineering applications. Here the engineering setup is embedded into the framework of functional analysis of modern mathematical physics. After an overview, the –Hilbert space approach to free Euler–Bernoulli bending vibrations of a beam in one spatial dimension is investigated. We analyze in detail the corresponding positive, selfadjoint differential operators of 4-th order associated to the boundary conditions in statics. A comparison with free string wave swinging is outlined.
Model-based hearing diagnosis based on wideband tympanometry measurements utilizing fuzzy arithmetic
(2019)
Today's audiometric methods for the diagnosis of middle ear disease are often based on a comparison of measurements with standard curves that represent the statistical range of normal hearing responses. Because of large inter-individual variances in the middle ear, especially in wideband tympanometry (WBT), specificity and quantitative evaluation are greatly restricted. A new model-based approach could transform today's predominantly qualitative hearing diganostics into a quantitative and tailored, patient-specific diagnosis, by evaluating WBT measurements with the aid of a middle-ear model. For this particular investigation, a finite element model of a human ear was used. It consisted of an acoustic ear canal and a tympanic cavity model, a middle-ear with detailed nonlinear models of the tympanic membrane and annular ligament, and a simplified inner-ear model. This model has made it possible to identify pathologies from measurements, by analyzing the parameters through senstivity studies and parameter clustering. Uncertainties due to the lack of knowledge, subjectivity in numerical implementation and model simplification are taken into account by the application of fuzzy arithmetic. The most confident parameter set can be determined by applying an inverse fuzzy method on the measurement data. The principle and the benefits of this model-based approach are illustrated by the example of a two-mass oscillator, and also by the simulation of the energy absorbance of an ear with malleus fixation, where the parameter changes that are introduced can be determined quantitatively through the system identification.
The incudo-malleal joint (IMJ) in the human middle ear is a true diarthrodial joint and it has been known that the flexibility of this joint does not contribute to better middle-ear sound transmission. Previous studies have proposed that a gliding motion between the malleus and the incus at this joint prevents the transmission of large displacements of the malleus to the incus and stapes and thus contributes to the protection of the inner ear as an immediate response against large static pressure changes. However, dynamic behavior of this joint under static pressure changes has not been fully revealed. In this study, effects of the flexibility of the IMJ on middle-ear sound transmission under static pressure difference between the middle-ear cavity and the environment were investigated. Experiments were performed in human cadaveric temporal bones with static pressures in the range of +/- 2 kPa being applied to the ear canal (relative to middle-ear cavity). Vibrational motions of the umbo and the stapes footplate center in response to acoustic stimulation (0.2-8 kHz) were measured using a 3D-Laser Doppler vibrometer for (1) the natural IMJ and (2) the IMJ with experimentally-reduced flexibility. With the natural condition of the IMJ, vibrations of the umbo and the stapes footplate center under static pressure loads were attenuated at low frequencies below the middle-ear resonance frequency as observed in previous studies. After the flexibility of the IMJ was reduced, additional attenuations of vibrational motion were observed for the umbo under positive static pressures in the ear canal (EC) and the stapes footplate center under both positive and negative static EC pressures. The additional attenuation of vibration reached 4~7 dB for the umbo under positive static EC pressures and the stapes footplate center under negative EC pressures, and 7~11 dB for the stapes footplate center under positive EC pressures. The results of this study indicate an adaptive mechanism of the flexible IMJ in the human middle ear to changes of static EC pressure by reducing the attenuation of the middle-ear sound transmission. Such results are expected to be used for diagnosis of the IMJ stiffening and to be applied to design of middle-ear prostheses.