Relative importance and interactions of parameters of finite-element models of human middle ear

In the last decades, finite-element models of the middle ear have been widely used to predict the middle-ear vibration outputs. Even with the simplest linear assumption for material properties of the structures in the middle ear, these models need tens of parameters. Due to the complexities of measurements of material properties of these structures, accurate estimations of the values of most of these parameters are not possible. In this study, we benefited from the stochastic finite-element model of the middle ear we had developed in the past, to perform global sensitivity analysis. For this aim, we implemented Sobol' sensitivity analysis which ranks the importance of all uncertain parameters and interactions among them at different frequencies. To decrease the computational costs, we found Sobol' indices from surrogate models that we created using stochastic finite-element results and the polynomial chaos expansion method. Based on the results, the Young's modulus and thickness of the tympanic membrane, Young's modulus and damping of the stapedial annular ligaments, and the Young's modulus of ossicles are among the parameters with the greatest impacts on vibrations of the umbo and stapes footplate. Furthermore, the most significant interactions happen between the Young's modulus and thickness of the tympanic membrane.

Mammalian middle ear mechanics: A review

The middle ear is part of the ear in all terrestrial vertebrates. It provides an interface between two media, air and fluid. How does it work? In mammals, the middle ear is traditionally described as increasing gain due to Helmholtz's hydraulic analogy and the lever action of the malleus-incus complex: in effect, an impedance transformer. The conical shape of the eardrum and a frequency-dependent synovial joint function for the ossicles suggest a greater complexity of function than the traditional view. Here we review acoustico-mechanical measurements of middle ear function and the development of middle ear models based on these measurements. We observe that an impedance-matching mechanism (reducing reflection) rather than an impedance transformer (providing gain) best explains experimental findings. We conclude by considering some outstanding questions about middle ear function, recognizing that we are still learning how the middle ear works.

A Novel Methodology to Obtain the Mechanical Properties of Membranes by Means of Dynamic Tests

A new, non-destructive methodology is proposed in this work in order to determine the mechanical properties of membrane using vibro-acoustic tests. This procedure is based on the dynamic analysis of the behavior of the membrane. When the membrane is subjected to a sound excitation it responds by vibrating based on its modal characteristics and this modal parameter is directly related to its mechanical properties. The paper is structured in two parts. First, the theoretical bases of the test are presented. The interaction between the sound waves and the membrane (mechano-acoustic coupling) is complex and requires meticulous study. It was broadly studied by means of numerical simulations. A summary of this study is shown. Aspects, such as the position of the sound source, the measuring points, the dimensions of the membrane, the frequency range, and the magnitudes to be measured, among others, were evaluated. The validity of modal analysis curve-fitting techniques to extract the modal parameter from the data measures was also explored. In the second part, an experimental test was performed to evaluate the validity of the method. A membrane of the same material with three different diameters was measured with the aim of estimating the value of the Young’s modulus. The procedure was applied and satisfactory results were obtained. Additionally, the experiment shed light on aspects that must be taken account in future experiments.

Statistical analysis of the human middle ear mechanical properties

Many experimental data on the human middle ear (ME) mechanics and dynamics can be found in the literature. Nevertheless, discussions about the uncertainties of these data are scarce. The present study compiles experimental data on the mechanical properties of the human ME. The summary statistics of mean and standard deviation of the data were collected and the coefficients of variation were computed and pooled. Moreover, the linear correlation and distribution were assessed for the ossicles' mass. Results show that, generally, the uncertainties of the stiffness properties of the tympanic membrane, ligaments, and tendons are larger than the uncertainties of the ossicles' mass. In addition, the uncertainties of the ME response vary across frequency. The vibration measures, such as the stapes' velocity normalized by the sound pressure at the tympanic membrane, are more uncertain than ME input impedance and reflectance. It is expected that the results presented in this study will provide the basis for the development of probabilistic models of the human ME.

Material Identification on Thin Shells Using the Virtual Fields Method, Demonstrated on the Human Eardrum

Characterization of material parameters from experimental data remains challenging, especially on biological structures. One of such techniques allowing for the inverse determination of material parameters from measurement data is the virtual fields method (VFM). However, application of the VFM on general structures of complicated shape has not yet been extensively investigated. In this paper, we extend the framework of the VFM method to thin curved solids in three-dimensional, commonly denoted shells. Our method is then used to estimate the Young's modulus and hysteretic damping of the human eardrum. By utilizing Kirchhoff plate theory, we assume that the behavior of the shell varies linearly through the thickness. The total strain of the shell can then be separated in a bending and membrane strain. This in turn allowed for an application of the VFM based only on data of the outer surface of the shell. We validated our method on simulated and experimental data of a human eardrum made to vibrate at certain frequencies. It was shown that the identified material properties were accurately determined based only on data from the outer surface and are in agreement with literature. Additionally, we observed that neither the bending nor the membrane strain in an human eardrum can be neglected and both contribute significantly to the total strain found experimentally.

Mimicking the Human Tympanic Membrane: The Significance of Scaffold Geometry

The human tympanic membrane (TM) captures sound waves from the environment and transforms them into mechanical motion. The successful transmission of these acoustic vibrations is attributed to the unique architecture of the TM. However, a limited knowledge is available on the contribution of its discrete anatomical features, which is important for fabricating functional TM replacements. This work synergizes theoretical and experimental approaches toward understanding the significance of geometry in tissue-engineered TM scaffolds. Three test designs along with a plain control are chosen to decouple some of the dominant structural elements, such as the radial and circumferential alignment of the collagen fibrils. In silico models suggest a geometrical dependency of their mechanical and acoustical responses, where the presence of radially aligned fibers is observed to have a more prominent effect compared to their circumferential counterparts. Following which, a hybrid fabrication strategy combining electrospinning and additive manufacturing has been optimized to manufacture biomimetic scaffolds within the dimensions of the native TM. The experimental characterizations conducted using macroindentation and laser Doppler vibrometry corroborate the computational findings. Finally, biological studies with human dermal fibroblasts and human mesenchymal stromal cells reveal a favorable influence of scaffold hierarchy on cellular alignment and subsequent collagen deposition.

Biomimetic Tympanic Membrane Replacement Made by Melt Electrowriting

The tympanic membrane (TM) transfers sound waves from the air into mechanical motion for the ossicular chain. This requires a high sensitivity to small dynamic pressure changes and resistance to large quasi-static pressure differences. The TM achieves this by providing a layered structure of about 100µm in thickness, a low flexural stiffness, and a high tensile strength. Chronically infected middle ears require reconstruction of a large area of the TM. However, current clinical treatment can cause a reduction in hearing. With the novel additive manufacturing technique of melt electrowriting (MEW), it is for the first time possible to fabricate highly organized and biodegradable membranes within the dimensions of the TM. Scaffold designs of various fiber composition are analyzed mechanically and acoustically. It can be demonstrated that by customizing fiber orientation, fiber diameter, and number of layers the desired properties of the TM can be met. An applied thin collagen layer seals the micropores of the MEW-printed membrane while keeping the favorable mechanical and acoustical characteristics. The determined properties are beneficial for implantation, closely match those of the human TM, and support the growth of a neo-epithelial layer. This proves the possibilities to create a biomimimetic TM replacement using MEW.

Mouse middle-ear forward and reverse acoustics

The mouse is an important animal model for hearing science. However, our knowledge of the relationship between mouse middle-ear (ME) anatomy and function is limited. The ME not only transmits sound to the cochlea in the forward direction, it also transmits otoacoustic emissions generated in the cochlea to the ear canal (EC) in the reverse direction. Due to experimental limitations, a complete characterization of the mouse ME has not been possible. A fully coupled finite-element model of the mouse EC, ME, and cochlea was developed and calibrated against experimental measurements. Impedances of the EC, ME, and cochlea were calculated, alongside pressure transfer functions for the forward, reverse, and round-trip directions. The effects on sound transmission of anatomical changes such as removing the ME cavity, pars flaccida, and mallear orbicular apophysis were also calculated. Surprisingly, below 10 kHz, the ME cavity, eardrum, and stapes annular ligament were found to significantly affect the cochlear input impedance, which is a result of acoustic coupling through the round window. The orbicular apophysis increases the delay of the transmission line formed by the flexible malleus, incus, and stapes, and improves the forward sound-transmission characteristics in the frequency region of 7-30 kHz.

Fabrication of tissue-engineered tympanic membrane patches using 3D-Printing technology

In recent years, scaffolds produced in 3D printing technology have become more widespread tool due to providing more advantages than traditional methods in tissue engineering applications. In this research, it was aimed to produce patches for the treatment of tympanic membrane perforations which caused significant hearing loss by using 3D printing method. Polylactic acid(PLA) scaffolds with Chitosan(CS) and Sodium Alginate(SA) added in various ratios were prepared for artificial eardrum patches. Different amounts of chitosan and sodium alginate added to PLA increased the biocompatibility of the produced scaffolds. The created patches were designed by mimicking the thickness of the natural tympanic membrane thanks to the precision provided by the 3D printed method. The produced scaffolds were analyzed separately for chemical, morphological, mechanical and biocompatibility properties. Scanning electron microscope (SEM), Fourier-transform infrared (FT-IR) spectroscopy was performed to observe the surface morphology and chemical structure of the scaffolds. Mechanical, thermal and physical properties, swelling and degradation behaviors were examined to fully analyze whole characteristic features of the samples. Cell culture study was also performed to demonstrate the biocompatibility properties of the fabricated scaffolds with human adipose tissue-derived mesenchymal stem cells (hAD-MSCs). 15 wt % PLA was selected as the control group and among all concentrations of CS and SA, groups containing 3 wt% CS and 3 wt% SA showed significantly superior and favorable features in printing quality. The research continued with these two scaffolds (3 wt% CS, and 3 wt% SA), which showed improved print quality when added to PLA. Overall, these results show that PLA/CS and PLA/SA 3D printed artificial patches have the potential to tissue engineering solutions to repair tympanic membrane perforation for people with hearing loss.

Mechanical Properties of Baboon Tympanic Membrane from Young to Adult

Mechanical properties of the tympanic membrane (TM) play an important role in sound transmission through the middle ear. While numerous studies have investigated the mechanical properties of the adult human TM, the effects of age on the TM's properties remain unclear because of the limited published data on the TM of young children. To address this deprivation, we used baboons in this study as an animal model for investigating the effect of age on the mechanical properties of the TM. Temporal bones were harvested from baboons (Papio anubis) of four different age groups: less than 1 year, 1-3 years, 3-5 years, and older than 5 years of age or adult. The TM specimens were harvested from baboon temporal bones and cut into rectangle strips along the inferior-superior direction, mainly capturing the influence of the circumferential direction fibers on the TM's mechanical properties. The elasticity, ultimate tensile strength, and relaxation behavior of the baboon TM were measured in each of the four age groups with a mechanical analyzer. The average effective Young's modulus of adult baboon TM was approximately 3.1 MPa, about two times higher than that of a human TM. The Young's moduli of the TM samples demonstrated a 26 % decrease from newborn to adult (from 4.2 to 3.1 MPa). The average ultimate tensile strength of the TMs for all the age groups was ~ 2.5 MPa. There was no significant change in the ultimate tensile strength and relaxation behavior among age groups. The preliminary results reported in this study provide a first step towards understanding the effect of age on the TM mechanical properties from young to adult.

Tympanic Membrane Collagen Expression by Dynamically Cultured Human Mesenchymal Stromal Cell/Star-Branched Poly(ε-Caprolactone) Nonwoven Constructs

The tympanic membrane (TM) primes the sound transmission mechanism due to special fibrous layers mainly of collagens II, III, and IV as a product of TM fibroblasts, while type I is less represented. In this study, human mesenchymal stromal cells (hMSCs) were cultured on star-branched poly(ε-caprolactone) (*PCL)-based nonwovens using a TM bioreactor and proper differentiating factors to induce the expression of the TM collagen types. The cell cultures were carried out for one week under static and dynamic conditions. Reverse transcriptase-polymerase chain reaction (RT-PCR) and immunohistochemistry (IHC) were used to assess collagen expression. A Finite Element Model was applied to calculate the stress distribution on the scaffolds under dynamic culture. Nanohydroxyapatite (HA) was used as a filler to change density and tensile strength of *PCL scaffolds. In dynamically cultured *PCL constructs, fibroblast surface marker was overexpressed, and collagen type II was revealed via IHC. Collagen types I, III and IV were also detected. Von Mises stress maps showed that during the bioreactor motion, the maximum stress in *PCL was double that in HA/*PCL scaffolds. By using a *PCL nonwoven scaffold, with suitable physico-mechanical properties, an oscillatory culture, and proper differentiative factors, hMSCs were committed into fibroblast lineage-producing TM-like collagens.

The effect of blast overpressure on the mechanical properties of the human tympanic membrane

The rupture of the tympanic membrane (TM) is one of the major indicators for blast injuries due to the vulnerability of TM under exposure to blast overpressure. The mechanical properties of the human TM exhibit a significant change after it is exposed to such a high intensity blast. To date, the published data were obtained from measurement on TM strips cut from a TM following an exposure to blast overpressure. The dissection of a TM for preparation of strip samples can induce secondary damage to the TM and thus potentially lead to data not representative of the blast damage. In this paper, we conduct mechanical testing on the full TM in a human temporal bone. A bulging experiment on the entire TM is carried out on each sample prepared from a temporal bone following the exposure to blast three times at a pressure level slightly below the TM rupture threshold. Using a micro-fringe projection method, the volume displacement is obtained as a function of pressure, and their relationship is modeled in the finite element analysis to determine the mechanical properties of the post-blast human TMs, the results of which are compared with the control TMs without an exposure to the blast. It is found that Young's modulus of human TM decreases by approximately 20% after exposure to multiple blast waves. The results can be used in the human ear simulation models to assist the understanding of the effect of blast overpressure on hearing loss.

Surface Motion Changes of Tympanic Membrane Damaged by Blast Waves

Eardrum or tympanic membrane (TM) is a multilayer soft tissue membrane located at the end of the ear canal to receive sound pressure and transport the sound into the middle ear and cochlea. Recent studies reported that the TM microstructure and mechanical properties varied after the ear was exposed to blast overpressure. However, the impact of such biomechanical changes of the TM on its movement for sound transmission has not been investigated. This paper reports the full-field surface motion of the human TM using the scanning laser Doppler vibrometry in human temporal bones under normal and postblast conditions. An increase of the TM displacement after blast exposure was observed in the posterior region of the TM in four temporal bone samples at the frequencies between 3 and 4 kHz. A finite element model of human TM with multilayer microstructure and orthogonal fiber network was created to simulate the TM damaged by blast waves. The consistency between the experimental data and the model-derived TM surface motion suggests that the tissue injuries were resulted from a combination of mechanical property change and regional discontinuity of collagen fibers. This study provides the evidences of surface motion changes of the TM damaged by blast waves and possible fiber damage locations.

Finite-Element Modelling of the Acoustic Input Admittance of the Newborn Ear Canal and Middle Ear

Admittance measurement is a promising tool for evaluating the status of the middle ear in newborns. However, the newborn ear is anatomically very different from the adult one, and the acoustic input admittance is different than in adults. To aid in understanding the differences, a finite-element model of the newborn ear canal and middle ear was developed and its behaviour was studied for frequencies up to 2000 Hz. Material properties were taken from previous measurements and estimates. The simulation results were within the range of clinical admittance measurements made in newborns. Sensitivity analyses of the material properties show that in the canal model, the maximum admittance and the frequency at which that maximum admittance occurs are affected mainly by the stiffness parameter; in the middle-ear model, the damping is as important as the stiffness in influencing the maximum admittance magnitude but its effect on the corresponding frequency is negligible. Scaling up the geometries increases the admittance magnitude and shifts the resonances to lower frequencies. The results suggest that admittance measurements can provide more information about the condition of the middle ear when made at multiple frequencies around its resonance.

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.

Mechanical damage of tympanic membrane in relation to impulse pressure waveform - A study in chinchillas

Mechanical damage to middle ear components in blast exposure directly causes hearing loss, and the rupture of the tympanic membrane (TM) is the most frequent injury of the ear. However, it is unclear how the severity of injury graded by different patterns of TM rupture is related to the overpressure waveforms induced by blast waves. In the present study, the relationship between the TM rupture threshold and the impulse or overpressure waveform has been investigated in chinchillas. Two groups of animals were exposed to blast overpressure simulated in our lab under two conditions: open field and shielded with a stainless steel cup covering the animal head. Auditory brainstem response (ABR) and wideband tympanometry were measured before and after exposure to check the hearing threshold and middle ear function. Results show that waveforms recorded in the shielded case were different from those in the open field and the TM rupture threshold in the shielded case was lower than that in the open field (3.4 ± 0.7 vs. 9.1 ± 1.7 psi or 181 ± 1.6 vs. 190 ± 1.9 dB SPL). The impulse pressure energy spectra analysis of waveforms demonstrates that the shielded waveforms include greater energy at high frequencies than that of the open field waves. Finally, a 3D finite element (FE) model of the chinchilla ear was used to compute the distributions of stress in the TM and the TM displacement with impulse pressure waves. The FE model-derived change of stress in response to pressure loading in the shielded case was substantially faster than that in the open case. This finding provides the biomechanical mechanisms for blast induced TM damage in relation to overpressure waveforms. The TM rupture threshold difference between the open and shielded cases suggests that an acoustic role of helmets may exist, intensifying ear injury during blast exposure.

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.

Feedback characteristics between implantable microphone and transducer in middle ear cavity

With the advent of implantable hearing aids, implementation and acoustic sensing strategy of the implantable microphone becomes an important issue; among the many types of implantable microphone, placing the microphone in middle ear cavity (MEC) has advantages including simple operation and insensitive to skin touching or chewing motion. In this paper, an implantable microphone was implemented and researched feedback characteristic when both the implantable microphone and the transducer were placed in the MEC. Analytical and finite element analysis were conducted to design the microphone to have a natural frequency of 7 kHz and showed good characteristics of SNR and sensitivity. For the feedback test, simple analytical and finite element analysis were calculated and compared with in vitro experiments (n = 4). From the experiments, the open-loop gain and feedback factor were measured and the minimum gain margin measured as 14.3 dB.

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.

Full-field thickness distribution of human tympanic membrane obtained with optical coherence tomography

The full-field thickness distribution, three-dimensional surface model and general morphological data of six human tympanic membranes are presented. Cross-sectional images were taken perpendicular through the membranes using a high-resolution optical coherence tomography setup. Five normal membranes and one membrane containing a pathological site are included in this study. The thickness varies strongly across each membrane, and a great deal of inter-specimen variability can be seen in the measurement results, though all membranes show similar features in their respective relative thickness distributions. Mean thickness values across the pars tensa ranged between 79 and 97 μm; all membranes were thinnest in the central region between umbo and annular ring (50-70 μm), and thickness increased steeply over a small distance to approximately 100-120 μm when moving from the central region either towards the peripheral rim of the pars tensa or towards the manubrium. Furthermore, a local thickening was noticed in the antero-inferior quadrant of the membranes, and a strong linear correlation was observed between inferior-posterior length and mean thickness of the membrane. These features were combined into a single three-dimensional model to form an averaged representation of the human tympanic membrane. 3D reconstruction of the pathological tympanic membrane shows a structural atrophy with retraction pocket in the inferior portion of the pars tensa. The change of form at the pathological site of the membrane corresponds well with the decreased thickness values that can be measured there.

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.

Fluorescent stereo microscopy for 3D surface profilometry and deformation mapping

Recently, mechanobiology has received increased attention. For investigation of biofilm and cellular tissue, measurements of the surface topography and deformation in real-time are a pre-requisite for understanding the growth mechanisms. In this paper, a novel three-dimensional (3D) fluorescent microscopic method for surface profilometry and deformation measurements is developed. In this technique a pair of cameras are connected to a binocular fluorescent microscope to acquire micrographs from two different viewing angles of a sample surface doped or sprayed with fluorescent microparticles. Digital image correlation technique is used to search for matching points in the pairing fluorescence micrographs. After calibration of the system, the 3D surface topography is reconstructed from the pair of planar images. When the deformed surface topography is compared with undeformed topography using fluorescent microparticles for movement tracking of individual material points, the full field deformation of the surface is determined. The technique is demonstrated on topography measurement of a biofilm, and also on surface deformation measurement of the biofilm during growth. The use of 3D imaging of the fluorescent microparticles eliminates the formation of bright parts in an image caused by specular reflections. The technique is appropriate for non-contact, full-field and real-time 3D surface profilometry and deformation measurements of materials and structures at the microscale.

Dynamic properties of human tympanic membrane based on frequency-temperature superposition

The human tympanic membrane (TM) transfers sound in the ear canal into the mechanical vibration of the ossicles in the middle ear. The dynamic properties of TM directly affect the middle ear transfer function. The static or quasi-static mechanical properties of TM were reported in the literature, but the dynamic properties of TM over the auditory frequency range are very limited. In this paper, a new method was developed to measure the dynamic properties of human TM using the Dynamic-Mechanical Analyzer (DMA). The test was conducted at the frequency range of 1-40 Hz at three different temperatures: 5, 25, and 37 °C. The frequency-temperature superposition was applied to extend the testing frequency range to a much higher level (at least 3800 Hz). The generalized linear solid model was employed to describe the constitutive relation of the TM. The storage modulus E' and the loss modulus E″ were obtained from 11 specimens. The mean storage modulus was 15.1 MPa at 1 Hz and 27.6 MPa at 3800 Hz. The mean loss modulus was 0.28 MPa at 1 Hz and 4.1 MPa at 3800 Hz. The results show that the frequency-temperature superposition is a feasible approach to study the dynamic properties of the ear soft tissues. The dynamic properties of human TM obtained in this study provide a better description of the damping behavior of ear tissues. The properties can be transferred into the finite element model of the human ear to replace the Rayleigh type damping. The data reported here contribute to the biomechanics of the middle ear and improve the accuracy of the FE model for the human ear.

Békésy's contributions to our present understanding of sound conduction to the inner ear

In our daily lives we hear airborne sounds that travel primarily through the external and middle ear to the cochlear sensory epithelium. We also hear sounds that travel to the cochlea via a second sound-conduction route, bone conduction. This second pathway is excited by vibrations of the head and body that result from substrate vibrations, direct application of vibrational stimuli to the head or body, or vibrations induced by airborne sound. The sensation of bone-conducted sound is affected by the presence of the external and middle ear, but is not completely dependent upon their function. Measurements of the differential sensitivity of patients to airborne sound and direct vibration of the head are part of the routine battery of clinical tests used to separate conductive and sensorineural hearing losses. Georg von Békésy designed a careful set of experiments and pioneered many measurement techniques on human cadaver temporal bones, in physical models, and in human subjects to elucidate the basic mechanisms of air- and bone-conducted sound. Looking back one marvels at the sheer number of experiments he performed on sound conduction, mostly by himself without the aid of students or research associates. Békésy's work had a profound impact on the field of middle-ear mechanics and bone conduction fifty years ago when he received his Nobel Prize. Today many of Békésy's ideas continue to be investigated and extended, some have been supported by new evidence, some have been refuted, while others remain to be tested.

Mechanical properties of human tympanic membrane in the quasi-static regime from in situ point indentation measurements

The tympanic membrane is a key component of the human auditory apparatus. Good estimates of tympanic membrane mechanical properties are important to obtain realistic models of middle ear mechanics. Current literature values are almost all derived from direct mechanical tests on cut-out strips. For a biomedical specimen like the tympanic membrane, it is not always possible to harvest strips of uniform and manageable geometry and well-defined size suitable for such mechanical tests. In this work, elastic and viscoelastic properties of human tympanic membrane were determined through indentation testing on the tympanic membrane in situ. Indentation experiments were performed on three specimens with a custom-built apparatus that was also used in previously published works. Two types of indentation tests were performed on each specimen: (i) sinusoidal indentation at 0.2 Hz yielding the quasi-static Young's modulus and (ii) step indentation tests yielding viscoelastic properties in the quasi-static regime (0-20 Hz). In the cyclic indentation experiments (type i), the indentation depth and resulting needle force were recorded. The unloaded shape of the tympanic membrane and the membrane thickness were measured and used to create a specimen-specific finite element model of the experiment. The Young's modulus was then found through optimization of the error between model and experimental data; the values that were found for the three different samples are 2.1 MPa, 4.4 MPa and 2.3 MPa. A sensitivity analysis showed that these values are very sensitive to the thickness used in the models. In the step indentation tests (type ii), force relaxation was measured during 120 s and the relaxation curves were fitted with a 5 parameter Maxwell viscoelastic model. The relaxation curves in the time domain were transformed to complex moduli in the frequency domain, yielding viscoelastic properties in the quasi-static regime only.

Experimental measurement and modeling analysis on mechanical properties of incudostapedial joint

The incudostapedial (IS) joint between the incus and stapes is a synovial joint consisting of joint capsule, cartilage, and synovial fluid. The mechanical properties of the IS joint directly affect the middle ear transfer function for sound transmission. However, due to the complexity and small size of the joint, the mechanical properties of the IS joint have not been reported in the literature. In this paper, we report our current study on mechanical properties of human IS joint using both experimental measurement and finite element (FE) modeling analysis. Eight IS joint samples with the incus and stapes attached were harvested from human cadaver temporal bones. Tension, compression, stress relaxation and failure tests were performed on those samples in a micro-material testing system. An analytical approach with the hyperelastic Ogden model and a 3D FE model of the IS joint including the cartilage, joint capsule, and synovial fluid were employed to derive mechanical parameters of the IS joint. The comparison of measurements and modeling results reveals the relationship between the mechanical properties and structure of the IS joint.