Nonlinear models of development, amplification and compression in the mammalian cochlea.

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.

Efferent-mediated control of basilar membrane motion.

Medial olivocochlear efferent (MOCE) neurones innervate the outer hair cells (OHCs) of the mammalian cochlea, and convey signals that are capable of controlling the sensitivity of the peripheral auditory system in a frequency-specific manner. Recent methodological developments have allowed the effects of the MOCE system to be observed in vivo at the level of the basilar membrane (BM). These observations have confirmed earlier theories that at least some of the MOCE's effects are mediated via the cochlea's mechanics, with the OHCs acting as the mechanical effectors. However, the new observations have also provided some unexpected twists: apparently, the MOCEs can enhance the BM's responses to some sounds while inhibiting its responses to others, and they can alter the BM's response to a single sound using at least two separate mechanisms. Such observations put new constraints on the way in which the cochlea's mechanics, and the OHCs in particular, are thought to operate.

Separate mechanical processes underlie fast and slow effects of medial olivocochlear efferent activity.

Sound-evoked vibrations of the basilar membrane (BM) in anaesthetised guinea-pigs are shown to be affected over two distinct time scales by electrical stimulation of the medial olivocochlear efferent system: one is fast (10-100 ms), the other much slower (10-100 s). For low and moderate level tones near the BM's characteristic frequency, both fast and slow effects inhibited BM motion. However, fast inhibition was accompanied by phase leads, while slow inhibition was accompanied by phase lags. These findings are consistent with a hypothesis that both fast and slow effects decrease sound amplification in the cochlea. However, the opposing directions of the phase changes indicate that separate mechanical processes must underlie fast and slow effects. One plausible interpretation of these findings is that efferent slow effects are caused by outer-hair-cell stiffness decreases, while efferent fast effects are caused by reductions in 'negative damping'.

An improved heterodyne laser interferometer for use in studies of cochlear mechanics.

A displacement-sensitive heterodyne laser interferometer is described which is suitable to measure the sound-evoked motion of various structures in the intact, living cochlea. Data are included to demonstrate the interferometer's low noise-floor ( < 1 pm Hz (-0.5)), wide bandwidth (from d.c. to 63 kHz) and linear dynamic range ( > 300 microm). The interferometer's optical sensitivity is sufficient to detect the motion of the basilar membrane and various components of the organ of Corti without the use of artificial reflectors: the reflectivity needed to achieve a 10 pm Hz(-0.5) noise-floor is approximately 0.0001%, and the optical sectioning depth is approximately 23 microm. These features make the interferometer ideally suited to measure acoustic vibrations in the living inner ear, but there may also be applications in other fields of neuroscience.

Harmonic distortion on the basilar membrane in the basal turn of the guinea-pig cochlea.

1. Mechanical responses to pure-tone stimuli were recorded from the basilar membrane in the basal turn of the guinea-pig cochlea using a displacement-sensitive laser interferometer. The harmonic content of the responses was evaluated using Fourier analysis. 2. Harmonic distortion products were observed in many of the basilar membrane responses. Response components locked to twice the frequency of the stimulus (i.e. 2F0) were the largest of the distortion products. 3. The second harmonic responses showed a bimodal frequency distribution at low to moderate sound pressure levels: one peak occurred around the preparation's best or most sensitive frequency (i.e. when F0 approximately 17 kHz), and another occurred around one-half of the best frequency (when F0 approximately 8.5 kHz). 4. The absolute levels of most distortion products increased progressively with increasing stimulus strength. When expressed with respect to the levels of the fundamental responses, however, the distortion levels usually decreased with increasing stimulus strength. 5. The levels of the distortion decreased (in both absolute and relative terms) with deterioration in the physiological condition of the cochlea. 6. Maximum second harmonic distortion levels amounted to approximately 3.5 and approximately 28 % of the fundamental responses to tones near and below the best frequency, respectively. 7. The above findings are shown to be consistent with a highly simplified model of cochlear mechanics which incorporates an asymmetric, saturating non-linearity in a positive feedback loop.

Mechanical responses to two-tone distortion products in the apical and basal turns of the mammalian cochlea.

Mechanical responses to one- and two-tone acoustic stimuli were recorded from the cochlear partition in the apical turn of the chinchilla cochlea, the basal turn of the guinea pig cochlea, and the hook region of the guinea pig cochlea. The most sensitive or "best" frequencies (BFs) for the sites studied were approximately 500 Hz, 17 kHz, and 30 kHz, respectively. Responses to the cubic difference tone (CDT), 2F1 - F2 (where F1 and F2 are the frequencies of the primary stimuli), were characterized at each site. Responses to the quadratic difference tone (QDT), F2 - F1, were also characterized in the apical turn preparations (QDT responses were too small to measure in the basal cochlea). The observed responses to BF QDTs and CDTs and to BF CDTs at each site appeared similar in many ways; the relative magnitudes of the responses were highest at low-to-moderate sound pressure levels (SPLs), for example, and the absolute magnitudes grew nonmonotonically with increases in the level of either primary (L1 or L2) alone. The peak effective levels of the CDT and QDT responses were also similar, at around -20 dB re L1 and/or L2. In other respects, however, the responses to CDTs and QDTs and to BF CDTs at each site behaved quite differently. At low-to-moderate SPLs, for example, most CDT phase leads decreased with increases in either L1 or L2, whereas most QDT phase leads increased with increasing L1 and varied little with L2. Most CDT responses also varied monotonically with equal-level primaries (i.e., when L1 = L2), whereas most QDT responses varied nonmonotonically. Different responses also varied in different ways when F1 and F2 were varied. Apical turn QDT responses were observed over a very wide F1/F2 range (F1 = 1-12 kHz), but were usually largest for stimuli <2-4 kHz. Apical turn CDT levels decreased (at rates of approximately 40-80 dB/octave) only when the frequency ratio F2/F1 increased beyond approximately 1.4-1.5. In the basal turn and hook regions, the CDT levels depended nonmonotonically on F2/F1 with the eventual rates of decrease being approximately 200 dB/octave. Optimal frequency ratios for the CDT increased from (F2 < 1.1F1) to (F2 approximately 1.2F1) with increasing SPL in the basal turn, but were stable at around F2/F1 approximately 1.05 in the hook region. CDT phase leads tended to increase with increasing F2/F1 in all three regions of the cochlea, particularly at low-to-moderate SPLs. These findings are discussed in relation to previous studies of cochlear mechanics, physiology, and psychophysics.

Two-tone suppression in cochlear mechanics.

Mechanical responses to one- and two-tone stimuli were recorded from the basilar membrane (BM) in the hook region of the guinea-pig cochlea. The most sensitive or "best" frequencies (BFs) for the sites studied were approximately 25-30 kHz. Two-tone suppression (2TS) of the responses to near BF probe tones was noted using suppressor tones either above or below the BF. Rates of growth of 2TS were highest (approximately 1 dB/dB) when the suppressor tones were presented below the BF. Below-BF suppression thresholds (the suppressor intensities causing approximately 10% reduction in the probe-evoked responses) corresponded to BM displacements of approximately 1-5 nm. Above-BF suppression thresholds corresponded to much smaller displacements at the location studied. Both above- and below-BF suppressor tones changed the phase of the probe tone responses in the same way that increases in the probe tone intensity did (they evoked small phase-lags for below-BF probes, and small phase-leads for near- and above-BF probes). Low-frequency suppressor tones ( < approximately 7 kHz) evoked a frequency- and intensity-dependent mixture of phasic (ac) and tonic (dc) suppression. Peak (ac) suppression was observed around the times of peak BM displacement (not velocity). These findings are discussed in relation to those of other workers.

Nonlinear mechanics at the apex of the guinea-pig cochlea.

A heterodyne laser interferometer was used to observe the sound-evoked displacement patterns of Reissner's membrane and various other structures in the apical turn of the guinea-pig cochlea. Most structures (including the basilar membrane) were similarly tuned, and had best frequencies in the 200-350Hz range. A distinct notch was usually observed approximately 0.7 octaves above the best frequency, and amplitude- and phase-plateaus were observed at higher frequencies. In most other respects, however, the mechanical tuning resembled the frequency-threshold curves of low frequency cochlear nerve fibers. In five reasonably intact, in vivo preparations, the frequency of the mechanical sensitivity notch was intensity-dependent: Compressive nonlinearities were observed above approximately 80 dB SPL on the low-frequency side of the notch, with antagonistically expansive nonlinearities on the high-frequency side. Two-tone suppression was observed in one of these preparations. Stimulus-related baseline position shifts were observed in another in vivo preparation. No such nonlinearities were observed in structurally damaged and/or > 1 hour post-mortem preparations. However, more robust nonlinearities were observed in all preparations at higher levels of stimulation (e.g. > 100-110 dB SPL). These high-level nonlinearities diminished only slowly after death, and gave rise to various effects, including time-dependent (i.e. adapting) and severely distorted (e.g. peak-split and/or dc-shifted) responses.

Nonlinear input-output functions derived from the responses of guinea-pig cochlear nerve fibres: variations with characteristic frequency.

Rate-versus-level functions (RLFs) were recorded from individual cochlear nerve fibres in anaesthetised guinea-pigs. Variations in the shapes of these functions with frequency were used to derive input-output (IO) relationships for the mechanical preprocessing mechanisms in the cochlea. It was assumed that these preprocessing mechanisms operated linearly at frequencies well below each fibre's characteristic frequency (CF). The IO functions derived at each fibre's CF provided strong evidence of compressively nonlinear preprocessing in most regions of the cochlea. However, the apparent degree of compression depended on the fibre's CF, and hence on the presumed site of cochlear innervation. For fibres with CFs of between 1.5 and 3.6 kHz, the CF derived IO functions grew at rates of around 0.5 dB/dB. For fibres with CFs above 4 kHz, the IO functions were more compressive, with high-intensity asymptotic slopes of around 0.13 dB/dB. In the highest (> or = 10 kHz) CF fibres, the degree of compression depended on the physiological condition of the cochlea; the derived IO functions becoming more linear as the cochlea became less sensitive. The derived IO technique was not well suited to analyse responses evoked by very low frequency (e.g., < 500 Hz) tones. Nonetheless, the CF RLFs from fibres with CFs lower than approximately 1 kHz provided little evidence of mechanical nonlinearity near the apex of the cochlea. These findings imply a longitudinal variation in the mechanisms of cochlear preprocessing, and provide important new tests for functional models of the cochlea.

Cochlear nerve fiber responses to amplitude-modulated stimuli: variations with spontaneous rate and other response characteristics.

1. Single-fiber responses to sinusoidally amplitude-modulated (AM) tones were recorded from the cochlear nerves of anesthetized guinea pigs. Stimuli were presented at the fiber's characteristic frequency (CF) and covered the intensity range between the fiber's minimum rate threshold and 90-100 dB SPL in 5- or 6-dB steps. The amount of modulation in each fiber's response and the average rate of the responses were quantified. The observed response modulation was compared with the modulation to be expected on the assumption that the instantaneous discharge rates varied with intensity in the same way that the average rates did (i.e., as predicted from each fiber's average-rate vs. level function). 2. The difference between the observed and expected response modulation varied widely across fibers. In most fibers' the responses to a limited range of stimulus intensities (typically between 20 and 30 dB above the fiber's rate threshold) were modulated far more than expected on the basis of their average rates, with responses to stimuli either above or below this range differing progressively less from expectation. Little or no response modulation was observed above approximately 70 dB SPL in these fibers. Other fibers exhibited response modulation that exceeded the expected modulation by smaller amounts, but maintained this modulation to much higher sound pressure levels. 3. The discrepancy between the observed and expected responses to AM stimuli also varied with the frequency of modulation (fm) within individual fibers. The discrepancies were least pronounced at low fms (e.g., 10 Hz) but became progressively larger as fm was increased to between 50 and 320 Hz (subject to the inter-fiber variations described in 2, above). 4. The AM response characteristics varied systematically with the fiber's spontaneous rate and other response characteristics (e.g., rate threshold, CF rate vs. level function type, and rapid adaptation characteristics). In particular, the most sensitive, high spontaneous rate fibers had responses that adapted rapidly after the onset of a stimulus, and showed the greatest enhancement of AM-related information at low-to-moderate stimulus intensities. However, these fibers appeared incapable of encoding AM-related information at high intensities, since their response rates "saturated" and their AM response enhancements diminished around 30 dB above threshold. In contrast, the less sensitive (i.e., higher threshold), lower spontaneous rate fibers showed less evidence of rapid adaptation near the onsets of their response, and lesser enhancements of the modulated responses predicted from their average-rate versus level functions.(ABSTRACT TRUNCATED AT 400 WORDS)

Two-tone suppression and distortion production on the basilar membrane in the hook region of cat and guinea pig cochleae.

Two-tone suppression and two-tone distortion were investigated at the level of the basilar membrane in the hook region of cat and guinea pig cochleae using a displacement-sensitive laser interferometric measurement system. The system allowed measurements to be performed at physiological stimulus levels in the cochlear region tuned to 30-35 kHz in cat and 29 kHz in guinea pig. The amplitude of vibration of the basilar membrane due to a probe tone at the characteristic frequency (CF) was attenuated during the presentation of a simultaneous suppressor tone either above or below CF. The amount of suppression depended on the intensities of both probe and suppressor, and the relationship of the suppressor frequency to the CF. Suppressors at frequencies more than an octave below the CF attenuated the responses to the CF probe at a rate of up to 1 dB/dB, with little variation based on suppressor frequency. As the suppressor frequency was increased above CF the rate of suppression decreased rapidly. The lowest suppressor intensity at which attenuation of the probe response was observed did not vary in direct proportion to the probe intensity. This suppression threshold often varied only a few dB SPL when the probe was varied over a 20 dB SPL range. In a few instances the rate of attenuation was as much as a factor of two greater at the lowest probe intensities than at higher intensities. It is noteworthy that suppression was found when the frequency of the suppressor was either above or below CF in the same preparation. Low frequency suppressor tones suppress basilar membrane motion at the CF when the basilar membrane undergoes displacement toward either scala. The maximum suppression occurs around 100 microseconds after the peak excursions caused by the low frequency biasing tone. Two-tone distortion products were often observed even at stimulus levels below those causing two-tone suppression at the site studied. The cubic difference tone (CDT) was the most prominent of the distortion products. The level of the CDT component varied nonmonotonically with the level of either of the primary tones. Responses at the difference frequency between the two primaries were usually below the noise floor of the recording system. The existence of both two-tone distortion and two-tone suppression was dependent on the presence of a cochlear nonlinearity.

Basilar membrane mechanics in the hook region of cat and guinea-pig cochleae: sharp tuning and nonlinearity in the absence of baseline position shifts.

A heterodyne laser interferometer was used to observe the movements of small (approximately 20 microns) stainless-steel beads placed on the basilar membrane in the hook region of cat and guinea-pig cochleae. In several preparations, the displacement patterns observed exhibited sharp nonlinear tuning; in one cat this tuning was comparable to that commonly observed in single auditory-nerve fibers. The most sensitive frequencies of the preparations ranged from 31-40 kHz in the cat, and 28-32 kHz in the guinea-pig. The sharp tuning and nonlinearity of the basilar membrane responses was not apparent in surgically or acoustically traumatized preparations. The response nonlinearities were susceptible to temporary threshold shifts and disappeared within a few minutes post-mortem. Stimulus-related shifts in the baseline position of the basilar membrane were not apparent at low stimulus levels. Such shifts were occasionally observed at higher stimulus levels (e.g., > 90 dB SPL), but never approached the fundamental (oscillatory) component of basilar membrane vibration in magnitude. These findings are discussed in relation to previous observations by other workers.

Basilar membrane tonotopicity in the hook region of the cat cochlea.

Middle-ear to basilar membrane (BM) velocity transfer functions are reported for seven locations in the hook region of a single cat cochlea. These transfer functions were recorded at high sound pressure levels in a linearized, or passive cochlea, and resemble those reported previously by Wilson and Evans (1983). They demonstrate longitudinal tonotopicity with a gradient of approximately 3.6 mm/octave. When allowances are made for the nonlinear mechanisms previously demonstrated in active hook region preparations (Cooper and Rhode, 1992), the data are also consistent with the tonotopic map derived from the intracellular dye-filling studies of Liberman (1982).