I. INTRODUCTION.

Transcription

1 Inner hair cell response patterns: Implications for low-frequency hearing M. A. Cheatham a) and P. Dallos Audiology and Hearing Sciences, Communication Sciences and Disorders, The Hugh Knowles Center, Frances Searle Building, 2299 North Campus Drive, Northwestern University, Evanston, Illinois Received 26 February 2001; revised 18 June 2001; accepted 29 June 2001 Inner hair cell IHC responses to tone-burst stimuli were measured from three locations in the apical half of the guinea pig cochlea. In addition to the measurement of ac receptor potentials, average intracellular voltages, reflecting both ac and dc components of the receptor potential, were computed and compared to determine how bandwidth changes with level. Companion phase measures were also obtained and evaluated. Data collected from turn 2, where best frequency BF is approximately 4000 Hz, indicate that frequency response functions are asymmetrical with steeper slopes above the best frequency of the cell. However, in turn 4, where BF is around 250 Hz, the opposite behavior is observed and the steepest slopes are measured below BF. The data imply that cochlear filters are generally asymmetrical with steeper slopes above BF. High-pass filtering by the middle ear serves to reduce this asymmetry in turn 3 and to reverse it in turn 4. Apical response patterns are used to assess the degree to which the middle ear transfer function, the IHC s velocity dependence and the shunting effect of the helicotrema influence low-frequency hearing in guinea pigs. Implications for low-frequency hearing in man are also discussed Acoustical Society of America. DOI: / PACS numbers: Ld, Nf, Tk LHC I. INTRODUCTION Since the time of Fletcher 1940, it has been assumed that the peripheral auditory system can be represented as a large number of independent channels with each channel preceded by an auditory filter. If differences among channels relate primarily to this initial stage of filtering, then characterizing the auditory filter bank should provide insights into the operation of the system as a whole Rosen and Howell, Consequently, recordings from different regions along the cochlear partition offer a basis for characterizing individual filters with different center frequencies. Admittedly, most of this information comes from single-unit activity where large numbers of auditory nerve fibers with widely varying best frequencies BF can be recorded in a single preparation Kiang, 1984; Ruggero, By comparison, recordings from mammalian inner hair cells IHC are much less numerous. Nevertheless, they also yield information about different cochlear locations, i.e., information that reflects the best frequency BF of any particular recording site. In this report, IHC recordings are used to study how bandwidth changes with level and how the frequencyspecific information associated with preceding mechanical events is transformed and modified prior to spike initiation. Inner hair cell receptor potentials were measured from three locations in the apical half of the guinea pig cochlea. In addition to ac receptor potentials, which are presented in another publication Cheatham and Dallos, 1998a, average voltages produced by individual cells were computed and compared. These average potentials reflect both ac and dc a Author to whom correspondence should be addressed; electronic mail: m-cheatham@nwu.edu components of the receptor potential that are integrated at the synapse and that presumably initiate transmitter release. Use of the average potential is appropriate because the ac component of the response cannot by itself initiate transmitter release at high frequencies due to filtering by the cell s basolateral membrane Russell and Sellick, Conversely, the dc receptor potential produced by IHCs located at the apex of the cochlea is insufficient to drive transmitter release at levels corresponding to behavioral threshold at low stimulus frequencies Cheatham and Dallos, 1993, In previous publications Cheatham and Dallos, 1993, 1998a, longitudinal comparisons were made for ac responses by using a generic compensation to adjust for decreases in the ac receptor potential due to filtering associated with resistances and capacitances in the cells basolateral membrane. Although not quantitative, this procedure facilitated comparisons at the level of the IHC transducer. Because the average potential includes contributions from voltage- and time-dependent ion channels in the cells basolateral membrane, it may provide a better indication of the signal initiating transmitter release. Hence, our decision was to compute the average potential when comparing hair cell responses recorded at different cochlear locations and when relating these results to behavioral sensitivity. By collecting iso-input functions and documenting the magnitude and phase changes obtained at a series of levels, it is possible to define the filter properties of each recording location and to determine the factors that influence how these properties vary along the cochlear partition. Although the middle ear shapes cochlear inputs, the primary mechanical frequency analysis is associated with the basilar membraneouter hair cell-tectorial membrane BM-OHC-TM complex 2034 J. Acoust. Soc. Am. 110 (4), October /2001/110(4)/2034/11/$ Acoustical Society of America

2 that determines the input to the IHC. Because the IHC transduces this information prior to its transfer to the auditory nerve, hair cell measurements are important to our understanding of how frequency and intensity are coded by the peripheral auditory system. Because mechanical and neural responses obtained at the base of the cochlea are well characterized, the primary focus of this article is to show how apical IHC responses differ from those recorded at more basal locations. The response patterns recorded from IHCs with low BFs are also used to determine how the coding of low-frequency signals impacts behavioral sensitivity in guinea pig. Implications for human hearing are also evaluated. II. METHODS The method used in these experiments to record from IHCs is based on that introduced by Dallos et al In this lateral approach, recordings are made from anesthetized guinea pigs in turns 2 4 where BFs are approximately 4000, 1000 and 250 Hz, respectively. Hence, this procedure allows outputs to be sampled from IHCs having BFs at two-octave intervals. In any given preparation, however, recordings are made from only one cochlear turn. Because second-turn measurements are taken at a location along the cochlear partition that is about half-way between base and apex Cheatham, 1993, the present results provide information about the apical half of the guinea pig cochlea. It is acknowledged that the data reported here are obtained from the same cells whose responses are presented elsewhere in a different form Cheatham and Dallos, 1998a. Although we show representative examples, one for each recording location, these preparations are the best in our collection. The latter contains 12 IHCs from turn 2, 19 from turn 3, and 2 from turn 4. The examples shown in this report are those where the recording time was long enough to acquire frequency response functions at several levels. Further details appear in previous publications Dallos, 1985, 1986; Cheatham and Dallos, All of the data reported here were collected in experiments approved by the National Institutes of Health and by Northwestern University s Animal Care and Use Committee. In the lateral approach for recording IHC responses, a window is made in the cochlear bone overlying the scala media fluid space. This allows the recording electrode to enter the sense organ from the side, along a track that is roughly parallel to, but slightly below, the reticular lamina. Inner hair cell responses to tone-burst stimuli were amplified and capacitance compensated Cell Explorer Model 8700, Dagan Corp., low-pass filtered to remove aliasing and gaincontrolled to prevent saturation of the analog-to-digital converter. Sound pressure levels, reported in db re: 20 Pa, were determined by placing a probe-tube microphone BT- 1751, Knowles Electronics, Elk Grove Village, IL close to the tympanic membrane. Averaged response waveforms, obtained for a series of frequencies and levels, were stored for off-line analysis using Igor Pro WaveMetrics, Lake Oswego, OR. Although the data were collected using a PDP 11/73 Digital Equipment Corp., the results were analyzed on a Macintosh IIfx or a Power Macintosh G3 Apple Computer, Inc.. Magnitude and phase data for the fundamental component of the ac receptor potential were taken from fast Fourier transforms of averaged response waveforms. In addition, half-wave rectified, average voltages were computed over an integer multiple of response cycles. The average voltage was then computed by adding together all sampled values above the baseline and dividing by the total number of data points. This procedure is virtually identical to computing the area under each half-cycle and dividing by the stimulus period. Because data were acquired over many years, the stimulus parameters were not the same for all measurements. Although gated sinusoids were used, the duration was 40 ms for results in turns 3 and 4, but only ms in turn 2, where inputs were not presented for frequencies less that 2000 Hz. In addition, the rise/fall time was ms in turns 3 and 4, but 2.5 ms in turn 2. The number of samples used in the averaging procedure was also variable. At low levels, at least 30 repetitions were collected while at high levels, and, in some cases, as few as 10 repetitions were averaged. Because hair cell receptor potentials do not adapt, a relatively short interstimulus interval was selected to facilitate data collection, but in no case was it less than 55 ms. III. RESULTS A. Frequency response functions The left panel in Fig. 1 shows the average receptor potential recorded from a third-turn IHC with a BF near 1000 Hz. At the lowest sound pressure level, in this case 20 db, the cell is narrowly tuned and response magnitude decreases at higher and lower stimulus frequencies. As level increases, however, both low- and high-frequency slopes become flatter and bandwidth increases. The customary measure, Q 10, decreases from 1.8 at 20 db to less than 0.4 at 80 db. This degradation in frequency selectivity is thought to result from an increase in damping at higher stimulus levels Anderson et al., 1971; Hubbard and Geisler, 1972; Kim et al., 1973; Hall, Relative magnitude functions, obtained by comparing responses at a given sound level with high-level responses at 80 db, are plotted in the center panel. In other words, plots are given that show how much greater the 80-dB response is than the comparison datum. At each frequency, this magnitude change in db is plotted relative to the value at 80 db. If this were a linear system, the three functions would be flat and separated from one another by 20, 40 and 60 db. The data indicate that the largest magnitude changes, i.e., the most linear responses, are achieved away from BF. In the region around 1000 Hz, the changes are relatively small, indicating that the cell is most nonlinear near BF. This compression reflects that associated with preceding mechanical events Rhode, 1971; Sellick et al., 1982; Robles et al., 1986; Nuttall and Dolan, 1996; Ruggero et al., 1992, 1997, as well as that produced by the asymmetry inherent in the IHC transducer Hudspeth and Corey, 1977; Russell and Sellick, The latter is important because the IHC cannot receive dc inputs due to the free-standing nature of its ste- J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns 2035

3 FIG. 1. Iso-input functions are presented for an IHC in the third turn of the guinea pig cochlea. The average receptor potential is plotted for inputs at 20 circles and solid lines, 40 open squares and dashed lines, 60 triangles and solid lines and 80 open triangles and dashed lines db. The center panel shows magnitude measured relative to the 80-dB condition that is given a value of 0 db. The vertical line indicates the BF of the cell. Phase data appear on the right where phase changes are also plotted relative to the 80-dB reference condition. By subtracting one measure from another, i.e., 20 from 80 db, etc., the frequency- and level-dependent changes in magnitude and phase are emphasized. reocilia Dallos et al., 1972; Lim, In other words, the sensory transducer is the source of the IHC s dc receptor potential Cheatham and Dallos, 1998b, which is included in the average voltage. Companion phase data are provided in the right panel of Fig. 1. These values were obtained from fast Fourier transforms of averaged IHC responses. The functions show changes in phase for the fundamental component of the ac receptor potential measured relative to the high-level response at 80 db. The latter was chosen because a high-level reference was used for neural responses in the original description of phase nonlinearity Anderson et al., The data indicate phase leads below BF; phase lags above, as reported previously Dallos, The phase changes in the BF region are small and the function passes through 0 degrees at this position. In fact, a pivot point at BF can be defined similar to that observed in the single-unit data obtained from neurons with similar BFs Anderson et al., 1971; Allen, The existence of a pivot point indicates that response phase is independent of level in the region around BF and that BF is relatively independent of level, except at very high intensities. Data from the third turn are, therefore, consistent with the idea that BF refers to that frequency where the cell is most sensitive and where response phase goes through its lead/lag transition. Before generalizing from these results, it is prudent to evaluate recordings from other regions along the cochlear spiral, as in Fig. 2 where results are shown for a second-turn IHC with BF around 3800 Hz. The magnitude functions on the left demonstrate that response areas change as level increases from 40 to 80 db and that high-frequency slopes are steeper than low-frequency slopes. There is also a greater tendency for the peak of the function to shift to lower frequencies, as shown in second turn of the gerbil cochlea Zwislocki and Chatterjee, 1995 and in the basal turn of the guinea pig cochlea Russell and Sellick, This behavior is thought to reflect similar response patterns observed in cochlear mechanics Rhode, 1971; Sellick et al., 1982; Nuttall and Dolan, 1996; Ruggero et al., As in Fig. 1, relative magnitude measures are shown in the center and companion phase changes are plotted on the right. Although the latter indicate a lead/lag behavior, the transitions occur above the best frequency of the cell. There is also a tendency for the pivot point to disperse as the zero crossing moves to higher frequencies with increasing level. A similar trend was observed in basilar membrane mechanical responses Rug J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns

4 FIG. 2. Data obtained in turn 2 are plotted here for iso-input levels of 40 circles and solid lines, 50 squares and dashed lines, 60 triangles and solid lines and 80 open triangles and dashed lines db. The BF for this cell is 3800 Hz. These results are also presented in three panels, as in Fig. 1. gero et al., 1997 and in auditory nerve fibers with BFs above 2000 Hz Allen, It is acknowledged that we may have underestimated the BF of this second turn IHC because 40 db was the lowest level used to collect the data shown in Fig. 2. Measurements from the fourth turn are depicted in Fig. 3 for an IHC with BF near 230 Hz. Again, bandwidth is level dependent and the measurements of relative magnitude, plotted in the center, indicate that the system is nonlinear at this apical recording location. Only at 700 Hz, when the input sound pressure level is decreased from 70 to 50 db triangles and solid lines, is response magnitude reduced by 20 db as expected in linear systems. When compared to center panels in Figs. 1 and 2, the functions from turn 4 are less V-shaped, indicating that the nonlinearity is expressed over more of the response area of the cell. This is consistent with measurements of basilar membrane mechanics at the apex of the cochlea Rhode and Cooper, Relative phase changes are plotted on the right. Although a lead/lag behavior is again recorded, the transition occurs below the best frequency of the cell. A similar pattern was also observed by Anderson et al for single units innervating the apex of the cochlea and having low BFs. Data plotted in Fig. 4 serve to emphasize the level- and frequency-dependent magnitude changes observed in turns 2 4. To facilitate the comparisons, the average receptor potential is normalized to its value at BF, i.e., 3800 Hz in turn 2, 1000 Hz in turn 3, and 230 Hz in turn 4. The frequency scale is also normalized to BF. Plots for the compensated ac receptor potential are provided in a previous publication Cheatham and Dallos, 1998a. At each recording location, functions are included for the 50- and 90-dB conditions. In turn 2, the largest level-dependent changes are observed below the BF of the cell and the peak of the function shifts to lower frequencies. Conversely, the data in turn 4 exhibit the largest changes above BF and the peak tends to move to higher frequencies. The reverse asymmetry exhibited in turn 4 is consistent with that reported for data from the auditory nerve Pfeiffer and Molnar, 1970; Rose et al., 1971; Kiang et al., 1977; Gibson et al., 1977; Liberman and Kiang, 1978; Evans, 1981 where the tails of tuning curves for units with BFs below 1000 Hz are on the high-frequency side of the tuning curve. This contrasts with units with higher BFs where the opposite is true. Data collected in turn 3, and plotted in the center panel, show a more symmetrical expansion of the response area to both lower and higher frequencies as stimulus level increases from 50 to 90 db. These place-specific changes in filter shape have important implications for the coding of acoustic signals, especially the reverse asymmetry recorded at the very apex of the cochlea and expressed in both inner hair cell and neural responses. Because filter shape is primarily determined by preceding mechanical events, data for the ac receptor potential are provided in Fig. 5. These results were collected at 50 db, the lowest level common to all three cells. In order to better represent filter shape at the input to the IHC, ac responses J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns 2037

5 FIG. 3. This plot is similar to those in Figs. 1 and 2 but the data are collected from turn 4 where BF is 230 Hz. The 70-dB condition was used as the reference for the relative magnitude changes plotted in the center panel and for the relative phase changes plotted on the right. The 90-dB condition was not chosen in order to avoid the level-dependent phase changes observed at high input levels Cheatham and Dallos, 1998b. were compensated for reductions associated with filtering by the cell s basolateral membrane and by the recording apparatus Cheatham and Dallos, 1993, Fig. 3C. In addition, the ac magnitude data were normalized at BF and plotted on a normalized, linear frequency scale. The latter choice was made because behavioral data on auditory filter shape are frequently plotted on a linear abscissa. These results are provided to demonstrate changes in filter shape as they appear at the level of IHC transducer. Data from turn 2 show steeper slopes above BF, while data from turn 4 show steeper slopes below BF. In turn 3, the response area is relatively symmetrical. These shape changes appear to reflect the large variations in high-frequency slope observed at the three cochlear locations. In turn 2, which is approximately 10 mm from the base of the guinea pig cochlea where basilar membrane length is 18 mm Cheatham, 1993, the high-frequency slope is 96 db/oct. In turn 3, where the center of the cochlear window is 14 mm from the base, the high-frequency slope is 32 db/oct. Finally, in turn 4, which is 17 mm from the base, the high-frequency slope is only about 10 db/oct. In contrast, the slopes of the functions below BF are fairly similar at the three recording locations. B. Implications for behavioral thresholds at low frequencies Information obtained from the apex of the cochlea is used to construct the schematic shown in Fig. 6, which includes features that would be expected to influence lowfrequency responses in the guinea pig cochlea. The middle ear transfer function is represented by the high-pass filter function plotted with dashed lines and decreasing at 6 db/oct below 600 Hz Johnstone and Taylor, 1971; Décory et al., 1990; Cooper and Rhode, In addition, a second highpass filter also shapes low-frequency responses. This stage of filtering is associated with ciliary mechanics and the resulting velocity dependence of the IHC. In this schematic, input to the IHC is attenuated by 6 db/oct below a corner frequency of 470 Hz Dallos, In contrast to filtering by the middle ear, this attenuation at the input to the IHC occurs after the frequency analysis that is associated with basilar membrane mechanics. Although more recent studies of haircell stereocilia are available Freeman and Weiss, 1990; Shatz, 2000, these models were primarily designed for and tested in the lizard cochlea. The degree to which these models reflect behavior in the mammalian cochlea has not been 2038 J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns

6 FIG. 4. Iso-input functions obtained in turns 2 4 are compared here at 50 squares and dashed lines and 90 circles and solid lines db. To facilitate comparisons, the average receptor potentials are normalized at BF. This is achieved by giving the potential at BF a value of 0 db and plotting all other values relative to this datum. The abscissa is also normalized by dividing stimulus frequency by BF. Thus, the latter has a value of 1.0 and is designated by the vertical arrow in each panel. Data for turn 3 at 50 and 90 db were not plotted in Fig. 1 for clarity. The 90-dB condition in Fig. 2 is also missing for the same reason. evaluated. Hence, our decision is to use the Dallos 1984 model that is based on IHC response patterns recorded in turn 3 of the guinea pig cochlea. The schematic in Fig. 6 serves to demonstrate how these two high-pass filters affect the shapes of response areas in fourth-turn IHCs. The attenuations due to the middle ear and the velocity dependence of the IHC provide a total, combined attenuation that decreases at a rate of 12 db/oct. This combined function is plotted with dotted lines. The vertical line demonstrates that the BFs of IHCs in turn 4 are below the corner frequencies of these two high-pass filters. Consequently, input to the cell is reduced by filtering at very low frequencies. The remaining function, plotted in Fig. 6 with solid lines, represents the behavioral threshold for guinea pigs Fay, 1988 compiled by averaging data from several investigators Miller and Murray, 1966; Heffner et al., 1971; Walloch and Taylor-Spikes, 1976; Prosen et al., These results are normalized at 1000 Hz so that all values are plotted relative to this datum, which is given a value of 0 db. Behavioral threshold decreases at a rate that exceeds the 6 db/oct provided by the middle ear transfer function alone, hence the similarities between the combined and behavioral functions. When considering these comparisons, it should be mentioned that the middle ear transfer function for guinea pig was determined with bulla open. This differs from the situation when behavioral thresholds are obtained in intact animals. However, it has been demonstrated that the CM is impervious to many alterations of the middle ear and that the low-frequency slope of the transfer function is not altered Dallos, 1970, Fig. 8. Dallos also demonstrated that the middle ear muscles do not influence the low-frequency slope of the middle ear transfer function Fig. 9. Consequently, the comparisons shown in Fig. 6 are not inappropriate. A similar exercise is provided for humans in Fig. 7. Again, filter functions are plotted with dashed lines. In this figure, the attenuation associated with the middle ear is adapted from Flanagan s computational model Flanagan, 1962; Dallos, This effect decreases input to the cochlea at a rate of 6 db/oct below 1000 Hz. For lack of a better alternative, the function for the IHC velocity dependence is based on guinea pig data and is replotted from the previous figure. Finally, the shunting effect of the helicotrema is appended. This third high-pass filter is required because the helicotrema in man, but not in guinea pig Dallos, 1970; Zwislocki, 1975, is large with the result that additional attenuation is expected below 100 Hz. The remaining curve, plotted with solid lines in Fig. 7, approximates the minimum audible pressure MAP curve for man redrawn from Killion, This curve represents the sound pressure of a tone, at the threshold of audibility, that is presented by an earphone and measured near the tym- J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns 2039

7 FIG. 5. This figure shows responses at 50 db for the ac receptor potential obtained from the same three IHCs plotted in Fig. 4. The magnitude data include corrections for filtering associated with resistances and capacitances in the cell s basolateral membrane, as well as low-pass filtering associated with the recording electrode. The latter was required in turn 2 only. As in Fig. 4, the magnitude data are normalized and plotted on a normalized frequency scale. The function for turn 2 is plotted with circles and solid lines; for turn 3, triangles and dashed lines; for turn 4, squares and solid lines. panic membrane. Because the MAP curve has been normalized, all responses are plotted relative to the response at 1000 Hz. The shape of the MAP curve is similar to the combined curve, which represents the total attenuation due to filtering. Although this schematic shows that these three stages of high-pass filtering approximate the changes in sensitivity exhibited in human subjects, it is acknowledged that the terminal slope of the MAP function is greater than 18 db/oct Dadson and King, 1952; Killion, 1978; Puria et al., This suggests that the additional reduction in sensitivity at very low frequencies Corso, 1958; Yeowart and Evans, 1974 may relate to physiological noise as suggested by others Moore, In other words, the MAP curve represents a masked threshold. IV. DISCUSSION A. Comparisons with mechanical and neural responses: Magnitude data Recordings from mammalian IHCs are consistent with the idea that nonlinearities in the cochlea shape auditory filters in both a frequency- and level-dependent fashion. Even when auditory filter shape is examined psychophysically Glasberg and Moore, 2000, the changes with level resemble the variations in tuning observed in basilar membrane responses. This association suggests that the fundamental character of auditory filters is determined in the organ of Corti and that this distorted peripheral representation is provided to the central auditory pathway for further analysis. This idea is supported by the similarities between single-unit Rose et al., 1971; Kiang et al., 1977; Møller, 1977; Gibson et al., 1977; Liberman and Kiang, 1978; Evans, 1981 and IHC data. When response areas are measured at a series of levels, for neurons with BFs around 1000 Hz, the iso-input functions expand symmetrically to both lower and higher stimulus frequencies. This response pattern is reminiscent of that shown in Figs. 1, 4, and 5 for IHCs in turn 3. For neurons with higher BFs, above 2000 Hz, the response area expands asymmetrically toward lower frequencies with the result that the slopes recorded above BF are steeper than are those below. These results are similar to those from second-turn IHCs and from basilar membrane Rhode, 1971; Sellick et al., 1982; Robles et al., 1986; Nuttall and Dolan, 1996; Ruggero et al., 1997 and IHC Russell and Sellick, 1978; Zwislocki and Chatterjee, 1995 responses recorded from more basal regions of the cochlea. Finally, data from neurons with low BFs indicate that response areas expand preferentially toward higher frequencies, i.e., the functions have steeper low-frequency slopes. These response patterns are similar to those shown in Figs. 3 5 for IHCs in the fourth turn. They are also similar to mechanical measurements at the very apex of the cochlea where the frequency of the peak of the response function increases with increasing level Zinn et al., 2000 and where steeper slopes are recorded below BF Khanna and Hao, 1999a. The level-dependent magnitude changes recorded at various cochlear locations should be considered when evaluating the alterations that result from various cochlear manipulations. For example, it has been observed that furosemide-induced changes in neural tuning curves differ depending on BF Sewell, When recordings were made from nerve fibers innervating the basal half of the cochlea, a downward shift in BF was observed. However, in nerve fibers with BFs below 800 Hz, an upward shift was recorded due to the effects of furosemide. Liberman 1984 suggested that this difference in the direction of BF shift may relate to the shape of the tuning curve because the tail is above below BF for low high BF fibers Pfeiffer and Molnar, 1970; Rose et al., 1971; Kiang et al., 1977; Møller, 1977; Liberman and Kiang, 1978; Evans, This implies that the BF shifts seen in compromised auditory systems due to furosemide or acoustic trauma Liberman and Mulroy, 1982; Liberman and Dodds, 1984 may be a result of the increase in level required to produce a criterion response. The IHC data presented here are consistent with this idea. Data shown in Fig. 4 indicate that responses obtained at the higher input levels required to obtain criterion responses in traumatized cochleae will exhibit magnitude peaks at lower frequencies when recorded at positions with BFs greater than 1000 Hz. In contrast, at the very apex of the cochlea, for BFs less than 400 Hz, magnitude peaks should occur at frequencies higher than those observed in healthy cochleae J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns

8 FIG. 6. This schematic depicts factors that influence low-frequency hearing in the guinea pig. The dashed lines indicate the high-pass filter functions associated with the middle ear and with the velocity dependence of the IHC. They decrease at a rate of 6 db/oct below 600 and 470 Hz, respectively. Their combined effect is plotted with dotted lines and decreases at 12 db/ oct. The average behavioral threshold obtained from five studies Fay, 1988 is also appended and plotted with solid lines. The vertical bar indicates the BFs of IHCs in turn 4. Taken together, the data imply that the cochlear filter responsible for mechanical frequency analysis is generally asymmetrical, with steeper high-frequency slopes above BF. As shown in Fig. 5, this asymmetry is reduced in turn 3 and reversed in turn 4 consistent with the high-pass filtering associated with the middle ear transfer function. Although filtering due to the middle ear can account for the reverse asymmetry of apical response patterns and the almost complete symmetry of turn 3 responses at low levels, it cannot account for their reverse nonlinearity. The latter observation refers to the appearance of tuning-curve tails above BF where more linear responses are recorded. This response pattern contrasts with that in the base where tuning-curve tails, and concomitant more linear behavior, are found below BF. It should also be mentioned that longitudinal variations are observed in the impulse responses of auditory-nerve fibers Carney et al., When instantaneous frequency is measured as a function of time, the impulse response exhibits an increasing frequency glide for fibers with BFs greater than 1500 Hz and a decreasing glide for fibers with BFs less than 750 Hz. Mechanical measurements recorded at the base of the cochlea also indicate that the frequency of the basilar membrane s impulse response changes with time, increasing from below, up to BF de Boer and Nuttall, 1997; Recio et al., Because response envelopes become skewed at high levels, i.e., their center of gravity shifts ear- FIG. 7. This schematic for humans is similar to that in Fig. 6 for guinea pigs. In this case, however, the middle ear function decreases at 6 db/oct below 1000 Hz. A function representing the helicotrema is also included and decreases at 6 db/oct below 100 Hz. The IHC velocity dependence is appended from Fig. 6. The combined filter function plotted with dotted lines decreases at 6, 12 and finally, 18 db/ oct as frequency decreases below 100 Hz. The function plotted with solid lines is the minimum audible pressure curve MAP for humans, re-drawn from Killion J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns 2041

9 lier in time Recio et al., 1998, the increasing glides are consistent with a downward shift in peak frequency as level increases. These observations imply that cochlear mechanics may differ near the apex of the cochlea. Consistent with this idea, Zinn et al reported a weak compressive nonlinearity below BF and an expansive nonlinearity above BF when making mechanical measurements near the helicotrema. These authors suggest that the expansive nonlinearity is associated with an active attenuation on the tails of tuning curves, which are above BF when the latter is below 400 Hz. This idea is compatible with results from experiments in which various cochlear insults are introduced. For example, acoustic overstimulation Liberman and Dodds, 1984, mechanical damage Robertson et al., 1980 and/or salicylate ototoxicity Murugasu and Russell, 1995 all serve to lower the tails of neural tuning curves, i.e., they become hypersensitive. At the base of the cochlea, this behavior is thought to reflect a negative gain below BF provided by the cochlear amplifier Mountain et al., Because amplification is vulnerable to insult, many manipulations result in more sensitive responses for the tails of tuning curves well below BF. At the apical end of the cochlea, removal of the active attenuation/negative gain observed in basilar membrane responses above BF Zinn et al., 2000 could also result in hypersensitive tuning-curve tails when cochlear function is compromised. It should also be mentioned that IHC responses recorded from turn 4 of the guinea pig cochlea are nonlinear at BF. This is consistent with mechanical data obtained in guinea pig from Reissner s membrane Cooper and Rhode, 1995 and in chinchilla from tectorial membrane Rhode and Cooper, 1996 but not with guinea pig results from reticular lamina Khanna and Hao, 1999a, b. The latter reports indicate that BF responses at the fundamental are linear, inspite of the fact that energy is present for both even and odd harmonic components. The authors argue that the linear behavior at the fundamental reflects negative feedback due to active cochlear mechanics. However, it is also possible that the discrepancy may relate to the observation that frequency response functions in the Khanna and Hao data have two peaks, which the authors acknowledge is associated with preparations that are more broadly tuned. Because Khanna and Hao do not provide data at low levels, it is possible that these preparations are not in good condition. In fact, no harmonic distortion is evident below 70 db and most of the frequency response functions are obtained for inputs at 96 db. Although it could be argued that the IHC results are nonlinear at BF because of asymmetries in the hair cell transducer, this would not explain the discrepancy between the Cooper/Rhode and the Khanna/Hao data. Hence, there is the possibility that the Khanna/Hao results reflect a less than adequate seal between the preparation and the recording/ observing apparatus. If the seal is not tight, then notches appear in frequency response functions and more than one peak is evident. In this case, the relatively linear behavior at BF could be explained by interactions between linear fast and nonlinear slow responses, as suggested by Cooper and Rhode If the preparations are not in good condition, then the two peaks on the function may not be very different in magnitude, which facilitates the interactions between fast and slow components. B. Comparisons with mechanical and neural responses: Phase data The phase data collected from IHCs in turns 2 4 are consistent with previous results Dallos, 1986 indicating that phase leads lags accumulate below above BF when stimulus level is reduced. If BF is relatively stable with increasing level, then the lead/lag transition occurs near the BF of the cell and a stationary pivot point can be defined. However, if the peak of the frequency response function is level dependent, the pivot point disperses. For example, in turn 4, the transitions occur below BF and, in turn 2, the transitions occur above BF. These response patterns have their counterparts at the single-unit level Anderson et al., These comparisons suggest that one should be cautious when using level-dependent phase changes to define BF Nuttall and Dolan, 1993, 1996; Cheatham and Dallos, If BF refers to that frequency where the cell is most sensitive Galambos and Davis, 1943, then the lead/lag transition in response phase represents BF only when center frequency is relatively independent of level. In the peripheral auditory system, this is observed but only in the region around 1000 Hz. At more basal recording locations, the lead/lag transition tends to overestimate BF; at more apical locations, the transition underestimates BF. In other words, the level-dependent changes in phase move in opposite directions at the two ends of the cochlea. C. Factors influencing behavioral thresholds at low frequencies Others have suggested that behavioral threshold correlates with a constant pressure measured inside the vestibule of the inner ear Lynch et al., 1982; Puria et al., In fact, the correlations between behavioral threshold and either constant pressure, constant power or constant stapes volume velocity are all very good for inputs between 200 and 1000 Hz. Below 200 Hz, however, behavioral thresholds increase at a faster rate than any one of these variables Puria et al., 1997, Fig. 16. The schematic in Fig. 7 indicates that this discrepancy in humans may relate to filtering occurring central to the middle ear/cochlea interface, as suggested by Lynch et al The most parsimonious explanation for the decrease in sensitivity, shown by the MAP curve at low frequencies, is that reductions are due to high-pass filtering associated with the velocity dependence of the IHC and with the shunting effect of the helicotrema. The latter serves to diminish the pressure difference between scala vestibuli and scala tympani. Because the basilar membrane is displaced as a result of this pressure difference, the helicotrema serves to decrease sensitivity at low frequencies below 100 Hz Dallos, 1973; Zwislocki, 1975 in animals where the helicotrema is relatively large. In fact, it has been demonstrated that the slope of the behavioral threshold curve at low frequencies is correlated with helicotrema size. Like humans, both cats and chinchillas have large helicotremas and steeper low J. Acoust. Soc. Am., Vol. 110, No. 4, October 2001 M. A. Cheatham and P. Dallos: IHC response patterns

10 ACKNOWLEDGMENTS This work was supported in part by Research Grant No. 5 R01 DC00089 from the National Institute on Deafness and Other Communication Disorders, the National Institutes of Health. We are grateful to Gulam Emadi for writing the computer program that calculates the average voltage. FIG. 8. The arbitrary function used by Moore et al. 1997, Fig. 4 is inverted and plotted here along with the combined attenuation due to highpass filtering by the IHC s velocity dependence and by the shunting effect of the helicotrema. The latter function is plotted with dashed lines and represents the combined reductions plotted individually in Fig. 7 for the helicotrema and IHC. The function from Moore et al. was reconstructed using the DIGIMATIC software program. frequency slopes below 100 Hz when compared to guinea pigs where the helicotrema is small Dallos, 1970; Fay, Consequently, high-pass filtering by the helicotrema was not included in the schematic for guinea pigs Fig. 6. Finally, Moore and colleagues 1997 developed a phenomenological model for predicting the rise of threshold at low frequencies in human listeners. They acknowledge that this decrease in sensitivity rises more steeply than the transmission characteristic of the middle ear would suggest. This discrepancy is dealt with by assuming that the excitation level at threshold increases with decreasing frequency below 500 Hz according to an arbitrary function Moore et al., 1997, Fig. 4 designed to match the thresholds specified by an international standard. This arbitrary function is inverted and plotted in Fig. 8 with solid lines to indicate the decreasing input to the central auditory system as stimulus frequency is reduced. Also included is a function showing the high-pass filtering associated with both the IHC s velocity dependence and the helicotrema shunt, as in Fig. 7. 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