Учебники / Hearing - From Sensory Processing to Perception Kollmeier 2007

rate responses (Delgutte 1987; Viemeister 1988), (2) spread of excitation (Siebert 1968; Heinz et al. 2001), and (3) the use of level-dependent response phase for low-frequency AN fibers (Colburn et al. 2003).

AM detection and discrimination performance predicted with central neural responses suggests a fundamentally different representation of modulation depth in the IC as compared to the representation of tone level in the AN. Specifically, at low modulation depths, changes in average rate cannot account for perceptual thresholds, while synchrony to the envelope can be significant at these low depths. In contrast, for higher modulation depths, rate-based MDFs are not as prone to saturation, whereas vector strength tends to saturate in most neurons and phase is not systematically depthdependent (Krishna and Semple 2000; Nelson 2006). These properties of the synchronized response are inconsistent with behavioral depth-discrimination thresholds which remain approximately constant above about −25 dB (Ewert and Dau 2004). In other words, a qualitative description of IC responses to AM suggests a transition from a temporal code at low depths to a rate-based code at high depths.

The current analysis was designed to further characterize IC responses with two specific encoding strategies in mind. The first hypothesis is that rate-based neural detection thresholds might improve by pooling information across a number of cells. The second hypothesis is that a single-neuron decision statistic incorporating both rate and temporal information will predict thresholds across a wider portion of the perceptually relevant range of AM depths than rate or synchrony alone.

2Methods

Detailed descriptions of the experimental methods are available elsewhere (Batra et al. 1989; Nelson 2006). Briefly, single-unit extracellular recordings over a wide range of AM depths were obtained in 152 single neurons in the ICs of three awake female Dutch-belted rabbits (oryctolagus cuniculus). Glass-coated tungsten microelectrodes were positioned with a stereotaxic system mounted on a steel cylinder that was affixed to the animal’s skull.

Parameters of the AM stimuli were designed for each neuron based on responses to a battery of simpler sounds. The best-frequency-tone carrier had an SPL on the ascending portion of the rate-level function. Sinusoidal AM was at the modulation frequency (fm) that elicited the largest value of synchronized rate (the product of vector strength and average rate) over a range of fm from 2 to 312 Hz. This fm almost always corresponded to the frequency that resulted in the highest value of the Rayleigh statistic (2nVS2, where n is the number of spikes and VS is the magnitude of vector strength at fm). Three repetitions of 2 s duration AM tones were presented at each tested frequency and depth. For statistical purposes, the responses were

thresholds were equal to or lower than their rate-based counterparts; Nelson 2006). For supra-threshold AM depths, this cell’s average rate increased monotonically over the remaining 15-dB dynamic range.

In contrast, its VS was effectively constant for depths higher than −10 dB; the period histograms illustrate the emergence of a bimodal distribution of spike times that contributed to the saturation of this timing metric. Figure 1 also shows the across-repetition variability of rate and synchrony estimates as a function of stimulus m. Rate estimates were slightly more variable at higher driven rates (and higher m) in this neuron than at lower rates, while the variability of VS showed the opposite trend. The enhanced precision of VS at high depths was mainly a result of the increase in the number of spikes, as opposed to a transition into the compressive region of the metric’s dynamic range. Further analysis (not shown) supported this notion: mean VS did not change, but its variability increased, when spikes were deleted to match the average rates at different modulation depths.

3.2Relationship Between Mean Count and Count Variance

One strategy used in comparisons of AN responses to intensity discrimination psychophysical thresholds is the simulation of a population of fibers based on assumed rate functions and dependence of spike count variance on the mean spike count (e.g. Delgutte 1987; Viemeister 1988). This approach provides an estimate of the number of fibers with a stereotypical rate function that would be required to account for psychophysical performance, and is justifiable for peripheral responses because of the systematic variability of count estimates in the AN (Young and Barta 1986; Winter and Palmer 1991): count variance is slightly less than that expected from a Poisson process. Here, we show that a similar strategy is not appropriate in the IC because rate variability is not predictable from the number of spikes.

Count variance as a function of the mean count for the population of neurons tested with a range of modulation depths (1168 observations) is shown in Fig. 2. The thin line in Fig. 2 indicates the dependence that would be expected from a Poisson process, while the thicker lines represent the best linear fit to the data (in a minimized sum-of-squares error sense). The slope of the best-fit line is approximately 0.8 (consistent with Hancock and Delgutte 2004); however, the raw data make it clear that a simple relationship between variance and count does not adequately describe these data.

In contrast to more peripheral auditory neurons (see above) and visual cortical neurons (e.g. Geisler and Albrecht 1997), the spike-count variance of IC neurons in the awake rabbit is clearly not proportional to the mean count. An inspection of variance-vs-count functions for individual neurons also revealed no systematic relationship for most cells (not shown). The neuron illustrated in Fig. 1 was atypical in this sense, in that its spike-count variance increased monotonically with firing rate.

mean spike count in 500 ms

Fig. 2 Spike count variance is not systematically dependent on the mean count in the IC. Linear axes are used in the left panel, focusing on measurements with counts and variances less than 50 (939/1168 observations); the logarithmic scale in the right panel allows for almost the entire population to be included (1115/1168)

The count-variance dependence of several subsets of cells was examined; no obvious differences were observed between groups with different puretone histogram types (onset or sustained), or rate-based sensitivities to AM depth (low versus high neural detection thresholds). Also, there were no clear trends that suggested a difference in this relationship for responses to stimuli with low vs high modulation depths (responses to all depths are included in Fig. 2).

3.3Combining Rate and Timing Information

The fact that synchronization to the envelope can become significant in the IC at AM depths near psychophysical thresholds and average rate often increases monotonically at higher values of m points towards a hybrid (e.g. synchronized-rate) metric as a decision statistic with the potential to account for perceptual thresholds across the entire AM depth dynamic range. We tested this idea by quantifying the average rate, synchrony, and the product of synchrony and rate. A transformation of synchrony, –ln(1–VS), compensated for the compressive nature of the vector strength metric and resulted in an equal-variance synchrony axis (Joris et al. 1994). Note that this transformation does not alter the count-dependence of across-repetition synchrony variance (Fig. 1).

Neural AM depth discrimination thresholds of one neuron for each tested standard depth and response metric are shown in Fig. 3; for reference, human psychophysical thresholds for high carrier frequencies and fm below 150 Hz are also included in the figure (from Ewert and Dau 2004). Two features of the neural thresholds are worth noting. First, predicted performance was essentially the same for all three of the tested decision statistics. Second, the trend toward higher thresholds at standard depths below −10 dB in the neural predictions was inconsistent with the human listeners’ ability to discriminate

Fig. 3 Comparison of neural and psychophysical AM depth discrimination thresholds across a wide range of standard depths. Perceptual data from Ewert and Dau (2004)

small changes in m for all standard depths above approximately −25 dB. Qualitatively similar results were observed for the 19 other neurons examined with high depth resolution.

One interpretation of these results (Fig. 3) is that a simple combination of rate and timing information does not carry adequate information to account for the low-depth psychophysical thresholds, as hypothesized above. Although synchrony was significant in the neuron at a depth of −19 dB, the variability of both synchrony and synchronized rate at depths near threshold was too high with respect to the slope of the modulation depth functions to predict the perceptual 1- or 2-dB discrimination thresholds (−6 to −2 dB on the ordinate axes shown in Fig. 3).

4Summary and Conclusions

The neural representation of AM stimuli in the IC was examined in terms of the mean and variance of several response quantifications. Spike-count variability had no systematic relationship with mean count. This finding has implications for modeling strategies that pool rate responses across a population of neurons. Rate codes are also affected by several other fundamental issues that raise serious questions regarding the feasibility of proposed decoding algorithms. For instance, spike counts computed over a finite duration depend on both the duration of the counting window and the absolute position of the window in time. Neural discharge rates exhibit temporal

correlations that can be modeled with a long-range dependent point process (e.g. Jackson and Carney 2005); therefore, to make efficient use of short-term changes in average rate, these slow temporal fluctuations must be correlated across populations of neurons that converge at a higher point in the system. There is no strong evidence either for or against the existence of such correlations in the central auditory system.

Although we conclude that a strict rate code is probably not used in the IC to represent AM (at least at low AM depths), we were also not able to identify an alternative single-neuron decision statistic that was capable of accounting for human performance across the entire perceptually relevant dynamic range of AM depths. The variability associated with estimates of VS computed using small numbers of spikes overwhelms the systematic changes in timing-based metrics that are present at lower AM depths. Taken together, these findings suggest one of three possibilities: (1) differences in percepts elicited by variations of AM depth are not directly mediated by the activity of single IC neurons, (2) rabbits and humans experience different AM-induced sensations, or (3) the system uses another single-neuron response metric that has yet to be identified. Future work will address these issues with simultaneous recordings of populations of IC neurons, measurement of behavioral rabbit AM detection and discrimination thresholds, and the testing of additional response quantifications.

Acknowledgements. We thank Anita Sterns for technical assistance and Shigeyuki Kuwada and Blagoje Filipovic for their generous contributions of time and electrode-making advice. This research was supported by NIHNIDCD F31-7268 (PCN) and NIH-NIDCD R01-01641 (LHC).

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Comment by Verhey

Would your data be in line with the following two interpretations?

1.The most sensitive units show similar thresholds as the psychophysical data on modulation detection.

2.Units with different thresholds are sensitive to different ranges of modulation depths, i.e. for the modulation discrimination task units may be used by the auditory system which have their thresholds close to modulation depth of the reference.

Reply

1.Although this aspect of the data was not emphasized here, it is true that a subset of neurons in our population with the lowest synchrony-based modulation depth thresholds can account for human AM detection performance [this is described more fully in Nelson (2006, PhD thesis), and in Nelson and Carney 2007]. One of the main points in the current presenta-

tion is that neural AM discrimination thresholds for standard depths below about −15 dB apparently cannot be predicted by changes in either

the average rate or strength of synchrony in single IC neurons when the across-repetition variability of these metrics is taken into account (this leads to Verhey’s second suggestion).

2.The recruitment of neurons with different AM depth sensitivities is certainly a reasonable mechanism to explain discrimination thresholds at low depths. We would only add that average rate alone in some neurons is suf-

ficient to predict discrimination psychoacoustics at high standard modulation depths (above −10 dB).

References

Nelson PC, Carney LH 2007 Neural rate and timing cues for detection and discrimination of amplitude-modulated tones in the awake rabbit inferior colliculus. J Neurophysiol 97:522–539