Prestrain in the eardrum investigated using laser-ablation perforation: A proof of principle study on the New Zealand white rabbit.

While the presence of residual stress (also called prestress) in the tympanic membrane (TM) was hypothesized more than 150 years ago by von Helmholtz (1869), little experimental data exists to date. In this paper, a novel approach to study residual stress is presented. Using a pulsed laser, the New Zealand white rabbit TM is perforated at seven predefined locations. The subsequent retraction of the membrane around the holes is computed using digital image correlation (DIC). The amount of retraction is the so-called prestrain, which is caused by the release of prestress due to the perforation. By measuring the prestrain using DIC, we show that residual stress is clearly present over the entire rabbit TM surface. In total, fourteen TMs have been measured in this work. An automated approach allows tracking the holes' deformation during the measurement process and enables a more robust analysis than was previously possible. We find similar strains (around 5%) as reported in previous work, in which slits were created manually using flattened surgical needles. However, the new approach greatly reduces measurement time, which minimizes dehydration artifacts. To investigate the effect of perforation location on the TM, the spatial decrease of the prestrain (α) around the perforation was quantified. Perforations inferior to the umbo showed the least negative α values, i.e., the most gradual decrease around the hole, and were the most consistent. Perforations on other locations showed more negative α values, i.e., steeper decrease in strain, but were less consistent across samples. We also investigated the effect of the holes' creation sequence but did not observe a significant change in the results. Overall, the presented method allows for consistent residual stress measurements over the TM surface. The findings contribute to our fundamental knowledge of the mechanics of the rabbit TM and provide a basis for future work on human TMs.

Blowing pressure stabilization method for the artificial excitation of reed instruments (L).

To investigate the acoustics of reed instruments without the need for a human player, blowing machines are needed, which can generate air pressures up to 8 kPa and flow rates up to 40 liters per minute. Due to reed flexibility and the changing pressure gradient across the reed, the relationship between flow and pressure is highly non-linear. Since the output pressure of ventilators is highly dependent on flow, non-linear pressure regulation is a difficult task that requires a closed-loop approach. Since reed vibration starts suddenly when blowing pressure is gradually increased, an abrupt change in airflow through the instrument is present, resulting in a change in pressure in the artificial mouth. To avoid that, a method is presented to achieve a fast response to abrupt flow changes, which is tested in an existing blowing machine. The enhanced blowing machine exhibits a settling time below 200 ms, which allows for the generation of blowing pressures with linear responses.

Finite element modelling of the human middle ear using synchrotron-radiation phase-contrast imaging.

Finite element (FE) models of the middle ear often lack accurate geometry of soft tissue structures, such as the suspensory ligaments, as they can be difficult to discern using conventional imaging modalities, such as computed tomography. Synchrotron-radiation phase-contrast imaging (SR-PCI) is a non-destructive imaging modality that has been shown to produce excellent visualization of soft tissue structures without the need for extensive sample preparation. The objectives of the investigation were to firstly use SR-PCI to create and evaluate a biomechanical FE model of the human middle ear that includes all soft tissue structures, and secondly, to investigate how modelling assumptions and simplifications of ligament representations affect the simulated biomechanical response of the FE model. The FE model included the suspensory ligaments, ossicular chain, tympanic membrane, the incudostapedial and incudomalleal joints, and the ear canal. Frequency responses obtained from the SR-PCI-based FE model agreed well with published laser doppler vibrometer measurements on cadaveric samples. Revised models with exclusion of the superior malleal ligament (SML), simplification of the SML, and modification of the stapedial annular ligament were studied, as these revised models represented modelling assumptions that have been made in literature.

Rabbit tympanic membrane thickness distribution obtained via optical coherence tomography.

Knowing the precise tympanic membrane (TM) thickness variation is crucial in understanding the functional properties of the TM and has a significant effect on the accuracy of computational models. Using optical coherence tomography, we imaged five left and five right TMs of domestic New Zealand rabbits. From these data, ten thickness distribution maps were computed. Although inter-specimen variability is present, similar features could be observed in all samples: The rabbit TM is thickest around the umbo, with values of 150 ± 32 µm. From the umbo towards the TM annulus, the thickness gradually decreases down to 38 ± 7 µm around the midway location, but increases up to 54 ± 19 µm at the TM annulus. The thickness values at the umbo are comparable to literature data for humans, but the rabbit TM is thinner at the TM annulus and in-between the umbo and annulus. Moreover, the rabbit TM thickness distribution is highly symmetrical, which is not the case for the human TM. The results improve our general understanding of TM structure in rabbits and may improve numerical models of TM dynamical behavior.

How does prestrain in the tympanic membrane affect middle-ear function? A finite-element model study in rabbit.

Experiments have shown that prestrain exists in the rabbit tympanic membrane (TM), also in the absence of external loads. To date, it is unclear how prestrain influences the vibration response of the middle ear (ME). In this study, a detailed 3D finite-element model of the rabbit ME was constructed based on experimentally validated material properties. The model incorporates different degrees of prestrain in the TM and simulates the ME vibration response to sound as a linear harmonic perturbation around the prestressed reference state. To account for finite deformations associated with large prestrains, a framework was developed that iteratively updates the initial unstrained geometry until the prestrained geometry is in agreement with the given reference geometry. After validating the model using quasi-static and acoustic measurement data, it was shown that small levels of prestrain already have a substantial impact on the normal umbo and footplate response due to a phenomenon known as prestress stiffening. Although the approach is not preferable, it was possible to replicate the effect of prestrain in the normal ME by appropriately scaling the elastic moduli and damping factors in the base model. To evaluate the effect of possible changes in TM prestrain when the normal state of the ear is altered due to pathological modifications in the ME structure, we created a model with a perforation in the TM. It was shown that the change in vibration response after perforation is affected at low frequencies by a release of TM prestrain. In future studies, it may be necessary to incorporate prestrain in ME models to better understand the function of the diseased or reconstructed ME, which may be relevant for the development of reconstructive tissue grafts in the middle ear.

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.

Three-dimensional vibration patterns of alto saxophone reeds measured on different mouthpieces under mimicked realistic playing conditions.

In single reed musical instruments, vibrations of the reed, in conjunction with the geometry of the mouthpiece and the acoustic feedback of the instrument, play an essential role in sound generation. Up until now, three-dimensional (3D) reed vibration patterns have only been studied under external acoustic stimulation, or at a single note and lip force. This paper investigates vibration patterns of saxophone reeds under imitated realistic playing conditions. On different notes displacement measurements on the entire optically accessible part of the reed are performed using stroboscopic digital image correlation. These vibration data are decomposed onto the harmonic frequencies of the generated note pitch and into the operational modes. Motion data as a function of time are shown on single points. All points on the reed predominantly move in phase, corresponding to the first flexural mode of the reed. At higher note harmonics very low amplitude higher vibration modes are superimposed on the fundamental mode. Mouthpiece characteristics and lip force influence the vibration patterns. Vibration patterns differ strongly from earlier measurements on free vibrating reeds. Results show that single-point measurements on the tip of the reed can give a good indication of the 3D vibration amplitude, also at higher note pitches.

Prestrain in the rabbit eardrum measured by digital image correlation and micro-incisions.

Prestrain in the absence of external loads can have an important effect on the vibrational behavior of mechanical systems such as the middle ear. Studies that measure tympanic membrane (TM) prestrain are scarce, however, and provide no conclusive answer on the existence and nature of the prestrain. In this study, prestrain is measured in the TM of cadaveric rabbit ears by stereo digital image correlation. To release the prestrain, straight incisions of 0.33 mm are made on different locations in the TM with a direction parallel to either the radial or circular fibers in the membrane. The effect of sample dehydration during different stages in the experimental procedure is assessed and eliminated by rehydrating the samples directly before each measurement. The measurements demonstrate average prestrain values around the incisions between 3.52±2.34% and 13.62±7.92% for the different locations, with a noise floor of 0.07%. No clear differences were found between the prestrain values obtained for radial and circular incisions. Observed local variations in TM prestrain could not be clearly related to specific locations on the TM. The results suggest that TM prestrain may need to be considered in future studies of middle-ear function if the findings can be confirmed in human ears.

Geometry Calibration of a Modular Stereo Cone-Beam X-ray CT System.

Compared to single source systems, stereo X-ray CT systems allow acquiring projection data within a reduced amount of time, for an extended field-of-view, or for dual X-ray energies. To exploit the benefit of a dual X-ray system, its acquisition geometry needs to be calibrated. Unfortunately, in modular stereo X-ray CT setups, geometry misalignment occurs each time the setup is changed, which calls for an efficient calibration procedure. Although many studies have been dealing with geometry calibration of an X-ray CT system, little research targets the calibration of a dual cone-beam X-ray CT system. In this work, we present a phantom-based calibration procedure to accurately estimate the geometry of a stereo cone-beam X-ray CT system. With simulated as well as real experiments, it is shown that the calibration procedure can be used to accurately estimate the geometry of a modular stereo X-ray CT system thereby reducing the misalignment artifacts in the reconstruction volumes.

Extended imaging volume in cone-beam x-ray tomography using the weighted simultaneous iterative reconstruction technique.

An issue in computerized x-ray tomography is the limited size of available detectors relative to objects of interest. A solution was provided in the past two decades by positioning the detector in a lateral offset position, increasing the effective field of view (FOV) and thus the diameter of the reconstructed volume. However, this introduced artifacts in the obtained reconstructions, caused by projection truncation and data redundancy. These issues can be addressed by incorporating an additional data weighting step in the reconstruction algorithms, known as redundancy weighting. In this work, we present an implementation of redundancy weighting in the widely-used simultaneous iterative reconstruction technique (SIRT), yielding the weighted SIRT (W-SIRT) method. The new technique is validated using geometric phantoms and a rabbit specimen, by performing both simulation studies as well as physical experiments. The experiments are carried out in a highly flexible stereoscopic x-ray system equipped with x-ray image intensifiers (XRIIs). The simulations showed that higher values of contrast-to-noise ratio could be obtained using the W-SIRT approach as compared to a weighted implementation of the simultaneous algebraic reconstruction technique (SART). The convergence rate of the W-SIRT was accelerated by including a relaxation parameter in the W-SIRT algorithm, creating the aW-SIRT algorithm. This allowed to obtain the same results as the W-SIRT algorithm, but at half the number of iterations, yielding a much shorter computation time. The aW-SIRT algorithm has proven to perform well for both large as well as small regions of overlap, outperforming the pre-convolutional Feldkamp-David-Kress algorithm for small overlap regions (or large detector offsets). The experiments confirmed the results of the simulations. Using the aW-SIRT algorithm, the effective FOV was increased by >75%, only limited by experimental constraints. Although an XRII is used in this work, the method readily applies to flat-panel detectors as well.

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.

Eardrum displacement and strain in the Tokay gecko (Gekko gecko) under quasi-static pressure loads.

The eardrum is the primary component of the middle ear and has been extensively investigated in humans. Measuring the displacement and deformation of the eardrum under different quasi-static loading conditions gives insight in its mechanical behavior and is fundamental in determining the material properties of the eardrum. Currently, little is known about the behavior and material properties of eardrums in non-mammals. To explore the mechanical properties of the eardrum in non-mammalian ears, we investigated the quasi-static response of the eardrum of a common lizard: the Tokay gecko (Gekko gecko). The middle ear cavity was pressurized using repetitive linear pressure cycles ranging from -1.5 to 1.5 kPa with pressure change rates of 0.05, 0.1 and 0.2 kPa/s. The resulting shape, displacement and in-plane strain of the eardrum surface were measured using 3D digital image correlation. When middle-ear pressure is negative, the medial displacement of the eardrum is much larger than the displacement observed in mammals; when middle-ear pressure is positive, the lateral displacement is much larger than in mammals, which is not observed in bird single-ossicle ears. Peak-to-peak displacements are about 2.8 mm, which is larger than in any other species measured up to date. The peak-to-peak displacements are at least five times larger than observed in mammals. The pressure-displacement curves show hysteresis, and the energy loss within one pressure cycle increases with increasing pressure rate, contrary to what is observed in rabbit eardrums. The energy lost during a pressure cycle is not constant over the eardrum. Most energy is lost at the region where the eardrum connects to the hearing ossicle. Around this eardrum-ossicle region, a 5% increase in energy loss was observed when pressure change rate was increased from 0.05 kPa/s to 0.2 kPa/s. Other parts of the eardrum showed little increase in the energy loss. The orientation of the in-plane strain on the eardrum was mainly circumferential with strain amplitudes of about +1.5%. The periphery of the measured eardrum surface showed compression instead of stretching and had a different strain orientation. The TM of Gekko gecko shows the highest displacements of all species measured up till now. Our data show the first shape, displacement and deformation measurements on the surface of the eardrum of the gecko and indicate that there could exist a different hysteresis behavior in different species.

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.

Evaluation of Artificial Fixation of the Incus and Malleus With Minimally Invasive Intraoperative Laser Vibrometry (MIVIB) in a Temporal Bone Model.

BACKGROUND: A significant number of adults suffer from conductive hearing loss due to chronic otitis media, otosclerosis, or other pathologies. An objective measurement of ossicular mobility is needed to avoid unnecessarily invasive middle ear surgery and to improve hearing outcomes. METHODS: Minimally invasive intraoperative laser vibrometry provides a method that is compatible with middle ear surgery, where the tympanic membrane is elevated. The ossicles were driven by a floating mass transducer and their mobility was measured using a laser Doppler vibrometer. Utilising this method, we assessed both the absolute velocities of the umbo and incus long process as well as the incus-to-umbo velocity ratio during artificial fixation of the incus alone or incus and malleus together. RESULTS: The reduction of absolute velocities was 8 dB greater at the umbo and 17 dB at the incus long process for incus-malleus fixations when compared with incus fixation alone. Incus fixation alone resulted in no change to the incus-to-umbo velocity ratio where incus-malleus fixations reduced this ratio (-11 dB). The change in incus velocity was shown to be the most suitable parameter to distinguish between incus fixation and incus-malleus fixation. When the whole frequency range was analyzed, one could also differentiate these two fixations from previously published stapes fixation, where the higher frequencies were less affected. CONCLUSION: Minimally invasive intraoperative laser vibrometry provides a promising objective analysis of ossicular mobility that would be useful intraoperatively.

De novo topology optimization of total ossicular replacement prostheses.

Conductive hearing loss, due to middle ear pathologies or traumas, affects more than 5% of the population worldwide. Passive prostheses to replace the ossicular chain mainly rely on piston-like titanium and/or hydroxyapatite devices, which in the long term suffer from extrusion. Although the basic shape of such devices always consists of a base for contact with the eardrum and a stem to have mechanical connection with the residual bony structures, a plethora of topologies have been proposed, mainly to help surgical positioning. In this work, we optimize the topology of a total ossicular replacement prosthesis, by maximizing the global stiffness and under the smallest possible volume constraint that ensures material continuity. This investigation optimizes the prosthesis topology in response to static displacement loads with amplitudes that normally occur during sound stimulation in a frequency range between 100 Hz and 10 kHz. Following earlier studies, we discuss how the presence and arrangement of holes on the surface of the prosthesis plate in contact with the umbo affect the overall geometry. Finally, we validate the designs through a finite-element model, in which we assess the prosthesis performance upon dynamic sound pressure loads by considering four different constitutive materials: titanium, cortical bone, silk, and collagen/hydroxyapatite. The results show that the selected prostheses present, almost independently of their constitutive material, a vibroacustic behavior close to that of the native ossicular chain, with a slight almost constant positive shift that reaches a maximum of ≈5 dB close to 1 kHz. This work represents a reference for the development of a new generation of middle ear prostheses with non-conventional topologies for fabrication via additive manufacturing technologies or ultraprecision machining in order to create patient-specific devices to recover from conductive hearing loss.

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%.

Deep neural networks for single shot structured light profilometry.

In 3D optical metrology, single-shot structured light profilometry techniques have inherent advantages over their multi-shot counterparts in terms of measurement speed, optical setup simplicity, and robustness to motion artifacts. In this paper, we present a new approach to extract height information from single deformed fringe patterns, based entirely on deep learning. By training a fully convolutional neural network on a large set of simulated height maps with corresponding deformed fringe patterns, we demonstrate the ability of the network to obtain full-field height information from previously unseen fringe patterns with high accuracy. As an added benefit, intermediate data processing steps such as background masking, noise reduction and phase unwrapping that are otherwise required in classic demodulation strategies, can be learned directly by the network as part of its mapping function.

Sound localization in the lizard using internally coupled ears: A finite-element approach.

A number of interesting differences become apparent when comparing the hearing systems of terrestrial vertebrates, especially between mammals and non-mammals. Almost all non-mammals possess only a single ossicle, enabling impedance matching and hearing below 10 kHz. The middle ear (ME) evolved as a chain of three ossicles in mammals, enabling sound transmission up to higher frequencies than in similar-sized non-mammals. The relatively low-frequency hearing in non-mammals is associated with audible wavelengths that are significantly larger than the head. Therefore, it is unlikely that localization of the sound source can be obtained by using external cues between the ears (intensity and time difference between both sides), especially when compared to similarly sized mammals. The heads of many non-mammals contain large air-filled cavities, which acoustically couple both MEs. This article studies acoustic responses and sound-source localization capabilities of the coupled MEs of the brown anole (Anolis sagrei), using finite-element modeling. Based on high-resolution µCT data, 3D finite-element models of the ME and interaural cavity were constructed. The parameter values in the ME model were determined such that the response of the isolated ME matches experimental data of literature and the velocity ratio between the tympanic membrane (apex) and footplate reflects the anatomical arrangement of the columellar lever in the anole. It was found from simulation of the coupled ME model that the interaural connection amplifies intensity differences between both sides and thus enhances the capability of sound-source localization. In addition, the interaural canal doubles the phase differences of the incident external sound waves between the eardrums. In isolated ears, generating such phase differences would require head sizes twice as large. Effects of the inner-ear loading on the sound-source localization of the coupled MEs were investigated as well. The inner-ear load lowered the peak velocity ratios between the ears, but created broader plateaus of useful directionality, indicating that inner-ear loading not only influences sound perception but also sound localization in internally connected ears.

The effect of single-ossicle ear flexibility and eardrum cone orientation on quasi-static behavior of the chicken middle ear.

In the single-ossicle ear of chickens, the quasi-static displacement of the umbo shows great asymmetry; umbo displacements are much larger for negative than for positive pressure in the middle ear, which is opposite to the typical asymmetry observed in mammal ears. To better understand this behavior, a finite-element model was created of the static response of the chicken middle ear. The role of flexibility of the extracolumella in the model was investigated, and the potential effect of the outward orientation of the tympanic-membrane cone was studied by building two adapted models with a flat membrane and an inverted conical membrane. It is found that the extracolumella must be made of flexible material to explain the large inward displacements of the umbo, and that displacements of the footplate are much smaller due to bending of the flexible extracolumella. However, increasing extracolumellar stiffness mostly reduces umbo displacement rather than increasing footplate displacement. The results suggest that the inverted orientation of the membrane cone is responsible for the change in asymmetry of the umbo displacement curve. The asymmetry of the footplate displacement curve in the normal model is smaller, but increases towards positive middle-ear pressure in the case of a flat or inverted membrane geometry.

Eardrum and columella displacement in single ossicle ears under quasi-static pressure variations.

Although most birds encounter large pressure variations during flight, motion of the middle ear components as a result of changing ambient pressure are not well known or described. In the present study, motion of the columella footplate and tympanic membrane (extrastapedius) in domestic chickens (Gallus gallus domesticus) under quasi-static pressure conditions are provided. Micro-CT scans were made of cadaveric heads of chickens under positive (0.25 kPa, 0.5 kPa, 1 kPa, and 1.5 kPa) and negative (-0.25 kPa, -0.5 kPa, -1 kPa, and -1.5 kPa) middle ear pressure. Both extrastapedius and columella footplate displacements show a non-linear S-shaped curve as a function of pressure indicating non-linear response characteristics of the middle ear components. The S-curve is also seen in mammals, but unlike in mammals, the lateral piston-like displacement of both the columella footplate and extrastapedius, which is caused by an increased middle ear pressure are smaller than the medial piston-like displacements, caused by a decreased middle ear pressure of the same magnitude. Columella footplate piston displacements are always smaller than the extrastapedius piston displacements, indicating the flexibility of the extracolumella. The cone-shape of the avian tympanic membrane with inverted apex in comparison to the mammalian tympanic membrane can cause the inverted shape of the pressure response curve.