A finite-element model of the cat eardrum is presented which includes the effects of the three-dimensional curved conical shape of the drum. The model is valid at low frequencies (below 1-2 kHz) and within the range of linear vibration amplitudes. The material properties used are based on a review of the literature. The critical material parameters are the stiffness (2 times 10(8) dyn cm(-2)) and thickness (40 micrometer) of the pars tensa. The model exhibits a vibration pattern and amplitude very similar to those observed experimentally using laser holography. A number of parameters are varied in order to study their relative importance in the model.
This article presents frequency responses calculated using a three-dimensional finite-element model of the cat eardrum that includes damping. The damping is represented by both mass-proportional and stiffness-proportional terms. With light damping, the frequency responses of points on the eardrum away from the manubrium display numerous narrow minima and maxima, the frequencies and amplitudes of which are different for different positions on the eardrum. The frequency response on the manubrium is smoother than that on the eardrum away from the manubrium. Increasing the degree of damping smooths the frequency responses both on the manubrium and on the eardrum away from the manubrium. The overall displacement magnitudes are not significantly reduced even when the damping is heavy enough to smooth out all but the largest variations. Experimentally observed frequency responses of the cat eardrum are presented for comparison with the model results.
The gerbil is a popular species for experimental middle-ear research. The goal of this study is to develop a 3D finite-element model to quantify the mechanics of the gerbil middle ear at low frequencies (up to about 1 kHz). The 3D reconstruction is based on a magnetic resonance imaging dataset with a voxel size of about 45 mm, and an x-ray micro-CT dataset with a voxel size of about 5.5 mm, supplemented by histological images. The eardrum model is based on moiré shape measurements. Each individual structure in the model was assumed to be homogeneous with isotropic, linear, and elastic material properties derived from a priori estimates in the literature. The behavior of the finite-element model in response to a uniform acoustic pressure on the eardrum of 1 Pa is analyzed. Sensitivity tests are done to evaluate the significance of the various parameters in the finiteelement model. The Young_s modulus and the thickness of the pars tensa have the most significant effect on the load transfer between the eardrum and the ossicles and, along with the Young_s modulus of the pedicle and stapedial annular ligament, on the displacements of the stapes. Overall, the model demonstrates good agreement with low-frequency experimental data. For example, (1) the maximum footplate displacement is about 35 nm; (2) the umbo/stapes displacement ratio is found to be about 3.5; (3) the motion of the stapes is predominantly piston-like; and (4) the displacement pattern of the eardrum shows two points of maximum displacement, one in the posterior region and one in the anterior region. The effects of removing or stiffening the ligaments are comparable to those observed experimentally.
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