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1Laboratory of Auditory Neurophysiology, Medical School, K.U.Leuven, Leuven, Belgium; and 2Department of Neuroscience, Erasmus MC, Rotterdam, The Netherlands
Submitted 7 February 2008; accepted in final form 11 August 2008
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ABSTRACT |
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INTRODUCTION |
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; Wightman and Kistler 1992). The physiological implementation of these comparisons is akin to a process of cross-correlation (Colburn 1977; Stern and Trahiotis 1997; Yin et al. 1986). For many wideband sounds encountered in natural environments, the cross-correlation function of the sound waveforms at the two ears shows a single narrow peak. This peak is at 0 ms for sounds sources in the midsagittal plane and is displaced from 0 ms if the sound source is moved to the right or left, reflecting the interaural time delay (ITD) of the sound between the near and the far ear.
Physiologically, the full bandwidth of the sound waveform is not available to individual binaural neurons because cochlear filtering restricts the spectral window at each point on the cochlear basilar membrane. Each inner hair cell, and its associated peripheral neurons, "listens" to a small range of frequencies. Therefore the effective temporal waveform at the two ears that is being compared by binaural neurons is only a narrowband part of the actual sound. Estimates of the cross-correlation function of the effective waveforms that drive these peripheral neurons show a damped oscillatory pattern, with a large central peak and smaller secondary peaks (Joris 2003; Louage et al. 2004, 2005). The periodicity of these functions matches the center frequency of the peripheral band-pass filter (Louage et al. 2004, 2005; Ruggero 1973), whereas their damping should reflect the filter's spectral bandwidth. Similarly, the so-called noise-delay (ND) functions of binaural neurons also show a damped oscillatory pattern (Geisler et al. 1969; Yin et al. 1986, 1987). Such ND functions are obtained by presenting broadband noise of varying ITD and plotting firing rate as a function of ITD. Psychoacoustically measured "masking-delay" functions also show a similar damped oscillatory shape (Langford and Jeffress 1964; van der Heijden and Trahiotis 1999).
In a prior study, we measured spectral bandwidth in responses of both binaural and monaural neurons (Mc Laughlin et al. 2008). We found that, at a population level, bandwidths were very similar in these two populations. In another study from this laboratory, damping was measured in responses of binaural and monaural neurons (Joris et al. 2005, 2008). Paradoxically, damping was found to be very different in these same two populations. Clearly, the relationship between bandwidth and damping is not straightforward. Whereas in linear systems damping and bandwidth are uniquely related to each other, in binaural and monaural neurons, other factor(s) complicate the relationship. The goal of this study was to identify such factor(s).
If binaural cells would literally perform a cross-correlation operation, their activity would be proportional to the interaural cross-correlation of the stimulus. In reality, the response of binaural cells to changes in interaural correlation is typically nonlinear and differs greatly between cells (Albeck and Konishi 1995; Coffey et al. 2006; Saberi et al. 1998; Shackleton and Palmer 2003; Shackleton et al. 2005; Yin et al. 1987). In addition, cross-correlation analysis of monaural cells also shows a nonlinear relation between stimulus correlation and coincidence rate, although it is more stereotyped than in binaural cells (Louage et al. 2006; Mc Laughlin et al. 2008). We hypothesized that differences in sensitivity to interaural correlation could account for the paradox that neurons of similar center frequency can strongly differ in their damping while having the same spectral bandwidth (BW). In this study, we measured ND functions and aimed at explaining their shapes in terms of both frequency selectivity and sensitivity to interaural correlation using an approach similar to van der Heijden and Trahiotis (1999). We found that indeed the shapes of ND functions are well captured in terms of frequency selectivity and correlation sensitivity.
Our results show an unexpected binaural response feature: in a substantial portion of binaural neurons, the responses depend in a compressive way on stimulus correlation, whereas this relationship is typically expansive in the auditory nerve (AN). Compression is not expected for the binaural circuit as it is commonly conceptualized: a succession of steps of monaural and binaural coincidence detection would predict increasingly expansive rather than compressive sensitivity to interaural correlation. A compressive relationship in binaural neurons has been observed in previous studies but received little attention (Coffey et al. 2006; Shackleton et al. 2005). We found that in the IC, compression is more frequent at very low than at mid-CFs. Consideration of this relationship enables us to give a coherent picture of the shape of ITD tuning in binaural neurons.
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METHODS |
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We recorded from the IC in nine cats and, in a separate series of experiments, from the AN in six cats. All procedures were approved by the K.U.Leuven Ethics Committee for Animal Experiments and were in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals. The experimental procedures were previously reported (Joris 2003; Louage et al. 2004; Mc Laughlin et al. 2008). Briefly, cats with clear eardrums were anesthetized with an intramuscular injection of a 1:3 mixture of acepromazine (0.2 mg/kg) and ketamine (20 mg/kg). Anesthesia for surgical preparation and recording was maintained with pentobarbital sodium infused through a femoral vein to eliminate the withdrawal reflex to toe pinch. The animals were placed on a heating pad in a sound-attenuated chamber. The IC was exposed anterior to the tentorium, and neurons were isolated using glass-insulated tungsten or indium electrodes. The dorsal border of the central nucleus of the IC was defined physiologically by the presence of background discharges phased-locked to binaural beats of low-frequency pure tones (Kuwada et al. 1979), and the IC was histologically processed to confirm the site of recording. In the AN experiments, micropipettes (3 M KCl) were inserted under visual control into the nerve trunk, exposed through a posterior fossa craniotomy.
In both procedures, sounds were presented through dynamic speakers attached to earbars that were tightly inserted into the cut ear canals. The stimuli were generated digitally using commercially available hardware (Tucker-Davis Technologies, Alachua, FL) and were compensated for the acoustic transfer function measured with a probe tube near the eardrum and a 12.7-mm condenser microphone (Brüel and Kjaer). The neural signal was amplified, filtered, displayed, and timed (1-µs resolution).
IC stimuli
NOISE DELAY FUNCTIONS.
We tested the neuron's sensitivity to ITDs by collecting ND functions (Yin et al. 1986). This stimulus consisted of a pair of correlated (A+A+) or anticorrelated (A+A–) pseudorandom broadband noise tokens (lower cut-off 50 or 100 Hz; upper cut-off between 8 and 10 kHz), where A+ represents the original noise token and A– is the same noise token with inverted polarity, which corresponds to a 
phase shift at all frequencies. The ITD within the A+A+ pair was systematically changed, and the response rate of the neuron was measured at each ITD to allow us to collect a "correlated" ND function. Positive ITDs corresponded to the token leading at the contralateral ear (i.e., the token at the ipsilateral ear delayed). The same procedure was repeated with the A+A– pair to measure an "anticorrelated" ND function. Figure 1 shows a cartoon representation of the stimulus and the corresponding response. Typical noise tokens were 1,000 ms in duration repeated between 10 or 20 times every 1,500 ms, or 5,000 ms in duration repeated three times every 6,000 ms. Based on a quick preliminary assessment, the range of ITDs and step increment were chosen to appropriately characterize the shape of the ND function in a reasonable amount of time (
4 min). The first ND function was presented at 60 or 70 dB SPL, and in some cases, ND functions were collected at multiple SPLs. The "best delay" (BD) of the neuron was defined as the ITD at which the difference between the correlated and anticorrelated responses is maximal. This is typically, but not always (see Fig. 6), also the ITD at which the response to correlated noise is maximal.
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) from ND functions. The difcor was calculated by subtracting the anticorrelated response from the correlated response and was normalized by its maximum. THRESHOLD CURVES. The spontaneous rate (SR) was measured, and a threshold tracking algorithm with ipsilateral, contralateral, and/or binaural stimulation (using an ITD equal to the BD) was used to determine the threshold curve characteristic frequency (CFthr). The binaural threshold curve was used in the further analysis. However, when this was not possible, the contralateral or ipsilateral threshold curve was used. The threshold curve bandwidth (BWthr) was measured at 10 dB above CFthr threshold.
Interaural correlation functions
To characterize the neuron's correlation sensitivity we collected rate versus interaural correlation functions (rICFs) for each neuron. Studies in a number of different species have shown that there is a wide variability in rICF shape between different neurons within the same animal (Albeck and Konishi 1995; Coffey et al. 2006; Saberi et al. 1998; Shackleton and Palmer 2003; Shackleton et al. 2005). To measure the rICF, the interaural correlation of the stimulus was varied by mixing independent tokens of broadband noise (Robinson and Jeffress 1963) (see Fig. 1, C and D). Two independent tokens of Gaussian broadband noise (lower cut-off 50 or 100 Hz; upper cut-off 8 or 10 kHz) were either presented unmixed as reference tokens or combined to produce different mixed tokens. By presenting different combinations of mixed and unmixed tokens, at the neuron's BD, we could change the interaural correlation of the stimulus between –1 and 1. For a more detailed description of this stimulus generation, see Fig. 1 or Louage et al. (2006). We measured the response of the neuron while changing the interaural correlation between –1 and 1 in steps of between 0.02 and 0.1. Stimulus duration, repetition interval, and SPL were chosen to be the same as for the noise delay stimulus. The number of repetitions was between 15 and 60 (typically 20) depending on SR.
To quantify the relationship between interaural correlation and spike rate, we fitted a positive or a negative power function (Eqs. 1.1 and 1.2, respectively) to the rICFs
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Shackleton et al. (2005) have shown that these power functions best describe the rICFs measured in guinea pigs. Although not explicitly stated by these authors, inspection of their Figs. 3 and 10 shows that they allowed b to have negative or positive values, whereas p was restricted to values >1. In the fitting procedure used here, b and p could have any positive value but could not be negative. This approach has the advantage that the curvature of the rICF (both for expansive and compressive functions) is completely expressed by one parameter, namely p. Using a power function gives a good fit to responses that are steep around interaural correlations of +1 or –1. The positive power function was fitted to monotonic rICFs, which showed an increasing response rate with increasing correlation (e.g., Fig. 3E), whereas the negative power function was fitted to monotonic rICFs, which showed a decreasing response rate with increasing correlation (Fig. 6E). For the correlation responses, which we visually categorized as nonmonotonic, we fitted Eq. 1.1 to the rising part of the rICF and separately fitted Eq. 1.2 to the decreasing part of the same rICF.
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In the AN, we used exactly the same stimuli as in the IC but presented the stimuli monaurally. An automated tracking algorithm was used to measure a monaural threshold curve from which CFthr, BWthr, and SR were obtained. The noise delay and interaural correlation stimuli were also presented monaurally, playing one token after the other. To allow comparison between the AN and IC responses, we performed a coincidence analysis on the AN data. This allows us to construct pseudo-binaural responses from monaural data. For a detailed description of the reasoning behind the analysis, the reader is referred to Joris (2003), Louage et al. (2004), and Joris et al. (2006).
To measure an ND function, we presented the same noise tokens that were used in IC experiments. The A+ token was presented to one ear, followed by the A– token to the same ear. Noise bandwidth, duration, repetition interval, and SPL range were all the same as for the IC. However, more repetitions were needed than in the IC to allow for better coincidence detection analysis: between 15 and 60 (typically 40).
Coincidence detection analysis consists of counting the number of coincidence spikes, within a particular bin width (50 µs), between two separate spike trains recorded from the same auditory nerve fiber. When there is no imposed delay between the spike trains, counting the number of coincident spikes gives the response at zero delay. To obtain the response at a particular delay, one spike train is time shifted relative to the other, and the number of coincident spikes counted again. To calculate the correlated ND function, this procedure is repeated for all possible pairs of spike trains from the A+ stimulus, and all these contributions are summed. The same procedure is used to calculate the anticorrelated ND function, but now spike trains in response to the A+ stimulus are paired with spike trains from the A– stimulus. As in the IC, we calculated a difcor by subtracting the anticorrelated ND function from the correlated ND function.
Noise tokens such as those used to measure rICFs in the IC were also presented while recording from the AN. Again, noise bandwidth, duration, repetition interval, and SPL were all the same as for the IC, but the number of repetitions was higher (15–60, typically 40). Interaural correlation values were either evenly spaced, as in the IC experiments, or spaced unequally to maximize the sampling close to an interaural correlation of 1 (1, 0.99, 0.96, 0.911, 0.844, 0.76,0, –1) (Louage et al. 2006). The rICF function for the AN was also calculated using coincidence detection analysis. The response to a reference token was compared with the response to a mixed token, giving varying interaural correlation values between –1 and +1. As in the IC, the relationship between interaural correlation and spike rate was quantified by fitting either Eq. 1.1 or 1.2 to the measured correlation function.
Henceforth, the terms ND function, difcor, and rICF refer to the respective functions from either the AN after coincidence analysis or the IC. We use the term "dataset" to refer to the ND functions (correlated and anticorrelated) and the rICF collected from one cell at one SPL.
Extracting BW and CF metrics: curve fitting method
Van der Heijden and Trahiotis (1999) measured ND functions psychoacoustically and used a curve fitting method to extract a BW measurement from their data. Here, we adopt a similar approach to measure BW from physiologically measured ND functions. As outlined in the Introduction, there are two key factors that shape the ND function of an individual neuron—its filter characteristics and its correlation sensitivity. In humans, the psychoacoustically measured relation between interaural correlation and threshold can be approximated by an exponential (van der Heijden and Trahiotis 1997). However, this is not the case for individual neurons, which show a wide range of responses (Albeck and Konishi 1995; Coffey et al. 2006; Saberi et al. 1998; Shackleton and Palmer 2003; Shackleton et al. 2005). To analyze the ND functions, we measure an rICF at the neuron's BD and fit it using the power function given in Eq. 1 (see Interaural correlation functions). Knowing the expected spike rate of a neuron for a given interaural correlation value allows us to directly compare estimated correlation versus delay functions with ND functions (which show spike rate vs. delay).
We can now proceed with determining the filter characteristics of the neuron. Conceptually, one can think of a ND function as the autocorrelation of filtered broadband noise; the correlation of the monaural output from one filter with the monaural output of another identical filter. For curve fitting purposes, we assumed that the power spectrum of the filtered noise had a Gaussian shape with a mean corresponding to the CF of the filter and a BW corresponding to twice the SD. Thus the magnitude spectrum of the filtered monaural input is
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To account for the delay between the two monaural filters, we assume the interaural phase difference (
) is a straight line
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and the intercept on the phase axis corresponds to a phase delay 0 between the two filters. These terms are necessary to account for the phase and time shifts away from zero ITD seen in the IC ND functions. In the AN ND functions, there are no delays, and accordingly, these terms are always zero. The complex transfer functions for the two ears, HL(f) and HR(f), are given by
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Here the (unknown) common phase response of the two ears has been divided out because it does not contribute to the interaural cross-correlation, which is used to predict the ND curves. The binaural filter transfer function was therefore completely determined by four parameters: CF, BW, 0, and . Taking the inverse Fourier transform of HL(f) 
, where the bar denotes complex conjugation, gave the cross-correlation function, i.e., correlation as a function of interaural delay. Using the measured rICF, we converted this cross-correlation function into a spike rate versus delay function, i.e., a predicted ND function. The frequency spectrum of the response to the anticorrelated ND function was estimated using the same parameters as for the response to the correlated ND function but adding to the estimated interaural phase difference. The estimated difcor was calculated by subtracting the estimated correlated ND function from the estimated anticorrelated ND function.
Using this curve fitting approach, we make the assumption that the only factors shaping the ND function are the rICF and the model parameters, namely BW, CF, 0, and . This means that, if there are other factors contributing to the shape of the ND function, they will be reflected in the BW and CF measurements derived from the fit to the ND function.
Extracting BW and CF metrics: application
The application of the curve fitting technique is shown schematically in Fig. 2.
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0 = 0, = 0). Step 2: Using these starting values, Eqs. 2–4 were used to compute an estimated correlated and anticorrelated interaural correlation versus delay function.
Step 3: We used the rICF to convert interaural correlation into spike rate and thus expressed the estimated interaural correlation versus delay functions as spike rate versus delay functions, i.e., estimated ND functions.
Step 4: We calculated the estimated difcor by subtracting the estimated anticorrelated ND function from the estimated correlated ND function and dividing by its maximum.
Step 5: The sum of the squared differences (SSDs) was calculated between the estimated difcor and measured difcor.
Step 6: A minimization method, based on standard built-in functions in Matlab (lsqcurvefit), was used to adjust CF, BW, 0, and .
Steps 2–6 were repeated until a minimum SSD was reached, giving the final estimated of the parameters (CF, BW, 0, ). We refer to this curve fitting method as the temporal method (as opposed to the spectral method; Mc Laughlin et al. 2008) and refer to the estimate of characteristic frequency as CFND and the estimate of bandwidth as BWND. The delay parameters (0 and ) describe the shift in the ND functions away from zero ITD. In this paper, we will not discuss the delay properties of the ND functions and thus will restrict our discussion to the first two parameters: CFND and BWND.
As a measure of the quality of fit, an accuracy factor (Q), based on the amount of variance accounted for by the curve fitting, was defined
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data2 is the variance of the measured difcor. Fits with accuracy factors <70% were excluded from the analysis. AN datasets without rICFs
In the AN, interaural correlation functions were not available for 119 of 167 datasets. Analysis of the datasets with rICFs (see Fig. 10A) showed that the shape of rICF function in the AN was rather constant compared with the shape of the rICF in the IC. Therefore for AN datasets without rICFs, we used a generic rICF with the following values for Eq. 1.1, P = 2, a = 0, and b = 1, matching the shape of the average rICF in the AN. The AN data shown in Figs. 12–14 are based on both measured rICFs and generic rICFs. The AN population data in Fig. 10, A and B, are based exclusively on measured rICFs.
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In both the IC and AN, we grouped the data based on CF. We used the same CF groupings and statistical methods as Mc Laughlin et al. (2008) because we wanted to compare the results of this temporal method for measuring BW with those from our previous study based on a spectral method. Four groups with CFs ranges spanning one octave (187.5<G1
375 Hz, 375<G2 750 Hz, 750<G3 1,500 Hz, 1,500<G4 3,000 Hz) were chosen. We used a two-way ANOVA to test for differences between the mean BW measurements in IC and AN across each CF group. We compared the variances of each CF group using an F-test corrected for multiple comparisons. P < 0.01 was considered statistically significant.
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RESULTS |
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. Inferior colliculus
A typical IC dataset is shown in Fig. 3. The responses to correlated noise (thick line) and anticorrelated noise (thin line) are shown in Fig. 3A. The neuron's BD is indicated by the dashed line on Fig. 3A. The binaural threshold curve, which was collected at the neuron's BD, is shown in Fig. 3B. The threshold curve CF was measured as the frequency at minimum threshold (vertical dashed line), and threshold curve bandwidth was measured as the width of the threshold function 10 dB above the minimum threshold (horizontal dashed line). Figure 3E shows an rICF (solid line), which was also collected at the neuron's BD. This rICF is relatively linear and is well described by the positive power function fit (dashed line; P = 0.88). The difcor, shown as the solid line in Fig. 3C, was calculated by subtracting the anticorrelated ND function from the correlated ND function and normalized to its maximum. The estimated difcor, which has been fitted to the measured difcor, is shown as the dashed line on Fig. 3C. The estimated difcor fits well to the measured difcor (Q = 97.5%), and the corresponding filter shape is shown in Fig. 3D (CFND = 540 Hz, BWND = 132 Hz).
Figure 4 shows an ND function that is heavily "rectified" compared with the ND curve in Fig. 3: the bottom half of the oscillatory pattern is clipped. However, it still follows the pattern of a damped oscillation centered on the BD. This rectification is also seen in the rICF (Fig. 4E, solid line); correlation values between –1 and –0.5 have a spike rate of zero. This nonlinear rICF is well described by the positive power fit (dashed line). The neuron is hardly driven when the correlations falls below zero. When we calculated the difcor (Fig. 4C, solid line), most of the rectification was removed from the response. In this dataset, we can see the estimated difcor (Fig. 4C, dashed line) fits well to the measured difcor. The resulting estimated filter shape is shown in Fig. 4D (CFND = 1,061 Hz, BWND = 354 Hz).
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). The envelope component is visible in Fig. 5A; the responses to the correlated and anticorrelated noise are similar except for a decrease in the response to anticorrelated noise near the cells BD and a slight increase in response at ITDs neighboring the BD. The rICF (Fig. 5B, solid line) shows that this cell has a minimum response to uncorrelated noise and a maximum response to correlated noise. The neuron also shows an increased response to anticorrelated noise, as expected from the ND function. The first part of this concave-shaped rICF was fitted by the negative power function and the second part by the positive power function, as described in Interaural correlation functions. The nonmonotonic response of the neuron to changes in interaural correlation is well described by this fit. Calculating the difcor (Fig. 5C, solid line) removed much of the envelope component from the response. The estimated difcor is shown in Fig. 5C as the dashed line and the corresponding filter shape is shown in Fig. 5D.
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Auditory nerve
A typical "pseudo-binaural" response calculated from AN data is shown in Fig. 7. The ND function shows the same damped oscillatory pattern as seen in the IC (Fig. 7C). The response to correlated noise (thick line) shows a peak at zero delay where the response to anticorrelated noise shows a trough (thin line). This is expected for a monaural response. This fiber has a nonlinear rICF (Fig. 7B, solid line), and the power fit captures the response well (dashed line; P = 1.67). The difcor is well fit by the estimate (Fig. 7E), and the resulting filter shape is shown in Fig. 7D (CFND = 463 Hz, BWND = 171 Hz).
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Correlation functions.
To show systematic differences between the shapes of the rICFs in the AN and the IC, we plot the power (p) of the fit from Eq. 1 as a function of CF (Fig. 10A). Here, we use functions from both this study and the previous study (Mc Laughlin et al. 2008). Nonmonotonic rICFs fitted by both the negative and positive power functions were excluded from this analysis. AN fibers with a low SR (SR < 18 spikes/s) are shown as gray triangles and high SR fibers (SR 
18 spikes/s) are shown as black triangles. There is no clear trend for low or high SR fibers to have a particular power. It is clear from Fig. 10A that the IC (
) shows a wider range of powers than in the AN. In the AN, across the entire CF range, virtually all rICFs (33/34) were expansive (power > 1). Only one rICF in the AN was found to be slightly compressive (P = 0.82). However, in the IC almost one third of the rICFs (9/31) were compressive (power < 1). Most of these neurons have CF <1 kHz (7/9).
As mentioned in the Introduction, one puzzle is that neurons in the AN and IC with similar CF have also similar BW (Mc Laughlin et al. 2008) (see also Fig. 12C, below), but differ in their damping (Joris et al. 2008). To examine whether the shape of the rICF function may explain this puzzle, we compare damping and p in Fig. 10B, using the peak ratio measure of the correlated ND function as used in Joris et al. (2005) based on Yin et al. (1986). We defined the central peak (CP) as the largest peak in the ND function and the secondary peaks (SP) as the next two closest peaks (Fig. 11G). The peak ratio was calculated as the height of the SP closest to zero delay divided by the height of the CP. The IC data show a clear negative correlation between the power of the fit to the rICF and the peak ratio of the correlated ND function. The range of powers and corresponding peak ratios seen in the AN are much smaller than in the IC and viewed alone would not show a strong correlation. However, the values measured in the AN overlap with those measured in the IC and, when viewed as part of a larger population, they support a general relationship between ND function damping and the expansiveness of the rICF. The three AN fibers with the highest CFs are marked 1–3 on Fig. 10. The ND functions of these fibers contain a strong envelope component, and the relationship between peak ratio and rICF expansiveness seems to be different from in fibers with lower CFs.
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CF versus BW
In the following population plots, AN data are shown as filled triangles and IC data are shown as open circles. Datasets recorded from the same cell at different SPLs are joined by a line.
Figure 12A shows the BWND as a function of CFND for the IC neurons. There is a clear positive correlation between CFND and BWND. The results from the AN data are shown in Fig. 12B. Again, there is a clear positive correlation between BWND and CFND. There are more data points at CFs >1.4 kHz for the AN than for the IC. This simply reflects our focus on binaural processing of fine structure and the fact that the transition from fine structure to envelope occurs at higher CFs in the AN than in the IC (Joris 2003; Louage et al. 2004). In the AN, as in the IC, there is a systematic increase in BWND with increasing CFND up to 2 kHz. Between 2 and 3.5 kHz, as the upper limit of phase-locking in the AN is approached, we see a less steep increase in BWND with increasing CFND. Figure 12C shows the same data as in A and B but now plotted together on log axes. There is no clear separation between BWND measured in the AN and BWND measured in the IC. In fact, there is considerable overlap between BW estimates from IC and AN data across the entire range of CFs. The inset in Fig. 12C shows the mean BWND in each octave-wide CF group in the AN (solid line) and the IC (dashed line). There were no data points in the highest CF group for the IC population. The error bars indicate the SD in each group. Using a two-way ANOVA, we did not find any statistically significant differences between the mean BWND measurements for IC and AN across each CF group. However, comparing the variances between the AN and IC, we found that the IC group centered at 551 Hz had a significantly greater variance than the corresponding AN group (F-test, P < 0.01). The differences in variance between the other AN and IC groups were not significant.
A number of psychoacoustic studies have used broadband stimuli to measure binaural critical bands in humans (Kohlrausch 1988; Kollmeier and Holube 1992; van der Heijden and Trahiotis 1999). They report BWs of between 80 and 120 Hz for filters centered at 500 Hz. This range is marked by the box centered at 500 Hz on Fig. 12C. Similar measurements of monaural critical bands centered at 500 Hz have been reported (Bourbon and Jeffress 1965; Fletcher 1940). This range of human critical bands is within the lower range of the BWs measured in cat IC cells with CFs 500 Hz. It is also lower than any BWs measured in the cat AN fibers with CFs 500 Hz. This finding is in line with a report on sharper frequency selectivity in humans compared with laboratory animals (Shera et al. 2002), but it should be noted that there are many uncertainties in relating physiological data from animals to psychophysical data from humans.
BW versus SPL
It has been shown that cochlear BW increases with increasing SPL (Evans 1977; Rhode 1971). In both the AN and the IC, we collected data at multiple SPLs for a number of cells. These data are shown in Fig. 13, where each animal is represented by a different symbol, and data from the same cell are joined by a line. In general, the IC data showed a mild tendency to increase in BWND with increasing SPL (Fig. 13A). Using linear regression, we fit a straight line through the data points for each fiber in Fig. 13A and used its slope as a measure of the change in BW. The average slope for all fibers showed an increase in BWND of 1.0 Hz per 1-dB increase in SPL. A stronger tendency for BWND to increase with increasing SPL was seen in the AN. Here, the average increase was 3.5 Hz/dB increase in SPL (Fig. 13B). When the AN data were restricted to the same range of CFs seen in the IC data, the average increase was 2.4 Hz/dB.
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To allow comparison between the temporally based BW measurement (BWND) described here and the spectrally based BW measurement (BWSP) described in Mc Laughlin et al. (2008), we collected both ND functions and "fflip functions" (obtained from noise with a spectrally varying interaural phase) from the same cells in the IC (50 datasets in 31 cells) and AN (40 datasets in 26 cells). Figure 14 compares the estimates of CF and BW obtained from these neurons using the two separate curve fitting methods. The estimates from the spectral method are denoted by CFSP and BWSP.
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DISCUSSION |
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). This result is confirmed in this study, using a different analysis (Fig. 12C). On the other hand, AN fibers and IC neurons behave differently regarding damping (Joris et al. 2005, 2008), which seems at odds with their similarity in BW. We show here that sensitivity to interaural correlation is key to understanding these differences. Whereas AN fibers show a stereotyped response to changes in interaural correlation, the response of IC neurons is more varied, and they can show compressive rICFs, particularly at CFs <1 kHz. These results show that understanding sensitivity to interaural correlation is a key issue to address in further studies of mechanisms of binaural hearing. Interpreting the ND function
The interaural correlation of a filtered broadband noise stimulus changes as the ITD of the stimulus is changed. Therefore a ND function will reflect the neuron's sensitivity to changes in interaural correlation as well as reflecting the characteristics of the auditory filter. In this study, we separated these two factors and obtained a measure of BW from the ND functions that was independent of interaural correlation.
The separation is shown in Fig. 11, which shows an AN fiber and an IC neuron with similar CFs. Although the ND functions have different damping patterns, the BW is very similar for the two neurons. This is because their rICFs are markedly different. The AN fiber has an rICF with power >1, which means that when the correlation between the stimuli increases, the coincidence rate increases expansively. This expansive behavior elevates the central peak of the ND function at 0 delay, which is the only delay at which the correlation approaches 1. In contrast, the correlation values at the secondary peaks are well below unity, leading to a reduced coincidence rate. This gives the ND functions of the AN a heavily damped shape. Conversely, the IC neuron has a compressive rICF, which suppresses the central peak of the ND function, giving it a less damped shape.
To allow us to separate the effects of the auditory filter from the effects of correlation sensitivity on the ND functions, we measured the rICF for individual neurons and incorporated this information into the curve fitting method. Another way to reduce the effect of the nonlinear rICFs on the ND function is by calculating a difcor (Joris 2003); this tends to remove much of the rectification and, more generally, has a linearizing effect (cf. A and C in Fig. 4). However, calculating the difcor does not always remove all nonlinearities from the response. Figure 11, J and K, illustrate this point: the difcor of the AN and TB fibers still show a strong central peak caused by a nonlinear response to changes in interaural correlation.
BW measurements
We showed that BW measurements can be derived from ND functions in both the IC and the AN. The BW measurements derived from the ND functions show a strong positive correlation with BW measurements obtained from a spectrally manipulated stimulus in a previous study. There was a fairly even spread of data points on either side of the line of equality for both the AN and the IC (Fig. 14A), indicating that there was no tendency for one method to estimated a higher BW than the other. The CF estimates from both methods were virtually identical.
Comparison of the BW estimates show that there is considerable overlap between the range of BWs seen in the AN and the IC (Fig. 12C). When we grouped the BWs based on CF (Fig. 12C, inset), we could find no statistically significant differences between the mean BWs in AN and IC. However, the variance of the IC group centered on 551 Hz was statistically greater than the variance in the equivalent AN group, indicating a greater spread of BWs in the IC at this CF range. The variances in the other groups were not significantly different. The ND function BW measurements support the main conclusion from Mc Laughlin et al. (2008) that BW in the IC is not significantly greater than in the AN.
The data presented here show a clear increase in measured BW with increasing CF in both the AN and the IC (Fig. 12). This finding is in agreement with the previous study (Mc Laughlin et al. 2008), as indicated by the strong correlation between the two measurements of CF (Fig. 14B), and also agrees with earlier studies carried out in the AN (Carney and Yin 1988; De Boer and de Jongh 1978; Evans 1977; Kiang et al. 1965; Liberman 1978; Pfeiffer and Kim 1972; Ruggero 1973) and the IC (Joris et al. 2005). As in the previous study, we found that an increase in SPL leads to an increase in BW in both the AN and the IC. In both studies, the effect of SPL on BW is rather small. In the previous study, we found an increase in BW in the IC of 3.4 Hz/dB; in this study, we found an increase of 1.0 Hz/dB. The discrepancy could be caused by the slightly different CF populations sampled in each study. The AN shows quite a consistent picture of increasing BW with increasing SPL whereas in the IC, there are some cells that show a decreasing or nonmonotonic dependence of BW on SPL.
Interaural correlation
Albeck and Konishi (1995) looked at rICFs in the barn owl at different levels in the binaural pathway. They classified them using three categories, linear, parabolic, and ramp, and found a predominance of different categories at different levels of the binaural pathway. They found that parabolic rICFs were dominant at the level of the nucleus laminaris (NL; the first site of binaural interaction in the owl—equivalent to the medial superior olive in the mammal). The anterior division of the lateral lemniscal nucleus (VLVa) and the core of the central nucleus of the IC (ICcC) were dominated by linear rICFs, whereas ramp rICFs were most common in the lateral shell of the central nucleus of the IC (ICcLS) and external nucleus of the IC (ICx). Fitting these data with a power fit showed a general progression from P = 2 in the NL to P = 1 in the VLVa and ICcC and finally back to P > 2 in the ICcLS and ICx. Shackleton et al. (2005) measured rICFs in the IC of the guinea pig and classified these using a power fit. They reported a wide range of shapes of rICF with powers ranging from 1 to 5 and the majority falling between 1 and 2. However, it should be noted that, although Shackleton et al. (2005) do show compressive rICFs in some figures, they do not report values of P < 1. This is because they used different constraints in their fitting procedure. Compressive rICFs were fit with positive P values but had a negative value for parameter b (Eq. 1). Using these constraints means that the curvature of the rICF cannot be expressed in one single parameter. Coffey et al. (2006) used power fits as well as linear, parabolic, and ramp categories to classify rICFs in subcollicular, IC, and cortex neurons in the rabbit. They found that most subcollicular and IC neurons had a linear or parabolic response, whereas in the auditory cortex, parabolic responses where most frequent. Coffey et al. (2006) also reported a minority of IC neurons with compressive rICFs. However, they did not observe that the majority of compressive rICFs came from neurons with CFs <1 kHz. This may be because of differences in the species.
Using our coincidence analysis technique (METHODS), we calculated what an rICF would look like at the level of the AN or more precisely: the rICF of a simple coincidence detector with two identical AN inputs. In Fig. 10, we plotted the shape of the rICF as a function of CF for the AN and the IC. The power of the fit for rICFs in the AN had a mean value of 2.2 and an SD of 0.70. Simple narrowband noise correlation models (Albeck and Konishi 1995; Shackleton et al. 2005) have shown that this shape of rICF results when a half-wave rectification step is included in the model. This suggests that at the level of the AN, most of the nonlinearities present in the rICF, measured at a constant SPL, are accounted for by half-wave rectification. A minority of AN responses show a more linear rICF, which may result from a deviation from half-wave rectification caused by a high spontaneous rate, resulting in a linearization of the response. Shackleton et al. (2005) found powers of between 1.1 and 1.8 when using a model of the hair cell (Meddis et al. 1990) for the transduction stage followed by a coincidence detector with one input on each side.
At the level of the IC, there is a large variation in the shapes of the rICFs that we measure (power = 2.02 ± 1.53). We see extremely expansive rICFs with powers as high as 5. We also see strongly compressive rICFs, particularly at lower CFs, which are not present at the level of the AN. Shackleton et al. (2005) also reported a wide range of shapes of rICF in the guinea pig, but direct comparison with their study is difficult given the differences in the fitting procedure.
Relationship between damping and bandwidth
In linear systems, BW and damping are uniquely related, but this is not the case for the neurons studied here. We found that BWs in the AN and the IC are the same across different CF groups (Fig. 12C and Mc Laughlin et al. 2008). This seems at odds with the finding that damping in the IC remains constant with CF (Joris et al. 2005), whereas it increases at low CFs (<500 Hz) in the AN (Joris et al. 2008). Clearly, there must be a factor(s) besides BW that affects damping. Our data show that sensitivity to correlation is at least part of the explanation. The rICF distribution in the IC shows that neurons with CFs <1 kHz are more likely to show a compressive rICF than neurons at higher CFs (Fig. 10A). Such compression affects the height of the central peak of ND functions more than the secondary peaks, resulting in ND functions with a less damped shape than AN fibers of a similar CF. At CFs >1 kHz, IC neurons are less likely to have compressive rICF powers and generate ND functions that are more strongly damped. This relationship between damping of the ND function and the expansiveness of the rICF is clearly shown in Fig. 10B. In summary, our data suggest that the different damping patterns seen in ND functions for AN and IC neurons with similar CFs, (Joris et al. 2005, 2008) are not caused by differences in BW but are caused by differences in correlation sensitivity, generated somewhere between the AN and the IC. Although AN fibers differ little in this sensitivity, it varies greatly in IC neurons.
At this point, we can only speculate regarding the mechanisms causing the changes in correlation sensitivity between AN and IC. It is straightforward to account for increased expansion in correlation functions by increasing the number of inputs to the coincidence detector or by invoking a second level of coincidence detection (Shackleton et al. 2005; Stern and Trahiotis 1992). Indeed, a preliminary analysis of data published in Louage et al. (2005) shows that for bushy cells, which provide input to the medial superior olive where the first temporal binaural interaction occurs, rICFs are even more expansive than in the AN (cf. Fig. 11, middle column). This is intriguing because it indicates an increase in importance of stimulus correlation between the AN and bushy cells, which is lost at the level of the IC. That loss does not seem to come at a cost in binaural performance at the single neuron level: neural thresholds are similar for bushy cells and IC neurons for the two binaural tasks of decorrelation detection and ITD discrimination (Louage 2007; Louage et al. 2006; Shackleton et al. 2003, 2005). Apparently the decreased sensitivity in terms of spike rate is offset by an improved "statistical quality" of the neural coding. It is unclear how to account for the more frequent occurrence of compressive rICFs in the IC, both in functional terms (does this benefit binaural hearing?) and in terms of mechanisms. The underlying mechanism(s) could be as simple as rate saturation or could reflect more complex convergence effects at monaural or binaural levels. Viewing of the drastically different ND functions in Fig. 11, G–I, obtained from neurons with very similar CF and BW, underscores the profound effects of correlation sensitivity on the shape of ND functions. Understanding the underlying mechanisms should be an aim of future studies, because it will certainly bring deeper insight in binaural hearing.
Comparison of temporal and spectral methods
As mentioned previously, if the binaural system was linear, the damping of the ND function would be directly related to the BW of the underlying filter. The output of binaural neurons, however, is not always linearly related to the interaural correlation of the stimulus. This complication must also be taken into consideration when we interpret the response to the spectral stimulus used in our previous study. Here, the independent stimulus variable was defined in the frequency domain: the flip frequency (fflip). For a given broadband binaural stimulus, all frequencies below fflip were anticorrelated and all frequencies above fflip were correlated. Again, if the binaural system was linear, the response to this spectral stimulus would directly reflect the amount of correlated stimulus energy falling within the filter for the given fflip, and a measurement of BW could be directly derived from the response of the neuron to changes in fflip. However, the response of the neuron is not linearly related to the correlation of the stimulus and so again we have to take the rICF into account before we can estimate BW from the response to the spectral stimulus. Figure 14A shows a direct comparison of the BW derived using both methods for the same neurons. Although there is some scatter, there is generally good agreement between the two measures of BW. This consistency across methods supports the notion that the output of binaural cells is well predicted by the interaural correlation of the effective monaural stimuli, regardless of the specific method in which the decorrelation is realized: interaural delay, frequency-dependent phase reversal, or frequency-independent mixing of independent noise sources. This is a nontrivial observation, because dependencies on the "origin" of correlation could easily arise by a convergence across CF or best ITD, either in monaural inputs or at the binaural level. From our data, however, there is no reason to assume that the sensitivity to interaural correlation of binaural cells depends on the origin of the correlation.
Concluding statement
We end by summarizing the series of studies from this laboratory regarding the comparison of damping, BW, and correlation sensitivity in AN and IC. We first give an overview in "absolute" terms (Hz, ms) and then in relative terms (normalized to CF).
BW, measured either spectrally (McLaughlin et al. 2008) or from delay functions (this study), increases with CF but does not differ on average between AN and IC (Fig. 12). If bandwidth would completely determine the damping of the delay functions, damping would also increase with CF. At a qualitative level, this is indeed the case: an increase in damping (measured as a decrease in half-width of delay functions) is observed both in the IC (Joris et al. 2005) and the AN (Joris et al. 2008).
If bandwidth would be constant relative to CF (traditionally measured with the Q10 value, i.e., CF/tuning curve bandwidth at 10 dB above threshold), damping would also be constant when expressed relative to the CF or the corresponding period. However, it is well known that the sharpness of tuning increases with CF. This increase of sharpness is apparent in Fig. 12B, where the growth of bandwidth with CF does not follow a fixed proportionality factor (for reference, the dashed line on Fig. 12B shows Q10 = 3), but instead shows an increase of Q10 with CF. Increased sharpness of tuning predicts that delay functions would be less damped (more oscillatory) at high CFs than at low CFs, when this damping is expressed in terms of number of characteristic periods (1/CF). Indeed, the half-width of delay functions in the AN occupies only about one characteristic period or less at low CFs and about two to four periods at mid-CFs (Fig. 6A in Joris et al. 2008). Thus the delay functions in the AN become more oscillatory with increasing CF, consistent with the increased sharpness of spectral tuning.
Against the backdrop of the rather stereotyped and expected results in the AN, the shape of delay functions in the IC proved to be surprisingly invariant with CF. ND functions in the IC show more scatter in the range of damping observed, but this range changes little with CF when expressed with a relative metric (Fig. 6C in Joris et al. 2008). These results show that this invariance is caused by a "compensating" effect of correlation sensitivity, shown in Fig. 15 with simulated difcors and their envelope (dashed lines) from which damping is measured as the width at half-height (vertical and horizontal lines, see Joris et al. 2005). Autocorrelation functions of cochlear basilar membrane motion (Fig. 15, A and B), have more characteristic periods within the damping envelope at mid-CFs than at low-CFs, reflecting the sharper frequency tuning. In the AN (Fig. 15, C and D), this difference between low and mid-CFs is amplified because of rectifying effects of inner hair cell transduction causing an expansive nonlinearity in the relationship between stimulus correlation and spike timing. Thus the difference in number of cycles contained within a half-width is larger between D and C than it was between B and A. In bushy cells recorded in the TB (Louage et al. 2005, 2006; unpublished results) this difference between low and mid-CFs is even more striking (not shown, but see Fig. 11). In the IC (Fig. 15, E and F), the shape of the ND functions is similar across CFs. At the population level, BWs are similar in AN and IC, and the invariance in shape in the IC seems to originate with a CF-dependent sensitivity to interaural correlation. In the IC, compressive relationships between rate and interaural correlation are seen at low CFs (<1 kHz; Fig. 15E, inset), whereas at high CFs, the relationship is more likely to be expansive (Fig. 15F, inset). As a result, an approximately equal number of cycles is present within the width at half-height of both "IC neurons," despite their difference in frequency tuning. Thus the net effect is that the shape of delay functions is more invariant in the IC (compare E to F) than in the AN (compare C to D).
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: P. X. Joris, Lab. of Auditory Neurophysiology, Campus Gasthuisberg O&N 2, Herestraat 49 bus 1021, B-3000 Leuven, Belgium (E-mail: Philip.Joris{at}med.kuleuven.be)
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ABSTRACT
INTRODUCTION
