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Laboratory of Auditory Neurophysiology, Medical School, K.U.Leuven, Leuven, Belgium
Submitted 27 May 2004; accepted in final form 25 August 2004
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). This phenomenon, which is called two-tone suppression (2TS), can be quite pronounced; under some conditions, the second tone (the suppressor) completely shuts down the neural activity evoked by the first tone (the probe). Psychophysically this would correspond to the suppressor rendering the probe inaudible: the suppressor is said to mask the probe. Indeed, the work of Delgutte (1990) has shown that, in addition to excitatory effects, 2TS is a major determinant of auditory masking and that many aspects of masking can be quantitatively understood from 2TS.
In most physiological studies of suppression, the frequency probe is chosen around the characteristic frequency (CF) of the fiber, while the frequency of the suppressor can either be slightly above or well below CF. These two cases are termed high- and low-side suppression, respectively. The mechanisms underlying suppression are not known in any detail, but contributions of cochlear-mechanical origin are likely. Two-tone suppression has indeed been demonstrated in the vibration of the basilar membrane (Rhode and Robles 1974), although it is presently unclear whether all aspects of suppression observed in the AN have a cochlear-mechanical origin (Robles and Ruggero 2001).
A striking feature of 2TS is its speed. Arthur et al. (1971), who used a gated suppressor to suppress a sustained probe, found that suppression begins and ends within 
2 ms of the beginning and end of the suppressor. This latency of suppression was sufficiently short for the authors to rule out efferent pathways as the source of 2TS. On the other hand, the method of gating the suppressor did not yield precise estimates of latency because "the latency measurement was complicated by the requirement that the [suppressor] rise decay had to be smoothed to avoid a transient response that obscured both the onset and the termination [of suppression]." More generally, it will be difficult to obtain precise estimates of latency from gated suppressors because latencies in the response to sharp stimulus onsets are poorly defined: different definitions of latency lead to different answers. These difficulties stem from the failure of any band-limited system to transmit ideal transients. To avoid the problems associated with the timing of transients, the speed of suppression might be examined from the way in which an ongoing suppressor shapes the response to the probe. This amounts to determining the delay of suppression rather than its latency (cf. Møller 1975).
For suppressors at sufficiently low frequencies ("bias tones"), the response to CF tones is modulated by the suppressor waveform in a cycle-by-cycle fashion as can be evaluated by computing cycle histograms at the suppressor frequency (Cai and Geisler 1996a; Sachs and Hubbard 1981; Temchin et al. 1997). This phasic or AC component of 2TS suppression is restricted to low-frequency suppressors (<4 kHz). The mere existence of an AC component at suppressor frequencies upto a few kilhertz confirms that 2TS is a fast phenomenon. In principle, the AC component could be used to quantify the delay of suppression by measuring how the phase of 2TS varies with the frequency of the bias tones, but we are not aware of any such attempts. It should be pointed out, however, that the method of bias tones has its limitations and drawbacks in this context. First, even at high suppressor levels, the AC component rapidly declines when the suppressor frequency exceeds 3 kHz (Cai and Geisler 1996a). Second, the high sound levels of bias tones often result in multimodal cycle histograms ("peak splitting") that complicate the temporal analysis.
In this study, we introduce an alternative method to measure the speed of suppression based on the use of narrowband rather than tonal suppressors. The fluctuating envelope of a sustained narrowband suppressor modulates the response to the probe in a simple way: maxima in the envelope of the suppressor cause minima in the response and vice versa. The speed with which the suppressor modulates the AN response can be determined by computing the group delay of the modulations. Unlike the method of low-frequency bias tones, in our method, there is no restriction in the choice of suppressor center frequency other than the requirement of suppression.
Group delays measured in this way reflect the delay between the acoustic presentation of the suppressor and its effect as a suppressor in the AN response. This delay includes traveling-wave delays, a potential build-up of the mechanism of suppression, and a synaptic delay. To tease apart these different contributions as much as possible, we also measured the group delay of the response to the probe and the group delay of the response to the suppressor when presented in isolation (i.e., when acting as an excitor rather than as a suppressor). Above-CF suppressors do not evoke a response when presented in isolation except when presented at very high sound levels. The comparison between excitation and suppression can thus not be made for high-side suppressors. We therefore restricted the present study to low-side suppression.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Cats with normal eardrums and air-filled middle ears were anesthetized with a mixture of acepromazine (0.2 mg/kg) and ketamine (20 mg/kg). A venous canula allowed infusion of Ringer solution and pentobarbital sodium at doses sufficient to maintain an areflexic state. After a tracheotomy, the pinna and temporalis muscle of one side were removed, and the bulla was exposed and vented with a 30-cm-long polyethylene tube (0.9 mm ID). The animal was placed in a double-walled soundproof room (Industrial Acoustics Company, Niederkrüchten, Germany). Through a posterior fossa craniotomy, a small portion of the cerebellum was aspirated and the auditory nerve exposed. A plastic base was glued to the skull to support a hydraulic microdrive (Trent Wells, Coulterville, CA). A glass micropipette, filled with 3 M NaCl, was positioned in the AN under visual control, and warm agar was poured over the exposure to reduce pulsations and prevent dissecation.
Hard- and software environment
A dynamic phone (supertweeter, Radio Shack, Forth Worth, TX) was connected to a hollow Teflon earpiece that fit in the transversely cut ear canal. Custom software, run within Matlab (The MathWorks, Natick, MA) on a personal computer, was used to calculate the stimuli and control the digital hardware (Tucker-Davis Technologies, Alachua, FL). The transfer function of the closed acoustic assembly was obtained via a probe, the tip of which was placed within a few millimeters of the tympanic membrane and which was coupled to a 1/2-in (12.7 mm) condensor microphone and conditioning amplifier (Bruel and Kjaer, Nærum, Denmark). All stimuli were compensated for this transfer function, and the stimuli were specified in SPL (dB re. 20 µPa). The stimuli were computed digitally and presented at a sampling rate of 125 kHz through a 16-bit D/A converter (Tucker Davis Technologies System II). The full 16-bit range was used to sample the stimuli; levels were adjusted by analog attenuation.
After conventional amplification and filtering (300 Hz to 3 kHz) of the neural signal, spikes were converted to standard TTL pulses with a custom-built peakpicker (Carney and Yin 1988). These pulses were time-stamped to an accuracy of 1 µs (ET-1, Tucker-Davis Technologies). Spontaneous rate (SR), minimum threshold, and CF of single fibers were determined with an automated tuning curve program.
Stimuli
Our aim is to determine the delays with which the envelopes of narrowband stimuli are coded by AN fibers. The basic idea is that the neural response decreases when the suppressor envelope increases. Rather than evaluating suppression in terms of average rate, we employ a temporal measure of suppression, namely, the way in which the response is modulated by the suppressor.
In principle, the delay of suppression could be estimated by varying the modulation rate of sinusoidally amplitude-modulated (SAM) tones. It is more efficient, however, to combine the different modulation frequencies into a single stimulus. To this end, we employed a particular type of tone complex the primary components of which are irregularly spaced in such a way that the frequency difference of any pair of primaries is unique among the set of all primary pairs. Tone complexes with this property are called zwuis stimuli (van der Heijden and Joris 2003). The usefulness of zwuis stimuli is based on the fact that the spectrum of the envelope of tone complexes is dominated by the frequency differences among the primaries ("beat frequencies"). The irregular frequency spacing of the six primaries results in a particularly rich envelope spectrum. For example, a zwuis complex with six primaries results in 15 distinct beat frequencies. In contrast, a six-component harmonic complex would yield no more than five different envelope components. The concurrent presence of many envelope components has the additional advantage that it justifies the use of linear analysis techniques (e.g., Fourier analysis) despite the nonlinear character of auditory peripheral coding: each component is one of many so that its effect, being small, may be linearized. The mathematical details of this argument are given in van der Heijden and Joris (2003); essentially the same argument underlies the use of reverse correlation techniques in auditory neurophysiology (de Boer 1967).
The spacing of the primaries in our stimuli was irregular but only slightly different from an evenly spaced complex. The average distance between adjacent primaries was varied between 100 and 300 Hz. Thus the beat frequencies of our stimuli ranged from 100 to 1,500 Hz. Such envelope frequencies are low enough to be coded by the AN of the cat (Joris and Yin 1992). Group delays were estimated by an analysis of the phases of the beat components in the AN response. This analysis is described in RESULTS.
Figure 1 schematically illustrates the two stimulus configurations of this study. In the first configuration (Fig. 1A), two different 6-tone complexes are simultaneously present: a probe complex and a low-side suppressor complex. In the example shown the probe is centered around 8 kHz; the low-side suppressor is centered around 3 kHz. Importantly, suppressor and probe each have their own, unique, set of beat frequencies. Study of the response envelope components at these frequencies allows the extraction of the delays of both the probe and the suppressor from a single response to a single stimulus.
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15 dB above threshold. The sound level of the suppressor was adjusted to partially suppress (modulate) the response to the probe in the way described in METHODS. This adjustment is critical: if the suppressor level is too low, it has no observable effect on the AN response to the probe; if the suppressor level is too high, the suppressor starts to drive the AN fiber on its own account instead of modulating the response to the probe. We found that, given a fixed probe level, there was usually only a narrow range (<15 dB) of suppressor levels for which the suppressor can be shown to modulate the AN response to the probe. The low-side suppressors used in this study were on the average 25 dB above the level of the probe. The second stimulus configuration (Fig. 1B) differs from the previous one by the absence of the CF probe—only the low-side suppressor is present. Because there is no probe to suppress, the suppressor can only act as an excitor by itself. It is important that the identical tone complex ("low-side suppressor") is playing two different roles in the two conditions: as a suppressor (Fig. 1A) and as an excitor (Fig. 1B). The comparison of delays across these two conditions is critical in the analysis of temporal aspects of suppression.
Stimuli were presented with 500-ms cos2 on- and offset ramps and had a duration of 45 s. Starting phases of the individual primaries were selected at random from a uniform distribution. If necessary (e.g., low spike rates), presentation was repeated. Adjustment of levels to meet the criteria described in the preceding text was based on on-line analysis of the data.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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The data presented in this study were obtained from from eight ears of six cats. The CFs of the fibers ranged from 2 to 37 kHz. A total of 633 datasets was collected from 120 AN units.
Figure 2 illustrates our method of extracting delays from the AN responses. Data obtained from a single AN fiber with a CF of 8,240 Hz serve as an example. We first discuss the suppressor-alone condition of Fig. 1B. In our example, the low-side complex consisted of primaries at 2,668, 2,856, 3,045, 3,231, 3,418, and 3,610 Hz. The spectrum of the envelope of this stimulus (Fig. 2A) is dominated by the 15 dominant beat frequencies, obtained by subtracting any two of the primary frequencies. These beat frequencies range from 186 to 942 Hz, which is well within the range of phase-locking to stimulus envelopes at this CF (Joris and Yin 1992). Indeed, the response showed significant vector strengths to each of the 15 beat frequencies at a confidence level of P = 0.001 according to Rayleigh statistics (Mardia and Jupp 2000).
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) approximates a straight line with zero intercept (Fig. 2B, —), indicating an overall delay of the envelope. Although the slope of this phase-frequency curve provides a direct estimate of the group delay amounting to 1,319 µs, we preferred a more elaborate analysis in which the relative phases of the primaries are constructed from the phases of the beats. For the details of this computation, the reader is referred to van der Heijden and Joris (2003). The resulting phases of the primaries (Fig. 2C) were fit with linear regression and yielded an estimated group delay of 1,323 µs. We now turn to the stimulus condition in which a CF probe and a low-side suppressor were presented together as displayed in Fig. 1A. Both tone complexes have their own, distinct, set of beat frequencies. This allows separate analyses of their delays from the response to a single stimulus. As before, the phases of the beat components are expressed re the corresponding phases of the stimulus. The beat phases of the probe are shown as x in Fig. 2B. Again, the frequency-phase pattern approximates a straight line with zero intercept. After reconstructing the primary phases, the delay of the response to the probe was computed, yielding a value of 1,960 µs (not shown). Note that this value is higher than the delay of the low-side suppressor when acting as an excitatory stimulus. This is consistent with the steeper descent of the envelope phases (Fig. 2B, x).
From the same response we reconstructed the phases of the low-side suppressor for the suppressor+probe condition. The phases of the beat frequencies of the suppressor are shown as 
in Fig. 2B. The frequency-phase curve again approximates a straight line, the downward slope of which indicates a delay. This time, however, the intercept of the line is close to 0.5 cycle. This implies that the envelope of the suppressor is coded by the AN fiber in an inverted fashion: maxima in the envelope correspond to minima in the response and vice versa. This is exactly the effect that a suppressor is supposed to have (see INTRODUCTION). In fact, during the experiments, we used this phase inversion as a criterion for the occurrence of suppression. After taking the phase inversion into account, the primary phases of the suppressor were reconstructed as before (Fig. 2C, ). The group delay derived from the primary phases amounts to 1,675 µs. This value is larger than the delay observed when the same low-side complex acted as a excitor (Fig. 2, B and C, ) but smaller than the delay associated with the probe centered around CF (x).
Note that the suppression phase at the highest beat frequency (942 Hz) is not plotted in Fig. 2B. It was omitted because phase-locking to this frequency did not reach a Rayleigh significance of P = 0.001. Beat components that did not reach this significance level were not included in the calculation of group delays. Moreover, we required a minimum of three beat frequencies per primary with significant phase-locking for that primary phase to be included in the analysis, and a minimum of four primaries had to be obtained for an estimate of group delay to be included.
For 100 different AN fibers, we were able to measure the delay of low-side suppression according to the preceding criterion. For many of these fibers, multiple sequential datasets showed suppression, yielding a total of 307 estimates of suppression delay. The center frequency fsup of the low-side suppressor was varied across measurements. An overview of the conditions is provided in Fig. 3, which displays fsup of the effective suppressors as a function of CF (an effective suppressor is one that yielded suppression). Low-side suppression occurred for a wide range of suppressor frequencies <0.8 x CF. This wide range of effective low-side suppressor frequencies is consistent with classic neural data on 2TS (Schmiedt 1982).
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Recall that our data yield estimates of three types of delays: the delay of the low-side complex acting as an excitor, the delay of the CF probe, and the delay of the low-side complex acting as a suppressor. Using the same symbols for the three different types as in Fig. 1, the corresponding population data are shown in Fig. 4, which displays the delays as a function of CF. In Fig. 4, — are best-fitting second-order polynominals; their coefficients are given in the legend.
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) and from AN recordings in the cat for CFs between 2 and 20 kHz (van der Heijden and Joris 2003). The delay of CF probes (Fig. 4B) decreases from 2,200 µs for CFs around 5 kHz to 1,700 µs for CFs of 
15 kHz. In contrast, the delay of low-side complexes (Fig. 4A) does not depend on CF; its value is 1,475 µs for the whole range of CFs. The remaining type of delay is that of the suppression evoked by the low-side tone complex (Fig. 4C). For CFs >15 kHz, this "suppressive delay" practically coincides with the excitatory delay of the same low-side stimuli. But unlike the latter data, suppressive delay does depend on CF, lower CFs yielding higher delays. For CFs <10 kHz, the suppressive delay lies between the excitatory delays of the low-side complex and the CF probe.
The difference in delay evoked by the same low-side stimulus in its two roles of excitor and suppressor is elaborated in Figs. 5 and 6. Figure 5 is a scatter plot of excitation delay (abcissa) versus suppression delay (ordinate). Each symbol represents a pair of measurements in which these delays were measured in the same cell and using the same low-side complex at the same intensity. Different symbols are used for different CF ranges. This plot shows that for CF >15 kHz, there is little difference in delay between excitation and suppression. For CF <10, suppression is systematically slower than excitation. In the intermediate range of CFs, the difference is smaller but still present. We will refer to this difference as the "excess delay" of suppression.
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400 µs for CFs <10 kHz and disappears for CF >15 kHz.
There is considerable scatter in the delay data of Figs. 4–6. Some of the scatter, but not all of it, is due to inter-animal differences (Fig. 6). We tested if this variation could be linked to any quantity other than CF and animal but were not able to find any systematic effect in our data. The parameters considered were suppressor frequency, ratio of suppressor frequency to CF, spacing of the suppressor components, threshold of the fibers, their spontaneous rate, and their driven rate. Some of these parameters certainly affect other aspects of suppression (e.g., Cai and Geisler 1996a, b; Delgutte 1990; Temchin et al. 1997), and we do not wish to imply that none of these factors can affect the temporal aspects of suppression addressed in the present study. Our data collection was restrained by an interactive search for those values of stimulus parameters that allowed an assesment of the timing of suppression (see METHODS). Considering the limited recording time per fiber, the experiments left little room for a systematic variation of stimulus parameters, let alone a balanced design.
Ability of suppression to follow the envelope of the suppressor
We tested whether suppression is more "sluggish" than excitation in the sense that fast fluctuations in the low-side stimulus would be effectively weakened when it acts as a suppressor. An example of such sluggishness can be observed in Fig. 2, where the highest beat frequency of the low-side complex (942 Hz) evoked phase-locking when the low-side complex acted as an excitor (), but not when it acted as a suppressor (). A direct comparison between suppression and excitation was possible because these two effects of a same low-side complex were examined in many fibers (Fig. 5). Significance (P < 0.001) of phase-locking to the envelope frequencies of the low-side complex was used as an index of temporal acuity. For different ranges of envelope frequencies, we counted the number of recordings in which these envelope frequencies evoked significant phase-locking and we expressed these numbers as a percentage of the measurements in which those beat frequencies were present in the stimulus. This was done separately for the excitation and suppression data.
Figure 7 displays the resulting histograms. For the excitation data (Fig. 7A), a high fraction (close to 80%) of the beat frequencies <500 Hz evoked phase-locking. For higher envelope frequencies, this fraction slowly decreases to 60% at 1,500 Hz (no data are available for envelope frequencies >1,500 Hz). This slow decline of phase-locking with modulation frequency agrees with data on phase-locking to SAM tones in the cat AN nerve (Joris and Yin 1992).
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The second difference between the panels of Fig. 7 is the dependence on envelope frequency. The suppression data (Fig. 7B) show a band-pass character rather than the low-pass character of the excitation data (Fig. 7A). The decline of phase-locking toward low frequency is suggestive of an adaptation to slow variations in suppressor level. The rather sharp decline at envelope frequencies >1,250 Hz is reminiscent of the decline of the AC component of suppression for pure tone suppressors >1 kHz (Cai and Geisler 1996a).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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In view of the compressive nature of the coding of sound by the auditory periphery, it is important to note that any instantaneous saturating nonlinearity will produce suppression. This is so because a secondary input acts as a bias that pushes the system away from the range of its steepest transfer, thus lowering the net gain. As a result, the response to the primary input is suppressed by the secondary input. Consistent with this theoretical observation, a memory-less saturating nonlinearity forms the core element of many models of 2TS (e.g., Pfeiffer 1970; Sachs and Abbas 1976). In physiologically oriented models, the nonlinearity is explicitly identified with a particular stage of transduction, e.g., the sigmoid curve relating transducer current of outer hair cells to deflections of the stereocilia (Geisler 1992).
In the following, we first illustrate that a saturating nonlinearity by itself is insufficient to explain 2TS because it is inconsistent with two fundamental aspects of 2TS in the AN. We then explore two alternative compressive schemes to explain suppression and discuss how our data can add to an understanding of the mechanisms underlying 2TS.
Asymmetry between probe and suppressor
In the AN, tones at frequencies well below CF are potent suppressors of CF probes but have not been observed to be suppressed themselves by tones of any frequency—be it above, around or below CF. This asymmetry of suppression is unexplained by a simple instantaneous nonlinearity because, to produce suppression, suppressor and probe must have comparable amplitudes at the input of the nonlinearity. This, however, will always result in the mutual suppression of the two stimulus components.
In many models, the observed spectral asymmetry is realized by a filter at the output of the nonlinearity that rejects the suppressor (e.g., Pfeiffer 1970). Now this creates a new problem: the filter will also reject low-frequency tones when they are presented alone, contradicting the observation that excitatory thresholds of tones below CF are often comparable to their thresholds for suppressing a CF probe (Schmiedt 1982).
The most straightforward way out of this dilemma is to add a "linear bypass" that allows the low-frequency components to play an excitatory role in addition to their role as suppressors. Stated independently of any particular model, we hypothesize that the excitation and suppression evoked by the same low-side suppressor reaches the AN fiber either by two independent mechanisms or via two different mechanical paths. This hypothesis provides the background of the remaining discussion.
Sluggishness of suppression
A second, perhaps more fundamental, shortcoming of an instantaneous nonlinearity as a model for 2TS is its failure to reproduce the observed sluggishness of suppression. The AC (phasic) component of 2TS in the AN declines at lower frequencies than does phase-locking to tones or SAM tones (Cai and Geisler 1996a) while the DC component persists. Remarkably, the AC component of 2TS in the vibration of the basilar membrane seems to be limited as well: the AC component declines >7 kHz (Cooper 1996), whereas, again, a DC component persists—there seems to be sluggishness even in the mechanical response of the cochlea. As discussed by Geisler and Nutall (1997), this poses a fundamental problem to the construction of a single compressive I/O function to account for 2TS on the basilar membrane. Our study was not specifically aimed at testing an upper frequency limit in the AC component of suppression, but Fig. 7 is nevertheless of relevance. Unlike the previous cases, where sluggishness was reflected in the reduced ability of suppression to follow the fine-structure of the suppressor, our data suggest a reduced inability to follow fast fluctuations of the envelope of the suppressor.
The sluggishness of suppression, both at the cochlear-mechanical stage and in the AN, suggests that suppression results from some type of automatic gain control (AGC) rather than from an instantaneous compression of the waveform. An AGC mechanism adapts its gain based on an integrated measure of the stimulus strength. In a typical implementation, this measure is obtained by rectification and low-pass filtering of the waveform (leaky integrator). Noninstantaneous compressive schemes of the AGC type produce the DC component of suppression that schemes based on instantaneous nonlinearities fail to explain. Cai and Geisler (1996c) present a model of suppression in the AN in which AGC plays a central role. Interestingly, a gain-control mechanism for 2TS in the basilar membrane was also considered by Cooper (1996) in an entirely different context, viz., phase shifts of the probe evoked by the suppressor.
For an AGC scheme to be compatible with the spectral asymmetry of suppression observed in the physiology, a careful distinction is needed between those stimulus components that control the gain and those that are controlled by it. The "controlled frequencies" are confined to a relatively narrow range around CF. The range of controlling frequencies is wider: it includes both frequencies above CF that do not evoke excitation by themselves (high-side suppressors) and frequencies below CF that do evoke excitation (low-side suppressors). The latter excitation, however, is not in turn suppressed by any other components. Thus as in the case with the instantaneous nonlinearity, it seems inevitable to postulate a linear "low-frequency route" that bypasses the compressive path (the compressive path now being represented by the AGC mechanism).
Two potential origins of the excess delay
We now consider the small but systematic excess delay of suppression re excitation (Fig. 6). The delays shown in Fig. 6 seem to have a phasic counterpart in the data of Rhode and Cooper (1993), who measured 2TS at the level of the basilar membrane. They observed a 100-µs delay between the displacement caused by a 1-kHz bias tone and its peak effectiveness in suppressing a CF tone at 30 kHz. While this delay is small, it is still about three times the period of the CF probe. Therefore suppression in this case cannot be explained by an instantaneous compressive nonlinearity of the type discussed above. The same is true for our Fig. 6: for CFs <10 kHz, the excess delay certainly exceeds the period of a CF tone (for reference, the · · · in Fig. 6 corresponds to 2 periods of the CF).
We can think of two potential origins of the excess delay associated with suppression. First, the very mechanism of suppression may take some time. Any AGC mechanism has an integration time, i.e., a window over which the level of the output is integrated. The excess delay observed would then reflect the time constant of the gain-control mechanism. Thus the existence of excess delay may be viewed as another argument (in addition to sluggishness) in favor of an AGC basis of 2TS. Cai and Geisler (1996c) do include in their model a low-pass filter at the control input of the AGC but do not evaluate the effect of such a filter on the delay of suppression.
The alternative explanation of the extra delay of suppression considers the location of the interaction between suppressor and probe. From basilar-membrane mechanics (Robles and Ruggero 2001) and from AN measurements (van der Heijden and Joris 2004), it is known that a traveling wave of a given frequency travels from base to apex at an initial high speed. Only when approaching its best site does it slow down. This underlies the observed larger delay of CF probes compared with that of the low-side stimulus (Fig. 4A). We will use the terms "fast wave" and "slow wave" for the traveling waves associated with the low-side suppressor and the CF probe, respectively (eventually also the fast wave will slow down when approaching its own best site, apically from the region of interest, but that is irrelevant here).
Figure 8 is a sketch of the situation. The waves are represented by their envelope. Vertical tick marks indicate the time it takes the waves to travel from point to point; they are like the ticks of a clock traveling with the wave. Thus densely spaced ticks correspond to slow wave propagation. The innervation site of the AN fiber from which the recording is obtained ("recording site" in brief) is indicated by the letter R.
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The two explanations of excess delay are readily stated in terms of the working hypothesis proposed in the preceding text: in the AGC scheme, the excess delay arises because suppression is mediated by a slower mechanism than excitation; in the travel time (TT) scheme, the excess delay is explained as a difference in travel time between two alternative routes. The two proposed explanations do not necessarily exclude each other but could coexist.
To test the TT scheme, it would be nice to be able to move the recording site basally while employing the same stimulus configuration. In terms of Fig. 8, this would amount to measuring along the path between R and S. If the TT scheme was correct, the excess delay would gradually decrease when moving toward S, and vanish when reaching S, the hypothetical site of suppression. Unfortunately, when recording from the AN, one cannot choose the CF of the fibers encountered. For a number of nerve fibers, though, we were able to do the mirror experiment, i.e., determine the excess delay for several different probe frequencies. This amounts to shifting the entire excitation and suppression pattern of Fig. 8 while fixing the recording site. The level and frequency of the suppressor was kept constant across measurements. Before presenting these data, we consider what each of the two proposed schemes would predict.
Figure 9 shows the predictions for a 10-kHz fiber. The suppressor frequency is well below CF (say 4 kHz) and the probe frequency is varied between 8 and 11 kHz. The horizontal line (· · ·) indicates the delay of the low-side complex in its excitatory role, that is, the delay of the fast wave. The symbols in Fig. 9 indicate the delay of the suppression () and the delay of the probe (X) as a function of probe frequency. The height of the above the line is the excess delay. Around CF (10 kHz), the probe arrives at the recording site with a large delay due to the slowing down of its traveling wave. As the frequency of the probe is lowered, the slow part of its traveling wave will shift apically. At the fixed recording site, the delay of the probe will decrease—eventually it will reach the low value corresponding to the fast wave marked ( · · · ). The effect of probe frequency on probe delay is purely a matter of traveling waves and is not affected by assumptions regarding suppression. The predictions of probe delay are therefore identical in the two panels of Fig. 9.
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9.5 kHz in Fig. 9B). Figure 10 shows the effect of probe frequency on delays measured in four fibers. The CFs of the fibers are indicated by diamonds on the abcissa. We would not call these data conclusive, but they do seem to favor the AGC scheme rather than the TT scheme.
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). In fact, the mere occurrence of suppression for probe frequencies below CF (Fig. 10) supports this notion of a "basal shift." It is true that such a shift will always result in travel-time differences of the type considered in the preceding text (Fig. 8). The crucial question, however, is whether these travel-time differences are sufficiently large to account for the excess delay of suppression. This is a fundamental issue: if the travel-time differences are insufficient (as suggested by Fig. 10), then the delayed action of suppression must be an inherent property of the interaction between suppressor and probe, implying that the very mechanism of suppression is not instantaneous.
It is important that the AGC invoked to account for the excess delay has to be operating in the mechanics of the cochlea as opposed to AGC-mechanisms that modify transduction by the hair-cell/nerve-fiber complex (Geisler and Greenberg 1986). The latter type of AGC cannot account for disparities between delays of suppression and excitation because these disparities preceed the transduction stage. For a discussion of cochlear-mechanical AGC, see Zwislocki et al. (1996).
Implications of AGC-related delays
What will be the most salient consequences of a delayed action of auditory compression (as in AGC) to the coding of sound in the auditory periphery? In the case of transient stimuli such as clicks, the compressive portion of the response is expected to lag an earlier linear reponse. The cochlear-mechanical click responses of Recio et al. (1998) indeed show such a delayed onset of compression. In the interpretation of such data, however, it is difficult to disentangle the effects of dispersion of the traveling wave from the effects of any inherent delay of auditory compression.
In the case of narrowband stimuli such as bands of noise or tone complexes, the adjustment of the gain will lag the envelope of the stimulus, causing the envelope of the AGC output to "overshoot" following each minimum of the stimulus envelope. A preliminary numerical analysis (not shown) revealed that the effects of the delayed gain control on the stimulus envelope are similar to the effects of adaptation: overshoot, a moderate (6 dB) boost of the higher envelope frequencies and a small (<80 µs) net advance of the envelope (the overshoot effectively advances the upward slopes of the envelope). These small effects of AGC-related delays on the peripheral coding of bandlimited stimuli are not expected to interfere much with the interpretation of physiological data for which temporal coding of envelope is essential, such as the estimation of group delays and the reconstruction of cochlear phase transfer from AN responses to tone complexes (van der Heijden and Joris 2003).
Even though AGC-related delays will have relatively little impact on envelope coding of bandlimited stimuli, the situation is drastically different for those aspects of peripheral coding that owe their existence to auditory nonlinearity, such as suppression and distortion. Because these are purely nonlinear phenomena, they are sensitive to the exact character of the nonlinearity that creates them. This includes the dynamical aspects of the nonlinearity. The delay and the sluggishness of suppression have been amply discussed in the foregoing. As for distortion products, AGC-related delays can be expected to significantly affect their phases. In all, there appear to be several promising openings for further investigation of the temporal aspects of cochlear nonlinearity.
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GRANTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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FOOTNOTES |
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Address for reprint requests and other correspondence: M. van der Heijden, Laboratory of Auditory, Neurophysiology, O. and N. Campus Gasthuisberg, Herestraat 49 - bus 801, B-3000 Leuven, Belgium (E-mail: Marcel.vanderHeyden{at}med.kuleuven.ac.be)
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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