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

Dynamic tensile viscoelastic properties of porcine periodontal ligament

The periodontal ligament plays a significant role in orthodontic and masticatory processes. To explicitly investigate the effects of dynamic force amplitude and frequency on the dynamic tensile properties of the periodontal ligament, in vitro tensile experiments were conducted using a dynamic mechanical analysis at various dynamic force amplitudes across a wide frequency range. Storage modulus, loss modulus, and loss factor values were measured. A Maxwell constitutive model based on modulus was established to describe the dynamic mechanical properties of the periodontal ligament. The results showed that the storage modulus ranged from 29.53 MPa to 158.24 MPa, the loss modulus ranged from 3.26 MPa to 76.16 MPa, and the loss factor values all increased with higher frequencies and higher dynamic force amplitudes. Based on the parameters obtained from the fitting results, it is evident that the short-term response has a more pronounced impact on the elastic response of the periodontal ligament than the long-term response. Increasing the dynamic force amplitude and its frequency amplified the viscous effects of the periodontal ligament and enhanced energy dissipation. The proposed constitutive model further demonstrated that the periodontal ligament acts as a viscoelastic biomaterial. These findings have implications for future research on the periodontal ligament.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

Characterization of middle ear soft tissue damping and its role in sound transmission

Damping plays an important role in the middle ear (ME) sound transmission system. However, how to mechanically characterize the damping of ME soft tissues and the role of damping in ME sound transmission have not yet reached a consensus. In this paper, a finite element (FE) model of the partial external and ME of the human ear, considering both Rayleigh damping and viscoelastic damping for different soft tissues, is developed to quantitatively investigate the damping in soft tissues effects on the wide-frequency response of the ME sound transmission system. The model-derived results can capture the high-frequency (above 2 kHz) fluctuations and obtain the 0.9 kHz resonant frequency (RF) of the stapes velocity transfer function (SVTF) response. The results show that the damping of pars tensa (PT), stapedial annular ligament (SAL) and incudostapedial joints (ISJ) can help smooth the broadband response of the umbo and stapes footplate (SFP). It is found that, between 1 and 8 kHz, the damping of the PT increases the magnitude and phase delay of the SVTF above 2 kHz while the damping of the ISJ can avoid excessive phase delay of the SVTF, which is important in maintaining the synchronization in high-frequency vibration but has not been revealed before. Below 1 kHz, the damping of the SAL plays a more important role, and it can decrease the magnitude but increases the phase delay of the SVTF. This study has implications for a better understanding of the mechanism of ME sound transmission.

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.

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.

Parameter Identification From Normal and Pathological Middle Ears Using a Tailored Parameter Identification Algorithm

Current clinical practice is often unable to identify the causes of conductive hearing loss in the middle ear with sufficient certainty without exploratory surgery. Besides the large uncertainties due to interindividual variances, only partially understood cause-effect principles are a major reason for the hesitant use of objective methods such as wideband tympanometry in diagnosis, despite their high sensitivity to pathological changes. For a better understanding of objective metrics of the middle ear, this study presents a model that can be used to reproduce characteristic changes in metrics of the middle ear by altering local physical model parameters linked to the anatomical causes of a pathology. A finite-element model is, therefore, fitted with an adaptive parameter identification algorithm to results of a temporal bone study with stepwise and systematically prepared pathologies. The fitted model is able to reproduce well the measured quantities reflectance, impedance, umbo and stapes transfer function for normal ears and ears with otosclerosis, malleus fixation, and disarticulation. In addition to a good representation of the characteristic influences of the pathologies in the measured quantities, a clear assignment of identified model parameters and pathologies consistent with previous studies is achieved. The identification results highlight the importance of the local stiffness and damping values in the middle ear for correct mapping of pathological characteristics and address the challenges of limited measurement data and wide parameter ranges from the literature. The great sensitivity of the model with respect to pathologies indicates a high potential for application in model-based diagnosis.

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.

Dynamic Properties of Microresonators with the Bionic Structure of Tympanic Membrane

The structure of a microresonator will affect the vibration characteristics and the performance of the system. Inspired by the structural characteristics of the human tympanic membrane, this paper proposed a microresonator with the bionic structure of a tympanic membrane. The structure of a tympanic membrane was simplified to a regular shape with three structural parameters: diameter, height, and thickness. To imitate the tympanic membrane, the contour surface of the bionic structure was modeled based on the formula of transverse vibration mode of a circular thin plate. The geometric model of the bionic structure was established by using the three structural parameters and the contour surface equation. The dynamic properties of the bionic model were studied by the finite element method (FEM). We discuss the modal characteristics of the bionic structure and study the effect of structural parameters and scale on the dynamic properties. The advantages of the bionic structure were investigated by a comparison with circular plate microresonators. The results illustrate that the bionic structure can significantly improve the resonant frequency and have a much larger effective area of vibration displacement.

Structural stiffening in the human middle ear due to static pressure: Finite-element analysis of combined static and dynamic middle-ear behavior

The vibration response of the middle ear (ME) to sound changes when static pressure gradients are applied across the tympanic membrane (TM). To date, it has not been well understood which mechanisms lead to these changes in ME vibration response. In this study, a 3D finite-element model of the human ME was developed that simulates the sound-induced ME vibration response when positive and negative static pressures of up to 4 kPa are applied to the TM. Hyperelasticity of the soft-tissue components was considered to simulate large deformations under static pressure. Some ME components were treated as viscoelastic materials to capture the difference between their static and dynamic stiffness, which was needed to replicate both static and dynamic ME behavior. The change in dynamic stiffness with static preload was simulated by linearization of the hyperelastic constitutive model around the predeformed state. For the preloaded harmonic response, we found that the statically deformed ME geometry introduced asymmetry in the vibration loss between positive and negative pressure, which was due to the TM cone shape. As opposed to previous assumptions, the prestress in the ME due to static pressure had a substantial impact on the vibration response. We also found that material nonlinearity led to a higher stiffening at the umbo but a less pronounced stiffening at the footplate compared to the linear elastic condition. The results suggest that flexibility of the incudomalleolar joint (IMJ) enhances the decoupling of static umbo and footplate displacements, and that viscosity and viscoelasticity of the IMJ could play a role in the transfer of sound-induced vibrations from the umbo to the footplate. The components of the incudostapedial joint had minimal effect on ME mechanical behavior.

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.

How flexibility and eardrum cone shape affect sound conduction in single-ossicle ears: a dynamic model study of the chicken middle ear

It is believed that non-mammals have poor hearing at high frequencies because the sound-conduction performance of their single-ossicle middle ears declines above a certain frequency. To better understand this behavior, a dynamic three-dimensional finite-element model of the chicken middle ear was constructed. The effect of changing the flexibility of the cartilaginous extracolumella on middle-ear sound conduction was simulated from 0.125 to 8 kHz, and the influence of the outward-bulging cone shape of the eardrum was studied by altering the depth and orientation of the eardrum cone in the model. It was found that extracolumella flexibility increases the middle-ear pressure gain at low frequencies due to an enhancement of eardrum motion, but it decreases the pressure gain at high frequencies as the bony columella becomes more resistant to extracolumella movement. Similar to the inward-pointing cone shape of the mammalian eardrum, it was shown that the outward-pointing cone shape of the chicken eardrum enhances the middle-ear pressure gain compared to a flat eardrum shape. When the outward-pointing eardrum was replaced by an inward-pointing eardrum, the pressure gain decreased slightly over the entire frequency range. This decrease was assigned to an increase in bending behavior of the extracolumella and a reduction in piston-like columella motion in the model with an inward-pointing eardrum. Possibly, the single-ossicle middle ear of birds favors an outward-pointing eardrum over an inward-pointing one as it preserves a straight angle between the columella and extrastapedius and a right angle between the columella and suprastapedius, which provides the optimal transmission.

The effects of varying tympanic-membrane material properties on human middle-ear sound transmission in a three-dimensional finite-element model

An anatomically based three-dimensional finite-element human middle-ear (ME) model is used to test the sensitivity of ME sound transmission to tympanic-membrane (TM) material properties. The baseline properties produce responses comparable to published measurements of ear-canal input impedance and power reflectance, stapes velocity normalized by ear-canal pressure (P_EC), and middle-ear pressure gain (MEG), i.e., cochlear-vestibule pressure (P_V) normalized by P_EC. The mass, Young's modulus (E_TM), and shear modulus (G_TM) of the TM are varied, independently and in combination, over a wide range of values, with soft and bony TM-annulus boundary conditions. MEG is recomputed and plotted for each case, along with summaries of the magnitude and group-delay deviations from the baseline over low (below 0.75 kHz), mid (0.75-5 kHz), and high (above 5 kHz) frequencies. The MEG magnitude varies inversely with increasing TM mass at high frequencies. Increasing E_TM boosts high frequencies and attenuates low and mid frequencies, especially with a bony TM annulus and when G_TM varies in proportion to E_TM, as for an isotropic material. Increasing G_TM on its own attenuates low and mid frequencies and boosts high frequencies. The sensitivity of MEG to TM material properties has implications for model development and the interpretation of experimental observations.

Panel 2: Anatomy (Eustachian Tube, Middle Ear, and Mastoid-Anatomy, Physiology, Pathophysiology, and Pathogenesis)

Objective In this report, we review the recent literature (ie, past 4 years) to identify advances in our understanding of the middle ear-mastoid-eustachian tube system. We use this review to determine whether the short-term goals elaborated in the last report were achieved, and we propose updated goals to guide future otitis media research. Data Sources PubMed, Web of Science, Medline. Review Methods The panel topic was subdivided, and each contributor performed a literature search within the given time frame. The keywords searched included middle ear, eustachian tube, and mastoid for their intersection with anatomy, physiology, pathophysiology, and pathology. Preliminary reports from each panel member were consolidated and discussed when the panel met on June 11, 2015. At that meeting, the progress was evaluated and new short-term goals proposed. Conclusions Progress was made on 13 of the 20 short-term goals proposed in 2011. Significant advances were made in the characterization of middle ear gas exchange pathways, modeling eustachian tube function, and preliminary testing of treatments for eustachian tube dysfunction. Implications for Practice In the future, imaging technologies should be developed to noninvasively assess middle ear/eustachian tube structure and physiology with respect to their role in otitis media pathogenesis. The new data derived from these structure/function experiments should be integrated into computational models that can then be used to develop specific hypotheses concerning otitis media pathogenesis and persistence. Finally, rigorous studies on medical or surgical treatments for eustachian tube dysfunction should be undertaken.

Dynamic property changes in stapedial annular ligament associated with acute otitis media in the chinchilla

Located at the end of the ossicular chain, the stapedial annular ligament (SAL) serves as a closed yet mobile boundary between the cochlear fluid and stapes footplate. It is unclear how SAL properties change with acute otitis media (AOM). This paper reports the measurements of SAL dynamic properties in chinchilla AOM model using dynamic mechanical analyzer (DMA) and frequency-temperature superposition (FTS) principle. AOM was analyzed in two infection groups: 4 days (4D) and 8 days (8D) post induction. SAL specimens were measured using DMA at three temperatures: 5, 25, and 37°C. To extend the testing frequencies to higher levels, FTS principle was employed. Then generalized Maxwell model was utilized to define the constitutive equations of the SAL. The complex shear moduli were obtained from seven samples of control, 4D, and 8D groups. Results show that the storage and loss shear moduli of SALs decreased due to AOM. The storage moduli for 4D and 8D ears were similar below 100Hz, and the loss modulus for 4D was significantly larger than 8D across the entire frequency range. This study reports data that contributes to ear biomechanics and improves understanding on the effects of AOM in middle ear tissues.

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.

The effect of actuator and its coupling conditions on eardrum-stimulated middle ear implants: A numerical analysis

Consisting of the actuator and coupling layer, a finite element model of the human middle ear was used to analyze the effect of the actuator and its coupling conditions on the performance of the eardrum-stimulated middle ear implants. This model which was based on the right ear of a healthy adult was built via microcomputed tomography imaging and the technique of reverse engineering. Based on this finite element model, the linear viscoelasticity of the human middle ear soft tissues and three-layer structure of the eardrum pars tensa which was orthotropic were considered. The validity of the model was verified by comparing the model calculated results with experimental data. After that, the influence of the three main design parameters of the actuator and two aspects of the coupling layer were investigated by the finite element model. The results show that (1) the manubrium tip is the optimal position for the actuator to stimulate; (2) the increased cross-section of the actuator would worsen its hearing compensation performance, especially in the low frequencies; (3) both the patients’ residual hearing and the actuator’s hearing compensation performance at high frequencies will be deteriorated with the increase in the actuator’s mass; and (4) a coupling layer with a small Young’s modulus and an area approximating 80% of the eardrum would reduce the stress of the eardrum effectively.

Numerical evaluation of implantable hearing devices using a finite element model of human ear considering viscoelastic properties

Finite element method was employed in this study to analyze the change in performance of implantable hearing devices due to the consideration of soft tissues' viscoelasticity. An integrated finite element model of human ear including the external ear, middle ear and inner ear was first developed via reverse engineering and analyzed by acoustic-structure-fluid coupling. Viscoelastic properties of soft tissues in the middle ear were taken into consideration in this model. The model-derived dynamic responses including middle ear and cochlea functions showed a better agreement with experimental data at high frequencies above 3000 Hz than the Rayleigh-type damping. On this basis, a coupled finite element model consisting of the human ear and a piezoelectric actuator attached to the long process of incus was further constructed. Based on the electromechanical coupling analysis, equivalent sound pressure and power consumption of the actuator corresponding to viscoelasticity and Rayleigh damping were calculated using this model. The analytical results showed that the implant performance of the actuator evaluated using a finite element model considering viscoelastic properties gives a lower output above about 3 kHz than does Rayleigh damping model. Finite element model considering viscoelastic properties was more accurate to numerically evaluate implantable hearing devices.

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.

Response of the human tympanic membrane to transient acoustic and mechanical stimuli: Preliminary results

The response of the tympanic membrane (TM) to transient environmental sounds and the contributions of different parts of the TM to middle-ear sound transmission were investigated by measuring the TM response to global transients (acoustic clicks) and to local transients (mechanical impulses) applied to the umbo and various locations on the TM. A lightly-fixed human temporal bone was prepared by removing the ear canal, inner ear, and stapes, leaving the incus, malleus, and TM intact. Motion of nearly the entire TM was measured by a digital holography system with a high speed camera at a rate of 42 000 frames per second, giving a temporal resolution of <24 μs for the duration of the TM response. The entire TM responded nearly instantaneously to acoustic transient stimuli, though the peak displacement and decay time constant varied with location. With local mechanical transients, the TM responded first locally at the site of stimulation, and the response spread approximately symmetrically and circumferentially around the umbo and manubrium. Acoustic and mechanical transients provide distinct and complementary stimuli for the study of TM response. Spatial variations in decay and rate of spread of response imply local variations in TM stiffness, mass, and damping.

3D finite element model of the chinchilla ear for characterizing middle ear functions

Chinchilla is a commonly used animal model for research of sound transmission through the ear. Experimental measurements of the middle ear transfer function in chinchillas have shown that the middle ear cavity greatly affects the tympanic membrane (TM) and stapes footplate (FP) displacements. However, there is no finite element (FE) model of the chinchilla ear available in the literature to characterize the middle ear functions with the anatomical features of the chinchilla ear. This paper reports a recently completed 3D FE model of the chinchilla ear based on X-ray micro-computed tomography images of a chinchilla bulla. The model consisted of the ear canal, TM, middle ear ossicles and suspensory ligaments, and the middle ear cavity. Two boundary conditions of the middle ear cavity wall were simulated in the model as the rigid structure and the partially flexible surface, and the acoustic-mechanical coupled analysis was conducted with these two conditions to characterize the middle ear function. The model results were compared with experimental measurements reported in the literature including the TM and FP displacements and the middle ear input admittance in chinchilla ear. An application of this model was presented to identify the acoustic role of the middle ear septa-a unique feature of chinchilla middle ear cavity. This study provides the first 3D FE model of the chinchilla ear for characterizing the middle ear functions through the acoustic-mechanical coupled FE analysis.

Dynamic Properties of Tympanic Membrane in a Chinchilla Otitis Media Model Measured With Acoustic Loading

Otitis media is the most common infectious disease in young children, which results in changes in the thickness and mechanical properties of the tympanic membrane (TM) and induces hearing loss. However, there are no published data for the dynamic properties of the TM in otitis media ears, and it is unclear how the mechanical property changes are related to TM thickness variation. This paper reports a study of the measurement of the dynamic properties of the TM in a chinchilla acute otitis media (AOM) model using acoustic loading and laser Doppler vibrometry (LDV). AOM was created through transbullar injection of Haemophilus influenzae into the middle ear, and AOM samples were prepared 4 days after inoculation. Vibration of the TM specimen induced by acoustic loading was measured via LDV over a frequency range of 0.1-8 kHz. The experiment was then simulated in a finite element (FE) model, and the inverse-problem solving method was used to determine the complex modulus in the frequency domain. Results from 12 ears (six control and six AOM) show that the storage modulus of the TM from AOM ears was on average 53% higher than that of control ears, while the loss factor was 17.3% higher in control ears than in AOM ears at low-frequency (f < 1 kHz). At high-frequency (e.g., 8000 Hz), there was a mean 40% increase in storage modulus of the TM from AOM compared to control samples. At peak frequency (e.g., 3 kHz), there was a 19.5% increase in loss factor in control samples compared to AOM samples. These findings quantify the changes induced by AOM in the chinchilla TM, namely, a significant increase in both the storage and loss moduli.

Dynamic properties of human stapedial annular ligament measured with frequency-temperature superposition

Stapedial annular ligament (SAL) is located at the end of human ear ossicular chain and provides a sealed but mobile boundary between the stapes footplate and cochlear fluid. Mechanical properties of the SAL directly affect the acoustic-mechanical transmission of the middle ear and the changes of SAL mechanical properties in diseases (e.g., otosclerosis) may cause severe conductive hearing loss. However, the mechanical properties of SAL have only been reported once in the literature, which were obtained under quasi-static condition (Gan, R. Z., Yang, F., Zhang, X., and Nakmali, D., 2011, "Mechanical Properties of Stapedial Annular Ligament," Med. Eng. Phys., 33, pp. 330-339). Recently, the dynamic properties of human SAL were measured in our lab using dynamic-mechanical analyzer (DMA). The test was conducted at the frequency range from 1 to 40 Hz at three different temperatures: 5 °C, 25 °C, and 37 °C. The frequency-temperature superposition (FTS) principle was applied to extend the testing frequency range to a much higher level. The generalized Maxwell model was employed to describe the constitutive relation of the SAL. The storage shear modulus G' and the loss shear modulus G" were obtained from seven specimens. The mean storage shear modulus was 31.7 kPa at 1 Hz and 61.9 kPa at 3760 Hz. The mean loss shear modulus was 1.1 kPa at 1 Hz and 6.5 kPa at 3760 Hz. The dynamic properties of human SAL obtained in this study provide a better description of the damping behavior of soft tissues than the classic Rayleigh type damping, which was widely used in the published ear models. The data reported in this study contribute to ear biomechanics and will improve the accuracy of finite element (FE) model of the human ear.

Viscoelastic properties of the human tympanic membrane studied with stroboscopic holography and finite element modeling

A new anatomically-accurate Finite Element (FE) model of the tympanic membrane (TM) and malleus was combined with measurements of the sound-induced motion of the TM surface and the bony manubrium, in an isolated TM-malleus preparation. Using the results, we were able to address two issues related to how sound is coupled to the ossicular chain: (i) Estimate the viscous damping within the tympanic membrane itself, the presence of which may help smooth the broadband response of a potentially highly resonant TM, and (ii) Investigate the function of a peculiar feature of human middle-ear anatomy, the thin mucosal epithelial fold that couples the mid part of the human manubrium to the TM. Sound induced motions of the surface of ex vivo human eardrums and mallei were measured with stroboscopic holography, which yields maps of the amplitude and phase of the displacement of the entire membrane surface at selected frequencies. The results of these measurements were similar, but not identical to measurements made in intact ears. The holography measurements were complemented by laser-Doppler vibrometer measurements of sound-induced umbo velocity, which were made with fine-frequency resolution. Comparisons of these measurements to predictions from a new anatomically accurate FE model with varied membrane characteristics suggest the TM contains viscous elements, which provide relatively low damping, and that the epithelial fold that connects the central section of the human manubrium to the TM only loosely couples the TM to the manubrium. The laser-Doppler measurements in two preparations also suggested the presence of significant variation in the complex modulus of the TM between specimens. Some animations illustrating the model results are available at our website (www.uantwerp.be/en/rg/bimef/downloads/tympanic-membrane-motion).