A geometrically nonlinear finite-element model of the cat eardrum

Performance of personalised prosthesis under static pressure: Numerical analysis and experimental validation

This study investigates the performance of personalised middle ear prostheses under static pressure through a combined approach of numerical analysis and experimental validation. The sound transmission performances of both normal and reconstructed middle ears undergo changes under high positive or negative pressure within the middle ear cavity. This pressure fluctuation has the potential to result in prosthesis displacement/extrusion in patients. To optimise the design of middle ear prostheses, it is crucial to consider various factors, including the condition of the middle ear cavity in which the prosthesis is placed. The integration of computational modelling techniques with non-invasive imaging modalities has demonstrated significant promise and distinct prospects in middle ear surgery. In this study, we assessed the efficacy of Finite Element (FE) analysis in modelling the responses of both normal and reconstructed middle ears to elevated static pressure within the ear canal. The FE model underwent validation using experimental data derived from human cadaveric temporal bones before progressing to subsequent investigations. Afterwards, we assessed stapes and umbo displacements in the reconstructed middle ear under static pressure, with either a columella-type prosthesis or a prosthetic incus, closely resembling a healthy incus. Results indicated the superior performance of the prosthetic incus in terms of both sound transmission to the inner ear and stress distribution patterns on the TM, potentially lowering the risk of prosthesis displacement/extrusion. This study underscores the potential of computational analysis in middle ear surgery, encompassing aspects such as prosthesis design, predicting outcomes in ossicular chain reconstruction (OCR), and mitigating experimental costs.

Strain distribution in rabbit eardrums under static pressure

Full-field strain maps of intact rabbit eardrums subjected to static pressures are presented. A stochastic intensity pattern was applied to 12 eardrums, and strain maps were measured at the medial site using a stereoscopic digital image correlation setup for pressures between -2 and 2 kPa. Ear canal overpressures induced circumferential orientated positive strains between manubrium and the eardrum border that increased almost linearly with pressure. Radially orientated negative strains were found at the border and manubrium. Ear canal underpressures caused negative circumferential strains between manubrium and the tympanic annulus but radially orientated positive strains at the borders. The magnitudes of these negative strains at underpressures were larger than those of positive strains at overpressures and were nonlinearly proportional to pressure. In three ears, strains were calculated with intact and removed cochlea. The effect of cochlea removal on the peak-to-peak strain was found to be no more than 3%.

Characterization of the nonlinear elastic behavior of chinchilla tympanic membrane using micro-fringe projection

The mechanical properties of an intact, full tympanic membrane (TM) inside the bulla of a fresh chinchilla were measured under quasi-static pressure from -1.0 kPa to 1.0 kPa applied on the TM lateral side. Images of the fringes projected onto the TM were acquired by a digital camera connected to a surgical microscope and analyzed using a phase-shift method to reconstruct the surface topography. The relationship between the applied pressure and the resulting volume displacement was determined and analyzed using a finite element model implementing a hyperelastic 2(nd)-order Ogden model. Through an inverse method, the best-fit model parameters for the TM were determined to allow the simulation results to agree with the experimental data. The nonlinear stress-strain relationship for the TM of a chinchilla was determined up to an equibiaxial tensile strain of 31% experienced by the TM in the experiments. The average Young's modulus of the chinchilla TM from ten bullas was determined as approximately 19 MPa.

Nonlinear Vibration Response Measured at Umbo and Stapes in the Rabbit Middle ear

Using laser vibrometry and a stimulation and signal analysis method based on multisines, we have measured the response and the nonlinearities in the vibration of the rabbit middle ear at the level of the umbo and the stapes. With our method, we were able to detect and quantify nonlinearities starting at sound pressure levels of 93-dB SPL. The current results show that no significant additional nonlinearity is generated as the vibration signal is passed through the middle ear chain. Nonlinearities are most prominent in the lower frequencies (125 Hz to 1 kHz), where their level is about 40 dB below the vibration response. The level of nonlinearities rises with a factor of nearly 2 as a function of sound pressure level, indicating that they may become important at very high sound pressure levels such as those used in high-power hearing aids.

Energy localization and frequency analysis in the locust ear

Animal ears are exquisitely adapted to capture sound energy and perform signal analysis. Studying the ear of the locust, we show how frequency signal analysis can be performed solely by using the structural features of the tympanum. Incident sound waves generate mechanical vibrational waves that travel across the tympanum. These waves shoal in a tsunami-like fashion, resulting in energy localization that focuses vibrations onto the mechanosensory neurons in a frequency-dependent manner. Using finite element analysis, we demonstrate that two mechanical properties of the locust tympanum, distributed thickness and tension, are necessary and sufficient to generate frequency-dependent energy localization.

A non-linear viscoelastic model for the tympanic membrane

The mechanical behavior of the tympanic membrane displays both non-linearity and viscoelasticity. Previous finite-element models of the tympanic membrane, however, have been either non-linear or viscoelastic but not both. In this study, these two features are combined in a non-linear viscoelastic model. The constitutive equation of this model is a convolution integral composed of a non-linear elastic part, represented by an Ogden hyperelastic model, and an exponential time-dependent part, represented by a Prony series. The model output is compared with the relaxation curves and hysteresis loops observed in previous measurements performed on strips of tympanic membrane. In addition, a frequency-domain analysis is performed based on the obtained material parameters, and the effect of strain rate is explored. The model presented here is suitable for modeling large deformations of the tympanic membrane for frequencies less than approximately 3 rad/s or about 0.6 Hz. These conditions correspond to the pressurization involved in tympanometry.

Estimation of the quasi-static Young's modulus of the eardrum using a pressurization technique

The quasi-static Young's modulus of the eardrum's pars tensa is an important modeling parameter in computer simulations. Recent developments in indentation testing and inverse modeling allow estimation of this parameter with the eardrum in situ. These approaches are challenging because of the curved shape of the pars tensa which requires special care during experimentation to keep the indenter perpendicular to the local surface at the point of contact. Moreover, they involve complicated contact modeling. An alternative computer-based method is presented here in which pressurization is used instead of indentation. The Young's modulus of a thin-shell model of the eardrum with subject-specific geometry is numerically optimized such that simulated pressurized shapes match measured counterparts. The technique was evaluated on six healthy rat eardrums, resulting in a Young's modulus estimate of 22.8±1.5MPa. This is comparable to values estimated using indentation testing. The new pressurization-based approach is simpler to use than the indentation-based method for the two reasons noted above.

Measuring the quasi-static Young's modulus of the eardrum using an indentation technique

Accurate estimation of the quasi-static Young's modulus of the eardrum is important for finite-element modeling. In this study, we adapted a tissue indentation technique and inverse finite-element analysis to estimate the Young's modulus of the eardrum. A custom-built indentation apparatus was used to perform indentation testing on seven rat eardrums in situ after immobilizing the malleus. Testing was done in most cases on the posterior pars tensa. The unloaded shape of each eardrum was measured and used to construct finite-element models with subject-specific geometries to simulate the indentation experiment. The Young's modulus of each specimen was then estimated by numerically optimizing the Young's modulus of each model so that simulation results matched corresponding experimental data. Using an estimated value of 12 microm for the thickness of each model eardrum, the estimated average Young's modulus for the pars tensa was found to be 21.7+/-1.2 MPa. The estimated average Young's modulus is within the range reported in some of the literature. The estimation technique is sensitive to the thickness of the pars tensa used in the model but is not sensitive to relatively large variations in the stiffness of the pars flaccida and manubrium or to the pars tensa/pars flaccida separation conditions.

Effects of ear-canal pressurization on middle-ear bone- and air-conduction responses

In extremely loud noise environments, it is important to not only protect one's hearing against noise transmitted through the air-conduction (AC) pathway, but also through the bone-conduction (BC) pathways. Much of the energy transmitted through the BC pathways is concentrated in the mid-frequency range around 1.5-2 kHz, which is likely due to the structural resonance of the middle ear. One potential approach for mitigating this mid-frequency BC noise transmission is to introduce a positive or negative static pressure in the ear canal, which is known to reduce BC as well as AC hearing sensitivity. In the present study, middle-ear ossicular velocities at the umbo and stapes were measured using human cadaver temporal bones in response to both BC and AC excitations, while static air pressures of +/-400 mm H(2)O were applied in the ear canal. For the maximum negative pressure of -400 mm H(2)O, mean BC stapes-velocity reductions of about 5-8 dB were observed in the frequency range from 0.8 to 2.5 kHz, with a peak reduction of 8.6(+/-4.7)dB at 1.6 kHz. Finite-element analysis indicates that the peak BC-response reduction tends to be in the mid-frequency range because the middle-ear BC resonance, which is typically around 1.5-2 kHz, is suppressed by the pressure-induced stiffening of the middle-ear structure. The measured data also show that the BC responses are reduced more for negative static pressures than for positive static pressures. This may be attributable to a difference in the distribution of the stiffening among the middle-ear components depending on the polarity of the static pressure. The characteristics of the BC-response reductions are found to be largely consistent with the available psychoacoustic data, and are therefore indicative of the relative importance of the middle-ear mechanism in BC hearing.

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.

A nonlinear finite-element model of the newborn middle ear

A three-dimensional static nonlinear finite-element model of a 22-day-old newborn middle ear is presented. The model includes the tympanic membrane (TM), malleus, incus, and two ligaments. The effects of the middle-ear cavity are taken into account indirectly. The geometry is based on a computed-tomography scan and on the published literature, supplemented by histology. A nonlinear hyperelastic constitutive law is applied to model large deformations. The middle-ear cavity and the Young's modulus of the TM have significant effects on TM volume displacements. The TM volume displacement and its nonlinearity and asymmetry increase as the middle-ear cavity volume increases. The effects of the Young's moduli of the ligaments and ossicles are found to be small. The simulated TM volume changes do not reach a plateau when the pressure is varied to either -3 kPa or +3 kPa, which is consistent with the nonflat tails often found in tympanograms in newborns. The simulated TM volume displacements, by themselves and also together with previous ear-canal model results, are compared with equivalent-volume differences derived from tympanometric measurements in newborns. The results suggest that the canal-wall volume displacement makes a major contribution to the total canal volume change, and may be larger than the TM volume displacement.

Finite-element analysis of middle-ear pressure effects on static and dynamic behavior of human ear

A finite-element analysis for static behavior of middle ear under variation of the middle-ear pressure was conducted in a 3D model of human ear by combining the hyperelastic Mooney-Rivlin material model and geometry nonlinearity. An empirical formula was then developed to calculate material parameters of the middle-ear soft tissues as the stress-dependent elastic modulus relative to the middle-ear pressure. Dynamic behavior of the middle ear in response to sound pressure in the ear canal was predicted under various positive and negative middle-ear pressures. The results from static analysis indicate that a positive middle ear pressure produces the static displacements of the tympanic membrane (TM) and footplate more than a negative pressure. The dynamic analysis shows that the reductions of the TM and footplate vibration magnitudes under positive middle-ear pressure are mainly determined by stress dependence of elastic modulus. The reduction of the TM and footplate vibrations under negative pressure was caused by both the geometry changes of middle-ear structures and the stress dependence of elastic modulus.

The discordant eardrum

At frequencies above 3 kHz, the tympanic membrane vibrates chaotically. By having many resonances, the eardrum can transmit the broadest possible bandwidth of sound with optimal sensitivity. In essence, the eardrum works best through discord. The eardrum's success as an instrument of hearing can be directly explained through a combination of its shape, angular placement, and composition. The eardrum has a conical asymmetrical shape, lies at a steep angle with respect to the ear canal, and has organized radial and circumferential collagen fiber layers that provide the scaffolding. Understanding the role of each feature in hearing transduction will help direct future surgical reconstructions, lead to improved microphone and loudspeaker designs, and provide a basis for understanding the different tympanic membrane structures across species. To analyze the significance of each anatomical feature, a computer simulation of the ear canal, eardrum, and ossicles was developed. It is shown that a cone-shaped eardrum can transfer more force to the ossicles than a flat eardrum, especially at high frequencies. The tilted eardrum within the ear canal allows it to have a larger area for the same canal size, which increases sound transmission to the cochlea. The asymmetric eardrum with collagen fibers achieves optimal transmission at high frequencies by creating a multitude of deliberately mistuned resonances. The resonances are summed at the malleus attachment to produce a smooth transfer of pressure across all frequencies. In each case, the peculiar properties of the eardrum are directly responsible for the optimal sensitivity of this discordant drum.