On a psychophysical transformed-rule up and down method converging on a 75% level of correct responses.

Transformed-rule up and down psychophysical methods have gained great popularity, mainly because they combine criterion-free responses with an adaptive procedure allowing rapid determination of an average stimulus threshold at various criterion levels of correct responses. The statistical theory underlying the methods now in routine use is based on sets of consecutive responses with assumed constant probabilities of occurrence. The response rules requiring consecutive responses prevent the possibility of using the most desirable response criterion, that of 75% correct responses. The earliest transformed-rule up and down method, whose rules included nonconsecutive responses, did not contain this limitation but failed to become generally accepted, lacking a published theoretical foundation. Such a foundation is provided in this article and is validated empirically with the help of experiments on human subjects and a computer simulation. In addition to allowing the criterion of 75% correct responses, the method is more efficient than the methods excluding nonconsecutive responses in their rules.

Place code for pitch: a necessary revision.

It is widely believed that the location of the cochlear excitation maximum, which has been shown by Békésy to depend on sound frequency and move from the cochlear apex to its base as the frequency increases, is a code for subjective pitch. The pitch of a tone is known to be practically independent of sound intensity. If the location does determine the pitch, it too must remain invariant. At the 1990 meeting of the Collegium held in Basel, however, the first author reported compelling indirect evidence indicating that this may not be true. It suggested that, at least in the mid-portion of the cochlea, the most important for speech frequencies, the maximum moves toward the cochlear base as sound intensity is increased. We now have a direct verification of this inference. Recording alternating Hensen's cell potentials at two or three second-turn locations of each of several Mongolian gerbil cochleas, we observed that the maximum response produced by a single tone moved substantially toward the cochlear base as sound intensity increased. For example, an intensity increment of only 10 dB caused the maximum to move by about 0.225 mm. Since Hensen's cells are known to reflect closely the excitation pattern of the outer hair cells, similar to that of the inner hair cells, the discovery makes it impossible for the cochlear excitation maximum to be an adequate code for pitch. We observed, on the other hand, that the apical excitation cut-off did not depend on sound intensity. Every cochlear location investigated had its invariant characteristic cut-off frequency. It is possible, therefore, that the cut-off location provides the place code for pitch. These findings may have profound consequences for our understanding of auditory mechanisms as well as for the technology of cochlear implants.

Cochlear mechanisms of frequency and intensity coding. II. Dynamic range and the code for loudness.

Our preceding paper described SPL-dependent changes in the shape of transfer functions recorded from inner and outer hair cells as well as supporting cells, in the 500-2500 Hz regions of the Mongolian gerbil cochlea. As SPL was increased, large shifts were observed in the peak of the transfer function. A strongly compressive nonlinearity was also observed at CF. This paper examines the data from the perspective of intensity coding in the auditory periphery. Based on the data, we offer a new explanation for the mechanisms underlying the different dynamic ranges of low and high threshold auditory neurons. We also find that, for pure tone stimuli, the growth of excitation at the characteristic place saturates rapidly, and cannot encode the wide dynamic range of loudness. The data are analyzed to explore other excitation pattern candidates for loudness coding. The growth of the peak of the IHC transfer function, as well as the growth of the response area, have been found to be linearly related to loudness growth over most of its dynamic range. Implications of the data for auditory intensity coding are discussed.

Cochlear mechanisms of frequency and intensity coding. I. The place code for pitch.

In the past, several researchers have reported a substantial shift in the peak of the tone-evoked excitation pattern toward the base of the cochlea following an increase in the SPL of the stimulating tone. Evidence for such peak shifts has been found in the responses of auditory nerve fibers, cochlear microphonics, and the responses of outer hair cells and supporting cells in the cochlea, as well as in basilar membrane vibration measurements, and indirectly, in psychophysical data. However, direct evidence for such a peak shift in inner hair cell (IHC) responses has been relatively sparse. If the peak shift is preserved in the information conveyed to the auditory nerve fibers by the IHCs, the classical 'place theory' for frequency coding in the cochlea requires modification. In this study, the nature and extent of the SPL-dependent peak shift is examined with the help of recordings in the IHCs and other cells of the organ of Corti in the 0.5-2.5 kHz region of the Mongolian gerbil cochlea. It is demonstrated that the peak shift is a universal phenomenon in the diverse cell types in this region of the cochlea. Most importantly, a large SPL-dependent peak shift is demonstrated in IHC responses. On the other hand, the recordings indicate that the apical cutoff of the spatial excitation pattern is SPL-independent. We conclude, therefore, that the place theory of pitch perception must be abandoned or at least modified.

Enhanced cochlear responses after sound exposure.

Alternating potentials produced in Hensen's cells of Mongolian gerbils by sinusoidal stimuli were enhanced or depressed after exposure to broad-band sound of moderately high intensity, depending on exposure- and stimulus intensities. Since Hensen's cell responses have been shown to be identical in phase and directly proportional in magnitude to outer hair cell (OHC) responses (Oesterle, E.C., Dallos, P., 1989, J. Acoust. Soc. Am. 86 (3), 1013-1032.; Zwislocki, J.J., Slepecky, N.B., Cefaratti, L., Smith, R.L., 1992, Hear. Res. 57, 175-194), it was assumed that these changes were reflections of changes in OHC receptor potentials, which were of main interest. The indirect method of intracellularly recording the Hensen's cell potentials rather than OHC potentials was used to minimize damage to the organ of Corti and reduce technical difficulties associated with repeated recordings from OHCs. Continuous magnitude and phase transfer functions (TFs) were obtained before and after the exposure over a range of sound pressure levels (SPLs) extending from 40-90 dB by using frequency sweeps ranging from 0.125-18 kHz. Cochlear microphonic (CM) TFs were also acquired over the same frequency and intensity ranges for monitoring purposes. The exposure stimuli were set at 80, 86, 90 or 100 dB SPL for periods ranging from 10-40 min. When response enhancement occurred, it was most clearly seen in the peak of the transfer function determined at 90 dB SPL. Enhancement ranged from approximately 12-230% of the original peak. In contrast, control Hensen's cell recordings obtained over periods of up to 130 min revealed great response stability. In all reliable recordings, response enhancement was associated with a phase lead or no phase change. The strongest exposure stimuli tended to produce sensitivity loss accompanied by phase lag at the lower SPLs, in agreement with previous work in this laboratory (Zhang and Zwislocki, 1995). In some preparations, both sensitivity loss at lower SPLs and enhancement at higher SPLs occurred simultaneously, suggesting involvement of two different mechanisms.

Relationships of intensity discrimination to sensation and loudness levels: dependence on sound frequency.

The main purpose of the experiments described in this article was to establish the frequency dependence of auditory intensity jnd's (just noticeable differences) for pure tones as functions of loudness level (LL). For this purpose, two sets of experiments were performed. In the first, the jnd's were measured as functions of sensation level (SL) at sound frequencies of 0.125, 0.5, 1, 2, 4, 6, and 8 kHz. The SLs were set at 10, 20, 40, 60, and 80 dB in a random order. In the second, LLs corresponding to the set of the SL at 1 kHz were obtained, and the relationship of the jnd's to LL was determined. We investigated to what extent the constant loudness-constant jnd relationship found previously intrafrequency can be applied interfrequency. The detection experiments were performed with a continuous-pedestal paradigm and an adaptive two-alternative, forced-choice (2AFC) procedure that converges on 75% of correct responses. We found that the jnd's in dB plotted versus SL decreased roughly according to power functions, the rate of decrease depending on sound frequency. The jnd's increased with sound frequency at low SLs but became practically constant at high SLs. According to the second experiment, the jnd's followed approximately the same function of LL at all sound frequencies, except for a multiplicative constant, irrespective of the slope of the loudness level function. Thus, the constant loudness-constant jnd relationship appears to apply interfrequency except for a multiplicative constant that, with the continuous-pedestal paradigm, grew monotonically with the frequency.

Effects of stimulus duration on the amplitude difference limen for vibrotaction.

Vibrotactile amplitude difference limens (DLs) were measured by the continuous pedestal and gated pedestal methods. In both cases, the relative DL decreased as a function of the intensity of the stimulus and the results, in most cases, could be described as a near miss to Weber's law. DLs measured by the continuous pedestal method were found to decrease substantially as a function of increases in stimulus duration over a range of 12 to 1000 ms. In contrast, DLs measured by the gated pedestal method were only slightly affected by changes in stimulus duration. It was concluded that the process of temporal summation can manifest itself in reducing the size of the DL in the continuous pedestal, but not the gated pedestal, paradigm.

Intensity-dependent peak shift in cochlear transfer functions at the cellular level, its elimination by sound exposure, and its possible underlying mechanisms.

Our systematic study of cochlear transfer functions has confirmed earlier results that, in a normal cochlea, the cochlear AC responses at any given cochlear location do not have a fixed best frequency at which the response is maximal. The best frequency depends on sound intensity, shifting to lower frequencies as the intensity is increased. This phenomenon may account for the so called 'half-octave shift' of maximum cochlear damage relative to the frequency of the damaging sound observed in studies of auditory noise exposure. Our experimental results combined with the results of others and with our model studies bring us to the conclusion that, at low to moderate sound intensities, the dependence of the best frequency on sound intensity is due to an effect of the active feedback, which decreases as sound intensity increases. Consequently, the feedback, when present, must shift the best frequency upward.

Cochlear precursors of neural pitch and loudness codes.

It has been believed by most auditory scientists for over a century that the place of maximum vibration in the cochlea provides the main pitch code. Recently, we have obtained experimental evidence showing that this is quite unlikely, because the maximum of cochlear excitation changes its location with sound intensity, moving over the useful sound intensity range toward the cochlear base by a distance equivalent to more than one octave, whereas the pitch remains almost constant. In the presence of outer hair cell damage, the maximum is shifted toward the base by a similar distance, whereas the pitch is hardly affected. Of interest, the location of the apical cutoff of excitation is practically unaffected by sound intensity or cochlear damage. For any given sound frequency, the shift of the maximum with sound intensity precludes any single cochlear location from coding for loudness over the entire useful intensity range. The code is very likely provided by the maximum, which changes its location with the intensity, or by the whole cochlear excitation area. Of significance in this respect is our determination that the growth of the output of the whole auditory nerve parallels the growth of the excitation area. These findings may be useful for the coding of sound in cochlear implants, as well as for hearing aid dynamics.

OHC response recruitment and its correlation with loudness recruitment.

After proper noise exposure, Hensen's cells, which have been shown to follow closely the response characteristics of the outer hair cells, suffered a loss of sensitivity at low and moderate SPLs. The lower the stimulus level, the greater was the loss. When the low-SPL loss did not exceed about 40 dB, input-output functions showed an increased rate of amplitude growth, so that the post-exposure response caught up with its pre-exposure counterpart between 60 and 90 dB SPL, depending on the severity of the loss. These results, together with preceding clinical observations, led us to the conclusion that loudness recruitment occurs at least in part at the hair cell level and is basically a local event as opposed to a pathological spread of excitation. The response recruitment we have discovered appears to result from a decreased effect of the active feedback when the passive cochlear mechanisms are intact. Evidence for these relationships is presented and an explanation is offered for previous experimental successes and failures in observing a steepening of rate-intensity functions in auditory nerve fibers after noise exposures or administration of ototoxic drugs.

The effects of masking on the growth of vibrotactile sensation magnitude and on the amplitude difference limen: a test of the equal sensation magnitude-equal difference limen hypothesis.

In this study, the hypothesis that the difference limen (DL) for the detection of differences in amplitude of vibrotactile stimuli is independent of the slope of the sensation magnitude function was tested. The slope of the sensation magnitude function was varied by presenting test stimuli in the presence of or in the absence of vibrotactile noise. The slopes of the sensation magnitude functions were determined through a matching technique in which the subject adjusted stimulus amplitudes of a 250-Hz stimulus presented alone and a 250-Hz stimulus presented simultaneously with a masking noise, so that their sensation magnitudes were equated. The slope of the matching function was found to increase as a function of the intensity of the masking noise. In the second phase of the experiment, the amplitude DL was measured by the gated-pedestal method for test stimuli presented under the same stimulus conditions as used in the matching procedure. At all levels of stimulus intensity, the DL was found to be independent of the masking condition provided the sensation magnitudes of the stimuli were the same. This finding supports the hypothesis that the size of the DL is independent of the slope of the sensation magnitude function, provided the sensation magnitudes of stimuli are the same. The generality of this principle, first discovered in hearing, is thus extended to another sense modality.

Relationships between the variability of magnitude matching and the slope of magnitude level functions.

Binaural loudness matching and intermodal magnitude matching experiments were performed to test systematically the origins of the phenomenon observed earlier that the variability of binaural loudness matches was larger when sound intensity was varied in the normal ear than when it was varied in the contralateral ear with raised threshold and loudness recruitment. In the experiments, the raised threshold and loudness recruitment were produced by masking a 1-kHz tone with narrow-band random noise. In intermodal experiments, magnitude matches were performed between the masked tone and the length of lines projected on a translucent window pan. The results are consistent with the earlier observations. They show in addition that the variability depends on the slope of the matching functions in a complicated, not previously anticipated way, irrespective of whether the functions are intra- or intermodal. More specifically, for moderate slopes, the variability in the ear with loudness recruitment decreased as the slope increased. The reverse was true for the unmasked ear or the line length--when the slope was large, the variability increased with the slope. Since the variability decreased in one ear and increased in the other, the ratio of the variabilities increased as the slope increased. When the slope was equal to one, both variabilities tended to be the same.

Just noticeable differences for intensity and their relation to loudness.

The present study examines the relation between the form of the loudness function and the size of the intensity just noticeable difference (jnd). The hypothesis that equal loudnesses at any given sound frequency yield equal-intensity jnd's was examined. In addition, Hellman et al.'s [J. Acoust. Soc. Am. 82, 448-453 (1987)] experiment, which showed that jnd's are independent of the slope of the loudness function was replicated. Threshold shifts and altered loudness-balance functions for 1-kHz tones were produced by using backgrounds of narrow- or wideband noise. The two types of background noise produced intersecting points on loudness-balance functions at which intensity jnd's were obtained. Intensity jnd's were also obtained at equal-loudness levels (corresponding to 30, 40, 50, and 60 dB SL in the unmasked ear) under each of the two noise conditions and in quiet. The results indicate that tones of equal loudness produce approximately equal jnd's and that there is no apparent relation between the slope of the loudness-balance functions and the size of the intensity jnd.

Intensity just-noticeable differences at equal-loudness levels in normal and pathological ears.

The relationship between loudness level and intensity discrimination was investigated in the frequency range 0.5-6.5 kHz by comparing the intensity just-noticeable differences (jnd's) at a number of equal-loudness levels in the better and poorer ears of eight individuals with essentially unilateral hearing loss of cochlear origin. Such hearing loss usually produces loudness recruitment, altering the relationships among the loudness, sound-pressure level (SPL), and sensation-level (SL) variables, so that their effects can be separated. In these experiments, the jnd's were correlated with loudness level, not SPL or SL. Although, in some listeners, there were significant differences between jnd's in the two ears at some binaurally equal-loudness levels, they were not systematic over the group of listeners. Statistically, there was no significant difference between equal-loudness jnd's in the two ears, whereas the corresponding SLs and SPLs were significantly different. The rate of loudness growth had no effect on the jnd's. As expected from the near-miss to Weber's law, the mean jnd's decreased with sound intensity. The corresponding decrease in the mean Weber fraction, delta I/I, was accompanied by a decrement in its intrasubject standard deviation. The latter was correlated with the mean, independent of its relationship to SPL or SL.

Ionic coupling among cells in the organ of Corti.

Gap junctions have been demonstrated morphologically among the supporting cells of the mammalian organ of Corti but, in contradistinction to reptiles, evidence for their existence between the supporting cells and hair cells is equivocal. The literature is ambiguous with respect to electrical coupling and dye coupling among the supporting cells, and no coupling of either kind has been demonstrated for the hair cells. We found strong coupling of both kinds among the supporting cells in the cochleas of live Mongolian gerbils and a less stable coupling between the supporting cells and the outer hair cells. The electrical coupling was established by recording alternating receptor potentials in the hair cells and following their decrement in the population of Hensen's cells; the dye coupling, by injecting Lucifer yellow electrophoretically into the hair cells or the supporting cells and investigating its spread to the neighboring cells. The electrical recordings were made by means of microelectrodes filled with either 1.5 or 3 M KCl or 1 M LiCl with 6% Lucifer yellow, the latter used for dye injection. The electrode resistances ranged from about 20 to 60 M omega in the first instance, and from about 50 to 110 M omega, in the second. The electrodes were inserted into the organ of Corti through scala media according to the method of Dallos, Santos-Sacchi and Flock (1982) modified by us. The alternating potential in Hensen's cells was usually larger than in the outer tunnel of Corti and remained practically constant up to the outer margin of the Hensen's-cell population. Its phase was the same as in the outer hair cells. When the dye was injected into a Hensen's cell, it always spread to neighboring Hensen's cells and often to Deiter's cells. Dye injected into outer hair cells (identified according to anatomical and physiological criteria) also spread to Deiter's and Hensen's cells and, usually, to other outer hair cells. Stained cells were identified in surface preparations and, on two occasions, in serial sections from plastic embedded cochleas.

What is the cochlear place code for pitch?

The advent of cochlear implants has increased the clinical interest in the cochlear code for pitch. It is widely believed that pitch is determined by the location of the excitation maximum in the cochlea. However, direct recordings from cochlear hair cells indicate that, for a given sound frequency, the location changes appreciably with sound intensity, whereas the corresponding pitch remains approximately constant. Correlated with this constancy is a surprising constancy of the location of the high-frequency cutoff of cochlear excitation.

Tectorial membrane. II: Stiffness measurements in vivo.

The tectorial membrane is assumed to play a crucial role in the stimulation of the cochlear hair cells and was thought for decades to serve as a stiff anchor for the tips of the hair-cell stereocilia, particularly those belonging to the OHCs. Yet, its stiffness has never been measured under conditions approximating its normal environment in live animals. We have developed a method for doing this. The tectorial membrane is approached through the lateral wall of scala media. The bony cochlear capsule is removed along scala media over somewhat less than 1/4 turn, and the underlying spiral ligament and stria vascularis are carefully reflected. With the help of a three axial hydraulic manipulator, a flexible micropipette filled with isotonic KCl is inserted into the tectorial membrane at one of two different angles and moved either transversally, away from the basilar membrane, or radially, toward or away from the modiolus. This causes the tectorial membrane to be deformed and the micropipette to bend. The micropipette stiffness is calibrated on an instrument of a new kind, so as to convert the bend into force. The calibration allows us to determine the point stiffness of the tectorial membrane from the amount of micropipette bend. The stiffness of the tectorial membrane per unit length has been calculated from the point stiffness with the help of the deformation pattern. Transversal and radial stiffness magnitudes have been determined in the second cochlear turn in Mongolian gerbils. Both are smaller by almost an order of magnitude than the corresponding aggregate stiffness of the OHC stereocilia. As a consequence, the tectorial membrane cannot act as a stiff anchor for the stereocilia but only as a mass load, except at relatively low sound frequencies where mass effects are negligible. This means that the classical model of shear motion between the tectorial membrane and the reticular lamina must be replaced.

Intensity discrimination determined with two paradigms in normal and hearing-impaired subjects.

The literature on auditory intensity jnd's is ambiguous with respect to the relationship between the jnd's measured with gated and continuous pedestals and with respect to changes in this relationship in the presence of loudness recruitment accompanying cochlear pathology. In an attempt to clarify these issues and to lay a foundation for systematic investigations of the dependence on the jnd's on loudness functions, the jnd's for pure tones with gated- and continuous-pedestal paradigms of two groups of subjects, one with normal hearing and one with hearing loss of cochlear origin, were measured. The experiments were performed at 0.5, 2, and 6 kHz, and at a wide range of sensation levels (SLs) by means of an adaptive two-alternative, forced-choice (2IFC) procedure. The jnd's obtained with the continuous-pedestal method were smaller than those obtained with the gated-pedestal method for both groups of subjects. They also had smaller intersubject standard deviations. When jnd's of the two groups were compared on the basis of equal SLs, the group with hearing loss showed smaller jnd values than the group with normal hearing for both pedestal paradigms. When the comparisons were made on the basis of equal sound-pressure levels (SPLs), both groups showed similar values for moderate and high SPLs. At relatively low SPLs, the group with hearing loss tended to have somewhat higher values.

Tectorial membrane. I: Static mechanical properties in vivo.

Although the tectorial membrane in the mammalian cochlea plays a crucial role in hair-cell stimulation, its mechanical properties have never been investigated under conditions approximating those under which it normally functions. For this reason, we performed such investigations in live Mongolian gerbils. Access to the tectorial membrane was gained through the lateral wall in the second cochlear turn. As far as possible, sodium ions were kept away from the tectorial membrane by avoiding injury to Reissner's membrane, relieving the perilymphatic pressure, and rinsing the scala media with an isotonic KCl solution. The tectorial membrane was manipulated with a flexible micropipette in three, approximately orthogonal, directions. Under these conditions the membrane was found to be highly compliant and resilient, and to have a relatively high tensile strength. Its viscosity was low. Some of these attributes were altered by sodium ions, dyes, or death.

Mechanical properties of the tectorial membrane in situ.

According to the classical model of cochlear hair-cell stimulation, the tectorial membrane moves in cross-section like a stiff beam, rotating around the lip of the spiral limbus. This produces a shearing motion against the reticular lamina and, as a result, a radial deflection of the hair-cell stereocilia. The deflection can be effectively produced by the tectorial membrane only if its stiffness in the radial direction is greater than that of the stereocilia. We were able to manipulate the tectorial membrane through a scala-media access in live Mongolian gerbils and to measure its transverse and radial stiffness. We found the membrane to behave like a rubber band and to be much less stiff than the stereocilia. This is incompatible with the classical model. The tectorial membrane must act on the stereocilia as a mass load rather than a stiff anchor.