A COCHLEAR MODEL USING THE TIME-AVERAGED LAGRANGIAN AND THE PUSH-PULL MECHANISM IN THE ORGAN OF CORTI

Otoacoustic emissions reveal the micromechanical role of organ-of-Corti cytoarchitecture in cochlear amplification

The intricate, crystalline cytoarchitecture of the mammalian organ of Corti presumably plays an important role in cochlear amplification. As currently understood, the oblique, Y-shaped arrangement of the outer hair cells (OHCs) and phalangeal processes of the Deiters cells serves to create differential "push-pull" forces that drive the motion of the basilar membrane via the spatial feedforward and/or feedbackward of OHC forces. In concert with the cochlear traveling wave, the longitudinal separation between OHC sensing and forcing creates phase shifts that yield a form of negative damping, amplifying waves as they propagate. Unlike active forces that arise and act locally, push-pull forces are inherently directional-whereas forward-traveling waves are boosted, reverse-traveling waves are squelched. Despite their attractions, models based on push-pull amplification must contend with otoacoustic emissions (OAEs), whose existence implies that amplified energy escapes from the inner ear via mechanisms involving reverse traveling waves. We analyze hybrid local/push-pull models to determine the constraints that reflection-source OAEs place on the directionality of cochlear wave propagation. By implementing a special force-mixing control knob, we vary the mix of local and push-pull forces while leaving the forward-traveling wave unchanged. Consistency with stimulus-frequency OAEs requires that the active forces underlying cochlear wave amplification be primarily local in character, contradicting the prevailing view. By requiring that the oblique cytoarchitecture produce predominantly local forces, we reinterpret the functional role of the Y-shaped geometry, proposing that it serves not as a push-pull amplifier, but as a mechanical funnel that spatially integrates local OHC forces.

Mechanical Effects of Cochlear Implant on Acoustic Hearing

Residual hearing loss in cochlear implant users is investigated using the mechanical-human-cochlear model. Hearing loss due to stiffening of the round window increases significantly as input frequencies decrease from 3 kHz to 1 kHz but remains constant at lower frequencies, whereas loss due to the presence of an electrode insert becomes significantly higher at lower frequencies ([Formula: see text] kHz). The latter also shifts the characteristic frequency map toward the basal end of the cochlea. In the region away from the end of the electrode insert, cochlear function recovers, but the user still suffers from hearing loss caused by round window stiffening.

Cochlear Outer-Hair-Cell Power Generation and Viscous Fluid Loss

Since the discovery of otoacoustic emissions and outer hair cell (OHC) motility, the fundamental question of whether the cochlea produces mechanical power remains controversial. In the present work, direct calculations are performed on power loss due to fluid viscosity and power generated by the OHCs. A three-dimensional box model of the mouse cochlea is used with a feed-forward/feed-backward approximation representing the organ of Corti cytoarchitecture. The model is fit to in vivo basilar membrane motion with one free parameter for the OHCs. The calculations predict that the total power output from the three rows of OHCs can be over three orders of magnitude greater than the acoustic input power at 10 dB sound pressure level (SPL). While previous work shows that the power gain, or the negative damping, diminishes with intensity, we show explicitly based on our model that OHC power output increases and saturates with SPL. The total OHC power output is about 2 pW at 80 dB SPL, with a maximum of about 10 fW per OHC.

Effects of basilar membrane arch and radial tension on the travelling wave in gerbil cochlea

The basilar membrane velocity of gerbil cochlea showed discrepancy between theoretical model and experimental measurements. We hypothesize that the reasons of such discrepancies are due to the arch towards the scala tympani and radial tension present in the basilar membrane of the gerbil cochlea. The arch changes the bending stiffness in the basilar membrane, reduces the effective fluid force on the membrane and increases the basilar membrane's inertia. The existence of the radial tension also dampens the acoustic travelling wave. In this paper, the wave number functions along the gerbil basilar membrane are calculated from experimentally measured physical parameters with the theoretical model as well as extracted from experimentally measured basilar membrane velocity with the wave number inversion formula. The two wave number functions are compared and the effects of the tension and membrane arch on the wave number are studied based on various parameters of the model. We found that the bending stiffness across the gerbil basilar membrane varies (1-2 orders along the cochlea in the section 2.2 mm-3 mm from base) more than the calculated value in the flat basilar membrane model and the radial tension increases the damping of the travelling wave in gerbil cochlea significantly (5 times more than that without radial tension). These effects of arch and radial tension in the basilar membrane elucidate the discrepancy between previous theoretical model and experimental measurements in gerbil cochlea.

Cytoarchitecture of the mouse organ of corti from base to apex, determined using in situ two-photon imaging

The cells in the organ of Corti are highly organized, with a precise 3D microstructure hypothesized to be important for cochlear function. Here we provide quantitative data on the mouse organ of Corti cytoarchitecture, as determined using a new technique that combines the imaging capabilities of two-photon microscopy with the autofluorescent cell membranes of the genetically modified mTmG mouse. This combination allowed us to perform in situ imaging on freshly excised tissue, thus minimizing any physical distortions to the tissue that extraction from the cochlea and chemical fixation and staining might have caused. 3D image stacks of the organ of Corti were obtained from base to apex in the cochlear duct, from which 3D lengths and relative angles for inner and outer hair cells, Deiters' cells, phalangeal processes, and inner and outer pillars were measured. In addition, intercellular distances, diameters, and stereocilia shapes were obtained. An important feature of this study is the quantitative reporting of the longitudinal tilts of the outer hair cells towards the base of the cochlea, the tilt of phalangeal processes towards the apex, and Deiters' cells that collectively form a Y-shaped building block that is thought to give rise to the lattice-like organization of the organ of Corti. The variations of this Y-shaped element along the cochlear duct and between the rows of outer hair cells are shown with the third row morphologically different from the other rows, and their potential importance for the cochlear amplifier is discussed.

A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery

Piston stapes prostheses are implanted in patients with refractory conductive or mixed hearing loss due to stapes otosclerosis to stimulate the perilymph with varying degrees of success. The overclosure effect described by the majority of researchers affects mainly low and medium frequencies, and a large number of patients report a lack of satisfactory results for frequencies above 2 kHz. The mechanics of perilymph stimulation with the piston have not been studied in a systematic manner. The objective of this study was to assess the influence of stapedotomy surgery on round window membrane vibration and to estimate the postoperative outcomes using the finite element (FE) method. The study hypothesis is that the three-dimensional FE model developed of the human inner ear, which simulates the round window (RW) membrane vibration, can be used to assess the influence of stapedotomy on auditory outcomes achieved after the surgical procedure. An additional objective of the study was to enable the simulation of RW membrane vibration after stapedotomy using a new type of stapes prosthesis currently under investigation at Warsaw University of Technology. A three-dimensional finite element (FE) model of the human inner ear was developed and validated using experimental data. The model was then used to simulate the round window membrane vibration before and after stapedotomy surgery. Functional alterations of the RW membrane vibration were derived from the model and compared with the results of experimental measurements from temporal bones of a human cadaver. Piston stapes prosthesis implantation causes an approximately fivefold (14 dB) lower amplitude of the RW membrane vibrations compared with normal anatomical conditions. A satisfactory agreement between the FE model and the experimental data was found. The new prosthesis caused an increase of 20–30 dB in the RW displacement amplitude compared with the 0.4-mm piston prosthesis. In all frequencies, the FE model predicted a RW displacement curve that was above the experimental curves for the normal ear. The stapedotomy can be well simulated by the FE model to predict the auditory outcomes achieved following this otosurgery procedure. The 3D FE model developed in this study may be used to optimize the geometry of a new type of stapes prosthesis in order to achieve a similar sound transmission through the inner ear as for a normal middle ear. This should provide better auditory outcomes for patients with stapedial otosclerosis.

Comparison of nonlinear mammalian cochlear-partition models

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a model highlighting the importance of the coupling between the nonlinear transduction current and somatic motility. It is found that for certain models precise tuning to any bifurcation is not necessary and that a compressively nonlinear response over a range similar to experimental observations and that the normal form of the Hopf bifurcation is not the only description that reproduces compression and tuning similar to experiment.

Estimation of optimal insertion angle in a mammalian outer hair cell stereocilium

Optimal insertion angle of mammalian stereocilia is estimated from the finite element analysis of the tip motion of outer hair cells (OHCs) stereocilia. The OHC stereocilia motion in the acousticolateral system appears to result in the mechanoelectrical transduction channels. Deflection of the hair bundle towards the tallest row of stereocilia causes increased probability of opening of ion channels. In this work, we focus on one of the physical features of the OHC stereocilium, the initial insertion angle of the tallest row into the tectorial membrane (TM), and its effects on the stereocilia's deflection motion. A three-dimensional model was built for the tallest stereocilium and the TM at the region where the best frequency was 500Hz. The mechanical interactions between the embedded stereocilia and the TM have been implemented into the finite element simulation. We found that, the optimum insertion angle of the tallest stereocilium into the TM was 69.8°, where the stereocilium is maximally deflected. This quantity is consistent with the histological observation obtained from the literature.

Biophysical mechanisms underlying outer hair cell loss associated with a shortened tectorial membrane

The tectorial membrane (TM) connects to the stereociliary bundles of outer hair cells (OHCs). Humans with an autosomal dominant C1509G mutation in alpha-tectorin, a protein constituent of the TM, are born with a partial hearing loss that worsens over time. The Tecta(C1509/+) transgenic mouse with the same point mutation has partial hearing loss secondary to a shortened TM that only contacts the first row of OHCs. As well, Tecta(C1509G/+) mice have increased expression of the OHC electromotility protein, prestin. We sought to determine whether these changes impact OHC survival. Distortion product otoacoustic emission thresholds in a quiet environment did not change to 6 months of age. However, noise exposure produced acute threshold shifts that fully recovered in Tecta (+/+) mice but only partially recovered in Tecta(C1509G/+) mice. While Tecta(+/+) mice lost OHCs primarily at the base and within all three rows, Tecta(C1509G/+) mice lost most of their OHCs in a more apical region of the cochlea and nearly completely within the first row. In order to estimate the impact of a shorter TM on the forces faced by the stereocilia within the first OHC row, both the wild type and the heterozygous conditions were simulated in a computational model. These analyses predicted that the shear force on the stereocilia is ~50% higher in the heterozygous condition. We then measured electrically induced movements of the reticular lamina in situ and found that while they decreased to the noise floor in prestin null mice, they were increased by 4.58 dB in Tecta(C1509G/+) mice compared to Tecta(+/+) mice. The increased movements were associated with a fourfold increase in OHC death as measured by vital dye staining. Together, these findings indicate that uncoupling the TM from some OHCs leads to partial hearing loss and places the remaining coupled OHCs at higher risk. Both the mechanics of the malformed TM and the increased prestin-related movements of the organ of Corti contribute to this higher risk profile.

Feed-forward and feed-backward amplification model from cochlear cytoarchitecture: an interspecies comparison

The high sensitivity and wide bandwidth of mammalian hearing are thought to derive from an active process involving the somatic and hair-bundle motility of the thousands of outer hair cells uniquely found in mammalian cochleae. To better understand this, a biophysical three-dimensional cochlear fluid model was developed for gerbil, chinchilla, cat, and human, featuring an active "push-pull" cochlear amplifier mechanism based on the cytoarchitecture of the organ of Corti and using the time-averaged Lagrangian method. Cochlear responses are simulated and compared with in vivo physiological measurements for the basilar membrane (BM) velocity, V(BM), frequency tuning of the BM vibration, and Q₁₀ values representing the sharpness of the cochlear tuning curves. The V(BM) simulation results for gerbil and chinchilla are consistent with in vivo cochlea measurements. Simulated mechanical tuning curves based on maintaining a constant V(BM) value agree with neural-tuning threshold measurements better than those based on a constant displacement value, which implies that the inner hair cells are more sensitive to V(BM) than to BM displacement. The Q₁₀ values of the V(BM) tuning curve agree well with those of cochlear neurons across species, and appear to be related in part to the width of the basilar membrane.