Broad nonlinearity in reticular lamina vibrations requires compliant organ of Corti structures.

In the mammalian cochlea, each longitudinal position of the basilar membrane (BM) has a nonlinear vibratory response in a limited frequency range around the location-dependent frequency of maximum response, known as the best frequency (BF). This nonlinear response arises from the electromechanical feedback from outer hair cells (OHCs). However, recent in vivo measurements have demonstrated that the mechanical response of other organ of Corti (OoC) structures, such as the reticular lamina (RL), and the electrical response of OHCs (measured in the local cochlear microphonic [LCM]) are nonlinear even at frequencies significantly below BF. In this work, a physiologically motivated model of the gerbil cochlea is used to demonstrate that the source of this discrepancy between the frequency range of the BM, RL, and LCM nonlinearities is greater compliance in the structures at the top of the OHCs. The predicted responses of the BM, RL, and LCM to pure tone and two-tone stimuli are shown to be in line with experimental evidence. Simulations then demonstrate that the sub-BF nonlinearity in the RL requires the structures at the top of the OHCs to be significantly more compliant than the BM. This same condition is also necessary for "optimal" gain near BF, i.e., high amplification that is in line with the experiment. This demonstrates that the conditions for OHCs to operate optimally at BF inevitably yield nonlinearity of the RL response over a broad frequency range.

Link between stimulus otoacoustic emissions fine structure peaks and standing wave resonances in a cochlear model.

In response to an external stimulus, the cochlea emits sounds, called stimulus frequency otoacoustic emissions (SFOAEs), at the stimulus frequency. In this article, a three-dimensional computational model of the gerbil cochlea is used to simulate SFOAEs and clarify their generation mechanisms and characteristics. This model includes electromechanical feedback from outer hair cells (OHCs) and cochlear roughness due to spatially random inhomogeneities in the OHC properties. As in the experiments, SFOAE simulations are characterized by a quasiperiodic fine structure and a fast varying phase. Increasing the sound pressure level broadens the peaks and decreases the phase-gradient delay of SFOAEs. A state-space formulation of the model provides a theoretical framework to analyze the link between the fine structure and global modes of the cochlea, which arise as a result of standing wave resonances. The SFOAE fine structure peaks correspond to weakly damped resonant modes because they are observed at the frequencies of nearly unstable modes of the model. Variations of the model parameters that affect the reflection mechanism show that the magnitude and sharpness of the tuning of these peaks are correlated with the modal damping ratio of the nearly unstable modes. The analysis of the model predictions demonstrates that SFOAEs originate from the peak of the traveling wave.

Anisotropic Material Properties of Wild-Type and Tectb-/- Tectorial Membranes.

The tectorial membrane (TM) is an extracellular matrix that is directly coupled with the mechanoelectrical receptors responsible for sensory transduction and amplification. As such, the TM is often hypothesized to play a key role in the remarkable sensory abilities of the mammalian cochlea. Genetic studies targeting TM proteins have shown that changes in TM structure dramatically affect cochlear function in mice. Precise information about the mechanical properties of the TMs of wild-type and mutant mice at audio frequencies is required to elucidate the role of the TM and to understand how these genetic mutations affect cochlear mechanics. In this study, images of isolated TM segments are used to determine both the radial and longitudinal motions of the TM in response to a harmonic radial excitation. The resulting longitudinally propagating radial displacement and highly spatially dependent longitudinal displacement are modeled using finite-element models that take into account the anisotropy and finite dimensions of TMs. An automated, least-square fitting algorithm is used to find the anisotropic material properties of wild-type and Tectb-/- mice at audio frequencies. Within the auditory frequency range, it is found that the TM is a highly viscoelastic and anisotropic structure with significantly higher stiffness in the direction of the collagen fibers. Although no decrease in the stiffness in the fiber direction is observed, the stiffness of the TM in shear and in the transverse direction is found to be significantly reduced in Tectb-/- mice. As a result, TMs of the mutant mice tend to be significantly more anisotropic within the frequency range examined in this study. The effects of the Tectb-/- mutation on the TM's anisotropic material properties may be responsible for the changes in cochlear tuning and sensitivity that have been previously reported for these mice.

Forward and Reverse Waves: Modeling Distortion Products in the Intracochlear Fluid Pressure.

Distortion product otoacoustic emissions are sounds that are emitted by the cochlea due to the nonlinearity of the outer hair cells. These emissions play an important role both in clinical settings and research laboratories. However, how distortion products propagate from their generation location to the middle ear remains unclear; whether distortion products propagate as a slow reverse traveling wave, or as a fast compression wave, through the cochlear fluid has been debated. In this article, we evaluate the contributions of the slow reverse wave and fast compression wave to the propagation of intracochlear distortion products using a physiologically based nonlinear model of the gerbil cochlea. This model includes a 3D two-duct model of the intracochlear fluid and a realistic model of outer hair cell biophysics. Simulations of the distortion products in the cochlear fluid pressure in response to a two-tone stimulus are compared with published in vivo experimental results. Whereas experiments have characterized distortion products at a limited number of locations, this model provides a complete description of the fluid pressure at all locations in the cochlear ducts. As in experiments, the spatial variations of the distortion products in the fluid pressure have some similarities with what is observed in response to a pure tone. Analysis of the fluid pressure demonstrates that although a fast wave component is generated, the slow wave component dominates the response. Decomposition of the model simulations into forward and reverse wave components shows that a slow forward propagating wave is generated due to the reflection of the slow reverse wave at the stapes. Wave interference between the reverse and forward components sometimes complicates the analysis of distortion products propagation using measurements at a few locations.

Viscoelastic multistable architected materials with temperature-dependent snapping sequence.

When an architected material with snap-through instabilities is loaded, the unit cells of the architected material snap sequentially to a series of deformed configurations. In this paper, we propose the novel concept of multimaterial viscoelastic architected materials whose snapping sequence can be tuned using temperature as a control parameter. Because different polymers have different temperature-dependent properties, it is possible that one polymer that is stiffer than another polymer at one temperature becomes softer at a higher temperature. A 3D printing inverse molding process is used to fabricate soft multimaterial architected materials that consist of two different polymers. Using finite element simulations and experiments, we demonstrate that the snapping sequence of these multimaterial architected materials depends on temperature. The influence of the geometrical parameters of the design on the critical temperature at which the snapping sequence switches from one sequence to another sequence is systematically analyzed using simulations and experiments. Being able to tune the snapping sequence using temperature makes it possible to obtain a large number of distinct stable configurations in response to compressive loads. To illustrate a potential application, we demonstrate that these materials can be used as soft reconfigurable metamaterials with tunable stiffness.

Middle-ear function in the chinchilla: Circuit models and comparison with other mammalian species.

The middle ear efficiently transmits sound from the ear canal into the inner ear through a broad range of frequencies. Thus, understanding middle-ear transmission characteristics is essential in the study of hearing mechanics. Two models of the chinchilla middle ear are presented. In the first model, the middle ear is modeled as a lumped parameter system with elements that represent the ossicular chain and the middle-ear cavity. Parameters of this model are fit using available experimental data of two-port transmission matrix parameters. In an effort to improve agreement between model simulations and the phase of published experimental measurements for the forward pressure transfer function at high frequencies, a second model in which a lossless transmission line model of the tympanic membrane is appended to the original model is proposed. Two-port transmission matrix parameter results from this second model were compared with results from previously developed models of the guinea pig, cat, and human middle ears. Model results and published experimental data for the two-port transmission matrix parameters are found to be qualitatively similar between species. Quantitative differences in the two-port transmission matrix parameters suggest that the ossicular chains of chinchillas, cats, and guinea pigs are less flexible than in humans.

Nonlinear response to a click in a time-domain model of the mammalian ear.

In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.

Effect of the attachment of the tectorial membrane on cochlear micromechanics and two-tone suppression.

The mechanical stimulation of the outer hair cell hair bundle (HB) is a key step in nonlinear cochlear amplification. We show how two-tone suppression (TTS), a hallmark of cochlear nonlinearity, can be used as an indirect measure of HB stimulation. Using two different nonlinear computational models of the cochlea, we investigate the effect of altering the mechanical load applied by the tectorial membrane (TM) on the outer hair cell HB. In the first model (TM-A model), the TM is attached to the spiral limbus (as in wild-type animals); in the second model (TM-D model), the TM is detached from the spiral limbus (mimicking the cochlea of Otoa(EGFP/EGFP) mutant mice). As in recent experiments, model simulations demonstrate that the absence of the TM attachment does not preclude cochlear amplification. However, detaching the TM alters the mechanical load applied by the TM on the HB at low frequencies and therefore affects TTS by low-frequency suppressors. For low-frequency suppressors, the suppression threshold obtained with the TM-A model corresponds to a constant suppressor displacement on the basilar membrane (as in experiments with wild-type animals), whereas it corresponds to a constant suppressor velocity with the TM-D model. The predictions with the TM-D model could be tested by measuring TTS on the basilar membrane of the Otoa(EGFP/EGFP) mice to improve our understanding of the fundamental workings of the cochlea.

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea.

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials.

Coupling active hair bundle mechanics, fast adaptation, and somatic motility in a cochlear model.

One of the central questions in the biophysics of the mammalian cochlea is determining the contributions of the two active processes, prestin-based somatic motility and hair bundle (HB) motility, to cochlear amplification. HB force generation is linked to fast adaptation of the transduction current via a calcium-dependent process and somatic force generation is driven by the depolarization caused by the transduction current. In this article, we construct a global mechanical-electrical-acoustical mathematical model of the cochlea based on a three-dimensional fluid representation. The global cochlear model is coupled to linearizations of nonlinear somatic motility and HB activity as well as to the micromechanics of the passive structural and electrical elements of the cochlea. We find that the active HB force alone is not sufficient to power high frequency cochlear amplification. However, somatic motility can overcome resistor-capacitor filtering by the basolateral membrane and deliver sufficient mechanical energy for amplification at basal locations. The results suggest a new theory for high frequency active cochlear mechanics, in which fast adaptation controls the transduction channel sensitivity and thereby the magnitude of the energy delivered by somatic motility.

Intracochlear distortion products are broadly generated by outer hair cells but their contributions to otoacoustic emissions are spatially restricted.

Detection of low-level sounds by the mammalian cochlea requires electromechanical feedback from outer hair cells (OHCs). This feedback arises due to the electromotile response of OHCs, which is driven by the modulation of their receptor potential caused by the stimulation of mechano-sensitive ion channels. Nonlinearity in these channels distorts impinging sounds, creating distortion-products that are detectable in the ear canal as distortion-product otoacoustic emissions (DPOAEs). Ongoing efforts aim to develop DPOAEs, which reflects the ear's health, into diagnostic tools for sensory hearing loss. These efforts are hampered by limited knowledge on the cochlear extent contributing to DPOAEs. Here, we report on intracochlear distortion products (IDPs) in OHC electrical responses and intracochlear fluid pressures. Experiments and simulations with a physiologically motivated cochlear model show that widely generated electrical IDPs lead to mechanical vibrations in a frequency-dependent manner. The local cochlear impedance restricts the region from which IDPs contribute to DPOAEs at low to moderate intensity, which suggests that DPOAEs may be used clinically to provide location-specific information about cochlear damage.

The effect of tectorial membrane and basilar membrane longitudinal coupling in cochlear mechanics.

Most mathematical models of the mammalian cochlea neglect structural longitudinal coupling. However, recent experimental data suggest that viscoelastic longitudinal coupling, in the basilar membrane (BM) and the tectorial membrane (TM), is non-negligible. In this paper, mathematical models for BM and TM longitudinal coupling are presented to determine the influence of such a coupling on the tuning of the BM. The longitudinal coupling models are added to a macroscopic linear model of the guinea pig cochlea that includes the micromechanics of the organ of Corti and outer hair cell (OHC) somatic motility. The predictions of the BM response to acoustic stimulus show that the characteristic frequency is controlled by a TM radial resonance and that TM longitudinal coupling has a more significant effect than BM longitudinal coupling. TM viscoelasticity controls the sharpness of the BM frequency response and the duration of the impulse response. The results with realistic TM longitudinal coupling are more consistent with experiments. The model predicts that OHC somatic electromotility is able to supply power to the BM at frequencies well above the cutoff of the OHC basolateral membrane. Moreover, TM longitudinal coupling is predicted to stabilize the cochlea and enable a higher BM sensitivity to acoustic stimulation.

Reducing tectorial membrane viscoelasticity enhances spontaneous otoacoustic emissions and compromises the detection of low level sound.

The mammalian cochlea is able to detect faint sounds due to the presence of an active nonlinear feedback mechanism that boosts cochlear vibrations of low amplitude. Because of this feedback, self-sustained oscillations called spontaneous otoacoustic emissions (SOAEs) can often be measured in the ear canal. Recent experiments in genetically modified mice have demonstrated that mutations of the genes expressed in the tectorial membrane (TM), an extracellular matrix located in the cochlea, can significantly enhance the generation of SOAEs. Multiple untested mechanisms have been proposed to explain these unexpected results. In this work, a physiologically motivated computational model of a mammalian species commonly studied in auditory research, the gerbil, is used to demonstrate that altering the viscoelastic properties of the TM tends to affect the linear stability of the cochlea, SOAE generation and the cochlear response to low amplitude stimuli. These results suggest that changes in TM properties might be the underlying cause for SOAE enhancement in some mutant mice. Furthermore, these theoretical findings imply that the TM contributes to keeping the mammalian cochlea near an oscillatory instability, which promotes high sensitivity and the detection of low level stimuli.

Investigation of the 2f1-f2 and 2f2-f1 distortion product otoacoustic emissions using a computational model of the gerbil ear.

In this work, a three-dimensional computational model of the gerbil ear is used to investigate the generation of the 2f1-f2 and 2f2-f1 distortion product otoacoustic emissions (DPOAEs). In order to predict both the distortion and reflection sources, cochlear roughness is modeled by introducing random inhomogeneities in the outer hair cell properties. The model was used to simulate the generation of DPOAEs in response to a two-tone stimulus for various primary stimulus levels and frequency ratios. As in published experiments, the 2f1-f2 DPOAEs are mostly dominated by the distortion component while the 2f2-f1 DPOAEs are dominated by the reflection component; furthermore, the influence of the levels and frequency ratio of the primaries are consistent with measurements. Analysis of the intracochlear response shows that the distortion component has the highest magnitude at all longitudinal locations for the 2f1-f2 distortion product (DP) while the distortion component only dominates close to the DP best place in the case of the 2f2-f1 DP. Decomposition of the intracochlear DPs into forward and reverse waves demonstrates that the 2f1-f2 DP generates reverse waves for both the distortion and reflection components; however, a reverse wave is only generated for the reflection component in the case of the 2f2-f1 DP. As in experiments in the gerbil, the group delay of the reflection component of the DPOAE is between 1× and 2× the forward group delay, which is consistent with the propagation of DP towards the stapes as slow reverse waves.

Simultaneously high stiffness and damping in nanoengineered microtruss composites.

Materials combining high stiffness and mechanical energy dissipation are needed in automotive, aviation, construction, and other technologies where structural elements are exposed to dynamic loads. In this paper we demonstrate that a judicious combination of carbon nanotube engineered trusses held in a dissipative polymer can lead to a composite material that simultaneously exhibits both high stiffness and damping. Indeed, the combination of stiffness and damping that is reported is quite high in any single monolithic material. Carbon nanotube (CNT) microstructures grown in a novel 3D truss topology form the backbone of these nanocomposites. The CNT trusses are coated by ceramics and by a nanostructured polymer film assembled using the layer-by-layer technique. The crevices of the trusses are then filled with soft polyurethane. Each constituent of the composite is accurately modeled, and these models are used to guide the manufacturing process, in particular the choice of the backbone topology and the optimization of the mechanical properties of the constituent materials. The resulting composite exhibits much higher stiffness (80 times) and similar damping (specific damping capacity of 0.8) compared to the polymer. Our work is a step forward in implementing the concept of materials by design across multiple length scales.

WITHDRAWN: Predicting the role of OHC somatic motility and HB motility in cochlear amplification using a mathematical model.

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.

WITHDRAWN: Predicting the role of OHC somatic motility and HB motility in cochlear amplification using a mathematical model.

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.