Intermodulation components in inner hair cell and organ of Corti responses M. A. Cheatham a) and P. Dallos Hugh Knowles Center, Department of Communication Sciences and Disorders, Frances Searle Building, Northwestern University, Evanston, Illinois 60208-3550 Received 23 December 1996; revised 2 April 1997; accepted 3 April 1997 Two-tone responses are recorded from inner hair cells and from the organ of Corti fluid space in second and third turns of the guinea pig cochlea where best frequencies BF are approximately 4000 and 1000 Hz, respectively. This allows both ac and dc response components to be obtained and facilitates comparisons with psychophysical investigations that have traditionally been conducted at low and moderate frequencies. The measurements of ac responses in the organ of Corti fluid space also allow comparisons with mechanical results because the cochlear microphonic is proportional to basilar membrane displacement. By using a constant frequency ratio ( f 2 / f 1 ) of 1.4, local distortion products generated at the recording location are prominent when the two primaries are near the BF of the cell. However, when the primary pairs increase above BF, quadratic and cubic difference tones are recorded even when responses to the primaries are not measurable. The presence of these traveling distortion products is consistent with the idea that both f 2 f 1 and 2 f 1 f 2 have their own traveling waves. Notches in the existence regions of quadratic and cubic difference tones were also observed and found to be influenced by mutual suppression between the two inputs. 1997 Acoustical Society of America. S0001-4966 97 01908-5 PACS numbers: 43.64.Ld, 43.64.Nf, 43.64.Tk RDF INTRODUCTION Approximately 150 years ago, Ohm 1843 proposed that combination tones are perceived by resolving a complex sound into its individual Fourier components. He believed that an individual pitch could be distinguished only when the stimulus contained the corresponding frequency. Helmholtz 1954 later suggested in 1863 that a mechanical nonlinearity in the middle ear introduces distortion products which are then perceived behaviorally as if they had been presented at the input to the ear. Evidence for Ohm s original notion was presented by Zwicker 1955 who demonstrated that a pitch at the cubic difference tone CDT frequency, 2 f 1 f 2, could be made to disappear by adjusting the amplitude and phase of an external tone whose frequency matched that of the CDT. A physiological correlate for these psychophysical results was provided in 1968 when Goldstein and Kiang 1968 reported time-locked responses to the CDT in single auditory nerve fibers recorded in the cat. It was also possible to cancel this response to the intermodulation component by adding a third tone to the stimulus which was equal in frequency to the distortion product. Goldstein and Kiang also demonstrated that even if f 1 and f 2 were outside the response area of the fiber, the response to the CDT was robust when the latter was near the best frequency BF of the cell. The implication of these results is that the difference tone is generated in the region of overlap between the two primaries. Energy at the distortion frequency is then fed back into the mechanics and resolved at its proper place along the cochlear partition. These ideas were supported by Kim et al. 1980 who studied the spatial distribution of cochlear responses to twotone stimuli by recording from hundreds of nerve fibers in a single cat. At low levels, the difference tones, f 2 f 1 and 2 f 1 f 2, emerge in the primary frequency region. With increasing level, these components show additional activity at their characteristic place so that they are clearly visible in the distortion frequency region as well as in the frequency region corresponding to the primaries, f 1 and f 2. Although the exact site of the nonlinearity is not known, it certainly does not reside in the middle ear Lewis and Reger, 1993; Wever et al., 1940; Guinan and Peake, 1967 as Helmholtz originally surmised. This is because the magnitude of these components is strongly dependent upon the frequency separation between the two primaries Goldstein, 1967; Goldstein and Kiang, 1968. In addition, it has been demonstrated Smoorenburg, 1972 that the CDT is perceived only when both primaries are audible. Consequently, any defect which causes a threshold shift is thought to precede the nonlinearity. In other words, stimulus components below the level of audibility do not reach the distortion generator. Smoorenburg s results, obtained in a patient with threshold shift, were subsequently confirmed in a behaviorally trained chinchilla Dallos, 1977 with an outer hair cell OHC loss produced by the ototoxic antibiotic, kanamycin. In fact, outer hair cell damage appears to linearize cochlear output Dallos et al., 1980; Patuzzi et al., 1989 implying that the nonlinearity occurs prior to inner hair cell IHC transduction. Based on these ideas, it is of interest to learn whether local and traveling distortion products can be resolved in IHC receptor potentials. For example, when the ear is stimulated with two primaries whose intertone ( f 1 f 2 )/2] correa Corresponding author address: 2-240 Frances Searle Building, 2299 North Campus Drive, Northwestern University, Evanston, IL 60208-3550. Electronic mail: m-cheatham@nwu.edu 1038 J. Acoust. Soc. Am. 102 (2), Pt. 1, August 1997 0001-4966/97/102(2)/1038/11/$10.00 1997 Acoustical Society of America 1038
sponds to the BF of the cell, a profusion of combination tones is measured. These responses reflect local components produced at the generation site. However, if the primaries are presented well above BF, such that the difference tone frequency coincides with the BF of the IHC, then traveling components should be resolved. The latter are thought to originate basal to the recording location and, via their own traveling waves, propagate apically to stimulate hair cells whose BFs correspond to the individual distortion product frequencies Goldstein, 1967. Although traveling components have been demonstrated in the cochlear microphonic CM Gibian and Kim, 1979, 1982; Dallos et al., 1980 and in the dc receptor potentials of IHCs with high BFs Nuttall and Dolan, 1990, no data are available for IHCs with lower BFs or for the ac receptor potential. The latter, as well as extracellular measures of both cubic and quadratic components, are important when trying to compare hair cell and mechanical responses Nuttall et al., 1990; Robles et al., 1991, 1997. It is also important to study cochlear nonlinearities in apical regions to foster comparisons with psychophysical investigations that have usually been restricted to low and moderate stimulus frequencies but have been compared to high-frequency physiological data. I. METHODS To avoid repetition, we provide a cursory description of the methods employed in these experiments. Further details can be obtained from previous publications Dallos et al., 1982; Dallos, 1985; Cheatham and Dallos, 1992. As before, all animal care procedures were approved by the National Institutes of Health and by Northwestern University s Institutional Review Committee. Young albino guinea pigs were anesthetized with urethane or with a combination of sodium pentobarbital and Innovar-Vet. The standard ventro-lateral approach Dallos et al., 1982 allowed access to the right auditory bulla which was opened widely. A small window was then made in the cochlear bone over scala media. The use of backlighting assisted electrode placement. After traveling through the endolymphatic space, Hensen s cells are encountered at the peripheral edge of the organ of Corti. Further advances allow recordings from individual hair cells as well as from the organ of Corti fluid space. Although data were collected in both second and third turns, only one opening was made in any given preparation. The two-tone inputs used in these experiments were generated by a single dynamic earphone Beyer DT-48 with the result that the two signals were electrically and not acoustically mixed. Sound-pressure levels in the external ear canal were determined using a subminiature microphone Knowles BT-1751. The latter was attached to a probe tube which was inserted into the sound tube in a concentric arrangement. Harmonic and intermodulation distortion was measured in a coupler using a 1/2 in. B&K condenser microphone and found to be at least 60 db down from the two stimulating primaries. These determinations, however, were made at maximum sound-pressure levels which were above those used to collect the data reported here. Consequently, these estimates are thought to be conservative. FIG. 1. The averaged response waveform at the top was recorded in a second turn IHC at a sound-pressure level of 70 db. This and all soundpressure levels are measured re: 20 Pa. The timing of the two inputs shown here is arranged so that responses to each individual primary can be recovered as well as responses to various components in the region of overlap. The center panel shows the spectrum obtained in window 1 for f 1 alone at 2800 Hz. When the FFT is obtained from window 2, the spectrum contains several distortion products with frequencies both above and below the primaries. All responses were amplified and capacitance compensated Dagan 8700, low-pass filtered to prevent aliasing and averaged for off-line analysis using Igor Pro WaveMetrics, Lake Oswego, OR 97035 and/or custom-designed software. An automatic gain control system was also used to optimize amplification, thereby avoiding saturation of the analog-todigital converter. The peak values of various response components were determined from fast Fourier transforms FFT of averaged response waveforms. Waveform segments of approximately 20 ms duration were windowed before transformation using a Hanning function. In some instances, peak ac values were increased by 6 db/octave above a corner frequency of 470 Hz Dallos, 1984 to compensate for filtering by the cell s basolateral membrane and by 12 db/octave above 3500 Hz to compensate for losses in the recording apparatus Baden-Kristensen and Weiss, 1983; Cody and Russell, 1987. Although these adjustments have been employed before Cheatham and Dallos, 1993, they yield qualitative, not quantitative, information. The protocol used in these experiments is provided in Fig. 1. This recording was made in second turn where BFs are approximately 4000 Hz. Because the onset of the second 1039 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1039
FIG. 2. Frequency response functions at 70 db are provided for a third-turn IHC. The broken vertical line at 1000 Hz indicates the BF of the cell. In both panels A and B, peak ac values mv-p are plotted for the lower frequency primary alone dot-dashed lines along with two-tone functions open symbols for components below f 1 at 2 f 1 f 2 and f 2 f 1. In addition to the frequency response function for f 1 alone at 70 db, a similar function is included for single-tone inputs at 20 db to facilitate comparisons between single- and two-tone responses. Data in A are plotted at the intertone; those in B at the frequency of the individual response component. tone at 3920 Hz is delayed relative to that of the lower frequency tone at 2800 Hz, it is possible to recover responses to each primary alone as well as those in the region of overlap where both tones are presented together. For example, the spectrum of the f 1 alone response in the center shows magnitude peaks for f 1 at 2800 Hz and its second harmonic at 5600 Hz. In contrast to this simple picture, the spectrum of the two-tone response at the bottom reveals a profusion of response peaks for difference and summation tones as well as harmonic components. Above the primaries, the combination tones f 2 f 1 and 2 f 2 f 1 as well as the second harmonic can be identified. In the region below f 1, magnitude peaks appear at f 2 f 1 and 2 f 1 f 2. Based on the power series approximation, these latter components are referred to as the quadratic difference tone QDT and cubic difference tone CDT. The unlabeled peak at 2240 Hz, just below f 1, could reflect one of a number of components produced by interactions between a primary and a combination tone or between two individual distortion products. In this example, and in all materials, the primaries were presented at equal levels. This choice was based on input output functions for the cochlear microphonic recorded in third turn where the largest cubic difference tone was produced at or near the point where the intensities of both primaries were equal Dallos, 1969. In addition, the frequency ratio f 2 / f 1 was kept constant at 1.4 except when small adjustments were made to assure that the two inputs were not harmonically related. This relatively large frequency ratio was used so that the primaries were not excitatory when quadratic and cubic difference tones were near the BF of the IHC. If a smaller frequency ratio at 1.2 had been employed, the primaries would need to be very high at 20 000 and 24 000 Hz to generate a QDT at 4000 Hz. In addition, to produce a CDT at 4000 Hz, the primaries at 5000 and 6000 Hz would probably cause excitation at the 4000 Hz place. Consequently, by using a frequency ratio of 1.4, traveling difference tones below f 1 can be recovered without being contaminated by excitation due to the primaries at the distortion product place. Although this choice of stimulus parameters has advantages, it is not optimal for all components especially those above the f 2 frequency. For example, when summation tones fall within the response area of the cell, the generating primaries also produce sizeable responses when presented alone. For primary pairs near and above BF, the summation tones as well as 2 f 2 f 1 are usually removed by filtering at the generation site. Hence, in the present experiments, it is not possible to distinguish local from traveling contributions. When responses are measured for these components, as in Fig. 1, they appear to reflect those produced locally for intertones near and below BF. II. RESULTS A. Traveling versus local difference tones Two-tone results are introduced using an IHC recording from third turn where BF is 1000 Hz. The ac frequency response functions in Fig. 2 are plotted for single- and two- 1040 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1040
FIG. 3. Results shown here were obtained from a second-turn IHC at 60 db. The components plotted are as in Fig. 2 except that three difference tones below f 1 are included. A frequency response function for f 1 alone is also provided for reference. tone inputs at 70 db. A second, single-tone function is appended to illustrate the response area at 20 db. In panel A, on the left, the functions are plotted either at f 1 for the single-tone functions or at the intertone, the average frequency of the two stimulating primaries, for the difference tones at f 2 f 1 and 2 f 1 f 2. The latter were generated by equal-intensity primary pairs that increased in frequency to map out the existence regions for individual distortion products. The two-tone functions, plotted for quadratic and cubic difference tones, exhibit two magnitude peaks. The first is produced by primaries with an intertone at 960 Hz which is near the BF of the cell as indicated by the broken vertical line at 1000 Hz. Here the CDT is 480 Hz. This local component is produced at the generation site. The second peak is associated with a CDT at 1080 Hz and with an intertone at 2040 Hz which is well above BF. A similar behavior is shown for the QDT at 960 Hz where the first peak occurs when BF ( f 1 f 2 )/2; the second peak, when BF f 2 f 1. To distinguish responses produced by primary pairs well above BF from those recorded at the generation site by lower-frequency primaries within the response area of the cell, the former are referred to as traveling rather than local components. In order to emphasize that large receptor potentials are produced when the distortion product coincides with the BF of the cell, the results are plotted in panel B, not at the intertone, but at the frequency of each individual difference tone. Single-tone functions at 70 and 20 db are again provided for reference. Both quadratic and cubic components exhibit peaks around 1000 Hz, the BF of the cell. It is assumed that these responses are generated at a more basal location and are distributed via their own traveling waves to the more apical location where they are recorded. The tuning and magnitude of these distortion products is commensurate with that observed for single tones at 20 db Dallos and Cheatham, 1992, Fig. 11. Comparisons with single-tone inputs, however, are made with caution because distortion products can suffer from the suppression that occurs between multiple components. In this plot B, both difference tones also have peaks below BF when the intertone frequency is near 1000 Hz. These maxima, corresponding to local components produced at the recording location, peak at BF in plot A. For these measures at 70 db, the magnitudes of the difference tones are similar for local and traveling distortion components and for the quadratic and cubic components. The results plotted in Fig. 2 emphasize that local distortion components are generated when the intertone is near the BF of the cell, as in panel A, while traveling components are expressed when the frequency of the distortion product approximates BF as in panel B. Companion measures for a second turn IHC are displayed in Fig. 3. Again, in order to provide an indication of the response area of the cell, the ac frequency response function for f 1 alone at 60 db is provided. In addition, several difference tones with frequencies below f 1 are also plotted at the intertone in panel A. These three functions all exhibit peaks when the intertone is near BF indicating the local nature of these responses. In the region above BF, all components decrease as primaries move out of the response area of the cell. However, with further increases, the response for 2 f 1 f 2 begins to rise when the distortion product is around the BF of the cell at 4080 Hz. This occurs when the intertone 1041 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1041
FIG. 4. Data from three IHCs located in second turn are plotted here on a normalized frequency scale where BF is indicated by the vertical bar at 1.0. The ac voltages have been compensated for filtering by the cell s basolateral membrane and by the microelectrode. These responses at 60 db are plotted for the CDT produced in response to primaries placed well above BF. Consequently, the functions peak near BF when the CDT is near 4000 Hz. frequency is 8160 Hz. These results are also plotted at the frequency of the distortion product in panel B to emphasize that components with frequencies at and around the BF of the cell behave very much as single-tone inputs of the same frequency. Unfortunately, in this example, the primary frequencies were not extended high enough to define the traveling CDT or to expose those for the other components. In other words, it is only the CDT frequency that approximates the BF of the cell. Consequently, additional examples are provided to explore the responses generated by higherfrequency, primary pairs. This information is presented in Fig. 4 for three secondturn IHCs where the primaries are also at 60 db. Since ac responses are filtered by the resistances and capacitances associated with the hair cell s basolateral membrane, they do not provide a good indication of the relative magnitudes of individual response components especially when recordings are made from more basal regions of the cochlea. Consequently, ac receptor potentials are compensated for these reductions, as well as those associated with the recording apparatus, using the corrections provided in Cheatham and Dallos 1993. Compensated ac responses are also plotted on a normalized frequency scale obtained by dividing the frequency of the difference tone by BF. However, in contrast to the third turn data plotted in Fig. 2, these estimates of BF were not determined from low-level responses in individual cells but are based on an average of cells recorded in this region. Notice that all functions peak near 1.0 when the frequency of the CDT corresponds to the BF of the recording FIG. 5. These results are similar to those in Fig. 4 except that examples are provided here for IHCs in second and third turns. These responses were measured at 70 db. location. Since these components are probably generated at a more basal location, the intertone frequencies associated with the magnitude peaks are well above BF at either 7680 or 8160 Hz. The functions have Q 10 s of 4.0 which is consistent with single units recorded from the guinea pig auditory nerve in this frequency region Evans, 1972. The primary motivation behind compensating ac responses was to foster comparisons between IHCs at different cochlear locations as well as between IHC and basilar membrane responses. Consequently, results from turns 2 and 3 are provided in Fig. 5. In order to facilitate these comparisons, the frequency scale has again been normalized by dividing the distortion product frequency by BF which is represented by the vertical line at 1.0. Data are plotted for the traveling CDT with the result that the functions peak at 1.0. This occurs when the primaries are well above BF so that the distortion product approximates the BF of the cell. As one might expect, the data from turn 3 where BF is approximately 1000 Hz, reflect broader tuning than those from the second turn where BF is 4000 Hz. In fact, the Q 10 for the third turn in 1.3 while that for the second turn is 3.7. Both of these values fall within the ranges reported for single units in the guinea pig auditory nerve Evans, 1972. Since these traveling distortion products behave as if a third tone had been added to the stimulus, they should reflect the filter shape exhibited at their BF locations. 1042 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1042
FIG. 6. These results, measured in another second-turn IHC at 70 db, provide responses for higher-frequency primaries to assure that both the CDT and the QDT coincide with BF. A bold vertical line appears at 4000 Hz which approximates the BF in this region of the cochlea. The responses in panel A are peak ac voltages obtained directly from the FFT; those in panel B, the voltages after compensating for filtering by the cell s basolateral membrane and by the recording electrode. The isolated pinwheel in each panel designates the intertone frequencies where f 2 suppresses f 1 by more than 6 db. B. The influence of mutual interference Figure 6 a provides another example from second turn where the intertone varied between 1440 and 13 440 Hz. Again the ac receptor potential for f 1 alone at 70 db is included to indicate the response area of the IHC. The BF is estimated by the bold vertical line. As the intertone increases above BF, two peaks emerge. The first is associated with the CDT at 4080 Hz which is produced when the intertone is at 8160 Hz. Another peak appears when the QDT is near BF at 4160 Hz and the intertone is at 12 480 Hz. In Fig. 3, a traveling component was only demonstrated for the CDT because the primary pairs were not high enough to place the QDT at BF. These responses were also compensated for losses due to filtering by the cell s basolateral membrane and by the recording apparatus and plotted in panel B using a different ordinate. After compensation, the response to f 1 alone exhibits a peak in the BF region and the peaks for the distortion products become more prominent. Because the maximum response to both difference tones occurs around 4100 Hz, when the primaries are well above BF, it is assumed that the distortion product propagates apically from its generation site to its own BF place where it is detected by the IHC. It is evident that the functions in Fig. 6 exhibit magnitude fluctuations. These notches are thought to reflect interactions between the two stimulating primaries as displayed in Fig. 7. In panel A, frequency response functions at 70 db are plotted for f 1 alone and for f 1 measured in the presence of f 2. When f 2 is at 3360 Hz, the f 1 response at 2400 Hz is suppressed to the largest extent. Companion data for f 2 are provided in panel B. Only when f 2 is near BF at 3360 Hz does it remain unchanged in the presence of f 1. Notice that f 2 is reduced by the lower frequency primary as f 2 increases above BF. This suggests that the large decreases in distortion product magnitude shown in Fig. 6 for intertones just above BF may reflect a combination of mutual suppression in which f 1 suppresses f 2 and the fact that the primaries are moving outside of the response area of the cell. The magnitude changes are also plotted in panel C of Fig. 7 at the intertone to facilitate comparisons with results in Fig. 6. In fact, the pinwheel symbol associated with the large decrease in f 1 for an intertone at 2880 Hz corresponds to similar symbols included in the previous figure. C. dc results from second turn It is emphasized that compensated ac responses provide qualitative, not quantitative information. Consequently, it is prudent to determine the degree to which distortion products are reflected in the dc receptor potential which is not affected by filtering. The dc results in Fig. 8 are the companion measures for the ac responses shown in Fig. 6. As before, the dc frequency response function for f 1 alone at 70 db is provided along with a reference line which approximates BF. The solid curve indicates dc responses produced when the two primaries are presented together. This two-tone function reflects a slightly broader tuning because the dc responses produced by f 1 and f 2 can sum. However, at this relatively high level, the single- and two-tone curves diverge mainly above BF where responses are not fully saturated. As the primaries increase above BF, two peaks emerge. The first 1043 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1043
FIG. 7. Panel A includes frequency response functions for f 1 at 70 db measured alone and in the presence of f 2, i.e., f 1 ( f 2 ). This latter function is plotted with dashed lines. A similar presentation is provided in panel B for f 2 measured in the presence of f 1. Panel C shows the magnitude changes due to the suppression of one primary on the other. If interactions between the two inputs did not occur, then all data points would fall on the horizontal line at 0 db. These magnitude changes are plotted at the intertone in panel C. occurs when the CDT is at 4080 Hz which corresponds to the ac response demonstrated in Fig. 6. In fact, the compensated ac response for this component is included and appears as a filled triangle. A second peak also emerges for higherfrequency primaries with an intertone of 12 480 Hz. This response represents the quadratic difference tone at 4160 Hz, again very near the BF of the cell. Its compensated ac response is also plotted as the open triangle. These results indicate that distortion products with frequencies near the BF of the cell produce large dc receptor potentials even when the two stimulating primaries generate little or no response in the cell. To illustrate this point, averaged response waveforms, corresponding to these two peaks in the dc function are shown in Fig. 9. The CDT is displayed at the top for the component at 4080 Hz. Window 1 indicates the region where f 1 at 6800 Hz is presented alone; window 2, the region of overlap where the two primaries are presented together and, finally, window 3 designates the time when only f 2 at 9520 Hz is present. The large dc receptor potential in window 2 reflects the response to a CDT which is generated at a more basal location and, via its own traveling wave, is distributed to its BF place. In other words, the dc receptor potential indicated here is produced by the transducer nonlinearity of the IHC in response to ac mechanical input at 2 f 1 f 2. Because of its velocity sensitivity, the IHC does not respond to dc. At the bottom, a similar figure shows the waveform obtained when the intertone equals 12 480 Hz. Again, because the quadratic difference tone is at 4160 Hz, a dc receptor potential is recorded in the region of overlap but no response is registered to either primary alone. D. Organ of Corti results from second turn Responses measured in the organ of Corti fluid space for f 2 f 1 and 2 f 1 f 2 are provided in Fig. 10. These extracellular dc responses were obtained from the same animal whose intracellular IHC responses are presented in the previous figure. In both cases, the responses in window 2, the FIG. 8. This figure provides dc frequency response functions for the same cell whose ac responses are shown in Fig. 6. The function for f 1 alone is included to indicate the response area of the cell. In addition, the function obtained for the two-tone input f 1 and f 2 is also provided and plotted at the intertone frequency. The two peaks above BF correspond to the CDT and the QDT. Both are produced by high-frequency, primary pairs. The corresponding compensated ac values are also indicated by the downward pointing triangles. 1044 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1044
FIG. 9. The waveforms pictured here correspond to the peaks in the twotone dc frequency response function shown in Fig. 8. That at the top is for the CDT while that at the bottom is for the QDT. The numbered boxes designate time intervals such that window 1 corresponds to the f 1 alone segment; window 2, the region of overlap, and window 3, the time when only f 2 is presented. region of overlap, are greater than responses to either primary alone indicating that traveling quadratic and cubic difference tones are also expressed in extracellular responses. In this example, the CDT is 6 db greater than the QDT. While this relationship may not hold at all levels, this magnitude disparity is smaller than that for the IHC results shown in Fig. 9. Since the data in Figs. 9 and 10 were obtained from the same animal, the magnitude differences between quadratic and cubic difference tones measured in the IHC could be overestimated. This may relate to the fact that the IHC response at f 2 f 1 was measured several minutes after that at 2 f 1 f 2. Consequently, it is possible that the organ of Corti results provide a better reflection of the relative magnitudes of individual components because the response profiles obtained here are more stable over time. Additional data collected from the organ of Corti fluid space in second turn is provided in Fig. 11. The ac response for f 1 alone is included to indicate the broad response area of this location at 80 db. As the intertone increases in frequency, response magnitudes for the local difference tones at f 2 f 1 and 2 f 1 f 2 decrease as expected from the shape of the f 1 alone response. However, with further increases in the intertone frequency, magnitude peaks are expressed when the distortion products are near the BF of the recording location. This occurs when the intertones are at 7200 Hz for the CDT at 3600 Hz and at 10 560 Hz for the QDT at 3520 Hz. In contrast to local components, traveling difference tones reflect narrower tuning because these distortion products, with frequencies near the BF of the recording location, are equivalent to low-level, single-tone inputs. In fact, the Q 10 for the FIG. 10. Additional waveforms recorded in the organ of Corti fluid space are included here for results collected at 70 db. These extracellular responses were obtained from the same preparation as the IHC data shown in Figs. 5 9. traveling 2 f 1 f 2 is 3.4, again consistent with the tuning of single auditory nerve fibers at the 4-kHz location in the guinea pig cochlea Evans, 1972. III. DISCUSSION A. Local components generated for intertones near BF The careful choice of stimulus parameters allows one to record locally generated distortion products when the two primaries are near the BF of the cell. As shown in Fig. 1, sum and difference tones above as well as below the primaries are prominent in ac receptor potentials recorded from individual IHCs. The magnitudes of these local components reflect the tuning of the recording location, such that distortion products with frequencies well away from BF are more severely attenuated by filtering than those closer to the BF of the cell. In addition, combination tones can be influenced by the complex interactions observed between the two stimulating primaries as in Fig. 7 C. Because the primary producing the largest response suppresses the weaker, the frequency dependence of these magnitude decreases will reflect the ways in which filter shape changes with BF and with level. In fact, at the moderately high levels used here, the largest potentials are not produced at BF because responses here are fully saturated. Frequency response functions are also broader which fosters nonlinear interactions over a wide fre- 1045 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1045
FIG. 11. The measures were made in the organ of Corti fluid space in the same general area as the second-turn IHC recordings. The voltages were obtained at 80 db but were not compensated for reductions associated with the microelectrode. quency range. Thus these alterations in filter shape are reflected in the frequency dependence of the suppressive interactions between the two stimulating primaries. It should also be evident that these high-level suppression patterns contrast with the general notion that two-tone suppression is greatest around BF Kiang and Moxon, 1974; Abbas and Sachs, 1976; Abbas, 1978; Javel et al., 1978; Geisler and Sinex, 1980. This characterization, however, is largely based on single unit results obtained with a BF probe presented 15 db above threshold. At these low levels, tuning is sharp and the largest magnitude reductions are measured near BF. Because more linear responses are observed well above and well below BF, interactions are minimized in these regions. This general description differs from that reported here for primary pairs that increase in frequency because these measures were not obtained for low-level, BF probe tones measured in the presence of a constantfrequency suppressor. However, when suppression patterns are measured in IHCs at low-levels for BF probes, response reductions behave as indicated by the single unit results Sellick and Russell, 1979; Cheatham and Dallos, 1989. It should also be emphasized that since the primaries used in the present experiments were not harmonically related, magnitude notches in the two-tone functions Fig. 6 cannot be explained by interactions between distortion products of the same frequency but of a different order Dallos, 1973; McAnally and Calford, 1992. In fact, when frequency ratio is held constant at 1.4, fluctuations in distortion product magnitude can coincide with regions of mutual suppression where one primary suppresses the other by large amounts Dallos and Cheatham, 1974. Suppression by the primaries on individual distortion products is also a possibility. Thus magnitude notches probably reflect a nonmonotonicity in the production of the distortion product as well as suppression upon the distortion component itself. These results imply that suppression does not follow the generation of intermodulation distortion but appears to be colocalized with the production of two-tone distortion. In other words, the same nonlinearity could be responsible for both. Because the notches reported in the two-tone functions are influenced by mutual suppression between the two primaries, this interaction should be considered when evaluating similar response patterns reported elsewhere. These hair cell results are consistent with the idea that the presence of magnitude notches does not necessarily indicate that different sources are involved. In other words, the presence of a notch need not imply phase cancellation between two components produced by separate sources Weiss and Leong, 1985. This conclusion, however, probably does not apply to input output functions obtained at other frequency ratios and demonstrated in human subjects Smoorenburg, 1972; Hall, 1975; Weber and Mellert, 1975 and in distortion product otoacoustic emissions Weiderhold et al., 1986; Brown, 1987; Zwicker and Harris, 1990; Whitehead et al., 1992. These latter results probably reflect contributions from relatively large segments along the basilar membrane. Thus the notches could correspond to interactions between sources located at different positions along the cochlear partition Furst et al., 1988; Sun et al., 1994a,b; Robles et al., 1997; Brown et al., 1996; Gaskill and Brown, 1996; Stover et al., 1996. They do not necessarily imply, however, that the individual sources are different in nature. B. Traveling components generated for intertones above BF When primary pairs are placed well above BF, IHC responses can also be measured for distortion products with frequencies near the BF of the cell. These results are consistent with those recorded from IHCs in the base of the cochlea Nuttall and Dolan, 1990 as well as those from the auditory nerve Goldstein and Kiang, 1968; Kim et al., 1980; Siegel et al., 1982. In fact, the magnitudes of these traveling distortion products tend to exceed those produced by the primaries at the recording location. In other words, distortion products can be measured when the primaries do not produce responses in the cell when presented alone. Because these descriptions apply equally well to quadratic and cubic difference tones, they confirm the single unit results Kim et al., 1980; Siegel et al., 1982 suggesting that both components have their own traveling waves. In other words, that both f 2 f 1 and 2 f 1 f 2 are generated at more basal locations, in the region of overlap between the two stimulating primaries, and are distributed to their own BF place. Although similar behavior has been observed in basilar membrane mechanics in the base of the cochlea for the CDT, a QDT has not yet been measured Robles et al., 1991, 1997; 1046 J. Acoust. Soc. Am., Vol. 102, No. 2, Pt. 1, August 1997 M. A. Cheatham and P. Dallos: Nonlinear IHC responses 1046
Nuttall and Dolan, 1993. These mechanical experiments, however, utilized primary pairs which produced a CDT near BF but a QDT well below BF. Thus the absence of a component at f 2 f 1 may reflect the fact that frequency combinations favorable to the QDT have not been used. This is important because only when distortion products are within the passband of the location under study is a response observed. This holds for both local and traveling components. This situation is similar in some ways to that in psychophysics where QDTs and CDTs were thought at one time to exhibit different characteristics and to be produced by different sources Zwicker, 1955, 1979; Goldstein, 1967. However, when both components were examined for primaries at similar input levels, the two difference tones behaved in a similar fashion Hall, 1972; Humes, 1985; Zwicker and Martner, 1990. Consequently, one should not rule out the possibility that they are produced by a single source which is consistent with the IHC results reported here. Although in vivo measurements are not available from OHCs, data from the organ of Corti fluid space are relevant. This is because the cochlear microphonic is thought to reflect ac receptor potentials produced by nearby OHCs Dallos and Cheatham, 1976. In addition, the CM is thought to mirror the displacement pattern of the basilar membrane at least for inputs below BF Dallos et al., 1974. Consequently, the QDT exhibited in the organ of Corti ac response suggests that further mechanical experiments are warranted. Use of higher-frequency primaries and larger frequency ratios should result in a QDT with a frequency nearer to the site of observation along the basilar membrane. If IHC and organ of Corti results do generalize to the base of the cochlea, then a traveling QDT may also be expressed in cochlear mechanics. It could be argued that a QDT will not be measured in high-frequency regions because the set point of OHCs, in contrast to IHCs and OHCs in the apex of the cochlea Dallos and Cheatham, 1992, is located at the place of maximum gain on the transducer operating curve Cody and Russell, 1987; Frank and Kössl, 1996. If true, then cubic rather than quadratic components should dominate. However, for the organ of Corti data reported in Figs. 10 and 11, traveling QDTs were produced by primaries with intertones of 12 480 and 10 560 Hz. Thus, these data suggest that quadratic components are produced in the 10 12 khz region of the guinea pig cochlea implying asymmetrical transfer functions. IV. CONCLUSION Results in this report indicate that intermodulation distortion components are prominent in the generation region when the intertone is placed near the BF of cochlear hair cells. 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