I. INTRODUCTION

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The present review, updating one by Patuzzi and Robertson (273), focuses on the mechanical processes leading to the stimulation of the inner hair cells of the mammalian cochlea, i.e., the vibrations of the basilar membrane (BM), the organ of Corti, and the tectorial membrane (TM). Otoacoustic emissions (for reviews, see Refs. 285, 362) are discussed only to the extent that they shed direct light on cochlear vibrations. Mathematical models of cochlear mechanics (for reviews, see Refs. 80, 81, 152) are mentioned, but rather selectively. The reader may want to consult two recent reviews that cover much the same ground as the present one, but from different perspectives. One (271) is especially useful because it provides theoretical contexts for many of the empirical findings, especially those dealing with micromechanics. The other (379) holds views, notably of experiments in excised cochleae, that clash strongly with our own.

The cochlea consists of three adjacent membranous tubes coiled in the form of a snail (hence its name; see Fig. 1) and enclosed by a bony shell, the otic capsule (For a review of cochlear structure, see Ref. 365). Two of the tubes, the scalae vestibuli and tympani, are filled with perilymph, a liquid whose ionic composition resembles that of other extracellular fluids. At the base of the approximately conical otic capsule, two membrane-covered windows open into the middle ear: the oval window in scala vestibuli, against which abuts the footplate of the stapes, the innermost of the three middle ear ossicles, and the round window in scala tympani. Between scala vestibuli and scala tympani is the scala media, which ends blindly near the "apex" of the otic capsule, allowing scala vestibuli and scala tympani to communicate (at the helicotrema). Scala media contains the organ of Corti, where the inner and outer hair cells transduce mechanical vibrations into electrical signals, endolymph, a fluid of unusual composition (with a high potassium concentration) sustaining a large positive electrical potential, and the TM, overlying the hair cells. The organ of Corti rests on the BM, which separates scala media from scala tympani. The length of the BM in mammals is positively correlated with body weight (e.g., 7, 18, 20, 21, 25, 34, 60, and 100 mm, respectively, in mouse, chinchilla, guinea pig, squirrel monkey, cat, human, elephant, and some whales) (206) and considerably greater than in reptiles or birds of comparable size (221).

View larger version (27K): [in this window] [in a new window]   Fig. 1. Sites of measurement of mechanical vibrations in mammalian cochleae. A: a schematic cross section of the guinea pig cochlea, indicating approaches to basilar membrane (BM) locations at the cochlear base, via an opening into scala tympani (ST), and to structures at the cochlear apex, via an opening into scala vestibuli (SV). The recording sites are also indicated in B, a diagram of the organ of Corti, the BM, and the TM. The numbers in A indicate the four cochlear turns. HC, Hensen's cells; IHC, inner hair cell; L, spiral limbus; OHC, outer hair cells; OSL, osseous spiral lamina; RM, Reissner's membrane; SL, spiral ligament; TM, tectorial membrane. [From Cooper (44), with permission from Elsevier Science.]

Pressure waves reaching the eardrum are transmitted via vibrations of the middle ear ossicles to the oval window at the base of the cochlea, where they create pressure differences between scala tympani and the other scalae, thus displacing the BM in a transverse direction. BM vibration causes shearing between the reticular lamina at the top of the organ of Corti and the TM, tilting the stereocilia that protrude from the outer hair cells. In the case of inner hair cells, whose stereocilia may not be firmly attached to the TM, stereocilia may be displaced by friction against the endolymphatic fluid. Tilting of the stereocilia, in turn, gates cationic channels located in their tips. Aided by the endolymphatic (or endocochlear) potential, the modulation of hair cell conductances produces transduction currents and receptor potentials in the hair cells (for reviews, see Refs. 64, 149, 153, 282, 409). Depolarizing receptor potentials in inner hair cells lead to the generation of action potentials in type I auditory nerve fibers, which constitute the vast majority (95%) of auditory nerve afferents and carry to the brain the bulk of the acoustic information processed by the cochlea.

The first measurements of the vibrational response to sound of the BM were carried out by Georg von Békésy (391), for which he was awarded the 1961 Nobel Prize for Physiology or Medicine. Working principally in the ears of human cadavers, Békésy showed that the cochlea performs a kind of spatial Fourier analysis, mapping frequencies upon longitudinal position along the BM. He described a displacement wave that travels on the BM from base to apex of the cochlea at speeds much slower than that of sound in water. As it propagates, the traveling wave grows in amplitude, reaches a maximum, and then decays. The location of the maximum is a function of stimulus frequency: high-frequency vibrations reach a peak near the base of the cochlea, whereas low-frequency waves travel all the way to the cochlear apex.

A turning point in the understanding of cochlear mechanics came in 1971 when Rhode (293) demonstrated that BM vibrations in live squirrel monkeys exhibit a compressive nonlinearity, growing in magnitude as a function of stimulus intensity at a rate of <1 dB/dB. Rhode also showed that the nonlinearity was frequency specific, being demonstrable only at or near the characteristic frequency (CF, the frequency to which the BM site is most sensitive) and that it was labile, disappearing after death. Rhode's discoveries had to wait longer than a decade for confirmation and extension (205, 307, 355), after several unsuccessful attempts (for review, see Ref. 297). However, by the time the confirmatory BM experiments were published, the existence of nonlinear and active cochlear processes consistent with Rhode's pioneering findings had received unexpected but influential support from Kemp's discovery of otoacoustic emissions, sounds emitted by the cochlea which grow at compressive rates with stimulus intensity (174). Kemp immediately revived Gold's prescient arguments (121) on the need for a positive electromechanical feedback to boost BM vibrations to compensate for the viscous damping exerted by the cochlear fluids. A few years later, a possible origin for both otoacoustic emissions and the hypothetical electromechanical feedback was identified by Brownell et al. (21), who showed that outer hair cells change their length under electrical stimulation.

	II. IN VIVO BASILAR MEMBRANE MECHANICS AT THE BASE OF THE COCHLEA

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Most of our knowledge of mechanics in normal inner ears is based on observations of BM motion at basal sites of the cochleae of guinea pigs, chinchillas, squirrel monkeys, and cats. Studies of BM vibrations at the base of the cochlea have now reached consensus on many issues, including how to judge the quality of recordings, regardless of species or precise CF. The situation is quite different with regard to in vivo studies of mechanical responses at the apex of the cochlea, with studies in chinchilla and guinea pig having yielded contradictory verdicts regarding several fundamental issues. Nevertheless, there is now sufficient evidence to conclude that responses at the apex of the cochlea differ at least quantitatively from those at the base. Accordingly, in vivo responses to "basic" stimuli (tones, clicks, and noise) of sites at the base and apex of the cochlea are described in sections II and III, respectively, of this review.

All techniques for measuring cochlear vibrations require a relatively unobstructed view of the site of measurement (see sect. XII). At basal locations, the BM can be reached directly via scala tympani, but the organ of Corti and the TM are inaccessible (Fig. 1). At the "hook" region of the cochlea (within 2 mm of the stapes), the BM is approached by way of the round window (41, 47, 179, 243). Slightly more apical locations (e.g., 3-4 mm from the stapes) are reached after perforating the otic capsule (43, 307, 355). An even more apical BM location (~8-9 mm from the stapes) in the squirrel monkey cochlea (293, 306) was reached from inside the posterior cranial fossa after removal of cerebral tissue and perforation of the temporal bone near the internal auditory meatus (the central exit of the auditory nerve).

A.  Responses to Single Tones

1.  Input/output functions

Figure 2 illustrates velocity-intensity functions for BM responses to tones recorded at a site of the chinchilla cochlea located 3.5 mm from the oval window (326). In contrast to the linear growth of responses to tones with higher or lower frequencies, responses to stimuli with frequencies near CF (10 kHz) exhibit highly compressive growth, i.e., response magnitude grows by only 28 dB as stimulus intensity increases by 96 dB. Compression is most prominent at moderate and high levels, with average rates of growth as low as 0.2 dB/dB at CF (measured for intensities between 40 and 90 dB SPL; i.e., sound pressure level referenced to 20 µPascals) and even lower rates at frequencies immediately above CF. The input/output functions for responses to CF tones at basal BM sites in guinea pig and cat resemble those in chinchilla (Fig. 3). Rates of growth for responses to CF tones measured in several studies are collected in Table 1.

View larger version (24K): [in this window] [in a new window]   Fig. 2. Velocity-intensity functions of BM responses to tones. A: responses to tones with frequency equal to and lower than characteristic frequency (CF; 10 kHz). B: responses to tones with frequency equal to and higher than CF. The straight dotted lines (bottom right in each panel) have linear slopes (1 dB/dB). Recordings were made at a site of chinchilla cochlea situated some 3.5 mm from its basal end. [From Ruggero et al. (326). Copyright, Acoustical Society of America, 1997.]

View larger version (19K): [in this window] [in a new window]   Fig. 3. Displacement-intensity functions for BM responses to CF tones recorded at basal cochlear sites in chinchilla, guinea pig, and cat. For comparison, the dotted line indicates linear growth. [Chinchilla data (squares) from Ruggero et al. (326); guinea pig data (solid and open circles) from Nuttal and Dolan (259) and Cooper (43), respectively; cat data (diamonds) from Cooper and Rhode (47).]

Early measurements of BM vibrations using the Mössbauer technique (see sect. XII) suggested, but did not establish conclusively, that responses to CF tones grow linearly at low stimulus intensities (307, 355). Newer measurements using optical techniques have provided confirmation (47, 237, 259, 326). Theoretical considerations suggest that input-output functions should also be linear at sufficiently high stimulus intensities (123, 164, 251, 279, 408). Indeed, the literature includes CF input-output curves in which compression decreases systematically above 80 dB SPL and slopes approach linearity at 90-100 dB SPL (272, 300, 322, 324, 332). In contrast, other reports (43, 259, 326) indicate that highly compressive growth is maintained essentially undiminished up to intensities as high as 100 dB SPL (e.g., Fig. 3). Complicating this issue is the fact that cochlear damage linearizes input-output BM functions (see sect. IXB1) and therefore the occasionally reported full linearization of input-output curves at high stimulus levels may reflect cochlear damage (326). On balance, it seems that although compression may be lessened in healthy cochleae above 80 dB SPL, full linearization occurs at levels >100 dB SPL, at which stimulation for longer than a few minutes is likely to result in permanent cochlear damage.

The variation of BM velocity as a function of stimulus frequency and intensity is depicted in Figure 4 as a family of isointensity functions (replotted from the data of Fig. 2). At low stimulus levels, the isointensity curves are sharply frequency tuned, with steep slopes arranged roughly symmetrically on both sides of CF. At higher stimulus levels, isointensity curves retain a steep high-frequency slope near CF but become more broadly tuned and increasingly asymmetrical as the peak responses shift toward lower frequencies. The response roll-off stops at a frequency about one-third octave higher than CF; at higher frequencies, response magnitude is relatively constant, i.e., it reaches a plateau, evident in responses to intense (70-90 dB) tones (Fig. 4).

View larger version (22K): [in this window] [in a new window]   Fig. 4. A family of isointensity curves representing the velocity of BM responses to tones as a function of frequency (abscissa) and intensity (parameter, in dB SPL). The isointensity curves represent the same chinchilla data of Fig. 2. [From Ruggero et al. (326). Copyright, Acoustical Society of America, 1997.]

Figure 5 shows curves of BM sensitivity (displacement per unit of stimulus pressure) as a function of frequency for basal sites of the chinchilla and guinea pig cochleae. If responses grew linearly, the sensitivity curves measured at different intensities would be identical. In fact, sensitivity grows systematically larger as a function of decreasing stimulus level at frequencies near CF so that the curves superimpose only at frequencies well removed from CF (i.e., frequencies lower than 0.7 CF or in the plateau region above CF).

View larger version (23K): [in this window] [in a new window]   Fig. 5. Families of isointensity curves representing the sensitivity (displacement divided by stimulus pressure) of BM responses to tones as a function of frequency (abscissa) and intensity (parameter, in dB SPL). The lower CF (10 kHz) data were recorded at the 3.5-mm site of the chinchilla cochlea. [Redrawn from Ruggero et al. (326).] The higher CF (17 kHz) data are from a basal site of the guinea pig cochlea. [Redrawn from Cooper and Rhode (52).]

The compressive nonlinearity is strongly dependent on stimulus frequency. As a result, both the bandwidth (or the sharpness of tuning) and the peak (or best) frequency of the sensitivity functions change as a function of stimulus level. At the highest stimulus levels, responses reach their maxima at frequencies about one-half octave lower than at the lowest stimulus levels and the sharpness of tuning decreases (e.g., from a Q₁₀ of 5 at 10 dB to only 1.4 at 90 dB SPL for the chinchilla data of Fig. 5). (Q₁₀ equals the frequency of the response peak divided by the bandwidth 10 dB below the peak.)

Normalizing BM sensitivity functions to stapes or incus motion yields estimates of cochlear gain as a function of stimulus frequency, permitting an assessment of cochlear contributions to frequency tuning in isolation from middle ear inputs. Figure 6 compares maximal cochlear gains (i.e., computed for low-level stimuli), as a function of frequency, for basal sites of the cochleae of cat, guinea pig, and chinchilla. (Also shown are curves for an apical site in chinchilla, to be discussed in sect. III.) At CF, the peak magnitudes of BM vibrations far exceed those of the middle ear ossicles, with cochlear gains ranging from 47 to 75 dB. At frequencies well below CF, BM vibration at basal cochlear sites exhibit slopes of ~6 dB/octave relative to stapes motion. This is as expected on the following assumptions, which apply to the relevant range of stimulus frequencies, from ~200 Hz to several kiloHertz in chinchilla (59, 73, 216, 328, 424): stapes velocity gain (re SPL) is roughly constant with respect to stimulus frequency; cochlear input impedance is real (or resistive) so that pressure in scala vestibuli near the stapes is proportional to stapes velocity (and greater than in scala tympani); BM displacement is proportional to the local pressure difference across the "cochlear partition" (the organ of Corti and the BM).¹

View larger version (20K): [in this window] [in a new window]   Fig. 6. Maximum gains of BM or TM responses, relative to middle-ear vibration, from basal and apical cochlear sites. Basal BM responses to low-level tones have been normalized to responses of the incus (guinea pig and cat) or the stapes (chinchilla). The TM data for the chinchilla apex, normalized to the vibrations of the umbo of the tympanic membrane, were selected to indicate the range of sensitivities. Chinchilla base (circles): CF = 8.4 kHz, data from Ruggero et al. (328); chinchilla apex (dashed lines): CF = 0.35-0.5 kHz, data from Rhode and Cooper (299); guinea pig (squares): CF = 17 kHz, data from Sellick et al. (360); cat (triangles): CF = 30 kHz, data from Cooper and Rhode (47).

Because the filter characteristics of the cochlea are distributed over space, wave propagation from base to apex (see sect. v) involves "pure" (i.e., frequency independent) delays as well as "filter" delays that vary with frequency. As a consequence of these delays, BM responses to tones exhibit increasing phase lag as a function of increasing frequency. Figure 7 displays the phases of BM vibrations, relative to middle ear motion, at basal cochlear sites of squirrel monkey, chinchilla, guinea pig, and cat. Most of the phase versus frequency curves are characterized by a shallow segment at low frequencies and a steep segment at frequencies around CF. The exception is the curve for the squirrel monkey site with CF = 6 kHz, with a low-frequency segment nearly as steep as the segment in the neighborhood of CF. At low frequencies, BM responses typically lead middle ear vibration by ~90 degrees. This phase lead and the 6-dB/octave slope of BM magnitude gain relative to the middle ear (see sect. IIA3) indicate that BM displacements are proportional to stapes velocity, consistent with the idea that cochlear input impedance is resistive (real) (424) (see footnote 1).

View larger version (20K): [in this window] [in a new window]   Fig. 7. The phases of BM responses to tones as a function of frequency. The phases of BM displacement toward scala tympani are expressed relative to inward ossicular displacement. The data were obtained at basal sites of the cochleae of squirrel monkey, chinchilla, guinea pig, and cat. CFs are indicated by closed symbols. Guinea pig (diamonds): data from Nuttall and Dolan (259); guinea pig (circles): data from Sellick et al. (360); chinchilla (X): CF = 9.7 kHz, data from Ruggero et al. (326); chinchilla (crosses): CF = 15 kHz, data from Narayan et al. (243); squirrel monkey (squares): data from Rhode (293); cat (triangles): data from Cooper and Rhode (47).

The slopes of the phase versus frequency curves are steepest just above CF. Because the slope of the phase curve can be interpreted as the (group) delay intervening between the launching of a wave near the stapes and its arrival at the measuring site, the increase in phase slope with frequency indicates that waves of higher frequency propagate more slowly than those of lower frequency. The phase-lag accumulation at CF, 1-2.5 periods, is not obviously correlated with CF, and one may conjecture that, in any single species, phase accumulation at CF may be a constant throughout the cochlea (415). We shall see below that such a conjecture is also supported by phase measurements at apical cochlear locations (see Fig. 12). At frequencies well above CF, some of the curves reach phase plateaus (discussed in the sect. IIA5). Table 2 provides a summary of the features of phase versus frequency curves, including those of Figure 7.

At the cochlear base, BM responses to tones with frequency well below CF grow linearly with stimulus intensity and, appropriately, response phases at those frequencies are invariant with respect to stimulus intensity. At near-CF stimulus frequencies, response magnitudes grow nonlinearly, and phases vary systematically with intensity. This intensity dependence is illustrated in Figure 8, which shows BM response phases in chinchilla and guinea pig normalized to the responses to moderately intense stimuli (80 and 74 dB SPL, respectively). Response phases increasingly lag with intensity for frequencies just below CF and lead for frequencies somewhat above CF, remaining relatively constant at a frequency close to CF. This pattern of phase shift with increasing stimulus level, first described in the responses of low-CF auditory nerve fibers (7), has been demonstrated in BM responses at the base of the cochlea in several species (47, 258, 259, 300, 301, 323, 326, 355). The intensity-dependent variation of responses around CF results in systematic changes of phase slope or group delay as a function of stimulus level. At the base of the chinchilla cochlea, for example, group delays around CF decrease from 990 to 610 µs as stimulus levels increase from 10 to 90 dB SPL (326). However, the accumulation of phase lag at CF (~1.5 periods, equivalent to a delay of 150 µs) remains essentially invariant over the same range of intensities.

View larger version (27K): [in this window] [in a new window]   Fig. 8. Intensity dependence of BM response phases around CF. BM phases in chinchilla (top) or guinea pig (bottom) are expressed relative to the phases of responses at a single stimulus intensity. Chinchilla data were normalized to 80 dB SPL and were from Ruggero et al. (326). Guinea pig data were normalized to 74 dB SPL and were from Nuttall and Dolan (258).

The sensitivity curves of Figure 5 include high-frequency plateaus, within which responses grow linearly and have sensitivities some 70-90 dB lower than for low-level stimulation at CF. Similarly, some of the phase curves in Figure 7 exhibit plateaus in the corresponding frequency regions. High-frequency plateaus have been observed in the cochleae of several species [e.g., curves for squirrel monkey (squares), chinchilla (crosses and X), and guinea pig (diamonds) in Fig. 7] (47, 243, 259, 293, 307, 326, 400, 402). The phase values at the plateaus have been variously reported as lagging middle ear vibration by 1.5 periods (165); 3.5, 4, or 4.5 periods (e.g., squares in Fig. 7; Refs. 293, 297); 2.5 periods (crosses and diamonds in Fig. 7; Refs. 243, 259; also see arrowhead in Fig. 19); 0.25 or 1.25 periods (400); 2.3 or 3.3 periods (328); or 3.75 periods (X in Fig. 7; Ref. 326). The phase plateaus often appear quantized in that, at any given BM site in each species, they occur at discrete values separated by one or more periods (307, 328, 400) (or, less commonly, 0.5 period; Ref. 293) (see also sect. VC and Fig. 15).²

It was once suggested that the plateaus arise from cochlear damage, including acoustic trauma incurred while testing for its presence (133). However, plateaus were subsequently demonstrated in normal cochleae using test stimuli that did not impair normal sensitivity (307). Plateaus do not appear to be instrumental artifacts, since they have been measured at the BM using such disparate methodologies as the Mössbauer technique, capacitive probes, and laser velocimetry. In addition, plateaus are present in pressure waves recorded in the perilymph of scala tympani, near the BM (266, 267) (see Fig. 15 and sect. VC). At the apex of the cochlea, plateaus appear to be artifacts resulting from opening the otic capsule over scala vestibuli (50; see sect. IIIC). At the base of the cochlea, however, it seems unlikely that opening the otic capsule over scala tympani would have a similar effect, since the round window membrane provides an effective pressure release even when the otic capsule is intact. Furthermore, plateaus are also evident in pressure recordings at basal sites of cochleae in which the hydraulic seal of the otic capsule was restored after introduction of the microphone into scala tympani (266, 267; see Fig. 15 and sect. VC). Interestingly, plateaus are present in BM vibrations but absent from the responses of high-CF auditory nerve fibers recorded under identical conditions in the same cochleae (see Fig. 1B of Ref. 244). In other words, BM vibrations at frequencies well above CF seemingly are not transmitted to inner hair cells (399). However, magnitude and phase plateaus are apparent in some responses of auditory nerve fibers as a function of CF (Fig. 10 of Ref. 188).

In conclusion, although BM vibrations at the plateau frequencies may not participate in determining responses of auditory nerve fibers, it is clear that the high-frequency amplitude and phase plateaus are normal features of BM displacement waves. By their very nature, which implies very high wave velocity, the phase plateaus indicate a mode of vibration distinct from the "slow" pressure and displacement waves that propagate in the cochlear fluids and on the BM (sect. V). The fixed, frequency-independent, phase relation between middle ear and BM vibrations (and also pressure in scala tympani; see sect. VC) suggests that the plateaus reflect, more or less directly, positive or negative components of stapes motion, transmitted as "fast" (acoustic) pressure waves or standing waves made up by the combination of a sound wave and its reflection (211). If the BM responds resistively to the fast pressure wave, its displacement must be in phase or antiphase with stapes displacement (rather than stapes velocity) (211), in agreement with many of the reported phase lags (165, 243, 259, 293, 297) (see footnote 2).

At the base of the cochlea, BM responses to tones contain fairly low harmonic distortion (43, 47, 326). Among distortion components, the second harmonic is the largest (47), attaining levels as high as 3.5% (or 29 dB) referred to the fundamental component (43). Harmonic distortion decreases with increasing stimulus level and with deterioration of cochlear function, an indication that harmonics arise as by-products of the mechanism that enhances cochlear sensitivity at low stimulus levels (43).

Although second-order harmonic distortion might be expected to be accompanied by direct current (DC) or tonic displacements (since all even-order distortions generate DC distortion), these have been measured at the base of the cochlea only following severe injury, in responses to very intense stimuli (203, 204). DC displacements were sought, but not found, in studies that used a displacement-sensitive interferometer to measure vibrations in near-normal cochleae (47).

For nonlinear systems, the responses to tones cannot generally be used to predict responses to arbitrary stimuli. Therefore, a thorough understanding of BM behavior requires the use of other stimuli, such as tone complexes, noise, and clicks. Clicks are especially useful because, being punctate and wide-band in nature, they permit precise timing of a system's response while simultaneously testing it over a wide range of frequencies. BM responses to clicks were first recorded in live animals using the Mössbauer technique (301, 306). Despite the severe distortion introduced by the Mössbauer recording technique (see sect. XIIA), these early studies revealed responses exhibiting compressive nonlinearities consistent with those of responses to tones (293). Those results have been confirmed and extended by laser-velocimetry recordings in chinchilla and guinea pig (84, 290, 323).

Figure 9 shows BM responses to clicks at the 10-kHz site of the chinchilla cochlea. Responses consist of lightly damped transient oscillations with latency of ~30 µs (referred to the onset of ossicular motion) and instantaneous frequency that increases rapidly and settles at CF within a few hundreds of microseconds (84, 290). The frequency increase is largely impervious to changes in stimulus intensity (84, 290) and remains after death (290). Response wave shape and sensitivity change systematically as a function of stimulus intensity. The responses to low-level clicks have high sensitivity and nearly symmetrical spindle-shaped envelopes, which reach their maxima roughly 1 ms after the onset of stapes motion. As click level is raised, most cycles of oscillation grow at highly compressive rates (thus decreasing in sensitivity), but the earliest cycle grows at faster, almost linear, rates. This produces a systematic skewing of the envelopes toward earlier times. Responses to clicks at a basal location of the guinea pig cochlea (CF = 18 kHz; Ref. 84) display nonlinear behavior similar to that illustrated in Figure 9.

View larger version (28K): [in this window] [in a new window]   Fig. 9. BM responses to rarefaction clicks. The response waveforms, recorded at a basal site of the chinchilla cochlea, are displayed with a uniform scale of sensitivity (velocity per unit pressure). The thin vertical line indicates the onset of vibration of the middle-ear ossicles. Positive values indicate velocity toward scala vestibuli. Peak stimulus pressures (in dB/20 µPa) are indicated above each trace. [Data from Recio et al. (290).]

Despite the level-dependent compressive nonlinearity, the magnitude and phase spectra of responses to clicks closely resemble the magnitudes (Fig. 10) and phases (data not shown) of responses to tones (290, 323). In other words, the features that characterize steady-state responses to tones are also expressed in the brief responses to clicks. This is made possible by the rapid development of compressive growth, which is detectable within 100 µs of the response onset (290). Taking into account the aforementioned frequency glide, it seems that compressive nonlinearity and its correlates, high sensitivity and frequency selectivity, all start nearly as soon as the BM begins to vibrate at CF. It is remarkable that these almost instantaneous level-dependent changes in gain are accomplished while generating relatively low harmonic and intermodulation distortion (see sects. IIA6 and VIIB). For comparison, electronic feedback systems in which gain is reduced as a function of increasing input magnitude typically incorporate relatively long time constants to prevent large harmonic and intermodulation distortion. In the case of the cochlea, harmonic and intermodulation distortion components appear to be minimized by the sharp frequency filtering that accompanies enhancement of BM responses to low-level stimuli and amplitude compression at high stimulus levels.

View larger version (23K): [in this window] [in a new window]   Fig. 10. BM responses to clicks and tones recorded at the same site in a chinchilla cochlea. Frequency spectra of BM responses to clicks (dashed and solid lines; peak pressures 24-104 dB) compared with the magnitudes of responses to tones (symbols). The thick solid line indicates the spectrum of responses to 104-dB clicks recorded 10-20 min postmortem. [Adapted from Recio et al. (290).]

Many nonlinear systems can be described by analyzing their responses to white noise using cross-correlation functions (96, 225). The first-order cross-correlation between the noise and the response, the first-order Wiener kernel, is identical to the impulse response in a linear system, but it also provides information on odd-order nonlinearities in the case of nonlinear systems. The second-order kernel provides information on quadratic and higher-order even nonlinearities. First-order Wiener kernels for BM vibration resemble responses to clicks (84, 289). This resemblance, as well as the fact that second-order Wiener kernels are small in magnitude, shows that even-order nonlinearities contribute little to BM responses to noise at the base of the cochlea (289). This is consistent with the relative weakness of harmonic distortion in BM responses to tones (see sect. IIA6; Refs. 43, 47, 326).

	III. IN VIVO MECHANICS AT THE APEX OF THE COCHLEA

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Mechanical responses to sound at the apex of the cochlea are still poorly understood in part because few such data have been obtained from cochleae that were reasonably free of experimenter-induced damage. Most methods for measuring cochlear vibrations require the placement of artifacts (mirrors, Mössbauer sources) on the vibrating structures and, therefore, studying the responses of the organ of Corti, the BM, or the TM at the apex (Fig. 1) often entails perforating Reissner's membrane, which alters the endolymph composition and reduces the endocochlear potential. The scarcity of data has been compounded by a lack of independent controls to assess the physiological state of the preparation. In particular, although compound action potential thresholds are very useful in testing the overall integrity of function of high-CF regions of the cochlea, when they have been (exceptionally) used in conjunction with mechanical measurements at the cochlear apex (49) they have been judged to be very insensitive as an indicator of damage. In addition, it is not clear whether compound action potential thresholds provide CF-specific information for cochlear regions with CFs lower than 500-1,000 Hz (68, 136, 166, 413).

A.  Responses to Single Tones

1.  Response magnitudes

Perhaps the recordings that are most representative of responses at apical sites in intact cochleae were obtained in chinchilla (50, 52, 299). Gold-coated polystyrene beads, introduced into scala media via small holes in Reissner's membrane, settled on the TM or Claudius cells (which line the scala media surface of the BM; see Fig. 1). When conditions were optimal, substantial compressive nonlinearities (reminiscent of those present in BM vibrations at the cochlear base) were demonstrated (50-52, 299). Figure 11 (open symbols) displays sensitivity functions (isointensity functions normalized to stimulus level) for TM responses to tones at a site of the chinchilla cochlea with CF ~500 Hz. Responses grow at mildly compressive rates (0.5-0.8 dB/dB) so that vibration sensitivity increases systematically with decreasing stimulus intensity (by as much as 22 dB between 90 and 30 dB SPL). The region of compressive nonlinearity encompasses the entire frequency range of responses so that both the peak frequency and bandwidth are largely independent of stimulus level (52, 299). Gains (computed relative to middle ear ossicular motion) for representative TM recordings at apical sites of the chinchilla cochlea are shown in Figure 6 (dashed lines) (299).

View larger version (32K): [in this window] [in a new window]   Fig. 11. Sensitivity (displacement divided by stimulus pressure) of responses to tones at the apex of guinea pig and chinchilla cochleae. Open symbols: chinchilla TM (CF = 500 Hz), data from Cooper and Rhode (52); solid symbols: guinea pig organ of Corti (CF = 400 Hz), data replotted from Zinn et al. (413); thick continuous line (no symbols): guinea pig BM (CF ~300 Hz), data replotted from Cooper and Rhode (49); thin lines (no symbols): responses to tones at three intensities spaced 10 dB apart, guinea pig organ of Corti (CF ~300 Hz), data replotted from Khanna and Hao (178).

Several investigations of mechanical vibration in apical regions of guinea pig and squirrel monkey cochleae have failed to detect compressive nonlinearities comparable to those observed in chinchilla (49, 52, 135, 178, 296, 413). Especially notable is the absence of nonlinearities in organ of Corti vibrations measured without rupturing Reissner's membrane (177, 178), since under such circumstances one would expect minimal disruption of normal function. A single investigation, however, has described a vulnerable expansive nonlinearity at an apical site of the guinea pig cochlea with CF ~300-400 Hz (Fig. 11, solid symbols) (413). The fact that the expansive nonlinearity disappeared postmortem (not shown in Fig. 11) suggests that this exceptional investigation is the only one that has managed to preserve the apex of the guinea pig cochlea in anything approaching its normal, undisturbed condition. As illustrated in Figure 11 (solid symbols), response magnitudes grew almost linearly at frequencies lower than CF. However, at CF and, especially, at a frequency just higher than CF, responses grew with stimulus intensity at rates higher than 1 dB/dB, i.e., expansively. In other words, for frequencies equal to and just higher than CF, responses became more sensitive as stimulus levels were raised. This level dependence of response magnitude is the opposite of the level dependence of responses at the apex of the chinchilla (Fig. 11, open symbols) or at basal locations (Figs. 2-5 and 10).

The mechanical responses of apical sites in guinea pig cochleae (Table 3 and Fig. 11) differ from responses in chinchilla in being less sensitive (by 20-30 dB for low-level CF stimuli), regardless of whether responses are linear (lines without symbols) or nonlinear (solid symbols). It is not clear whether this difference in sensitivity reflects differences in species or the locations of the recording sites, ~17 mm from the oval window (CFs = 200-400 Hz) in guinea pig versus 14 mm (CFs = 400-800 Hz) in chinchilla. Despite other differences, apical responses of chinchilla and guinea pig display similar sharpness of frequency tuning (Q₁₀ ~0.6-1.3; Fig. 11, Table 3).

Figure 12 shows the variation of phase as a function of frequency for TM responses to tones at apical sites of chinchilla and guinea pig cochleae (42, 49, 50, 299). The curves show phase lags (expressed relative to motion of the middle ear ossicles) that increase monotonically with almost constant slope. At CF, the phase accumulation amounts to ~0.8 periods in the cochleae of Figure 12, but larger phase accumulations (1-1.4 periods), nearly comparable to those at the base of the cochlea (Fig. 7), have also been measured at apical sites in other cochleae (50, 299). At frequencies lower than 150 Hz, response phases in chinchilla lead those in guinea pig by nearly 180 degrees, perhaps partly reflecting differences in the cochlear input impedance in the two species associated with the disparate sizes of their helicotremas (58).

View larger version (12K): [in this window] [in a new window]   Fig. 12. Vibration phases at the tectorial membrane (TM) of the cochleae of chinchilla and guinea pig. Displacements toward scala tympani (for the "slow" traveling wave) are shown relative to inward displacement of the middle ear ossicles. CFs are indicated by closed symbols. Solid line: chinchilla, at a site ~14 mm from base (CF ~500 Hz); reference, umbo. Dashed line: guinea pig, at a site ~16.5 mm from base (CF ~400 Hz); reference, incus. [Data from Cooper (42).]

At apical sites of chinchilla cochleae that display compressive nonlinearity (Fig. 11, open symbols), the response phases vary systematically with stimulus level (data not shown), exhibiting leads and lags as a function of increasing stimulus level for frequencies lower and higher than CF, respectively (299). At the apex of the guinea pig cochlea, nonlinearity (when it exists) is expansive (Fig. 11, solid symbols), but it is also accompanied by labile changes in response phases with stimulus level (data not shown). However, responses exhibit phase leads as a function of increasing stimulus level at all frequencies (413).

TM vibrations at the apex of the chinchilla cochlea exhibit DC components (299). These are typically tonic displacements toward scala vestibuli that accompany alternating current (AC) responses within the range of compressive growth. The DC displacements (35 nm in response to 40- to 80-dB SPL tones) are much smaller than the corresponding AC responses.

One study of the apex of the guinea pig cochlea reported that, paradoxically, even though organ of Corti vibrations grew at linear rates, they contained enormous harmonic distortion (e.g., second harmonic magnitude as high as 50% of the fundamental) for tone frequencies slightly lower than CF (177). At apical sites of the chinchilla cochlea, TM responses to tones with frequency lower than CF also exhibit harmonic distortion (299). Although their magnitude was not reported, perusal of the published waveforms (299) suggests that harmonic distortion at apical cochlear sites is much lower in chinchilla than in guinea pig (177).

Responses to clicks at the third turn of the chinchilla cochlea and the fourth turn of the guinea pig cochlea (50) consist of transient oscillations at frequencies corresponding to CF. These oscillations, which have a latency of ~1-1.5 ms relative to the onset of middle ear ossicular vibration, grow at compressive rates in the chinchilla throughout their duration.

In addition to the aforementioned "slow" components, with latencies of 1-1.5 ms, responses to clicks from apical turns of chinchilla and guinea pig cochleae include a linear "fast" component with an onset delay of ~20-50 µs. This fast wave is believed to be an experimental artifact (related to the propagation of the sound wave in the cochlea; see sect. V), since it disappears when the hydraulic seal of the cochlea is restored (50). Similarly, high-frequency magnitude and phase plateaus become less prominent or disappear upon closing the otic capsule.

	IV. COCHLEAR VIBRATIONS AS A FUNCTION OF LONGITUDINAL POSITION

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As first shown by von Békésy (388), the systematic mapping of CF upon longitudinal position on the BM is a general and fundamental principle of the mechanical processing of acoustic signals in the cochleae of mammals. Because such "tonotopic" mapping can be demonstrated in vitro, it is clear that spatial frequency analysis arises from the passive mechanical properties of cochlear fluids and tissues (see sect. VB). The tonotopic cochlear map has been worked out in some species, such as cat and Mongolian gerbil, by measuring the sites of innervation of auditory nerve fibers of known CF (208, 240). In these cochleae, as well as in the cochleae of several other species that are known with less precision, the tonotopic map follows Equation 1

(1)

where CF is expressed in kHz (127, 128). If x, the distance from the apex, is expressed as a proportion of BM length, from 0 to 1, the constant  is the same (2.1) in many cochleae differing widely in length (11.1 to 60 mm), including those of gerbil, chinchilla, guinea pig, cat, macaque monkey, humans, cow, and elephant (127, 129). The constant k also varies only slightly in many species (between 0.8 and 1, typically 0.85). This is a remarkable result, implying that in all these species, where  and k are (nearly) the same, every octave arranged "by rank, from highest to lowest in an animal's frequency range, subtends the same proportion of the length of the cochlea" (129). For the basal 75% of the cochlea (i.e., for x > 0.25), Equation 1 describes a simple linear relation between BM position and the logarithm of CF; for the 25% apical region, CF octaves are relatively compressed, occupying BM lengths shorter than at more basal locations. The constant A (0.456 in cat, 0.164 in chinchilla, 0.35 in guinea pig; 0.36 in the macaque monkey, and 0.4 in gerbil) determines the range of CFs.

Because the length of the BM tends to be greater in mammals with larger body size (see sect. IB), the actual length (e.g., in mm) subtended by a particular octave of CF varies from species to species. Thus, for example, the uppermost octaves represented in the cochleae of cat and gerbil occupy 14% of BM length, which translates to 1.57 mm in gerbil and 3.55 mm in cat (129). The corresponding BM distances are substantially shorter in nonmammalian species, which have short BMs (e.g., ~0.6 mm in several birds, 0.13 mm in the red-eared turtle, and 1 mm in the monitor lizard) (221). Because, in general, the hearing range in mammals extends to much higher frequencies than in nonmammals (95, 105), it seems reasonable to speculate that the reptilian ancestors of mammals had relatively short basilar papillae and that increased length of mammalian cochleae was associated with the evolution of mechanical processes (221), absent (or only present in primitive form) in reptiles, which led to the development of high-frequency hearing (371) and a consequent improvement in the ability to localize sounds (227).

1) BM vibrations are less sharply tuned at the apex of the cochlea than at the base (378, 391), regardless of stimulus level or the physiological state of the cochlea. In the chinchilla, for example, responses to intense stimuli of BM sites distant 3.5 and 14 mm from the oval window have Q₁₀ values of 1.6 and 0.9, respectively (Fig. 13).

View larger version (24K): [in this window] [in a new window]   Fig. 13. Comparison of vibration sensitivity (velocity per unit pressure) at the base and apex of the chinchilla cochlea. For each family of curves, stimulus frequencies are shown normalized to CF (500 Hz and 9 kHz). At either site, sensitivity decreases as function of stimulus level. At the base of the cochlea, responses to CF tones differ by as much as 56 dB as a function of stimulus level; peak sensitivities at the highest and lowest stimulus levels differ by 48 dB. At the apex, the two measures of the intensity dependence of sensitivity are the same, 15 dB. The upward arrows indicate the frequencies of peak sensitivity (BF) for responses to the highest level tones, which resemble postmortem data. [Basal BM data from Ruggero et al. (326); apical TM data from Cooper and Rhode (52).]

2) Whereas a compressive nonlinearity is a prominent feature of BM vibrations at the base of the cochlea, the presence and/or nature of nonlinearities at apical sites have not been well established. Some studies have reported that apical vibrations are linear (49, 178), others have demonstrated a relatively weak compressive nonlinearity (52, 299), and still another has found a weak expansive nonlinearity (413).

3) At the base of the cochlea, compressive nonlinearity is confined near CF, and vibrations grow linearly at frequencies lower than 0.7CF (Fig. 13). In contrast, at apical sites, when a compressive nonlinearity exists (chinchilla), it extends uniformly throughout the frequency range of responses; when an expansive nonlinearity exists (guinea pig), it is prominent only for frequencies higher than CF (413).

4) At the cochlear base, the strength of the compressive nonlinearity and sharpness of tuning are highly correlated (and perhaps inextricably linked; Figs. 5, 10, 13, 19, and 20). At the apex of the chinchilla cochlea, frequency tuning is largely independent of stimulus level (Figs. 11 and 13) even in the presence of a compressive nonlinearity (50, 52, 299). At the apex of the guinea pig, however, when an expansive nonlinearity exists, frequency tuning is labile and level dependent (413) but to a much lesser extent than at the base of the cochlea.

5) In chinchilla cochleae, responses to clicks at apical sites differ from those at basal sites in that the former grow at compressive rates throughout their duration, whereas at the base onset oscillations grow linearly. This difference is consistent with the contrasting distribution of compressive nonlinearity as a function of frequency in responses to tones at both cochlear sites (see point 3 above).

Some of the aforementioned differences between BM responses at the base and the apex are consistent with results of several studies of auditory nerve fibers. One study derived putative BM input-output functions for CF tones from the responses of auditory nerve fibers, on the assumption that at frequencies well below CF the BM at the nerve fiber site vibrates linearly (see sect. VIIIA), and found that the compressive nonlinearity became weaker with decreasing CF (53). Other studies found that the modulation or suppression exerted by low-frequency tones on auditory nerve fiber responses to CF tones (see sect. VIIA3) grows weaker as a function of decreasing CF (27, 86, 376). All these results on single- and two-tone stimulation could be interpreted as evidence that the strength of compression diminishes systematically with decreasing CF or, alternatively, as evidence that at the apex of the cochlea BM responses grow at similarly compressive rates at all frequencies. Both interpretations may turn out to be correct, in light of the contrasting apical mechanical data from chinchilla and guinea pig (see sect. III).

The base versus apex differences are also consistent with the dependence on CF of the effects of furosemide on the responses of auditory nerve fibers (361). Furosemide elevates the thresholds of high-CF auditory nerve fibers at all frequencies, but preferentially at CF. In light of the effects of furosemide on BM vibration at the base of the cochlea (Fig. 20; see sect. IXB3), it is clear that the CF specificity reflects the reduction of BM vibrations, whereas threshold elevations at other frequencies (and partially near CF) result from the reduced drive for mechanoelectrical transduction in inner hair cells. In other words, the decrease in endocochlear potential produced by furosemide affects high-CF inner hair cells directly at all frequencies and indirectly (via the outer hair cells and BM vibrations) only near CF. In the case of low-CF fibers, the effects of furosemide are less marked than for high-CF fibers and are similar at all response frequencies. The former finding is consistent with the lesser extent of compressive nonlinearity in the mechanical responses to sound at the apex of the cochlea. The latter finding agrees with the fact that at the apex the compressive nonlinearity is nearly evenly distributed over the entire frequency range of responses (see sect. IIIA1 and Fig. 11). Finally, differences between mechanical responses at the base and apex of the cochlea may underlie the finding that low-frequency hearing thresholds are relatively immune to the loss of apical outer hair cells (286).

In section IIA4 it was noted that the phase versus frequency curves of BM responses at basal sites (within 4 mm of the stapes) consist of three distinct segments: one with shallow slope at low frequencies, another with steep slope around CF, and a high-frequency phase plateau (Fig. 7). At the apex of the cochlea (Fig. 12), phase versus frequency curves differ from those at the base mainly in that there is no distinct separation between the low-frequency and the near-CF segments so that phase accumulates at a roughly constant rate. Nevertheless, the accumulation of phase lag at CF is similar at the base (1-2.2 periods at the base; Fig. 7, excluding the squirrel monkey data) and at the apex (0.8-1.4 periods), and in both cases the curves possess high-frequency plateaus. The squirrel monkey data for a BM site with CF ~6 kHz, presumably located ~9.5 mm (41% of total BM length) from the stapes (128), may represent a region of transition between base and apex. Low-frequency and near-CF segments are distinguishable in this phase versus frequency curve (Fig. 7), but their slopes do not differ as much as at more basal BM sites, and the phase accumulation at CF (2.5 periods) is larger than at sites closer to the stapes. A maximal phase accumulation at CF near the middle of the cochlea has been predicted on theoretical grounds (126). Systematic changes in phase slope as those noted above have been observed in cochlear microphonics and in responses of auditory nerve fibers (281).

Apical responses to tones with frequency lower and higher than CF exhibit systematic leads and lags, respectively, as a function of increasing stimulus intensity in chinchilla (see sect. IIIA2). These level dependencies of response phases are reversed from those that hold both for BM vibrations at basal cochlear regions (see sect. IIA4) and for the responses of low-CF auditory nerve fibers (7) as well as low-CF (30, 33, 62) and high-CF (335) inner hair cells.

	V. COCHLEAR TRAVELING WAVES

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One of von Békésy's fundamental contributions to auditory physiology was the discovery of cochlear mechanical traveling waves, i.e., "slow" displacement waves that propagate on the BM from base to apex (391). Although strictly speaking sound waves are also traveling waves, in the context of mammalian cochlear physiology "traveling waves" refers to displacement waves (or pressure waves; see sect. VC) that are slower by orders of magnitude than ordinary (acoustic) pressure waves, which propagate in the cochlear fluids at speeds of 1,550 m/s and traverse the entire cochlea in a few microseconds. There has been some confusion regarding what is meant by a traveling wave. Wever and Lawrence (394) originally rejected the applicability of the term to the mammalian cochlea because they thought that the term implied that energy is transmitted directly from one segment of the BM to another (rather than via the cochlear fluids; see sect. VC). Eventually, however, Wever, Lawrence, and von Békésy (395) jointly agreed that the patterns of motion described by von Békésy "can be referred to as ... a traveling wave, provided that ... nothing is implied about the underlying causes" (i.e., "how any given segment of the basilar membrane gets the energy that makes it vibrate").

The traveling-wave displacement patterns that von Békésy observed on the BM are characterized by three properties. 1) Displacements exhibit increasing phase lags as a function of distance from the oval window. At a given cochlear location, BM responses increasingly lag the motion of the stapes as a function of stimulus frequency, reaching phase accumulations far exceeding the 90-degree lag expected from simple resonances. For example, at the 300-Hz characteristic place of the BM in the human temporal bone, von Békésy measured phase accumulations equivalent to about one period at CF. In experimental animals, the phase accumulation reaches values as high as 4 periods at frequencies higher than CF (Figs. 7 and 12). 2) Displacement magnitudes have an asymmetrical envelope around the characteristic place, with the apical slope being steeper than the basal slope. At a single cochlear location, BM displacements are asymmetrically tuned around CF, with the high-frequency slope being steeper than the low-frequency slope (211, 399). 3) Traveling waves are demonstrable in the absence of normal cellular processes, when cochlear vibrations are entirely linear, such as in the temporal bones of human cadavers. In other words, traveling waves are manifestations of the "passive" mechanical characteristics (mass, stiffness, and damping) of cochlear tissues and fluids and constitute the first stage of frequency filtering and spatial analysis of auditory signals.³

A direct demonstration of the traveling wave is obtained by measuring the phases of responses to identical stimuli at closely spaced BM locations (50, 191, 243, 267, 293, 300, 338). Detailed measurements using 15-kHz tones at the base of one guinea pig cochlea (Fig. 14) (338) reveal phase lags that accumulate as a function of distance from the stapes. Over a range of 1 mm straddling the CF site, the phase accumulation for 35-dB tones amounts to 1.5 periods, indicating a wavelength at CF of ~0.67 mm and a wave velocity of 10 m/s, computed according to the following equations

(2)

(3)

(4)

where t is the travel time, is the phase difference between responses at the two sites (radians), f is the stimulus frequency (Hz), and x is the distance between the sites.

View larger version (25K): [in this window] [in a new window]   Fig. 14. Magnitudes and phases of BM responses to 15-kHz tones as functions of cochlear longitudinal position (expressed in mm from the apex). Data for BM positions apical to the dotted line were obtained from a single guinea pig, whereas data from more basal sites came from four other subjects. [Guinea pig data reprinted from Russell and Nilsen (338). Copyright 1997 National Academy of Sciences, USA.]

Wavelengths and wave velocities at CF for cochlear sites in several species are gathered in Table 4. The relation between distance from the oval window and velocities is generally consistent with the slowing down of the traveling wave as it approaches the cochlear apex. For any given stimulus frequency, wave velocities are as high as 100 m/s at sites basal to the characteristic place and decrease rapidly as the wave approaches the characteristic site (with CF = stimulus frequency) (300). For stimulus frequencies close to CF, wave velocities are more than one order of magnitude greater near the oval window than at sites close to the apex (e.g., 28 m/s at the 1.7-mm site vs. 1.55 m/s at the 12.8-mm site in the guinea pig cochlea). The wavelengths of responses to CF tones also appear to vary as a function of cochlear position, increasing from 0.5-0.9 mm near the oval window to 1.2-1.6 mm at apical sites in the guinea pig and chinchilla cochleae. A somewhat different conclusion was reached on the basis of the variation with CF of the phases of responses of cat auditory nerve fibers to near-CF tones: in the CF range 300-2,400 Hz, wavelength was found to be approximately constant, 2.2 mm or ~10% of the length of the BM (186).

The finite speed of the traveling wave also causes delays in the onsets of BM and neural responses to clicks that grow systematically longer as a function of distance from the cochlear base. In the case of the chinchilla, the delays have been measured directly at basal and apical cochlear sites, as well as indirectly, from the latencies of neural responses, throughout the cochlea. The delay between the onset of ossicular motion and BM vibration at the 3.5-mm site of the chinchilla cochlea (CF = 9-10 kHz) is 30 µs (289, 290). At the third cochlear turn (14 mm from the base: CF = ~500 Hz), delays are considerably longer, ~1-1.5 ms (50). Appropriately, the response latencies of auditory nerve fibers in chinchilla (as well as other species) increase syste