Thickness Distribution of Fresh Eardrums of Cat Obtained with Confocal Microscopy

The aim of this study was to measure the spatial thickness distribution of the cat tympanic membrane (TM), a very thin, virtually transparent and delicate biological membrane. Axial fluorescence images taken perpendicular through isolated TM were recorded for five different cats using confocal laser scanning microscopy. Thickness was measured on the cross-section of the membranes in the axial images. A correction for focal shift due to refractive-index mismatch was applied. Similar thickness distributions were obtained in all measured samples (n = 9). The pars tensa had a rather constant thickness in the central region between the annulus and manubrium. The thickness increased steeply toward the peripheral rim. Thickness was smallest in the inferior region, with values ranging between 5.5 and 9 μm in the central part and up to 50 μm near the annulus. More superiorly, thickness was slightly higher, up to 20 μm, between the annulus and manubrium. The anterior part was thicker than the posterior side. These findings are strongly different from a current value in the literature. Our data allow a more precise representation of the eardrum in mathematical models, which are a prerequisite for a better understanding of middle-ear mechanics. The optical sectioning technique of the confocal microscope did not result in any preparation artifacts and was therefore also used to quantify shrinkage due to preparation of histological sections of TMs

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 μm, and an x-ray micro-CT dataset with a voxel size of about 5.5 μm, 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

On the Coupling Between the Incus and the Stapes in the Cat

The connection between the long process and the lenticular process of the incus is extremely fine, so much so that some authors have treated the lenticular process as a separate bone. We review descriptions of the lenticular process that have appeared in the literature, and present some new histological observations. We discuss the dimensions and composition of the lenticular process and of the incudostapedial joint, and present estimates of the material properties for the bone, cartilage, and ligament of which they are composed. We present a preliminary finite-element model which includes the lenticular plate, the bony pedicle connecting the lenticular plate to the long process, the head of the stapes, and the incudostapedial joint. The model has a much simplified geometry. We present simulation results for ranges of values for the material properties. We then present simulation results for this model when it is incorporated into an overall model of the middle ear of the cat. For the geometries and material properties used here, the bony pedicle is found to contribute significant flexibility to the coupling between the incus and the stapes

Tympanic Membrane Boundary Deformations Derived from Static Displacements Observed with Computerized Tomography in Human and Gerbil

The middle ear is too complex a system for its function to be fully understood with simple descriptive models. Realistic mathematical models must be used in which structural elements are represented by geometrically correct three-dimensional (3D) models with correct physical parameters and boundary conditions. In the past, the choice of boundary conditions could not be based on experimental evidence as no clear-cut data were available. We have, therefore, studied the deformation of the tympanic membrane (TM) at its boundaries using X-ray microscopic computed tomography in human and gerbil while static pressure was applied to the ear canal. The 3D models of the TM and its bony attachments were carefully made and used to measure the deformation of the TM with focus on the periphery and the manubrium attachment. For the pars flaccida of the gerbil, the boundary condition can, for the most part, be described as simply supported. For the human pars flaccida, the situation is more complicated: superiorly, the membrane contacts the underlying bone more and more when pushed further inward, and it gradually detaches from the wall when sucked outward. In gerbil, the attachment of the TM to the manubrium can be described as simply supported. In human, the manubrium is attached underneath the TM via the plica mallearis and the contact of the TM with the bone is indirect. For both human and gerbil, a simple boundary condition for the peripheral edge of the pars tensa is not appropriate due to the intricate structure at the edge: the TM thickens rapidly before continuing into the annulus fibrosis which finally makes contact with the bone

Quasi-static Transfer Function of the Rabbit Middle Ear‚ Measured with a Heterodyne Interferometer with High-Resolution Position Decoder

Due to changes in ambient pressure and to the gas-exchange processes in the middle ear (ME) cavity, the ear is subject to ultra-low-frequency pressure variations, which are many orders of magnitude larger than the loudest acoustic pressures. Little quantitative data exist on how ME mechanics deals with these large quasi-static pressure changes and because of this lack of data, only few efforts could be made to incorporate quasi-static behavior into computer models. When designing and modeling ossicle prostheses and implantable ME hearing aids, the effects of large ossicle movements caused by quasi-static pressures should be taken into account. We investigated the response of the ME to slowly varying pressures by measuring the displacement of the umbo and the stapes in rabbit with a heterodyne interferometer with position decoder. Displacement versus pressure curves were obtained at linear pressure change rates between 200 Pa/s and 1.5 kPa/s, with amplitude ±2.5 kPa. The change in stapes position associated with a pressure change is independent of pressure change rate (34 μm peak-to-peak at ±2.5 kPa). The stapes displacement versus pressure curves are highly nonlinear and level off for pressures beyond ±1 kPa. Stapes motion shows no measurable hysteresis at 1.5 kPa/s, which demonstrates that the annular ligament has little viscoelasticity. Hysteresis increases strongly at the lowest pressure change rates. The stapes moves in phase with the umbo and with pressure, but the sense of rotation of the hysteresis loop of stapes is phase inversed. Stapes motion is not a simple lever ratio mimic of umbo motion, but is the consequence of complex changes in ossicle joints and ossicle position. The change in umbo position produced by a ±2.5 kPa pressure change decreases with increasing rate from 165 μm at 200 Pa/s to 118 μm at 1.5 kPa/s. Umbo motion already shows significant hysteresis at 1.5 kPa/s, but hysteresis increases further as pressure change rate decreases. We conclude that in the quasi-static regime, ossicle movement is not only governed by viscoelasticity, but that other effects become dominant as pressure change rate decreases below 1 kPa/s. The increasing hysteresis can be caused by increasing friction as speed of movement decreases, and incorporating speed-dependent friction coefficients will be essential to generate realistic models of ossicle movements at slow pressure change rates