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J Neurophysiol 78: 261-270, 1997;
0022-3077/97 $5.00
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The Journal of Neurophysiology Vol. 78 No. 1 July 1997, pp. 261-270
Copyright ©1997 by the American Physiological Society

Mechanical Responses to Two-Tone Distortion Products in the Apical and Basal Turns of the Mammalian Cochlea

N. P. Cooper and W. S. Rhode

Department of Neurophysiology, University of Wisconsin-Madison, Madison, Wisconsin 53706

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Cooper, N. P. and W. S. Rhode. Mechanical responses to two-tone distortion products in the apical and basal turns of the mammalian cochlea. J. Neurophysiol. 78: 261-270, 1997. Mechanical responses to one- and two-tone acoustic stimuli were recorded from the cochlear partition in the apical turn of the chinchilla cochlea, the basal turn of the guinea pig cochlea, and the hook region of the guinea pig cochlea. The most sensitive or "best" frequencies (BFs) for the sites studied were ~500 Hz, 17 kHz, and 30 kHz, respectively. Responses to the cubic difference tone (CDT), 2F1 - F2 (where F1 and F2 are the frequencies of the primary stimuli), were characterized at each site. Responses to the quadratic difference tone (QDT), F2 - F1, were also characterized in the apical turn preparations (QDT responses were too small to measure in the basal cochlea). The observed responses to BF QDTs and CDTs and to BF CDTs at each site appeared similar in many ways; the relative magnitudes of the responses were highest at low-to-moderate sound pressure levels (SPLs), for example, and the absolute magnitudes grew nonmonotonically with increases in the level of either primary (L1 or L2) alone. The peak effective levels of the CDT and QDT responses were also similar, at around -20 dB re L1 and/or L2. In other respects, however, the responses to CDTs and QDTs and to BF CDTs at each site behaved quite differently. At low-to-moderate SPLs, for example, most CDT phase leads decreased with increases in either L1 or L2, whereas most QDT phase leads increased with increasing L1 and varied little with L2. Most CDT responses also varied monotonically with equal-level primaries (i.e., when L1 = L2), whereas most QDT responses varied nonmonotonically. Different responses also varied in different ways when F1 and F2 were varied. Apical turn QDT responses were observed over a very wide F1/F2 range (F1 =1-12 kHz), but were usually largest for stimuli <2-4 kHz. Apical turn CDT levels decreased (at rates of ~40-80 dB/octave) only when the frequency ratio F2/F1 increased beyond ~1.4-1.5. In the basal turn and hook regions, the CDT levels depended nonmonotonically on F2/F1, with the eventual rates of decrease being ~200 dB/octave. Optimal frequency ratios for the CDT increased from (F2 < 1.1F1) to (F2 approx  1.2F1) with increasing SPL in the basal turn, but were stable at around F2/F1 approx  1.05 in the hook region. CDT phase leads tended to increase with increasing F2/F1 in all three regions of the cochlea, particularly at low-to-moderate SPLs. These findings are discussed in relation to previous studies of cochlear mechanics, physiology, and psychophysics.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

The mammalian cochlea's response to an acoustic stimulus that has spectral components at two frequencies (denoted as F1 and F2, where F1 < F2; see Table 1) normally includes a group of distortion products (DPs) whose frequencies are determined by simple mathematical combinations of F1 and F2 (e.g., 2F1 - F2, 3F1 - 2F2, 2F2 - F1, 3F2 - 2F1,F2 - F1, etc.). These DPs are of potential importance in many areas of hearing research: they clearly influence the perception of some pitch-producing sounds (Smoorenburg 1970; but also see Plomp 1965), and they provide the basis for one of the few objective tests that can be performed in an audiology clinic (Lonsbury-Martin et al. 1993).

 
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  		TABLE 1. Definition of terms, units, and abbreviations

The largest, most easily perceived and most extensively studied DP occurs at a frequency equal to 2F1 - F2; this DP is known as the cubic difference tone (CDT). CDTs have been characterized in numerous psychophysical and physiological studies, and have often led to fundamental improvements in our understanding of the cochlea (e.g., see Goldstein 1967; Smoorenburg 1972). Another extensively studied DP occurs at a frequency of F2 - F1. This DP is known as the simple or quadratic difference tone (QDT). The QDT has been shown to differ from the CDT in several respects (Brown 1993; Hall 1972; Zwicker 1979), even though both DPs appear to be generated in the cochlea and to propagate along the cochlear partition in the same way as any other stimulus component (Kim et al. 1980; Siegel et al. 1982).

Over the past few years, observations of CDTs have been made in several studies of cochlear mechanics (Nuttall et al. 1990; Rhode and Cooper 1993; Robles et al. 1990, 1991, 1997). In contrast to earlier mechanical studies (Rhode 1977; Wilson and Johnstone 1975), these modern studies show that significant amounts of distortion exist on the cochlear partition at physiologically relevant sound pressure levels (SPLs). To date, however, very little systematic information has been provided: only two studies have presented any information regarding the phases of the mechanical responses (Rhode and Cooper 1993; Robles et al. 1997), for example, and only one has provided systematic information with respect to the CDT's tuning characteristics (Robles et al. 1997). In view of the discrepancies that exist between psychophysical and otoacoustic emission (OAE) DPs (see below), the tuning characteristics of the mechanical DPs are particularly interesting. Robles et al. (1997) observed the amplitude of fixed-frequency CDTs to decline monotonically when the frequencies of the primary tones (and thus their ratio, F2/F1) were increased. Such "low-pass" tuning characteristics are similar to those observed in numerous psychophysical investigations (e.g., Goldstein 1967; Smoorenburg 1972; Zwicker 1955, 1981), and contrast strongly with the broad band-pass tuning that is observed in DP OAE studies (e.g., Allen and Fahey 1993; Brown et al. 1992; Harris et al. 1989). It should be noted that counterexamples to the low-pass mechanical tuning observed by Robles et al. (1997) have been published before, however (e.g., see experiment L47 in Ruggero et al. 1992). Additional systematic studies may thus be warranted.

Another limitation of the mechanical DP studies that have been performed to date is that they have all concentrated on the basal regions of the cochlea. These regions process sounds that are much higher in frequency than those used in most OAE and psychophysical studies, such that direct comparisons between disciplines are hampered. There is clear evidence that the DP tuning characteristics measured in both psychophysical and OAE experiments depend on the absolute frequencies of the primary stimuli, which in turn implies that the tuning varies with intracochlear position (e.g., Goldstein 1967; Hall 1972; Harris et al. 1989; Zwicker 1981).

The present study provides new information regarding the CDT in three separate regions of the cochlea, including the little-studied apical turn. It also provides what we believe to be the first direct observations of mechanical QDTs (at physiologically relevant SPLs) in the mammalian cochlea. An abstract of some of this work has been reported previously (Cooper and Rhode 1996a).

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Most of the methods used in this study have been described in detail elsewhere. Thus only a brief outline is given here, along with details of specific modifications.

Mechanical responses to one- and two-tone acoustic stimuli were recorded from the apical turns of 12 chinchilla cochleae, from the basal turns of five guinea pig cochleae, and from the hook regions of a further seven guinea pig cochleae. These preparations were selected from much larger groups of animals on account of the fact that their mechanical responses to single-tone stimuli exhibited substantial amounts of compressive nonlinearity. The animals were deeply anesthetized throughout the experimental procedures, and were overdosed with anesthetic at the end of each experiment. Tracheal cannulas were used to maintain a patent airway, and artificial ventilation was provided whenever necessary. The animal's core temperatures were maintained at ~37.6°C using a thermostatically controlled heating blanket. The physiological condition of the cochlea was monitored using compound action potential (CAP) audiogram recordings (Johnstone et al. 1979). The care and use of the animals reported in this study were approved by the Animal Care and Use Committee of the University of Wisconsin at Madison.

The cochlear partition was exposed using methods described elsewhere (Cooper and Rhode 1992, 1996b; also see Sellick et al. 1982). Gold-coated polystyrene microbeads (~25 µm diam, Polysciences) were then introduced onto the partition to reflect the laser beam used in the measurement technique. The opening into the cochlea was then covered with an optically flat glass window to stabilize the interface between the perilymph and air, and mechanical responses were monitored using a displacement-sensitive heterodyne laser interferometer (Cooper and Rhode 1992).

Acoustic stimuli were presented closed-field from two independent transducers: One of these was a reverse-driven condenser microphone cartridge (Bruel & Kjaer type 4134, with digital precompensation for 2nd-order nonlinearity), and the other was either a dynamic loudspeaker (Radio Shack Super-Tweeter) or a second (identically operated) condenser microphone. The dynamic loudspeaker was used only to generate single-tone stimuli in the apical turn (chinchilla) experiments, because the output levels of the condenser microphones were limited to ~70 dB SPL below200-400 Hz [note: 0 dB SPL = 20 µPa root mean square (rms)]. The levels of all intermodulation DPs in the two-channel system (as tested in a small sealed cavity using 100-dB SPL primary tones) were >= 66 dB below the levels of the primary tones. Ear canal SPLs were monitored at various points in time (typically just before and just after the two-tone experiments, and once more at the end of each experiment) using a calibrated probe tube microphone whose tip was placed within 3 mm of the animal's umbo (<1 mm in the basal turn experiments). The initial SPL calibrations were used to generate a digital compensation table for the sound generation system, such that absolute SPLs could be specified more readily in later parts of the experiments. Typically, errors in the specified SPLs (as revealed through the repeated measurements) only became appreciable (greater than ±3 dB) at very high frequencies (e.g., >26 kHz).

Single-tone tuning and/or input-output (IO) functions were determined with the use of short tone pips. Stimulus durations varied according to the preparation, typically being 50 ms in the apical turn and 30 ms in the basal turn. These durations include identical rise and fall times of 5 and 1 ms, respectively, with the rise and fall periods being shaped by a raised cosine envelope. Various two-tone stimuli were then presented to the animal (see Fig. 1 for an example). The primary frequencies of these stimuli were normally selected to align the CDT, 2F1 - F2, with the most sensitive or "best" frequency (BF) of the site under study. Experiments were also performed with the QDT, F2 - F1, aligned with the BF in the apical turn preparations. The levels of the primaries (L1, L2) were either varied one at a time, or L1 was set close (usually equal) to L2 and the two stimuli were varied together. Within each run of data collection, L1 and/or L2 were usually varied from high to low level in 5-dB steps. The time courses of the two-tone stimuli were arranged such that each response contained information about each of the primary tones (alone) as well as information about the two-tone combination: 30-ms-long tone pips were normally staggered by 10 ms, and 50-ms-long tone pips were staggered by 15 ms (see Fig. 1). The overall repetition periods for most stimuli were ~100 ms. Longer stimulus durations (e.g.,100-200 ms) and repetition periods were used to increase the spectral resolution in some experiments (e.g., when F1 = 525 Hz and F2 = 550 Hz in Fig. 4).


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  		FIG. 1. Time course of two-tone stimulus and illustration of response analysis technique. This example was taken from apical turn of the chinchilla cochlea, with cubic difference tone (CDT) selected to equal preparation's best frequency (BF) of 500 Hz, F2/F1 set to 1.545 (where F1 and F2 are frequencies of primary stimuli), and L1 = L2 = 54 dB SPL (where L1 and L2 are primary sound pressure levels; preparation CH52, response waveform averaged 32 times). Top traces: waveforms of primary stimulus components. Bottom traces: tectorial membrane's response to two-tone complex. Displacements toward scala tympani (ST) are plotted upward [scala vestibuli (SV) is down]. Periods marked A-C below response waveform; analysis windows used to evaluate amplitudes and phases of various response components: F2 alone during period A; F1, F2, 2F1 - F2, and F2 - F1 during period B; F1 alone during period C. Delta tau , delay factor (see METHODS). Plot at bottom: comparison of spectrum of entire two-tone response () with response amplitudes evaluated as described in METHODS (black-diamond , odot , square , black-square, open circle , bullet ). Amplitude mismatches between various symbols and spectrum are caused by uneven distribution of spectral components across time [spectrum was evaluated using a Hanning window spanning from start of period A to end of period C].


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  		FIG. 4. Dependence of CDT responses on stimulus frequency in 3 regions of the mammalian cochlea (a, d, and g, apex; b, e, and h, basal turn; c, f, and i, hook region).a-c: amplitudes of response to BF CDTs for various combinations of primary frequencies. F1 and F2 values for each curve are indicated in key, with corresponding F2/F1 ratios indicated with appropriate symbols in g-i. Dotted lines: growth rates of 1 dB/dB (as in Fig. 3, a-c). d-f: response phases corresponding to amplitude data in a-c. g-i: effective levels of CDTs, relative to primary stimuli, as function of primary stimulus frequency ratio (F2/F1). Effective levels of CDT indicate SPLs of single tones at CDT frequency (= BF in this instance) that would produce the same amplitudes of response as the CDT, and express these levels relative to the SPLs of the lowest frequency primary (L1). This metric facilitates comparison of distortion products across physiological (acoustic, mechanical, and neural) and psychophysical studies. Stimulus levels are indicated by numbered symbols, in multiples of 10 dB SPL (i.e., circled 3 = 30 dB SPL, circled 4 = 40 dB SPL, etc.). Negatively sloping dotted lines approximate high-frequency cutoff slopes of CDT tuning characteristics.

The mechanical responses were digitized at rates of ~100,000 or 250,000 samples per second (in the apical/basal turn experiments, respectively). Digitized responses were averaged across multiple presentations of a given stimulus (typically 32-64 times) and stored for off-line analysis. The amplitudes and phases of the response components locked to any particular frequency were evaluated by fitting sinusoids to the various steady-state portions of the responses (labeled A-C in Fig. 1---a delay factor Delta tau was used to compensate for the effects of propagation delays in the sound delivery system and in the cochlea itself). The length of the analysis window used in the sine fitting procedure was always adjusted to include an integer number of response cycles (where 1 cycle = 2pi radians = 360°; in the case of two-tone stimulation, the analysis window included integer numbers of F1, F2, 2F1 - F2, and F2 - F1 cycles). Figure 1 includes a comparison of this procedure's output with that of a more conventional Fourier transform. Response amplitudes are expressed in terms of their peak ac values (peak amplitude = <RAD><RCD>2</RCD></RAD> × rms amplitude) throughout this paper, and phases are expressed in fractions of a cycle. To facilitate cross-frequency comparisons, the CDT and QDT response phases are corrected by factors of 2alpha  - beta  and beta  - alpha , where alpha  and beta  are the phases of the F1 and F2 stimuli, respectively. [As an example, the CDT and QDT responses in Fig. 1 were analyzed in the period between 26.5 and 46.5 ms after the onset of the F2 stimulus, or (equivalently) between 11.5 and 31.5 ms after the onset of the F1 stimulus. The stimulus phases at the start of the analysis window were thus alpha  = rem (0.0115 × F1) = 0.65 cycles and beta  =rem (0.0265 × F2) = 0.05 cycles, and the CDT and QDT response phases (as illustrated in Figs. 3d and 5b) were corrected byrem (2 × 0.65 - 0.05) = 0.25 cycles and rem (0.05 - 0.65) = 0.4 cycles, respectively.]


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  		FIG. 3. Dependence of CDT responses on stimulus level in 3 regions of the mammalian cochlea (a, d, and g, apex; b, e, and h, basal turn; c, f, and i, hook region). a-c: comparison of CDT response amplitudes (bell-shaped curves with symbols) with responses to single tones at each preparation's BF (solid lines without symbols). L2 values for bell-shaped curves are indicated at top. Three single-tone data sets are shown in a-c to illustrate stability of recordings across time: 1 set was collected before two-tone data, 1 was collected in middle of two-tone experiments, and 1 was collected after two-tone experiments. Dotted lines: growth rates of 1 dB/dB. d-f: response phases corresponding to amplitude data in a-c. g-i: isoamplitude contours for CDT responses as function of stimulus levels L1 and L2. Contour criteria are separated by 6-dB steps, with absolute amplitude of smallest criterion being labeled. Increasing line weights are used for successively larger criteria.

The responses locked to the two primary stimulus components in isolation (e.g., during periods A and C in Fig. 1) were used to monitor the preparation's short-term stability, as well as to assess the response's susceptibility to two-tone suppression (see DISCUSSION). Repeated presentations of various stimuli (both one- and two-tone), as well as occasional checks of the CAP audiogram, were used to monitor longer-term stability (e.g., see the single-tone IO functions in Figs. 3, a-c, and 5a, and the square /bullet QDT data in Fig. 6a).


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  		FIG. 6. Dependence of QDT responses on stimulus frequency in the apical turn of the cochlea. a: amplitudes of response to BF QDTs for various combinations of primary frequencies. F1 and F2 values for each curve are indicated in key [F1 values are also indicated with appropriate symbols in c]. Solid curves without symbols: responses to single tones at preparation's BF (500 Hz) before, during, and after two-tone experiments. One two-tone stimulus condition was also repeated to demonstrate stability of recordings across time (square  were recorded near beginning of series, bullet  at end). Note that when F1 = 1 kHz (black-square), F2 - F1 = 2F1 - F2. b: response phases corresponding to amplitude data in a. c: relative effective levels of QDTs as function of primary stimulus frequency (F2 = F1 + BF). Effective levels of QDT, and numeric symbols, are as defined for CDT in Fig. 4, g-i.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Three individual preparations were selected to illustrate the main findings of this study. These preparations were selected for several reasons: they exhibited minimal(<3-dB) threshold losses in their CAP audiograms; their responses to single tones in the vicinity of their BF became compressively nonlinear at reasonably low SPLs (see Figs. 2, 3, a-c, and 5a); they remained stable for a considerable period of time; and they provided data that were consistent with (although generally more extensive than) those collected in the majority of other preparations.


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  		FIG. 2. Single-tone tuning characteristics in 3 regions of the mammalian cochlea (a, apex; b, basal turn; c, hook region). Numbered symbols: sound pressure levels (SPLs) of single-tone stimuli in multiples of 10 dB SPL (i.e., circled 3 = 30 dB SPL, circled 4 = 40 dB SPL, etc.). Vertical dotted lines: preparation's BF. Negatively sloping dotted lines approximate high-frequency cutoff slopes of preparation's tuning characteristics. (Note: 1 Pa = 94 dB SPL.)

The basic tuning characteristics at the three different cochlear sites are illustrated in Fig. 2. The apical turn preparation (CH52) has a BF of 500 Hz and is relatively broadly tuned at all SPLs; its Q10dB (a measure of the sharpness of tuning obtained by dividing the BF by the bandwidth of the tuning characteristic 10 dB below its peak level) is ~0.8. The basal turn preparation (GP204) has a higher BF (17 kHz) and is more sharply tuned, particularly at low SPLs; its Q10dB is ~5.5 at 40 dB SPL. The hook region preparation (GP201) has the highest BF (~30 kHz) and exhibits the sharpest tuning of all, particularly at low-to-moderate SPLs; its Q10dB is ~6.0 at 50 dB SPL. It should be noted 1) that the pure tone sensitivity1 of each preparation depends on both the frequency and the SPL of the stimulus, and 2) that this dependence varies quantitatively from one preparation to another. The responses to near-BF tones become compressively nonlinear at ~30 dB SPL in the apical turn, ~20 dB SPL in the basal turn, and ~50 dB SPL in the hook region (individual IO functions are given in Fig. 3, a-c, to illustrate this point more directly).

CDT responses as a function of primary SPL

BF CDT responses varied strongly with primary SPL in all three regions of the cochlea. As shown in Fig. 3, a-c and g-i, CDT response amplitudes grew nonmonotonically with increases in either L1 or L2 alone. However, when L1 and L2 were increased simultaneously (and by equal amounts), the CDT responses grew more monotonically (see Fig. 4, a-c, for direct illustration, or follow the diagonal dotted lines across the contour plots in Fig. 3, g-i). Peak CDT response amplitudes were normally observed when L1 was close, but not necessarily equal, to L2. When viewed as a set of isoamplitude contours in (L1, L2) space (Fig. 3, g-i), systematic deviations were observed between 1) the conditions necessary to produce maximal response amplitudes at any given L1 or L2 and 2) the L1=L2 line. In most instances, these deviations involve a nonparallel shift of the contour's "axis of symmetry" from the L1 = L2 line. Thus, at low-to-moderate SPLs [e.g., when (L1 + L2)/2 approx  40 dB SPL], the peak CDT responses were observed when L1 > L2, whereas at higher SPLs [e.g., (L1 + L2)/2 approx  80 dB SPL], they were observed when L1 approx  L2. The fact that the hook region data of Fig. 3i do not conform to this pattern may be due to errors in the calibration of the high-frequency acoustic signals involved (see Khanna and Stintson 1985). Data from the hook regions of two other animals showed more pronounced tilts to their axes of symmetry, despite variation in their absolute position in (L1, L2) space.

The phases of the CDT responses also behaved consistently when the SPLs of the primaries were varied. In most instances, CDT phase leads decreased quite strongly at low SPLs with increases in either L1 or L2. At slightly higher SPLs (e.g., for L1 approx  60 dB in Fig. 3d, for L1 approx  65-80 dB in Fig. 3e, and for L1 approx  70-80 dB in Fig. 3f) the phase leads tended to increase with increasing L2, but still decreased with increasing L1. It should be noted that the phase changes occurring when either L1 or L2 were altered were usually much larger than (and generally in the opposite direction to) those that could be predicted on the basis of the amplitudes of the responses to the BF CDTs. The solid lines without symbols in Fig. 3, a-f, show the amplitudes and phases of the three preparation's responses to single tones at their respective BFs. In each instance, the single-tone responses accumulate very little phase as their amplitudes grow across the range covered by the CDT responses, whereas (at least at the low-to-moderate SPLs associated with the ascending limbs of the bell-shaped CDT amplitude curves) the CDT phase leads decrease considerably with increases in either L1 or L2.

CDT responses as a function of primary frequency separation

BF CDT responses varied systematically with primary frequency separation in all three regions of the cochlea. When the relative levels of the two primary stimuli were held fixed, as shown in Fig. 4, both the shape and the sensitivity of the CDT IO functions and the slope of the phase-versus-level curves changed as F1 and F2 were varied. The IO function shape changes were more dramatic in the basal turn and hook region than in the apical turn preparations, and usually involved a transition from almost straight-line IO functions for closely separated primaries (e.g., black-square and square  in Fig. 4, b and c) to more convex, saturating IO functions (e.g., bullet  and open circle ) for wider separations. The phase-versus-level curves (Fig. 4, d-f) ranged from positively sloping functions of increasing SPL for closely spaced primaries (e.g., black-square and square ) to negatively sloping functions for wider spacings (black-diamond , odot ; note that there is a reversal in the phase trends above ~70 dB SPL in the apical turn preparation). In most instances there was a clear accumulation of phase lead with increasing frequency separation, particularly at low-to-moderate SPLs (the basal turn data of Fig. 4e illustrate this point particularly well).

The manner in which the CDT response amplitudes varied with primary frequency separation depended on the level of stimulation and on the region of the cochlea being studied (see Fig. 4, g-i). In the apical turn, CDT responses were largest (in a relative sense---note the effective level metric described in Fig. 4) for F2/F1 ratios below ~1.4, and decreased only moderately as F2/F1 was increased beyond this value (typical rates of decrease were between 40 and 80dB/octave; see Fig. 4g). In the basal turn (Fig. 4h), the largest CDTs were produced at frequency spacings that depended strongly on the levels of the primary stimuli. At low SPLs (e.g., 30 dB), the only CDTs to rise above the noise floor (~40 pm in this instance) were those associated with very closely spaced primary frequencies (i.e., for F2/F1 <=  1.1). At slightly higher SPLs, more widely spaced primaries (e.g., F2/F1 ~ 1.1-1.3) evoked the largest CDTs. Once the F2/F1 ratio increased beyond its optimal value (at any given SPL) in the basal turn, however, the CDT amplitudes fell at a much faster rate than in the apex (note the -200-dB/octave reference line in Fig. 4h). In the hook region (Fig. 4i), the optimal F2/F1 ratios (typically2 between ~1.05 and 1.1) were somewhat lower than those encountered in the basal turn, and the dependence on primary level was less notable. However, the rate of decrease in CDT amplitudes with increasing F2/F1 was similar (typically ~200 dB/octave above F2/F1 approx  1.1). The eventual rates of decrease in CDT amplitudes with increasing frequency ratio (F2/F1) were always reasonably similar to the high-frequency cutoff slopes of the preparation's pure tone tuning characteristics (compare negatively sloping dotted lines in Figs. 2, a-c, and 4, g-i, and see DISCUSSION).

QDT responses

Many of the responses to two-tone stimuli in the apical turn preparations included components at a frequency corresponding to the QDT, F2 - F1 (e.g., see Fig. 1). In some respects, the QDT responses resembled the CDT responses described above, but in other respects the two DP classes differed widely (see below). QDT responses were not explored systematically in either basal turn or hook region preparations (ad hoc measurements of sub-BF QDTs in these regions were always below the noise floor of our measurement technique).

The apical turn QDT responses varied much more than the CDT responses both within and across preparations. This might indicate that the QDTs were more vulnerable to the physiological condition of the preparation. The outcome of some experimental manipulations was certainly consistent with this view. When the two classes of DPs were observed around the time of an animal's death, for example, the QDT responses decreased much more rapidly than the CDTs (this observation is based on data from only 2 animals). However, the QDT responses appeared quite robust in terms of their sensitivity to acoustic overstimulation; when two preparations were subjected to repeated 1-min exposures to high-level (80- to 90-dB SPL) tones at frequencies close to the two-tone primaries (cf. Siegel et al. 1982), two sets of QDT responses suffered only minor decreases in their amplitudes (~2-dB loss recovering progressively over ~2 min) and one set incurred a transient amplitude increase (initially ~3 dB; not illustrated).

Figure 5 illustrates the dependence of one set of QDT responses on the levels of the two primary stimuli, L1 and L2. The stimuli and the preparation responsible for these responses are identical to those in Fig. 3, a, d, and g; only the response component chosen for analysis differs (the BF of the preparation was equal to the CDT, whereas the QDT was 100 Hz higher). IO functions for a single tone at the same frequency as the QDT (600 Hz) are also shown in Fig. 5a ( without symbols). The relative levels of the QDT responses for low-level primaries are very similar to those of the CDT responses. For example, with L1 =L2 = 44 dB SPL, the QDT response in Fig. 5a amounts to 3 nm, which is equivalent to the response evoked by a single 600-Hz tone at 21 dB SPL, whereas the CDT response in Fig. 3a amounts to 2.5 nm, which is equivalent to the response evoked by a single BF (500-Hz) tone at 18 dB SPL. The similar magnitudes of certain CDT and QDT responses often resulted in visible interactions in the response waveforms (note the waveform "beats" in the 2-tone response of Fig. 1, for example).


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  		FIG. 5. Dependence of quadratic difference tone (QDT) responses on stimulus level in the apical turn of the cochlea. Layout and stimulus conditions as in Fig. 3, a, d, and g, with exception that single-tone data (only 2 data sets) relate to QDT frequency of 600 Hz (CH52, BF = 500 Hz).

In most animals, the low-level growth of the QDT response amplitudes with either L1 or L2 was similar to that for the CDT. However, the response phases varied very differently for the QDT and CDT, even when the response amplitudes were well matched. For example, most of the QDT responses in Fig. 5b accumulate phase leads with increases in L1 and phase lags with increasing L2 over the 40- to 60-dB SPL range, whereas the CDT responses (Fig. 3d) accumulate phase lags with increases in either L1 or L2. There are also marked differences in the growths of the two classes of DP at moderate-to-high SPLs, as evidenced by the isoamplitude contours in (L1, L2) space (compare Figs. 3g and 5c). The differences between the QDT and CDT responses do not reflect differences between the processing of sounds at different frequencies (e.g., BF/non-BF); similar results were observed when the QDT was set equal to the preparation's BF and/or when the CDT was set well away from the BF.

Figure 6 illustrates the dependence of the QDT responses in an apical turn preparation on the absolute frequencies of the primary stimuli (F1 and F2, with L1 = L2). In three of the six experiments in which this frequency dependence was tested, the amplitudes of the QDT responses decreased rapidly when F1 and F2 were increased between 2 and 4 kHz, as shown in the figure. In the other experiments, no such decrease was seen, although the relative amplitudes of the QDTs were low even in the range <2 kHz. It should be noted that all of the QDT levels shown in Fig. 6c are significantly higher than those that could be attributed to intermodulation distortion in the stimulus generation system. Effective QDT levels in excess of -60 dB re L1 and/or L2 were observed for at least one (L1, L2) combination (in the 50- to 90-dB SPL range) at every frequency tested in every animal (F1s typically ranged from 2 to 10 kHz in 2-kHz steps).

For the lowest frequencies illustrated in Fig. 6 (F1 = 1 kHz, F2 = 1.5 kHz; black-square), the CDT and QDT coincide at the preparation's BF (500 Hz) and the DP IO function (Fig. 6a) shows an interesting combination of characteristics; its general form is that of a CDT IO function (cf. Fig. 4a), but there is a clear "bump" at ~40 dB SPL where the CDT and QDT seem to interfere constructively. In other preparations, similar stimulus conditions led to distinct notches in the DP amplitudes, presumably reflecting destructive interference between similarly sized QDT and CDT response components (not illustrated).

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

CDT response amplitudes

Mechanical responses to various two-tone DPs (including the CDT, as well as various other 3rd-order DPs) have been noted and/or characterized in several previous reports (Nuttall et al. 1990; Rhode and Cooper 1993; Robles et al. 1990, 1991, 1997). The characteristics of the CDT responses described in the present report are consistent with these reports in almost every respect. The only qualitative difference lies in our observation of nonmonotonic frequency dependencies for some of the CDT response amplitudes. The basal turn data of our Fig. 4h, in particular, are clearly inconsistent with the monotonic, low-pass tuning characteristics described recently by Robles et al. (1997) (see footnote 2 for some concerns about the nonmonotonicities in our own hook region data). The nonmonotonic tuning functions are not without precedent, however; both Robles et al. (1990; experiment L29) and Ruggero et al. (1992; experiment L47) have reported basal turn data from the chinchilla cochlea that are consistent with the present report.

Various rationales have been proposed to explain the tuning properties of the CDT in previous studies. The most basic of these hypothesize that the decreases in CDT levels that accompany an increase in the primary frequency ratio F2/F1 (i.e., the descending, high-frequency limb of the CDT tuning functions) are caused by decreases in the spatial overlap of the mechanical excitation patterns locked to F1 and F2 on the basilar membrane (Goldstein 1967). The data of the present report are entirely consistent with this hypothesis. It is particularly noteworthy that the high-frequency cutoff slopes of the CDT (Fig. 4, g-i) and single-tone (Fig. 2,a-c) tuning functions vary in much the same way with cochlear location. The most likely explanation for this is that the single-tone tuning characteristics underlie the CDT tuning, as proposed by Goldstein (1967). Even the fact that the cutoff slope of the apical turn CDT tuning function (Fig. 4g) is slightly steeper than the relevant single-tone data (Fig. 2a) can be accounted for with the use of Goldstein's proposal, because the site of maximal interaction between the two primary tones (and thus maximal CDT generation) is undoubtedly basal to the site under study, and more basal cochlear locations are generally associated with sharper single-tone tuning.

The origin of the ascending, low-frequency limb3 of the CDT tuning functions, when present, is a matter of speculation. There are presently two schools of thought regarding similar features in DP OAE studies (e.g., Harris et al. 1989). One of these attributes the low-frequency limb of the tuning functions to the effects of a discrete "second filter" in the cochlea (e.g., Allen and Fahey 1993; Brown et al. 1992), whereas the other attributes it to the effects of spatial integration (allowing destructive interference between out-of-phase DP generators) along the length of the cochlear partition (e.g., Neely and Stover 1997; also see Zwicker 1986). Unfortunately, our observations of nonmonotonic frequency dependencies at the level of the basilar membrane do not allow us to distinguish between these two hypotheses. The existence of nonmonotonic tuning at a single point on the basilar membrane can be interpreted as making the second hypothesis unnecessary, but it does not address the issue of the second filter in the first hypothesis directly.4

One further hypothesis regarding the low-frequency limb of the CDT tuning functions is that two-tone suppression might come into effect as both the primary frequencies and the CDT converge (i.e., as F2/F1 decreases toward 1). In fact, the data of the present report strongly support the idea that suppression plays a role in determining the shape of the CDT tuning functions (regardless of their monotonic/nonmonotonic nature). For the most closely spaced primary frequencies (F2/F1 < 1.1) in all three sets of data shown in Fig. 4, for example, F1 is known to have suppressed the F2 responses, and F2 is known to have suppressed the F1 responses, by ~6 dB. [The suppression effects are not illustrated directly in Fig. 4; they were observed by comparing the various response components during either one- or two-tone stimulation, cf. square  and black-square and open circle  and bullet  in Fig. 1 (note that F2/F1 > 1.5 in this instance---more suppression was usually observed between more closely spaced primaries).] It is very likely, therefore, that F1 (and/or F2) was also suppressing the CDTs by >= 6 dB (recall that the effective levels of the CDT were always >= 20 dB below the primary levels. The amount of mechanical two-tone suppression is known to increase both with increasing suppressor level and with decreasing suppressee level; cf. Cooper 1996; Cooper and Rhode 1996b; Ruggero et al. 1992). Because the amount of mutual (F1, F2) suppression always decreased with increasing frequency separation, it is likely that the CDT will also have become progressively more "unsuppressed" as F2/F1 grew. Two-tone suppression thus offers a rather simple explanation for the present mechanical data. Because two-tone suppression is stronger in the basal cochlea than it is in the apex (Cooper and Rhode 1996b; Delgutte 1990), it could even explain the change from monotonic CDT tuning in the apex to nonmonotonic tuning in the base. Two-tone suppression is also likely to have played an important role in other CDT studies (e.g., see Buunen and Rhode 1978; Greenwood et al. 1976; Nuttall and Dolan 1990; Smoorenburg 1972). It should be noted that suppression cannot account fully for the tuning observations made in some DP OAE studies, however, because multiple orders of DP (e.g., 2F1 - F2, 3F1 - 2F2) have been shown to exhibit similar dependencies on absolute frequency when F2 is fixed (see Allen and Fahey 1993; Brown et al. 1992; note that different DPs should be suppressed by different amounts by a given (F1, F2) combination, according to their different separations from the primaries---this is not as observed in the DP OAE studies).

CDT phases

As stated in the INTRODUCTION, only two previous studies have considered the phases of cochlear mechanical responses to the CDT. Rhode and Cooper (1993) reported CDT phases to vary very little with either L1 or L2 in the hook region of the cat cochlea (although phase leads of up to 0.25 cycles were observed above ~90 dB SPL; F2/F1 = 1.056). On the other hand, Robles et al. (1997) reported data from the basal turn of the chinchilla cochlea in which low F2/F1 (<= 1.1) ratio CDTs accumulated phase leads of up to 0.25 cycles as the levels of the primary stimuli (L1 = L2) were increased, whereas high F2/F1 (>= 1.3) ratio CDTs accumulated phase lags of 0.35-0.75 cycles. Most of the phase changes occurred in the 60- to 80-dB SPL range. The data of the present report are consistent with both of these previous reports. The hook region data of Fig. 3f, for example, show low F2/F1 (1.09) ratio CDT phases that vary slowly with L1, and even more slowly with L2, up to ~90 dB SPL. The data of Fig. 4, d-f, confirm the trends revealed by Robles et al. (1997), as well as suggesting that the "definition" of high and low F2/F1 ratios might vary with cochlear location (and/or absolute frequency); the transition between relative lead accumulation and relative lag accumulation occurs at F2/F1 ratios of ~1.2 in the apical turn, ~1.1 in the basal turn, and ~1.05 in the hook region.

The data of Fig. 4, d-f, also reveal a trend in the absolute phases of the CDT responses as the primary frequency spacing (i.e., the F2/F1 ratio) is increased: the responses for high F2/F1 ratios lead those for low ratios by as much as one complete cycle (i.e., 360°). The phase leads are larger in the basal turn than in either the apex or the hook region, and tend to decrease progressively with increasing SPL. These characteristics are remarkably consistent with those observed in previous psychophysical studies. Hall (1972) and Zwicker (1979, 1981), for example, showed CDT phase leads to increase over several cycles with increasing F2/F1. The psychophysical phase changes were largest at low-to-moderate SPLs, and also tended to increase with absolute frequency.

The fact that the phase changes observed in this report (particularly the level-dependent changes) were considerably smaller in the apical turn than in the basal turn may also be relevant to other physiological studies of the CDT. These studies have had mixed results concerning the frequency and level dependence of CDT response phases (see Goldstein et al. 1978). Most studies of CDT responses in the cochlear nerve and anteroventral cochlear nucleus (e.g., Buunen and Rhode 1978; Goldstein and Kiang 1968; Smoorenburg et al. 1976) have found little or no dependence of phase on stimulus level, whereas one (Greenwood et al. 1976) has found systematic phase changes that resemble those observed in psychophysical data (e.g., Goldstein 1967; Hall 1972; Zwicker 1981). Large CDT phase changes have also been observed in inner hair cells in the high-frequency region of the guinea pig cochlea (Nuttall and Dolan 1990). Robles et al. (1997) have recently suggested that at least part of the discrepancy between the physiological and psychophysical findings might have originated in the limited selection of F2/F1 ratios used (and/or the pooling of data across F2/F1 ratios) in the physiological studies. Another possibility, which is supported by the present data, is that the magnitudes of the phase changes vary systematically with cochlear position. With this point in mind, it should be noted that most of the neural data reported to date have been obtained with the use of relatively low-frequency stimuli, such that the observed CDTs fell within the phase-locking range of the auditory periphery (2F1 - F2 << 4 kHz). The only exceptions to this observation occur in the study by Greenwood et al. (1976; their Fig. 9), and it is interesting to note that all of the units that showed large phase shifts with level in that study were relatively high-frequency units (the only unit not to show a large phase shift had a BF of 725 Hz).

QDTs

Many psychophysical investigations have suggested that QDT levels are insignificant at low-to-moderate stimulus levels, and that the QDTs observed at higher SPLs might indicate little about cochlear filtering (for historical reasons, DPs generated by high-level stimuli have often been attributed to nonlinearities in the mechanisms of the middle ear; see Goldstein 1967; Zwicker 1979). Previous studies of the QDT in cochlear mechanics are quite consistent with this view: Rhode (1977) only observed significant QDTs at >100 dB SPL in the first turn of the squirrel monkey cochlea, and Nuttall and Dolan (1993) were unable to observe mechanical QDTs using 30- to 90-dB SPL primaries in the first turn of the guinea pig cochlea. Other physiological data (including those from the apical turn in the present report) demonstrate that QDTs do exist in the cochlea at low SPLs, however. Data from both the cochlear nerve (e.g., Goldstein and Kiang 1968; Kim et al. 1980; Siegel et al. 1982) and the anteroventral cochlear nucleus (Smoorenburg et al. 1976), for example, show QDT phase locking to be prominent at levels well below 60 dB SPL. Nuttall and Dolan (1993) also observed significant levels of QDT response in a series of electrophysiological recordings from the organ of Corti, which [given 1) the apparent lack of a macromechanical input at the QDT frequencies in their study and 2) evidence from physiologically compromised preparations that the inner hair cells in "normal" cochleas were responding to mechanically generated QDTs] led them to suggest that the local QDT must arise in the realm of cochlear micromechanics. The observations of Nuttall and Dolan had little or no impact on propagated QDTs, however [if the locally generated QDTs do not feed back to the basilar membrane (i.e., into the macromechanics of the cochlea), they are unlikely to propagate in the same way that acoustic stimuli do]. The observations made in the apical turn preparations of the present report, as well as the indirect observations made in previous studies (e.g., Kim et al. 1980), imply that QDTs are likely to exist at the macromechanical level throughout the cochlea. Failures to detect mechanical responses to QDTs in the basal turns of the cochlea (such as those reported by Nuttall and Dolan in 1993, and those in the present study) are thus likely to reflect nothing more than limitations of measurement technique.

    ACKNOWLEDGEMENTS

  This work was supported by National Institute of Deafness and Other Communications Disorders Grant 5 R01 DC-01910 to W. S. Rhode and by a Royal Society University Research Fellowship to N. P. Cooper.

    FOOTNOTES

1   It will be noted that the absolute sensitivities shown in Fig. 2 vary by several orders of magnitude across the three preparations. One factor that contributes toward this variation is the radial location of the recording sites: in the apical turn experiment, the recordings were made from a reflective bead placed near the lateral margin of the tectorial membrane (very close to the center of the cochlear partition's cross section); in the basal turn the bead was situated on the basilar membrane beneath the foot of an inner pillar cell (the amplitudes of vibration at this site are typically ~20 dB lower than those near the center of the partition); and in the hook region the bead was within ~40 µm of the center of the basilar membrane. Another factor that contributes strongly to the base-to-apex sensitivity differences is the transfer function of the middle ear: under the open bulla conditions of these experiments, the chinchilla's middle ear is ~2 orders of magnitude more sensitive at 500 Hz than the guinea pig's middle ear is in the 10- to 40-kHz range. 2   Extreme caution must be applied to the interpretation of the tuning data for the hook region, because difficulties often arise in calibrating and controlling stimulus levels in the 30- to 40-kHz region (even when the SPLs are monitored within 1 mm of the tympanic membrane) (see Khanna and Stintson 1985). Having said this, however, nonmonotonic CDT tuning was observed in three of the four hook region preparations where sufficient F2/F1 combinations were used, and a hint of nonmonotonicity was observed in the fourth. Nonmonotonic CDT tuning was also observed in three of the four basal turn preparations where sufficient F2/F1 combinations were used (the 4th preparation was insufficiently stable to comment on its tuning properties). Nonmonotonic CDT tuning was never observed in the apical turn. 3   Our use of the terms "ascending"/"descending" and "low-frequency"/"high-frequency" to describe particular features of the CDT tuning functions deserves some clarification. These terms strictly refer to sections of the amplitude-versus-F2/F1 curves, as observed in the present report (with the use of a fixed DP, variable F1 and F2 paradigm). Researchers in other studies have used different paradigms to study the tuning characteristics of various DPs, such that what we refer to as an ascending low-frequency limb may actually appear as a negatively sloping section on the high-frequency side of some published tuning functions [e.g., in the fixed F2, variable F1 OAE studies of Allen and Fahey (1993) and Brown et al. (1992)]. 4   One way to test the existence of a discrete second filter would be to monitor the amplitudes of several orders of DP (e.g., 2F1 - F2, 3F1 - 2F2, etc.) while F2 is held constant and F1 is varied (e.g., see Allen and Fahey 1993; Brown et al. 1992). This proposition will form the basis of further studies.

  Present address and address for reprint requests: N. P. Cooper, Dept. of Physiology, University of Bristol, Bristol BS8 1TD, England.

  Received 2 January 1997; accepted in final form 21 March 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society



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