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The Journal of Neuroscience, July 1, 2001, 21(13):4844-4851
Tuning to Interaural Time Differences across Frequency
Douglas C. Fitzpatrick1 and Shigeyuki Kuwada2 1 Department of Surgery, University of North Carolina, Chapel Hill, North Carolina 27599-7070, and 2 Department of Neuroscience, University of Connecticut Health Center, Farmington, Connecticut 06030-3405
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Interaural time differences (ITDs) are an important cue for azimuthal sound localization. Sensitivity to this cue depends on temporal synchrony to the waveform (i.e., phase locking) that begins in the hair cells and is relayed to the neural comparators. The synchrony function is low-pass. Therefore, it is expected that neural tuning to ITDs will become narrower with frequency according to a 1/frequency function. To test this, we measured ITD tuning across frequency in neurons from the superior olivary complex, the dorsal nucleus of the lateral lemniscus, the inferior colliculus, the auditory thalamus, and the auditory cortex. For some neurons in each nucleus, the ITD tuning width did become systematically narrower by the expected 1/frequency relationship. However, in other neurons the ITD tuning width was nearly constant across frequency. Constant ITD tuning width was infrequently observed in neurons of the superior olivary complex but was common in neurons in structures above the superior olivary complex. The nearly constant ITD tuning was caused both by sharper ITD tuning at low frequencies and broader tuning at higher frequencies within the low-frequency band. Neurons with nearly constant tuning to ITDs may be the mechanism underlying the perception of ITDs in humans in which just-noticeable differences to changes in ITD decrease by less than the 1/frequency prediction.
Key words: auditory neurophysiology; auditory pathways; interaural temporal disparities; sound localization; low-frequency hearing; low-frequency signals
INTRODUCTION
An important cue for the azimuthal location of sound sources is the difference in the times of arrival of sounds at the two ears or interaural time differences (ITDs). The neural coding of ITDs begins in the superior olivary complex (SOC), where inputs from the two sides first converge. After this, the ITD information is sent to higher centers, e.g., the dorsal nucleus of the lateral lemniscus (DNLL), the inferior colliculus (IC), the auditory thalamus, and the auditory cortex.
The cochlea is arrayed according to frequency, and each of the major brain centers where ITD is encoded has a cochleotopic organization. Thus, the frequency of sounds is an important parameter that is likely to influence the manner in which ITDs are encoded. Indeed, critical to modern models is the mechanism by which ITD is integrated across frequency (Colburn, 1973
; Stern and Colburn, 1978
However, if the loss of sensitivity at low frequencies were caused entirely by a constant degree of synchrony, the behavioral function would be expected to decline by 1/frequency (1/f) as the frequency is lowered. Instead, the actual decline is considerably <1/f. A possible reason is that synchrony beyond the auditory nerve is not constant with frequency, as has been shown recently for some neurons in the anteroventral cochlear nucleus (Joris et al., 1994b
MATERIALS AND METHODS
Single and multiunit recording was performed in female Dutch-Belted rabbits (1.5-2.5 kg). Surgical and experimental procedures have been described previously (Kuwada et al., 1987
Surgical procedures. All surgery was performed using aseptic techniques on rabbits with clean external ears. Under anesthesia (ketamine, 35 mg/kg, i.m.; xylazine, 5 mg/kg, i.m.), a square brass rod was anchored to the skull using screws and dental acrylic. Several days later, the animal was reanesthetized, and a small rectangular hole (~3 × 4 mm) was made in the skull overlying the intended structure. The hole was covered with sterilized medical elastopolymer. At this time, custom ear molds were made for sound delivery.
Recording procedures and data collection. All recordings were conducted in a double-walled, sound-insulated chamber. The awake rabbit was placed in a body stocking from which its head protruded, seated in a padded cradle, and further restrained using nylon straps. The stocking and straps provided only mild restraint, their primary purpose being to discourage movements that might cause injury to the rabbit. The rabbit's head was fixed in a constant position by clamping to the surgically implanted brass rod. After the rabbit was secured, the elastopolymer covering was removed to expose the opening in the skull. To eliminate possible pain or discomfort during the penetration of the electrode, a topical anesthetic (lidocaine) was applied to the dura for ~5 min and then removed by aspiration. With these procedures, rabbits remained still for a period of
2 hr, an important criterion for single-neuron recording. Typically, a rabbit participated in daily recording sessions over a period of 2-6 months. A session was terminated if the rabbit showed any signs of discomfort. The rabbit's comfort was a priority both for ethical reasons and because movements made it difficult to record from single neurons.
Extracellular recordings were made with glass-coated, platinum-tungsten microelectrodes (tip diameter of 1-2 µm; impedances of 10-30 M
). The action potentials of single neurons or small clusters of neurons (two to three neurons) were amplified 5,000-20,000 times, isolated with the aid of a time/amplitude window discriminator (BAK Electronics, Germantown, MD), and timed relative to the stimulus onset with an accuracy of 10 µsec. Recordings that consisted of more than a few relatively large spikes were not included. For the "small cluster" recordings, we set the amplitude trigger high and used a narrow time window. Consequently, the small cluster recordings were probably dominated by the response of a single unit.
Acoustic stimulation. Stimuli were generated by a two-channel digital stimulation system (Rhode, 1976
Sensitivity to ITDs was primarily assessed using binaural-beat stimuli. For low-frequency sounds (<2.5 kHz), the binaural-beat stimulus was created by delivering tones to the two ears that differed by 1 Hz, which resulted in a continuously varying ITD that ranged over (±) a period of the tonal frequency (Kuwada et al., 1979
Data analysis. We divided our sample into peak- and trough-like neurons on the basis of their characteristic phase (Fitzpatrick et al., 2000
We used the width of ITD tuning at the 50% response level between the maximum and minimum responses as a measure of the tuning to ITDs. To calculate these 50% ITD tuning widths, a 20-bin period histogram was first converted to interaural time on the basis of the frequency of the stimulus. Twenty bins were empirically found to be optimal for achieving an accurate measure of the tuning width (i.e., adding more bins did not substantially influence the width) while maintaining a smooth enough curve that the width could be reliably measured. As a test of whether the curve was in fact smooth enough, the 50% width was calculated in two ways: first, by starting from the peak of response and then traveling down the curve on both sides until the points of 50% response were reached and, second, by starting from the trough of response on each side and traveling up the curves until the points of 50% response were reached. If the widths calculated from these two measures differed by >50%, the data were not used; otherwise the two measures were averaged.
After the ITD tuning width was determined for each frequency, the points were plotted as log frequency versus log width, and a regression line was computed. If the widths decreased by 1/frequency, the slope of the regression line was expected to be
1. The correlation of the regression line (r) was not a reliable test for linearity because it is affected by the slope of the line. A test that overcomes this problem compares the mean square error of the best-fit line with that obtained from a random simulation (Yin and Kuwada, 1983
RESULTS
The recordings were of either single neurons or small clusters of neurons (two to three neurons). The illustrated examples are all from single neurons. The summary data are from pooled single neurons and clusters of neurons because no notable differences were found when multiple-neuron recordings were included. A total of 712 neurons were recorded. Of these, 47 (23 single) were from the SOC, 138 (57 single) were from the DNLL, 301 (186 single) were from the IC, 90 (48 single) were from the auditory thalamus, and 136 (73 single) were from the auditory cortex.
Neurons had different forms of ITD tuning across frequency
Some peak-like neurons displayed ITD tuning functions that followed a 1/f relationship (e.g., Fig. 1A). In this example, the width of the ITD curves systematically increased as frequency was decreased (Fig. 1A, top panel). When the log width was plotted against log frequency (Fig. 1A, bottom panel), the slope was nearly
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Figure 1. Examples of different forms of ITD tuning for peak-like neurons. A-F, For each neuron, the top panel displays the ITD functions across frequency, and the bottom panel plots log frequency versus log peak width (solid lines). Dashed lines in bottom panels are the predicted 1/f function (slope =
However, other peak-like neurons did not follow a 1/f relationship. For example, the neuron in Figure 1B displayed ITD tuning widths that changed by <1/f (slope =
The responses in Figure 1A-C were recorded from neurons in the IC. A similar range of ITD tuning functions was seen at other brain levels (Fig. 1D-F). Figure 1D shows an example of an SOC neuron in which the change in ITD tuning width across frequency closely followed a 1/f relationship. Figure 1E is an example from a DNLL neuron in which the ITD tuning width changed by <1/f, and Figure 1F is an example of a neuron from the auditory cortex in which the ITD tuning width was nearly constant across frequency.
Figure 2 compares the distribution of slopes of the log width versus log frequency for different structures along the auditory pathway. The primary difference in the distributions was that whereas in the SOC (Fig. 2E) there was approximately an equal number of neurons with slopes steeper or flatter than 1/f (dashed line, slope =
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Figure 2. Distribution of the slopes of the log peak width versus log frequency function for peak-like neurons at different levels along the auditory pathway. The number of neurons and the mean slope for each level are indicated. The distributions, especially above the level of the SOC, are skewed to the right of a slope of
Curiously, the mean slopes of the DNLL and IC were similar but then became slightly steeper at the thalamic and cortical levels. This change was primarily caused by an increase in the number of neurons in the thalamus and cortex with slopes that were steeper than 1/f. Thus, although the proportion of neurons with constant or near-constant tuning widths increased above the level of the SOC, the proportion of neurons with slopes steeper than 1/f also increased above the level of the IC. It is difficult to explain these changes. Perhaps neuron with slopes steeper or flatter than 1/f serve different functions. It is also possible that the steeper slopes were an artifact of behavioral state. Although our preparation is unanesthetized, the behavioral state of the animal is unknown. Thalamic and cortical neurons are especially vulnerable to behavioral state (e.g., alert or sleeping, anesthetized or unanesthetized).
What frequencies are associated with relatively constant ITD tuning?
It is of interest whether the tendency toward constant ITD tuning widths across frequency is created via broader tuning to ITDs at higher frequencies or sharper tuning at lower frequencies. It appears that both occur. Figure 3 compares the average ITD tuning widths as a function of frequency for a group of neurons that displayed slopes near 1/f (i.e., slopes ±0.25 of
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Figure 3. Mean peak widths in cycles as a function of frequency for two populations of neurons: those that had slopes (log width versus log frequency) that were near a 1/f relationship (i.e., ±0.25 of
A mechanism for creating neurons with constant peak widths
Inhibitory mechanisms may play a role in maintaining constant peak widths across frequency (Fig. 4). Figure 4A-L is a series of poststimulus time histograms, each showing the response to 1.1-sec-long tones in each ear at a frequency of 900 Hz at a different static ITD. As the static ITD was systematically changed, the response to the tone was suppressed below the spontaneous rate (dashed lines) at some ITDs (Fig. 4A-C,G-I) and enhanced at others (Fig. 4D-F,J-L). These differences resulted in a cyclic response to ITD (Fig. 4M, closed circles). When the ITD was suppressive, there was a response when the tone was turned off (Fig. 4A-C,G-I), and this off response was also cyclic with ITD (Fig. 4M, open circles). The suppression below the spontaneous rate at unfavorable ITDs along with an off response is consistent with an inhibitory input onto this IC neuron. Without this inhibition, it is likely that the peak width of the excitatory response would be broader.
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Figure 4. An IC neuron that shows excitatory-inhibitory interactions that may serve to create constant peak widths. A-L, Poststimulus time histograms to different static ITDs. The tones were 1100 msec long and were presented every 1300 msec. Dashed lines reflect the mean spontaneous activity. M, ITD functions plotted separately for the on response (filled circles, 100-1100 msec) and off response (open circles, 1120-1300 msec). Labeled responses refer to histograms. The rebound, off response, and suppression below the spontaneous rate at unfavorable ITDs suggest local inhibition. Because the inhibitory ITD function is out-of-phase and overlaps the excitatory ITD function, it could serve to decrease the peak width of an excitatory input. SPL, Sound pressure level.
Figure 5 plots the on and off response as a function of ITD at several stimulating frequencies for the neuron in Figure 4. The on response displays a near-constant ITD tuning width across frequencies (Fig. 5A). This neuron was the same as that shown in Figure 1C, so the constancy in peak widths across frequency was similar whether the change in ITD was dynamic (Fig. 1C) or static (Fig. 5A). When the peak portion of the on response was plotted with the off response (Fig. 5B), the trough portions of the off response flanked and overlapped the borders of the peak response at all frequencies. The relation between the on and off functions was more clearly visualized when the on and off ITD functions were averaged separately across frequency (Fig. 5C). Here, the inhibition at unfavorable ITDs (inhibitory surround) was almost symmetrical about the excitation at favorable ITDs (excitatory center). In a simple scheme, the trough widths of the inhibitory surround should be constant across frequency to create peak responses of constant width. However, our estimates of the shape of the inhibitory surround are prone to error because this shape is solely based on the magnitude of the off response. Moreover, constant peak width also depends on the shape and magnitude of the excitatory peak before sharpening, the shape and magnitude of the inhibitory trough, and the threshold of the interaction. Nonetheless, it appears that for this neuron, constant ITD tuning width was created by an ever-increasing inhibitory surround as frequency was decreased.
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Figure 5. The on and off ITD functions of the neuron in Figure 4 plotted for several frequencies. A, The normalized on ITD functions display a constant peak width across frequency. B, The normalized on and off ITD functions were plotted together. For clarity, only the peak portion of the on ITD functions were plotted. C, The on and off ITD functions in A and B were averaged separately to create a mean on and a mean off ITD function. Note that the inhibitory off ITD function centers around and flanks the excitatory on ITD function. In this way, constant peak widths across frequency could be created. contra, Contralateral; ipsi, ipsilateral.
Responses as a function of characteristic phase
Until now we have considered only peak-like responses. We now consider neurons with trough-like responses. Recall that these are neurons with CPs between 0.25 and 0.5. Similar to some peak-like neurons (e.g., Fig. 1A,D), the width of ITD tuning across frequency in some trough-like neurons decreased by nearly 1/f (Fig. 6A). In this example, the troughs align across frequency, and systematic changes can be observed in the trough widths. The slope of log frequency versus log trough width was very close to that predicted by a 1/f relationship.
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Figure 6. Examples of different forms of ITD tuning for trough-like neurons. The organization is similar to that in Figure 1. A, An IC neuron that decreased its trough tuning widths with frequency according to a 1/f relationship. B, An IC neuron that displayed near-constant trough width with frequency.
However, in other trough-like neurons (e.g., Fig. 6B), the widths of the troughs were nearly constant with frequency, analogous to the constant widths of some peak-like neurons (e.g., Fig. 1B,C,E,F). The slope of log frequency versus log trough width in this neuron (Fig. 6B, bottom panel, slope =
The distribution of slopes for trough-like neurons in the IC clustered around a slope of
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Figure 7. A, Distribution of the slopes of the log trough width versus log frequency function for trough-like neurons in the IC (open bars). The distribution of peak widths for peak-like neurons is shown for comparison (dashed line). B, Mean slopes of peak widths as a function of CP for neurons in the IC. Note that the slopes were flattest for peak-type neurons (i.e., CPs near 0 cycles) and steepest for trough-type neurons (i.e., CPs near 0.5 cycles).
The distributions described above are from groups of neurons that span wide ranges of CP, so that many intermediate-type neurons (CPs near ±0.25) are included. When these intermediate-type neurons were considered separately by plotting the results as a function of CP, a clear trend emerged. In Figure 7B, the average slopes of the peak widths are plotted as a function of CP for pooled neurons from the DNLL through the auditory cortex. The slopes were flattest for peak-type neurons (i.e., CPs near 0 cycles) and systematically increased with CP. For the slope of trough widths, the opposite trend occurred but over a smaller range (data not shown). Thus, it appears that there were systematic effects of CP on the changes of peak and trough widths with frequency and that the greatest difference from a 1/f relationship occurred for peak widths in peak-type neurons.
DISCUSSION
We have shown that in many neurons, especially above the level of the SOC, the tuning to ITDs tends toward constancy with frequency. In the following, we will first consider the degree to which the ITD tuning across brain levels is likely to be derived from central or peripheral processing. We will then discuss the functional implications of the results.
Neurons with nearly constant ITD tuning across frequency: central or peripheral processing?
There was an increase in the proportion of neurons with near-constant ITD tuning widths across frequency as information ascended from the SOC to midbrain levels. This suggests that the creation of such response properties occurs, at least in part, between the SOC and the midbrain. It is also likely that inhibitory mechanisms play a role in this central processing. In support of this, we showed an example of a neuron (Figs. 4, 5) in which inhibitory inputs in the IC appeared to create constant ITD tuning widths across frequency.
It is puzzling that neurons with constant or near-constant tuning widths show a broadening at higher frequencies (Fig. 3). A simple inhibitory mechanism cannot explain both a sharpening at lower frequencies and a broadening at higher frequencies. However, it is important to note that the difference in tuning width (expressed as a proportion of a cycle) between the two populations at high frequencies translates to a much smaller difference in absolute time than does the difference at low frequencies. Thus, in a functional sense, the sharpening at low frequencies may be the major contributor to the neural population that displays constant or near-constant tuning widths.
Our results from the SOC should be approached with some caution. The difficulty of recording from the SOC is well known, and we recorded many fewer neurons there than in the other brain levels. It is therefore necessary to examine evidence from previous studies to consider the possible contribution of sites peripheral to the SOC in creating neurons with relatively constant ITD tuning widths across frequency.
Although previous studies did not specifically examine the tuning to ITDs as a function of frequency, many examples of ITD tuning curves or synchronization functions across frequency exist. In most cases, these examples show the expected broader ITD tuning as the frequency is lowered. However, there are examples of neurons with ITD tuning widths that are nearly constant across frequency in the IC of the cat (Yin and Kuwada, 1983
There is evidence that at least some of the constancy we have described is caused by processing peripheral to the SOC. For example, in the auditory nerve there are several examples from individual fibers in which the synchrony declined with increasing frequency (Anderson, 1973
Functional importance of neurons with nearly constant ITD tuning across frequency
Differences between peak- and trough-type neurons
Most of the neurons in which ITD tuning width with frequency tended toward constancy were peak-like. In some trough-like neurons the change was in the other direction, with the trough widths tending toward constancy. In these neurons it is reasonable to assume that the processing emphasis was on the troughs rather than on the peaks. However, on average the trough-like neurons did not show a deviation from 1/f, whereas the peak-like neurons did. In addition, the effect of characteristic phase was systematic, such that on average neurons with CPs close to 0 cycles showed the strongest trend toward constancy of peak widths and the trend decreased as the CP approached 0.5. Thus, characteristic phase is an important factor in determining the degree to which a neuron is likely to deviate from 1/frequency. Peak-like neurons are generally most active for small ITDs associated with sound sources near the midline, whereas trough-like neurons are generally inhibited by these small ITDs and are most active for larger ITDs (Fitzpatrick et al., 2000Correlation of neural and behavioral results
An expected behavioral consequence of peak-like neurons that tend toward constant ITD tuning widths is to reduce the effect of frequency on sound localization acuity. Figure 8 shows that the just-noticeable differences (JNDs) from humans to ITDs in tones (closed circles) decrease with frequency. However, the change across frequency is much less than that predicted by a 1/f relationship (X symbols; note that the 1/f function is "anchored" to the JND function at 500 Hz to correspond with our finding that the tuning broadened at high frequencies and narrowed at low frequencies). The JND function closely resembles the function predicted from peak-like neurons recorded from the DNLL to cortex (open circles; also anchored to the JND function at 500 Hz). In fact, the slope of the log values of the human JND function is
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Figure 8. Comparison of behavioral JNDs from humans to ITDs in tones of different frequencies (closed circles) with that predicted by a 1/f relationship (X symbols) and estimates based on our neural responses (open circles). Neural estimates were derived by assuming a slope of log JND versus log frequency of
FOOTNOTES Received Jan. 8, 2001; revised March 23, 2001; accepted April 6, 2001.
This study was supported by National Institutes of Health Grants DC01366 and DC03948. We thank Lisa M. Fitzpatrick for technical assistance and Ranjan Batra, Talong Ju, and Robert Manfredi for computer programming.
Correspondence should be addressed to Dr. Douglas C. Fitzpatrick at the above address. E-mail: dcf{at}med.unc.edu.
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