A Non-linear Viscoelastic Model of the Incudostapedial Joint.

The ossicular joints of the middle ear can significantly affect middle-ear function, particularly under conditions such as high-intensity sound pressures or high quasi-static pressures. Experimental investigations of the mechanical behaviour of the human incudostapedial joint have shown strong non-linearity and asymmetry in tension and compression tests, but some previous finite-element models of the joint have had difficulty replicating such behaviour. In this paper, we present a finite-element model of the joint that can match the asymmetry and non-linearity well without using different model structures or parameters in tension and compression. The model includes some of the detailed structures of the joint seen in histological sections. The material properties are found from the literature when available, but some parameters are calculated by fitting the model to experimental data from tension, compression and relaxation tests. The model can predict the hysteresis loops of loading and unloading curves. A sensitivity analysis for various parameters shows that the geometrical parameters have substantial effects on the joint mechanical behaviour. While the joint capsule affects the tension curve more, the cartilage layers affect the compression curve more.

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound.

We present a finite-element model of the gerbil middle ear that, using a set of baseline parameters based primarily on a priori estimates from the literature, generates responses that are comparable with responses we measured in vivo using multi-point vibrometry and with those measured by other groups. We investigated the similarity of numerous features (umbo, pars-flaccida and pars-tensa displacement magnitudes, the resonance frequency and break-up frequency, etc.) in the experimental responses with corresponding ones in the model responses, as opposed to simply computing frequency-by-frequency differences between experimental and model responses. The umbo response of the model is within the range of variability seen in the experimental data in terms of the low-frequency (i.e., well below the middle-ear resonance) magnitude and phase, the main resonance frequency and magnitude, and the roll-off slope and irregularities in the response above the resonance frequency, but is somewhat high for frequencies above the resonance frequency. At low frequencies, the ossicular axis of rotation of the model appears to correspond to the anatomical axis but the behaviour is more complex at high frequencies (i.e., above the pars-tensa break-up). The behaviour of the pars tensa in the model is similar to what is observed experimentally in terms of magnitudes, phases, the break-up frequency of the spatial vibration pattern, and the bandwidths of the high-frequency response features. A sensitivity analysis showed that the parameters that have the strongest effects on the model results are the Young's modulus, thickness and density of the pars tensa; the Young's modulus of the stapedial annular ligament; and the Young's modulus and density of the malleus. Displacements of the tympanic membrane and manubrium and the low-frequency displacement of the stapes did not show large changes when the material properties of the incus, stapes, incudomallear joint, incudostapedial joint, and posterior incudal ligament were changed by ±10 % from their values in the baseline parameter set.

Effect of opening middle-ear cavity on vibrations of gerbil tympanic membrane.

This paper presents in vivo experimental measurements of vibrations on the pars flaccida, along the manubrium and at several points on the pars tensa in the gerbil with open middle-ear cavity. The effects of progressive opening of the middle-ear cavity are presented, with up to five different extents of opening. In all manubrial, pars-tensa and pars-flaccida responses, opening the cavity causes an increase in the low-frequency magnitude and a shift of the main middle-ear resonance to lower frequencies and introduces an antiresonance. However, opening the cavity has little or no effect on either the mode of vibration of the manubrium or the breakup frequency of the pars tensa. When the opening is gradually widened, the antiresonance frequency moves to higher frequencies. When the opening is made as wide as anatomically possible, the antiresonance moves to almost 10 kHz. The main increase in the low-frequency response magnitude happens upon making the smallest hole in the cavity wall, and further progressive enlarging of the opening has little or no effect on the low-frequency magnitude. The antiresonance interferes with the response shapes. An identification method is suggested for eliminating the effect of the antiresonance in order to estimate the ideal open-cavity response. The method is validated and then applied to manubrial and pars-tensa responses. Estimating the ideal open-cavity responses will simplify comparison of the data with numerical models which do not include the air cavity. The data collected at intermediate stages of opening will be useful in validating models that do include the cavity.

Experimental study of vibrations of gerbil tympanic membrane with closed middle ear cavity.

The purpose of the present work is to investigate the spatial vibration pattern of the gerbil tympanic membrane (TM) as a function of frequency. In vivo vibration measurements were done at several locations on the pars flaccida and pars tensa, and along the manubrium, on surgically exposed gerbil TMs with closed middle ear cavities. A laser Doppler vibrometer was used to measure motions in response to audio frequency sine sweeps in the ear canal. Data are presented for two different pars flaccida conditions: naturally flat and retracted into the middle ear cavity. Resonance of the flat pars flaccida causes a minimum and a shallow maximum in the displacement magnitude of the manubrium and pars tensa at low frequencies. Compared with a flat pars flaccida, a retracted pars flaccida has much lower displacement magnitudes at low frequencies and does not affect the responses of the other points. All manubrial and pars tensa points show a broad resonance in the range of 1.6 to 2 kHz. Above this resonance, the displacement magnitudes of manubrial points, including the umbo, roll off with substantial irregularities. The manubrial points show an increasing displacement magnitude from the lateral process toward the umbo. Above 5 kHz, phase differences between points along the manubrium start to become more evident, which may indicate flexing of the tip of the manubrium or a change in the vibration mode of the malleus. At low frequencies, points on the posterior side of the pars tensa tend to show larger displacements than those on the anterior side. The simple low-frequency vibration pattern of the pars tensa becomes more complex at higher frequencies, with the breakup occurring at between 1.8 and 2.8 kHz. These observations will be important for the development and validation of middle ear finite-element models for the gerbil.

Reverse transmission along the ossicular chain in gerbil.

In a healthy cochlea stimulated with two tones f (1) and f (2), combination tones are generated by the cochlea's active process and its associated nonlinearity. These distortion tones travel "in reverse" through the middle ear. They can be detected with a sensitive microphone in the ear canal (EC) and are known as distortion product otoacoustic emissions. Comparisons of ossicular velocity and EC pressure responses at distortion product frequencies allowed us to evaluate the middle ear transmission in the reverse direction along the ossicular chain. In the current study, the gerbil ear was stimulated with two equal-intensity tones with fixed f (2)/f (1) ratio of 1.05 or 1.25. The middle ear ossicles were accessed through an opening of the pars flaccida, and their motion was measured in the direction in line with the stapes piston-like motion using a laser interferometer. When referencing the ossicular motion to EC pressure, an additional amplitude loss was found in reverse transmission compared to the gain in forward transmission, similar to previous findings relating intracochlear and EC pressure. In contrast, sound transmission along the ossicular chain was quite similar in forward and reverse directions. The difference in middle ear transmission in forward and reverse directions is most likely due to the different load impedances-the cochlea in forward transmission and the EC in reverse transmission.

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.

Evaluation of a model for studies on sequelae after acute otitis media in the Mongolian gerbil.

CONCLUSIONS: The model appears relevant for studies on sequelae after acute otitis media (AOM), and may be the seed of a new, chronic tympanic membrane perforation model in the gerbil. OBJECTIVES: To evaluate an experimental model for abortive otitis media and to assess the structural and functional changes of the tympanic membrane in the resolving phase. MATERIALS AND METHODS: The middle ears of 16 Mongolian gerbils were inoculated with type 6a Streptococcus pneumoniae. Half of the animals were treated with antibiotics on days 4-6, when otoscopy was performed as well. After 1, 2, 3 or 4 weeks the animals were sacrificed and their tympanic membranes were examined by otoscopy, dissection microscopy, light microscopy and moire interferometry. RESULTS: On days 4 and 6 AOM was produced in approximately 80% of the animals and perforations prevailed in approximately 30% at the study end points. Clinical signs of AOM and oedema of the tympanic membrane had already started to reduce after 1 week, and often resolved within 2 weeks. The mechanical stiffness of the tympanic membrane remained relatively unharmed in the non-perforated ears. The antibiotic treatment seemed to reduce the duration of oedema but not the perforation rate.

Do Swiftlets have an ear for echolocation? The functional morphology of Swiftlets' middle ears.

The Oilbird and many Swiftlet species are unique among birds for their ability to echolocate. Echolocaters may benefit from improved hearing sensitivity. Therefore, morphological adaptations to echolocation might be present in echolocating birds' middle ears. We studied the functional morphology of the tympano-ossicular chain of seven specimens of four echolocating Swiftlet species and one specimen each of five non-echolocating species. Three dimensional (3D) reconstructions were made from micro-Computer-Tomographic (muCT) scans. The reconstructions were used in functional morphological analyses and model calculations. A two dimensional (2D) rigid rod model with fixed rotational axes was developed to study footplate output-amplitudes and to describe how changes in the arrangement of the tympano-ossicular chain affect its function. A 3D finite element model was used to predict ossicular-chain movement and to investigate the justification of the 2D approach. No morphological adaptations towards echolocation were found in the middle-ear lever system or in the mass impedance of the middle ear. A wide range of middle-ear configurations result in maximum output-amplitudes and all investigated species are congruent with these predicted best configurations. Echolocation is unlikely to depend on adaptations in the middle ear tympano-ossicular chain.

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 microm 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 microm at 200 Pa/s to 118 microm 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.

A geometrically nonlinear finite-element model of the cat eardrum.

Current finite-element (FE) models of the eardrum are limited to low pressures because of the assumption of linearity. Our objective is to investigate the effects of geometric nonlinearity in FE models of the cat eardrum with an approximately immobile malleus for pressures up to +/-2.2 kPa, which are within the range of pressures used in clinical tympanometry. Displacements computed with nonlinear models increased less than in proportion to applied pressure, similar to what is seen in measured data. In both simulations and experiments, there is a shift inferiorly in the location of maximum displacement in response to increasingly negative middle-ear pressures. Displacement patterns computed for small pressures and for large positive pressures differed from measured patterns in the position of the maximum pars-tensa displacement. Increasing the thickness of the postero-superior pars tensa in the models shifted the location of the computed maximum toward the measured location. The largest computed pars-tensa strains were mostly less than 2%, implying that a linearized material model is a reasonable approximation. Geometric nonlinearity must be considered when simulating eardrum response to high pressures because purely linear models cannot take into account the effects of changing geometry. At higher pressures, material nonlinearity may become more important.

Thickness distribution of fresh and preserved human eardrums measured with confocal microscopy.

HYPOTHESIS: In this study, the thickness distribution of the fresh human eardrum was measured and possible thickness changes in successive stages of preservation and preparation were studied. METHODS: The thickness measurement was performed on axial fluorescence images taken perpendicularly through the membrane with a confocal microscope. The influence of fixation and preservation (in Cialit solution) on the thickness was also investigated. The same eardrum was prepared (decalcified, dehydrated, and stained) for histologic sectioning and the thickness was measured on the sections using conventional light microscopy. RESULTS: Similar thickness distributions in the measured samples (n = 3) were observed. The pars tensa has a rather constant thickness in a central region curving as a horseshoe upward around the manubrium. The membrane thickens slightly from the inferior to the superior side. The anterior region is thicker than the posterior region. In narrow bands along the manubrium, peripheral rim, and in the region inferior to the umbo, a much larger thickness in comparison with that in the central region was found. Mean thicknesses of approximately 40, 50, and 120 microm were observed in the central region of the studied eardrums, respectively. CONCLUSION: Whereas the thickness distribution of the human eardrums shows similar features, the absolute thickness seems to vary a lot from one specimen to another. There is no significant difference in thickness of the same membrane in fresh, fixed, or preserved condition. Thus, human eardrums may be safely preserved in fixative for later thickness measurements. The histologic preparation process, however, causes a significant location-dependent shrinkage.

Refractive index of tissue measured with confocal microscopy.

Refractive index of tissue is an essential parameter in many bio-optical experiments, yet little data can be found in literature. Several methods have been proposed to measure refractive index in tissue samples, but all have specific limitations, such as low accuracy, the need for large amounts of tissue, or the complexity of the measurement setup. We propose a new method using a standard confocal microscope and requiring only small tissue samples. A thin slice of tissue is put next to a layer of immersion fluid of exactly the same thickness. The actual thickness of the fluid layer is directly measured with the microscope, as there is no refractive index mismatch. A difference between index of refraction of the tissue and of the immersion medium causes an axial scaling factor. The optical thickness of the specimen is thus measured with the microscope, and as its actual thickness equals the known thickness of the fluid layer, the axial scaling factor is readily determined. From this factor, we calculate the refractive index of the tissue. We use a diffraction model to take the point spread function (PSF) of the microscope into account, so we can determine the index of refraction to a very high accuracy. We demonstrate the method on bovine muscle tissue and find a value of n=1.382+/-0.004, at 592 nm.

Thickness of the gerbil tympanic membrane measured with confocal microscopy.

Thickness data for the gerbil tympanic membrane, an extremely thin biological membrane, are presented. Thickness measurements were performed on fresh material using fluorescence images taken perpendicular through the membrane with a commercial confocal microscope. Thickness varies strongly across the membrane. Similar thickness distributions in all samples (pars tensa n = 11; pars flaccida n = 3) were observed. The pars tensa has a rather constant thickness of about 7 microm in the central region curving as a horse shoe upwards around the manubrium. In the most superior parts of the pars tensa thickness becomes gradually twice as large. Thickness increases also steeply from the central region towards the edges (about 35 microm near the annulus and 20 microm near the manubrium). A pronounced, local thickening of about 30 microm is present close to the edge and extends as a ring along the entire annular periphery of the pars tensa. Overall, the pars flaccida is thicker than the pars tensa and has a rugged surface. Its central region has a mean thickness of about 24 microm with a mean variation of about 4 microm. The average thickness in the inferior region is slightly larger than in the superior region. The pars flaccida thickens steeply, up to about 80 microm, near the edges.

Three approaches for estimating the elastic modulus of the tympanic membrane.

The function of the middle ear is to resolve the acoustic impedance mismatch between the air in the ear canal and the fluid of the inner ear. Without this impedance matching, very little acoustic energy would be absorbed into the cochlea. The first step in this process is the tympanic membrane (TM) converting sound in the ear canal into vibrations of the middle ear bones. Understanding how the TM manages its task so successfully over such a broad frequency range should lead to more satisfactory and less variable TM repairs (myringoplasty). In addition, understanding the mechanics of the TM is necessary to improve the coupling between ossicular prostheses and the TM. Mathematical models have played a central role in helping the research community understand the mechanics of the eardrum. However, all models require parameters as inputs. Unfortunately, most of the parameters needed for modeling the TM are not well known. In this work, several approaches for inferring the material properties of the TM are explored. First, constitutive modeling is used to estimate an elastic modulus based on the elastic modulus of collagen and experimentally observed fiber densities. Second, experimental tension and bending test results from the literature are re-interpreted using composite laminate theory. Lastly, dynamic measurements of the cat TM are used in conjunction with a composite shell model to bound the material parameters. Values from the literature, both measurement and modeling efforts, and from the present analysis are brought together to form a coherent picture of the TM's material properties. In the human, the data bound the elastic modulus between 0.1 and 0.3 GPa. In the cat, the data suggest a range of 0.1-0.4 GPa. These values are significantly higher than previous estimates.

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.

Response of the cat eardrum to static pressures: mobile versus immobile malleus.

A phase-shift shadow moiré interferometer was used to measure the shape of the cat eardrum with a normal mobile malleus and with an immobile malleus as it was cyclically loaded with static middle-ear pressures up to +/-2.2 kPa. The shape was monitored throughout the loading and unloading phases, and three complete cycles were observed. The mobile-manubrium measurements were made in five ears. In three ears, the malleus was then immobilized with a drop of glue placed on the head of the malleus. Eardrum displacements were calculated by subtracting shape images pixel by pixel. The measurements are presented in the form of gray-level full-field shape and displacement images, of displacement profiles, and of pressure-displacement curves for selected points. Displacement patterns with a mobile malleus show that pars-tensa displacements are larger than manubrial displacements, with the maximum pars-tensa displacement occurring in the posterior region in all cats except one. Displacements vary from cycle to cycle and display hysteresis. For both the mobile-malleus and immobile-malleus cases, the eardrum response is nonlinear. The response is asymmetric, with lateral displacements being larger than medial displacements. With a mobile malleus, manubrial displacements exhibit more pronounced asymmetry than do pars-tensa displacements.

Pars flaccida displacement pattern in purulent otitis media in the gerbil.

HYPOTHESIS: Our hypothesis is that purulent otitis media and otitis media with effusion cause stiffness loss of the tympanic membrane. This loss of stiffness may be persistent and precede the development of retraction pockets and cholesteatoma. BACKGROUND: Postinflammatory changes such as retraction pockets and cholesteatoma develop in the pars flaccida and in the pars tensa of the tympanic membrane. In our previous experimental studies, stiffness changes were shown to develop early in the pars tensa in response to purulent otitis media and otitis media with effusion. These changes are suggested to be precursors to a later development of retraction pockets and cholesteatoma. In the clinical situation, retraction pockets are often found in the pars flaccida only. The aim of the current study was thus to investigate whether stiffness changes appear also in the pars flaccida during purulent otitis media. METHODS: Streptococcus pneumoniae type 3 was injected into the middle ear to induce purulent otitis media. As a measure of pars flaccida stiffness, peak displacement versus middle ear pressure was used. The peak displacement measurements were obtained from full-field moiré; interferometry, which is a noncontacting optical technique for deformation measurements. RESULTS: Ears with purulent otitis media showed increased peak displacement of the pars flaccida at a middle ear pressure of 200 daPa, compared with normal controls. CONCLUSION: There was a decreased mechanical stiffness of the pars flaccida in acute purulent otitis media. This decreased stiffness may predispose for future retraction pocket formation and cholesteatoma development.