The mechanical waveform of the basilar membrane. III. Intensity effects

Regional differences in cochlear nonlinearity across the basal organ of Corti of gerbil: Regional differences in cochlear nonlinearity

Auditory sensation is based in nanoscale vibration of the sensory tissue of the cochlea, the organ of Corti complex (OCC). Motion within the OCC is now observable due to optical coherence tomography. In a previous study (Cooper et al., 2018), the region that includes the electro-motile outer hair cells (OHC) and Deiters cells (DC) was observed to move with larger amplitude than the basilar membrane (BM) and surrounding regions and was termed the "hotspot." In addition to this quantitative distinction, the hotspot moved qualitatively differently than the BM, in that its motion scaled nonlinearly with stimulus level at all frequencies, evincing sub-BF activity. Sub-BF activity enhances non-BF motion; thus the frequency tuning of the OHC/DC region was reduced relative to the BM. In this work we further explore the motion of the gerbil basal OCC and find that regions that lack significant sub-BF activity include the BM, the medial and lateral OCC, and the reticular lamina (RL) region. The observation that the RL region does not move actively sub-BF (already observed in Cho and Puria 2022), suggests that hair cell stereocilia are not exposed to sub-BF activity in the cochlear base. The observation that the lateral and RL regions move approximately linearly sub-BF indicates that linear forces dominate non-linear OHC-based forces on these components at sub-BF frequencies. A complex difference analysis was performed to reveal the internal motion of the OHC/DC region and showed that amplitude structure and phase shifts in the directly measured OHC/DC motion emerge due to the internal OHC/DC motion destructively interfering with BM motion.

The Shape of Noise to Come: Signal vs. Noise Amplification in the Active Cochlea

According to the dominant view, the mammalian cochlea spatially amplifies signals by actively pumping energy into the traveling wave. That is, signals are amplified as they propagate through a region where the medium's resistance is effectively negative. While signal amplification has been extensively studied in active cochlear models, the same cannot be said for amplification of internal noise. According to transmission-line theory, signals are amplified more than internal noise in regions where the net resistance is negative. Here we generalize this finding by showing that a distributed system composed of cascaded "noisy" amplifiers boosts signals more rapidly than the internal noise; the larger the amplifier gain, the larger the signal-to-noise ratio (SNR) of the amplified signal. We further show that this mechanism operates in existing active cochlear models: the cochlear amplifier increases the SNR of cochlear responses, and thus enhances cochlear sensitivity. When considering also that the cochlear amplifier narrows the bandwidth of the "cochlear filters", activation of the cochlear amplifiers dramatically increases the SNR (by about one order of magnitude in our simulations) from the tail to the peak of the traveling wave. We further demonstrate that the tapered ear-horn-like cochlear geometry significantly improves the SNR of basilar-membrane responses.

Intracochlear overdrive: Characterizing nonlinear wave amplification in the mouse apex

In this study, we explore nonlinear cochlear amplification by analyzing basilar membrane (BM) motion in the mouse apex. Through in vivo, postmortem, and mechanical suppression recordings, we estimate how the cochlear amplifier nonlinearly shapes the wavenumber of the BM traveling wave, specifically within a frequency range where the short-wave approximation holds. Our findings demonstrate that a straightforward mathematical model, depicting the cochlear amplifier as a wavenumber modifier with strength diminishing monotonically as BM displacement increases, effectively accounts for the various experimental observations. This empirically derived model is subsequently incorporated into a physics-based "overturned" framework of cochlear amplification [see Altoè, Dewey, Charaziak, Oghalai, and Shera (2022), J. Acoust. Soc. Am. 152, 2227-2239] and tested against additional experimental data. Our results demonstrate that the relationships established within the short-wave region remain valid over a much broader frequency range. Furthermore, the model, now exclusively calibrated to BM data, predicts the behavior of the opposing side of the cochlear partition, aligning well with recent experimental observations. The success in reproducing key features of the experimental data and the mathematical simplicity of the resulting model provide strong support for the "overturned" theory of cochlear amplification.

A frame and a hotspot in cochlear mechanics

Auditory sensation is based in nanoscale vibration of the sensory tissue of the cochlea, the organ of Corti complex (OCC). Motion within the OCC is now observable due to optical coherence tomography. In the cochlear base, in response to sound stimulation, the region that includes the electro-motile outer hair cells (OHC) was observed to move with larger amplitude than the basilar membrane (BM) and surrounding regions. The intense motion is based in active cell mechanics, and the region was termed the "hotspot" (Cooper et al., 2018, Nature comm). In addition to this quantitative distinction, the hotspot moved qualitatively differently than the BM, in that its motion scaled nonlinearly with stimulus level at all frequencies, evincing sub-BF activity. Sub-BF activity enhances non-BF motion; thus the frequency tuning of the hotspot was reduced relative to the BM. Regions that did not exhibit sub-BF activity are here defined as the OCC "frame". By this definition the frame includes the BM, the medial and lateral OCC, and most significantly, the reticular lamina (RL). The frame concept groups the majority OCC as a structure that is largely shielded from sub-BF activity. This shielding, and how it is achieved, are key to the active frequency tuning of the cochlea. The observation that the RL does not move actively sub-BF indicates that hair cell stereocilia are not exposed to sub-BF activity. A complex difference analysis reveals the motion of the hotspot relative to the frame.

Place Coding in the Human Cochlea

The cochlea's capacity to decode sound frequencies is enhanced by a unique structural arrangement along its longitudinal axis, a feature termed 'tonotopy' or place coding. Auditory hair cells at the cochlea's base are activated by high-frequency sounds, while those at the apex respond to lower frequencies. Presently, our understanding of tonotopy primarily hinges on electrophysiological, mechanical, and anatomical studies conducted in animals or human cadavers. However, direct in vivo measurements of tonotopy in humans have been elusive due to the invasive nature of these procedures. This absence of live human data has posed an obstacle in establishing an accurate tonotopic map for patients, potentially limiting advancements in cochlear implant and hearing enhancement technologies. In this study, we conducted acoustically-evoked intracochlear recordings in 50 human subjects using a longitudinal multi-electrode array. These electrophysiological measures, combined with postoperative imaging to accurately locate the electrode contacts allow us to create the first in vivo tonotopic map of the human cochlea. Furthermore, we examined the influences of sound intensity, electrode array presence, and the creation of an artificial third window on the tonotopic map. Our findings reveal a significant disparity between the tonotopic map at daily speech conversational levels and the conventional (i.e., Greenwood) map derived at close-to-threshold levels. Our findings have implications for advancing cochlear implant and hearing augmentation technologies, but also offer novel insights into future investigations into auditory disorders, speech processing, language development, age-related hearing loss, and could potentially inform more effective educational and communication strategies for those with hearing impairments.

Significance Statement

The ability to discriminate sound frequencies, or pitch, is vital for communication and facilitated by a unique arrangement of cells along the cochlear spiral (tonotopic place). While earlier studies have provided insight into frequency selectivity based on animal and human cadaver studies, our understanding of the in vivo human cochlea remains limited. Our research offers, for the first time, in vivo electrophysiological evidence from humans, detailing the tonotopic organization of the human cochlea. We demonstrate that the functional arrangement in humans significantly deviates from the conventional Greenwood function, with the operating point of the in vivo tonotopic map showing a basal (or frequency downward) shift. This pivotal finding could have far-reaching implications for the study and treatment of auditory disorders.

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

The cochlea of the mammalian inner ear includes an active, hydromechanical amplifier thought to arise via the piezoelectric action of the outer hair cells (OHCs). A classic problem of cochlear biophysics is that the RC (resistance-capacitance) time constant of the hair-cell membrane appears inconveniently long, producing an effective cut-off frequency much lower than that of most audible sounds. The long RC time constant implies that the OHC receptor potential-and hence its electromotile response-decreases by roughly two orders of magnitude over the frequency range of mammalian hearing, casting doubt on the hypothesized role of cycle-by-cycle OHC-based amplification in mammalian hearing. Here, we review published data and basic physics to show that the "RC problem" has been magnified by viewing it through the wrong lens. Our analysis finds no appreciable mismatch between the expected magnitude of high-frequency electromotility and the sound-evoked displacements of the organ of Corti. Rather than precluding significant OHC-based boosts to auditory sensitivity, the long RC time constant appears beneficial for hearing, reducing the effects of internal noise and distortion while increasing the fidelity of cochlear amplification.

Cochlear Amplification in the Short-Wave Region by Outer Hair Cells changing Organ-of-Corti area to Amplify the Fluid Traveling Wave

Many details of the operation of the mammalian cochlea are known, but how they all work together to produce cochlear amplification is not understood. Outer-hair-cell (OHC) motility produces two kinds of amplification: non-propagating amplification (NPA) that is from local OHCs, and traveling-wave amplification (TWA) that increases basilar-membrane (BM) motion. Proposed here are a series of hypotheses that provide a new explanation, the "OoC-area-pump", for TWA: (1) In the short-wave region OHC vibrations cause cyclic longitudinal motion of fluid in the organ of Corti (OoC) and peri-Deiters-cell tissue, (2) the longitudinal motion changes the local OoC area, which (3) by reticular-lamina (RL) movement drives the fluid in scala media in a way that amplifies the fluid-pressure traveling wave. (4) At the NPA-TWA changeover frequency, an abrupt change in the OoC frequency-wavenumber relationship is due to positive feedback between TWA and the mode of cochlear motion that is dominant, aided by focusing of the pressure traveling wave. It is hypothesized that OoC radial expansion and radial force from the Deiters-cell phalangeal process act to advance RL and/or lateral-compartment phase. Finally, it is hypothesized that human and lab-animal frequency tuning have similar bandwidths in distance along the cochlea because their traveling-wave wavelengths are similar in the corresponding short-wave regions. Experiments are needed to test these hypotheses and to determine for TWA whether the OoC-area-pump hypothesis replaces or supplements the "OHCs-act-on-BM" hypothesis. Several tests are outlined that can be done with current methodology. A key step in the evolution of mammalian hearing was the development of the complex OoC anatomy, including Deiters cells and OoC fluid spaces that allow local wide-band NPA to produce TWA that enables small local increments of gain to accumulate in the traveling wave and sharpen tuning.

Overturning the mechanisms of cochlear amplification via area deformations of the organ of Corti

The mammalian ear embeds a cellular amplifier that boosts sound-induced hydromechanical waves as they propagate along the cochlea. The operation of this amplifier is not fully understood and is difficult to disentangle experimentally. In the prevailing view, cochlear waves are amplified by the piezo-electric action of the outer hair cells (OHCs), whose cycle-by-cycle elongations and contractions inject power into the local motion of the basilar membrane (BM). Concomitant deformations of the opposing (or "top") side of the organ of Corti are assumed to play a minor role and are generally neglected. However, analysis of intracochlear motions obtained using optical coherence tomography calls this prevailing view into question. In particular, the analysis suggests that (i) the net local power transfer from the OHCs to the BM is either negative or highly inefficient; and (ii) vibration of the top side of the organ of Corti plays a primary role in traveling-wave amplification. A phenomenological model derived from these observations manifests realistic cochlear responses and suggests that amplification arises almost entirely from OHC-induced deformations of the top side of the organ of Corti. In effect, the model turns classic assumptions about spatial impedance relations and power-flow direction within the sensory epithelium upside down.

Rectifying and sluggish: Outer hair cells as regulators rather than amplifiers

In the cochlea, mechano-electrical transduction is preceded by dynamic range compression. Outer hair cells (OHCs) and their voltage dependent length changes, known as electromotility, play a central role in this compression process, but the exact mechanisms are poorly understood. Here we review old and new experimental findings and show that (1) just audible high-frequency tones evoke an ∼1-microvolt AC receptor potential in basal OHCs; (2) any mechanical amplification of soft high-frequency tones by OHC motility would have an adverse effect on their audibility; (3) having a higher basolateral K+ conductance, while increasing the OHC corner frequency, does not boost the magnitude of the high-frequency AC receptor potential; (4) OHC receptor currents display a substantial rectified (DC) component; (5) mechanical DC responses (baseline shifts) to acoustic stimuli, while insignificant on the basilar membrane, can be comparable in magnitude to AC responses when recorded in the organ of Corti, both in the apex and the base. In the basal turn, the DC component may even exceed the AC component, lending support to Dallos' suggestion that both apical and basal OHCs display a significant degree of rectification. We further show that (6) low-intensity cochlear traveling waves, by virtue of their abrupt transition from fast to slow propagation, are well suited to transport high-frequency energy with minimal losses (∼2-dB loss for 16-kHz tones in the gerbil); (7) a 90-dB, 16-kHz tone, if transmitted without loss to its tonotopic place, would evoke a destructive displacement amplitude of 564 nm. We interpret these findings in a framework in which local dissipation is regulated by OHC motility.

Nonlinearity of intracochlear motion and local cochlear microphonic: Comparison between guinea pig and gerbil

Studying the in-vivo mechanical and electrophysiological cochlear responses in several species helps us to have a comprehensive view of the sensitivity and frequency selectivity of the cochlea. Different species might use different mechanisms to achieve the sharp frequency-place map. The outer hair cells (OHC) play an important role in mediating frequency tuning. In the present work, we measured the OHC-generated local cochlear microphonic (LCM) and the motion of different layers in the organ of Corti using optical coherence tomography (OCT) in the first turn of the cochlea in guinea pig. In the best frequency (BF) band, our observations were similar to our previous measurements in gerbil: a nonlinear peak in LCM responses and in the basilar membrane (BM) and OHC-region displacements, and higher motion in the OHC region than the BM. Sub-BF the responses in the two species were different. In both species the sub-BF displacement of the BM was linear and LCM was nonlinear. Sub-BF in the OHC-region, nonlinearity was only observed in a subset of healthy guinea pig cochleae while in gerbil, robust nonlinearity was observed in all healthy cochleae. The differences suggest that gerbils and guinea pigs employ different mechanisms for filtering sub-BF OHC activity from BM responses. However, it cannot be ruled out that the differences are due to technical measurement differences across the species.

Nonlinear cochlear mechanics without direct vibration-amplification feedback

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.

Unified cochlear model for low- and high-frequency mammalian hearing

The spatial variations of the intricate cytoarchitecture, fluid scalae, and mechano-electric transduction in the mammalian cochlea have long been postulated to provide the organ with the ability to perform a real-time, time-frequency processing of sound. However, the precise manner by which this tripartite coupling enables the exquisite cochlear filtering has yet to be articulated in a base-to-apex mathematical model. Moreover, while sound-evoked tuning curves derived from mechanical gains are excellent surrogates for auditory nerve fiber thresholds at the base of the cochlea, this correlation fails at the apex. The key factors influencing the divergence of both mechanical and neural tuning at the apex, as well as the spatial variation of mechanical tuning, are incompletely understood. We develop a model that shows that the mechanical effects arising from the combination of the taper of the cochlear scalae and the spatial variation of the cytoarchitecture of the cochlea provide robust mechanisms that modulate the outer hair cell-mediated active response and provide the basis for the transition of the mechanical gain spectra along the cochlear spiral. Further, the model predicts that the neural tuning at the base is primarily governed by the mechanical filtering of the cochlear partition. At the apex, microscale fluid dynamics and nanoscale channel dynamics must also be invoked to describe the threshold neural tuning for low frequencies. Overall, the model delineates a physiological basis for the difference between basal and apical gain seen in experiments and provides a coherent description of high- and low-frequency cochlear tuning.

Nonlinearity and amplification in cochlear responses to single and multi-tone stimuli

Mechanical displacements of the basilar membrane (BM) and the electrophysiological responses of the auditory outer hair cells (OHCs) are key components of the frequency tuning and cochlear amplification in the mammalian cochlea. In the work presented here, we measured the responses of (1) the extracellular voltage generated by OHCs (V_OHC) and (2) displacements within the organ of Corti complex (OCC) to a multi-tone stimulus, and to single tones. Using optical coherence tomography (OCT), we were able to measure displacements of different layers in the OCC simultaneously, in the base of the gerbil cochlea. We explored the effect of the two types of sound stimuli to the nonlinear behavior of voltage and displacement in two frequency regions: a frequency region below the BM nonlinearity (sub-BF region: f < ∼0.7 BF), and in the best frequency (BF) region. In the sub-BF region, BM motion (X_BM) had linear growth for both stimulus types, and the motion in the OHC region (X_OHC) was mildly nonlinear for single tones, and relatively strongly nonlinear for multi-tones. Sub-BF, the nonlinear character of V_OHC was similar to that of X_OHC. In the BF region X_BM, V_OHC and X_OHC all possessed the now-classic nonlinearity of the BF peak. Coupling these observations with previous findings on phasing between OHC force and traveling wave motions, we propose the following framework for cochlear nonlinearity: The BF-region nonlinearity is an amplifying nonlinearity, in which OHC forces input power into the traveling wave, allowing it to travel further apical to the region where it peaks. The sub-BF nonlinearity is a non-amplifying nonlinearity; it represents OHC electromotility, and saturates due to OHC current saturation, but the OHC forces do not possess the proper phasing to feed power into the traveling wave.

A FPGA Implementation of the CAR-FAC Cochlear Model

This paper presents a digital implementation of the Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) cochlear model. The CAR part simulates the basilar membrane's (BM) response to sound. The FAC part models the outer hair cell (OHC), the inner hair cell (IHC), and the medial olivocochlear efferent system functions. The FAC feeds back to the CAR by moving the poles and zeros of the CAR resonators automatically. We have implemented a 70-section, 44.1 kHz sampling rate CAR-FAC system on an Altera Cyclone V Field Programmable Gate Array (FPGA) with 18% ALM utilization by using time-multiplexing and pipeline parallelizing techniques and present measurement results here. The fully digital reconfigurable CAR-FAC system is stable, scalable, easy to use, and provides an excellent input stage to more complex machine hearing tasks such as sound localization, sound segregation, speech recognition, and so on.

Comparisons of transient evoked otoacoustic emissions using chirp and click stimuli

Transient-evoked otoacoustic emission (TEOAE) responses (0.7-8 kHz) were measured in normal-hearing adult ears using click stimuli and chirps whose local frequency increased or decreased linearly with time over the stimulus duration. Chirp stimuli were created by allpass filtering a click with relatively constant incident pressure level over frequency. Chirp TEOAEs were analyzed as a nonlinear residual signal by inverse allpass filtering each chirp response into an equivalent click response. Multi-window spectral and temporal averaging reduced noise levels compared to a single-window average. Mean TEOAE levels using click and chirp stimuli were similar with respect to their standard errors in adult ears. TEOAE group delay, group spread, instantaneous frequency, and instantaneous bandwidth were similar overall for chirp and click conditions, except for small differences showing nonlinear interactions differing across stimulus conditions. These results support the theory of a similar generation mechanism on the basilar membrane for both click and chirp conditions based on coherent reflection within the tonotopic region. TEOAE temporal fine structure was invariant across changes in stimulus level, which is analogous to the intensity invariance of click-evoked basilar-membrane displacement data.

A comparative study of seven human cochlear filter models

Auditory models have been developed for decades to simulate characteristics of the human auditory system, but it is often unknown how well auditory models compare to each other or perform in tasks they were not primarily designed for. This study systematically analyzes predictions of seven publicly-available cochlear filter models in response to a fixed set of stimuli to assess their capabilities of reproducing key aspects of human cochlear mechanics. The following features were assessed at frequencies of 0.5, 1, 2, 4, and 8 kHz: cochlear excitation patterns, nonlinear response growth, frequency selectivity, group delays, signal-in-noise processing, and amplitude modulation representation. For each task, the simulations were compared to available physiological data recorded in guinea pigs and gerbils as well as to human psychoacoustics data. The presented results provide application-oriented users with comprehensive information on the advantages, limitations and computation costs of these seven mainstream cochlear filter models.

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.

Tone-burst auditory brainstem response wave V latencies in normal-hearing and hearing-impaired ears

The metric used to equate stimulus level [sound pressure level (SPL) or sensation level (SL)] between ears with normal hearing (NH) and ears with hearing loss (HL) in comparisons of auditory function can influence interpretation of results. When stimulus level is equated in dB SL, higher SPLs are presented to ears with HL due to their reduced sensitivity. As a result, it may be difficult to determine if differences between ears with NH and ears with HL are due to cochlear pathology or level-dependent changes in cochlear mechanics. To the extent that level-dependent changes in cochlear mechanics contribute to auditory brainstem response latencies, comparisons between normal and pathologic ears may depend on the stimulus levels at which comparisons are made. To test this hypothesis, wave V latencies were measured in 16 NH ears and 15 ears with mild-to-moderate HL. When stimulus levels were equated in SL, latencies were shorter in HL ears. However, latencies were similar for NH and HL ears when stimulus levels were equated in SPL. These observations demonstrate that the effect of stimulus level on wave V latency is large relative to the effect of HL, at least in cases of mild-to-moderate HL.

Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave

Traveling waves in the inner ear exhibit an amplitude peak that shifts with frequency. The peaking is commonly believed to rely on motile processes that amplify the wave by inserting energy. We recorded the vibrations at adjacent positions on the basilar membrane in sensitive gerbil cochleae and tested the putative power amplification in two ways. First, we determined the energy flux of the traveling wave at its peak and compared it to the acoustic power entering the ear, thereby obtaining the net cochlear power gain. For soft sounds, the energy flux at the peak was 1 ± 0.6 dB less than the middle ear input power. For more intense sounds, increasingly smaller fractions of the acoustic power actually reached the peak region. Thus, we found no net power amplification of soft sounds and a strong net attenuation of intense sounds. Second, we analyzed local wave propagation on the basilar membrane. We found that the waves slowed down abruptly when approaching their peak, causing an energy densification that quantitatively matched the amplitude peaking, similar to the growth of sea waves approaching the beach. Thus, we found no local power amplification of soft sounds and strong local attenuation of intense sounds. The most parsimonious interpretation of these findings is that cochlear sensitivity is not realized by amplifying acoustic energy, but by spatially focusing it, and that dynamic compression is realized by adjusting the amount of dissipation to sound intensity.

Stationary noise responses in a nonlinear model of cochlear mechanics: iterative solutions in the frequency domain

To examine quasilinear filtering properties in cochlear mechanics, Liu and Neely [(2012). What Fire is in Mine Ears: Progress in Auditory Biomechanics, edited by C. A. Shera and E. S. Olson (AIP, Melville, NY), pp. 218-223] calculated Wiener kernels of a nonlinear cochlear model; it was verified that the model's responses to noise could be accurately predicted by treating the kernels as the impulse responses of an equivalent linear system. However, this previous work fell short of showing that the quasilinear filters could be realized under the same structure of the model, a property predicted by de Boer [(1997). Aud. Neurosci. 3, 377-388]. To address the issue of realizability, this paper presents a method that computes the cochlear model's responses to noise iteratively in the frequency domain. First, cochlear transfer functions are calculated as if the system is linear; then, the efficiency of the outer hair cell electromechanical transduction is adjusted. The two steps repeat until the transfer functions converge. Simulation shows that, as the stimulus level increases, the magnitude response of the cochlea decreases and the latency shortens. The corresponding impulse responses are approximately equal to the Wiener kernels obtained in time-domain simulation; as the stimulus varies, the approximation error is <5% in terms of energy. Thus, the Wiener kernels are effectively computed via the present method, which guarantees that the structure of the model is preserved.

Frequency selectivity without resonance in a fluid waveguide

This study analyzes a waveguide consisting of two parallel fluid-filled chambers connected by a narrow slit that is spanned by two coupled elastic beams. A stiffness gradient exists in the longitudinal direction. This simple linear system, which contains no lumped mass, is shown to act as a spectral analyzer. Fluid waves traveling in the waveguide exhibit a distinct amplitude peak at a longitudinal location that varies systematically with frequency. The peaking is not based on resonance, but entirely on wave dispersion. When entering its peak region, the wave undergoes a sharp deceleration associated with a transition in which two propagation modes exchange roles. It is proposed that this mode shape swapping underlies the frequency analysis of the mammalian cochlea.

Detection of cochlear amplification and its activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.

Single-unit labeling of medial olivocochlear neurons: the cochlear frequency map for efferent axons

Medial olivocochlear (MOC) neurons are efferent neurons that project axons from the brain to the cochlea. Their action on outer hair cells reduces the gain of the "cochlear amplifier," which shifts the dynamic range of hearing and reduces the effects of noise masking. The MOC effects in one ear can be elicited by sound in that ipsilateral ear or by sound in the contralateral ear. To study how MOC neurons project onto the cochlea to mediate these effects, single-unit labeling in guinea pigs was used to study the mapping of MOC neurons for neurons responsive to ipsilateral sound vs. those responsive to contralateral sound. MOC neurons were sharply tuned to sound frequency with a well-defined characteristic frequency (CF). However, their labeled termination spans in the organ of Corti ranged from narrow to broad, innervating between 14 and 69 outer hair cells per axon in a "patchy" pattern. For units responsive to ipsilateral sound, the midpoint of innervation was mapped according to CF in a relationship generally similar to, but with more variability than, that of auditory-nerve fibers. Thus, based on CF mappings, most of the MOC terminations miss outer hair cells involved in the cochlear amplifier for their CF, which are located more basally. Compared with ipsilaterally responsive neurons, contralaterally responsive neurons had an apical offset in termination and a larger span of innervation (an average of 10.41% cochlear distance), suggesting that when contralateral sound activates the MOC reflex, the actions are different than those for ipsilateral sound.

Effect of metabolic presbyacusis on cochlear responses: a simulation approach using a physiologically-based model

In the presented model, electrical, acoustical, and mechanical elements of the cochlea are explicitly integrated into a signal transmission line where these elements convey physiological interpretations of the human cochlear structures. As a result, this physiologically-motivated model enables simulation of specific cochlear lesions such as presbyacusis. The hypothesis is that high-frequency hearing loss in older adults may be due to metabolic presbyacusis whereby age-related cellular/chemical degenerations in the lateral wall of the cochlea cause a reduction in the endocochlear potential. The simulations quantitatively confirm this hypothesis and emphasize that even if the outer and inner hair cells are totally active and intact, metabolic presbyacusis alone can significantly deteriorate the cochlear functionality. Specifically, in the model, as the endocochlear potential decreases, the transduction mechanism produces less receptor current such that there is a reduction in the battery of the somatic motor. This leads to a drastic decrease in cochlear amplification and frequency sensitivity, as well as changes in position-frequency map (tuning pattern) of the cochlea. In addition, the simulations show that the age-related reduction of the endocochlear potential significantly inhibits the firing rate of the auditory nerve which might contribute to the decline of temporal resolution in the aging auditory system.

Masking of sounds by a background noise--cochlear mechanical correlates

In the search for cochlear correlates of auditory masking by noise stimuli, we recorded basilar membrane (BM) vibrations evoked by either tone or click signals in the presence of varying levels of background noise. The BM vibrations were recorded from basal regions in healthy cochleae of anaesthetized chinchilla and gerbil. Non-linear interactions that could underpin various aspects of psychophysical masking data, including both compression and suppression at the BM level, were observed. The suppression effects, whereby the amplitude of the responses to each stimulus component could be reduced, depended on the relative intensities of the noise and the tones or clicks. Only stimulus components whose frequencies fell inside the non-linear region of the recording site, i.e. around its characteristic frequency (CF), were affected by presentation of the 'suppressing' stimulus (which could be either the tone or the noise). Mutual suppression, the simultaneous reduction of the responses to both tones and noise components, was observed under some conditions, but overall reductions of BM vibration were rarely observed. Moderate- to high-intensity tones suppressed BM responses to low-intensity Gaussian stimuli, including both broadband and narrowband noise. Suppression effects were larger for spectral components of the noise response that were closer to the CF. In this regime, the tone and noise stimuli became the suppressor and probe signals, respectively. This study provides the first detailed observations of cochlear mechanical correlates of the masking effects of noise. Mechanical detection thresholds for tone signals, which were arbitrarily defined using three criteria, are shown to increase in almost direct proportion to the noise level for low and moderately high noise levels, in a manner that resembles the findings of numerous psychophysical observations.

Instrumentation for studies of cochlear mechanics: from von Békésy forward

Georg von Békésy designed the instruments needed for his research. He also created physical models of the cochlea allowing him to manipulate the parameters (such as volume elasticity) that could be involved in controlling traveling waves. This review is about the specific devices that he used to study the motion of the basilar membrane thus allowing the analysis that lead to his Nobel Prize Award. The review moves forward in time mentioning the subsequent use of von Békésy's methods and later technologies important for motion studies of the organ of Corti. Some of the seminal findings and the controversies of cochlear mechanics are mentioned in relation to the technical developments.

Von Békésy and cochlear mechanics

Georg Békésy laid the foundation for cochlear mechanics, foremost by demonstrating the traveling wave that is the substrate for mammalian cochlear mechanical processing. He made mechanical measurements and physical models in order to understand that fundamental cochlear response. In this tribute to Békésy we make a bridge between modern traveling wave observations and those of Békésy, discuss the mechanical properties and measurements that he considered to be so important, and touch on the range of computational traveling wave models.

Half-octave shift in mammalian hearing is an epiphenomenon of the cochlear amplifier

The cochlear amplifier is a hypothesized positive feedback process responsible for our exquisite hearing sensitivity. Experimental evidence for or against the positive feedback hypothesis is still lacking. Here we apply linear control theory to determine the open-loop gain and the closed-loop sensitivity of the cochlear amplifier from available measurements of basilar membrane vibration in sensitive mammalian cochleae. We show that the frequency of peak closed-loop sensitivity is independent of the stimulus level and close to the characteristic frequency. This implies that the half-octave shift in mammalian hearing is an epiphenomenon of the cochlear amplifier. The open-loop gain is consistent with positive feedback and suggests that the high-frequency cut-off of the outer hair cell transmembrane potential in vivo may be necessary for cochlear amplification.

Basilar membrane responses to tones and tone complexes: nonlinear effects of stimulus intensity

The mammalian inner ear combines spectral analysis of sound with multiband dynamic compression. Cochlear mechanics has mainly been studied using single-tone and tone-pair stimulation. Most natural sounds, however, have wideband spectra. Because the cochlea is strongly nonlinear, wideband responses cannot be predicted by simply adding single-tone responses. We measured responses of the gerbil basilar membrane to single-tone and wideband stimuli and compared them, while focusing on nonlinear aspects of the response. In agreement with previous work, we found that frequency selectivity and its dependence on stimulus intensity were very similar between single-tone and wideband responses. The main difference was a constant shift in effective sound intensity, which was well predicted by a simple gain control scheme. We found expansive nonlinearities in low-frequency responses, which, with increasing frequency, gradually turned into the more familiar compressive nonlinearities. The overall power of distortion products was at least 13 dB below the overall power of the linear response, but in a limited band above the characteristic frequency, the power of distortion products often exceeded the linear response. Our results explain the partial success of a "quasilinear" description of wideband basilar membrane responses, but also indicate its limitations.

In vivo outer hair cell length changes expose the active process in the cochlea

Background

Mammalian hearing is refined by amplification of the sound-evoked vibration of the cochlear partition. This amplification is at least partly due to forces produced by protein motors residing in the cylindrical body of the outer hair cell. To transmit power to the cochlear partition, it is required that the outer hair cells dynamically change their length, in addition to generating force. These length changes, which have not previously been measured in vivo, must be correctly timed with the acoustic stimulus to produce amplification.

Methodology/Principal Findings

Using in vivo optical coherence tomography, we demonstrate that outer hair cells in living guinea pigs have length changes with unexpected timing and magnitudes that depend on the stimulus level in the sensitive cochlea.

Conclusions/Significance

The level-dependent length change is a necessary condition for directly validating that power is expended by the active process presumed to underlie normal hearing.

Outer hair cell somatic electromotility in vivo and power transfer to the organ of Corti

The active amplification of sound-induced vibrations in the cochlea, known to be crucial for auditory sensitivity and frequency selectivity, is not well understood. The outer hair cell (OHC) somatic electromotility is a potential mechanism for such amplification. Its effectiveness in vivo is putatively limited by the electrical low-pass filtering of the cell's transmembrane potential. However, the transmembrane potential is an incomplete metric. We propose and estimate two metrics to evaluate the effectiveness of OHC electromotility in vivo. One metric is the OHC electromechanical ratio defined as the amplitude of the ratio of OHC displacement to the change in its transmembrane potential. The in vivo electromechanical ratio is derived from the recently measured in vivo displacements of the reticular lamina and the basilar membrane at the 19 kHz characteristic place in guinea pigs and using a model. The ratio, after accounting for the differences in OHC vibration in situ due to the impedances from the adjacent structures, is in agreement with the literature values of the in vitro electromechanical ratio measured by others. The second and more insightful metric is the OHC somatic power. Our analysis demonstrates that the organ of Corti is nearly optimized to receive maximum somatic power in vivo and that the estimated somatic power could account for the active amplification.

Tracing Distortion Product (DP) Waves in a Cochlear Model

In many cases a cochlear model suffices to explain (by simulation) the properties of waves in the cochlea. This is not so in the case of a distortion product (DP) set up by presenting two primary tones to the cochlea. A three-dimensional model predicts, apart from a DP wave traveling in the apical direction, a DP wave that travels from the region of overlap of the two tone patterns towards the stapes-setting the stapes in motion so as to produce an otoacoustic emission at the DP frequency. Experimental research has shown, however, that the actual DP wave in the cochlea appears to travel in the opposite direction, from near the stapes to the overlap region. This feature has been termed "inverted direction of wave propagation" (IDWP). The forward wave could result from an unknown process such as a "hidden source" near the stapes. In the present study we have disproved this notion, by using a one-dimensional model of the cochlea. It is found that both reverse and forward waves are set up by the source of nonlinearity, in the same way as has been published in an earlier work. The present results reveal that IDWP in the data corresponds to the region where the DP wave, originally created as a reverse wave but reflected from the stapes, has received so much amplification that it starts to dominate over the reverse wave. Hence we conclude that IDWP in a one-dimensional model is a direct manifestation of cochlear amplification.

Measurement of cochlear power gain in the sensitive gerbil ear

The extraordinary sensitivity of the mammalian ear is commonly attributed to the cochlear amplifier, a cellular process thought to locally boost responses of the cochlear partition to soft sounds. However, cochlear power gain has not been measured directly. Here we use a scanning laser interferometer to determine the volume displacement and volume velocity of the cochlear partition by measuring its transverse vibration along and across the partition. We show the transverse displacement at the peak-response location can be >1,000 times greater than the displacement of the stapes, whereas the volume displacement of an area centred at this location is approximately tenfold greater than that of the stapes. Using the volume velocity and cochlear-fluid impedance, we discover that power at the peak-response area is >100-fold greater than that at the stapes. These results demonstrate experimentally that the cochlea amplifies soft sounds, offering insight into the mechanism responsible for the cochlear sensitivity.

A differentially amplified motion in the ear for near-threshold sound detection

The ear is a remarkably sensitive pressure fluctuation detector. In guinea pigs, behavioral measurements indicate a minimum detectable sound pressure of ∼20 μPa at 16 kHz. Such faint sounds produce 0.1-nm basilar membrane displacements, a distance smaller than conformational transitions in ion channels. It seems that noise within the auditory system would swamp such tiny motions, making weak sounds imperceptible. Here we propose a new mechanism contributing to a resolution of this problem and validate it through direct measurement. We hypothesized that vibration at the apical side of hair cells is enhanced compared with that at the commonly measured basilar membrane side. Using in vivo optical coherence tomography, we demonstrated that apical-side vibrations peaked at a higher frequency, had different timing and were enhanced compared with those at the basilar membrane. These effects depend nonlinearly on the stimulus sound pressure level. The timing difference and enhancement of vibrations are important for explaining how the noise problem is circumvented.

Timing of cochlear responses inferred from frequency-threshold tuning curves of auditory-nerve fibers

Links between frequency tuning and timing were explored in the responses to sound of auditory-nerve fibers. Synthetic transfer functions were constructed by combining filter functions, derived via minimum-phase computations from average frequency-threshold tuning curves of chinchilla auditory-nerve fibers with high spontaneous activity (Temchin et al., 2008), and signal-front delays specified by the latencies of basilar-membrane and auditory-nerve fiber responses to intense clicks (Temchin et al., 2005). The transfer functions predict several features of the phase-frequency curves of cochlear responses to tones, including their shape transitions in the regions with characteristic frequencies of 1 kHz and 3-4 kHz (Temchin and Ruggero, 2010). The transfer functions also predict the shapes of cochlear impulse responses, including the polarities of their frequency sweeps and their transition at characteristic frequencies around 1 kHz. Predictions are especially accurate for characteristic frequencies <1 kHz.

The biophysical origin of traveling-wave dispersion in the cochlea

Sound processing begins at the peripheral auditory system, where it undergoes a highly complex transformation and spatial separation of the frequency components inside the cochlea. This sensory signal processing constitutes a neurophysiological basis for psychoacoustics. Wave propagation in the cochlea, as shown by measurements of basilar membrane velocity and auditory nerve responses to sound, has demonstrated significant frequency modulation (dispersion), in addition to tonotopic gain and active amplification. The physiological and physical basis for this dispersion remains elusive. In this article, a simple analytical model is presented, along with experimental validation using physiological measurements from guinea pigs, to identify the origin of traveling-wave dispersion in the cochlea. We show that dispersion throughout the cochlea is fundamentally due to the coupled fluid-structure interaction between the basilar membrane and the scala fluids. It is further influenced by the variation in physical and geometrical properties of the basilar membrane, the sensitivity or gain of the hearing organ, and the relative dominance of the compression mode at about one-third octave beyond the best frequency.

The remarkable cochlear amplifier

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

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.

In vivo impedance of the gerbil cochlear partition at auditory frequencies

The specific acoustic impedance of the cochlear partition was measured from 4 to 20 kHz in the basal turn of the gerbil cochlea, where the best frequency is approximately 40 kHz. The acoustic impedance was found as the ratio of driving pressure to velocity response. It is the physical attribute that governs cochlear mechanics and has never before been directly measured, to our knowledge. The basilar membrane velocity was measured through the transparent round window membrane. Simultaneously, the intracochlear pressure was measured close to the stapes and quite close to the cochlear partition. The impedance phase was close to -90 degrees and the magnitude decreased with frequency, consistent with stiffness-dominated impedance. The resistive component of the impedance was relatively small. Usually the resistance was negative at frequencies below 8 kHz; this unexpected finding might be due to other vibration modes within the cochlear partition.

Basilar membrane responses to noise at a basal site of the chinchilla cochlea: quasi-linear filtering

Basilar membrane responses to clicks and to white noise were recorded using laser velocimetry at basal sites of the chinchilla cochlea with characteristic frequencies near 10 kHz. Responses to noise grew at compressive rates and their instantaneous frequencies decreased with increasing stimulus level. First-order Wiener kernels were computed by cross-correlation of the noise stimuli and the responses. For linear systems, first-order Wiener kernels are identical to unit impulse responses. In the case of basilar membrane responses, first-order Wiener kernels and responses to clicks measured at the same sites were similar but not identical. Both consisted of transient oscillations with onset frequencies which increased rapidly, over about 0.5 ms, from 4-5 kHz to the characteristic frequency. Both first-order Wiener kernels and responses to clicks were more highly damped, exhibited slower frequency modulation, and grew at compressive rates with increasing stimulus levels. Responses to clicks had longer durations than the Wiener kernels. The statistical distribution of basilar membrane responses to Gaussian white noise is also Gaussian and the envelopes of the responses are Rayleigh distributed, as they should be for Gaussian noise passing through a linear band-pass filter. Accordingly, basilar membrane responses were accurately predicted by linear filters specified by the first-order Wiener kernels of responses to noise presented at the same level. Overall, the results indicate that cochlear nonlinearity is not instantaneous and resembles automatic gain control.

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

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Interaural correlation fails to account for detection in a classic binaural task: dynamic ITDs dominate N0Spi detection

Binaural signal detection in an NoSπ task relies on interaural disparities introduced by adding an antiphasic signal to diotic noise. What metric of interaural disparity best predicts performance? Some models use interaural correlation; others differentiate between dynamic interaural time differences (ITDs) and interaural level differences (ILDs) of the effective stimulus. To examine the relative contributions of ITDs and ILDs in binaural detection, we developed a novel signal processing technique that selectively degrades different aspects (potential cues) of binaural stimuli (e.g., only ITDs are scrambled). Degrading a particular cue will affect performance only if that cue is relevant to the binaural processing underlying detection. This selective scrambling technique was applied to the stimuli of a classic N0Sπ task in which the listener had to detect an antiphasic 500-Hz signal in the presence of a diotic wideband noise masker. Data obtained from five listeners showed that (1) selective scrambling of ILDs had little effect on binaural detection, (2) selective scrambling of ITDs significantly degraded detection, and (3) combined scrambling of ILDs and ITDs had the same effect as exclusive scrambling of ITDs. Regarding the question which stimulus properties determine detection, we conclude that for this binaural task (1) dynamic ITDs dominate detection performance, (2) ILDs are largely irrelevant, and (3) interaural correlation of the stimulus is a poor predictor of detection. Two simple stimulus-based models that each reproduce all binaural aspects of the data quite well are described: (1) a single-parameter detection model using ITD variance as detection criterion and (2) a compressive transformation followed by a crosscorrelation analysis. The success of both of these contrasting models shows that our data alone cannot reveal the mechanisms underlying the dominance of ITD cues. The physiological implications of our findings are discussed.

Outer hair cell electromechanical properties in a nonlinear piezoelectric model

A nonlinear piezoelectric circuit is proposed to model electromechanical properties of the outer hair cell (OHC) in mammalian cochleae. The circuit model predicts (a) that the nonlinear capacitance decreases as the stiffness of the load increases, and (b) that the axial compliance of the cell reaches a maximum at the same membrane potential for peak capacitance. The model was also designed to be integrated into macro-mechanical models to simulate cochlear wave propagation. Analytic expressions of the cochlear-partition shunt admittance and the wave propagation function are derived in terms of OHC electro-mechanical parameters. Small-signal analyses indicate that, to achieve cochlear amplification, (1) nonlinear capacitance must be sufficiently high and (2) the OHC receptor current must be sensitive to the velocity of the reticular lamina.

Inverse-solution method for a class of non-classical cochlear models

Measurements of distortion-product (DP) waves inside the cochlea have led to a conception of wave propagation that is at variance with the "classical" attitude. Of the several alternatives that have been proposed to remedy this situation, the feed-forward model could be a promising one. This paper describes a method to apply the inverse solution with the aim to attain a feed-forward model that accurately reproduces a measured response. It is demonstrated that the computation method is highly successful. Subsequently, it is shown that in a feed-forward model a DP wave generated by a two-tone stimulus is almost exclusively a forward-traveling wave which property agrees with the nature of the experimental findings. However, the amplitude of the computed DP wave is only substantial in the region where the stimulation patterns of the two primary tones overlap. In addition, the model developed cannot explain coherent reflection for single tones. It has been suggested that a forward transversal DP wave induced by a (retrograde) compression wave could be involved in DP wave generation. This topic is critically evaluated.

High-frequency click-evoked otoacoustic emissions and behavioral thresholds in humans

Relationships between click-evoked otoacoustic emissions (CEOAEs) and behavioral thresholds have not been explored above 5 kHz due to limitations in CEOAE measurement procedures. New techniques were used to measure behavioral thresholds and CEOAEs up to 16 kHz. A long cylindrical tube of 8 mm diameter, serving as a reflectionless termination, was used to calibrate audiometric stimuli and design a wideband CEOAE stimulus. A second click was presented 15 dB above a probe click level that varied over a 44 dB range, and a nonlinear residual procedure extracted a CEOAE from these click responses. In some subjects (age 14-29 years) with normal hearing up to 8 kHz, CEOAE spectral energy and latency were measured up to 16 kHz. Audiometric thresholds were measured using an adaptive yes-no procedure. Comparison of CEOAE and behavioral thresholds suggested a clinical potential of using CEOAEs to screen for high-frequency hearing loss. CEOAE latencies determined from the peak of averaged, filtered temporal envelopes decreased to 1 ms with increasing frequency up to 16 kHz. Individual CEOAE envelopes included both compressively growing longer-delay components consistent with a coherent-reflection source and linearly or expansively growing shorter-delay components consistent with a distortion source. Envelope delays of both components were approximately invariant with level.

Dynamic spectrotemporal feature selectivity in the auditory midbrain

The transformation of auditory information from the cochlea to the cortex is a highly nonlinear process. Studies using tone stimuli have revealed that changes in even the most basic parameters of the auditory stimulus can alter neural response properties; for example, a change in stimulus intensity can cause a shift in a neuron's preferred frequency. However, it is not yet clear how such nonlinearities contribute to the processing of spectrotemporal features in complex sounds. Here, we use spectrotemporal receptive fields (STRFs) to characterize the effects of stimulus intensity on feature selectivity in the mammalian inferior colliculus (IC). At low intensities, we find that STRFs are relatively simple, typically consisting of a single excitatory region, indicating that the neural response is simply a reflection of the stimulus amplitude at the preferred frequency. In contrast, we find that STRFs at high intensities typically consist of a combination of an excitatory region and one or more inhibitory regions, often in a spectrotemporally inseparable arrangement, indicating selectivity for complex auditory features. We show that a linear-nonlinear model with the appropriate STRF can predict neural responses to stimuli with a fixed intensity, and we demonstrate that a simple extension of the model with an intensity-dependent STRF can predict responses to stimuli with varying intensity. These results illustrate the complexity of auditory feature selectivity in the IC, but also provide encouraging evidence that the prediction of nonlinear responses to complex stimuli is a tractable problem.

Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.

The role of organ of Corti mass in passive cochlear tuning

The mechanism for passive cochlear tuning remains unsettled. Early models considered the organ of Corti complex (OCC) as a succession of spring-mass resonators. Later, traveling wave models showed that passive tuning could arise through the interaction of cochlear fluid mass and OCC stiffness without local resonators. However, including enough OCC mass to produce local resonance enhanced the tuning by slowing and thereby growing the traveling wave as it approached its resonant segment. To decide whether the OCC mass plays a role in tuning, the frequency variation of the wavenumber of the cochlear traveling wave was measured (in vivo, passive cochleae) and compared to theoretical predictions. The experimental wavenumber was found by taking the phase difference of basilar membrane motion between two longitudinally spaced locations and dividing by the distance between them. The theoretical wavenumber was a solution of the dispersion relation of a three-dimensional cochlear model with OCC mass and stiffness as the free parameters. The experimental data were only well fit by a model that included OCC mass. However, as the measurement position moved from a best-frequency place of 40 to 12 kHz, the role of mass was diminished. The notion of local resonance seems to only apply in the very high-frequency region of the cochlea.

A mechanism for active hearing

The remarkable sensitivity, frequency selectivity, and nonlinearity of the cochlea have been attributed to the putative 'cochlear amplifier', which consumes metabolic energy to amplify the cochlear mechanical response to sounds. Recent studies have demonstrated that outer hair cells actively generate force using somatic electromotility and active hair-bundle motion. However, the expected power gain of the cochlear amplifier has not been demonstrated experimentally, and the measured location of cochlear nonlinearity is inconsistent with the predicted location of the cochlear amplifier. We instead propose a 'cochlear transformer' mechanism to interpret cochlear performance.