Low-frequency finite-element modeling of the gerbil middle ear

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 microm, and an x-ray micro-CT dataset with a voxel size of about 5.5 microm, 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 finite-element 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.