A long-standing quest in audition concerns understanding relations between behavioral measures and neural representations of changes in sound intensity. Here, we examined relations between aspects of intensity perception and central neural responses within the inferior colliculus of unanesthetized rabbits (by averaging the population's spike count/level functions). We found parallels between the population's neural output and: (1) how loudness grows with intensity; (2) how loudness grows with duration; (3) how discrimination of intensity improves with increasing sound level; (4) findings that intensity discrimination does not depend on duration; and (5) findings that duration discrimination is a constant fraction of base duration.

Over the past several decades, there have been many attempts to determine relations between behavioral and neural representations of changes in sound intensity. The majority of the efforts have focused on the neural responses of auditory nerve fibers, most of which have a limited (25 dB or so) dynamic range. The bulk of such studies featured mathematical modeling to assess the degree to which the physiological data could account for or explain perceptual phenomena, such as intensity discrimination and loudness, e.g., Refs. 1–6. Central to these efforts were several assumptions about how the neural data could be linked to behavior decision variables (e.g., optimal processing). The purpose here is to show, using virtually no such assumptions, that a population of neurons in the inferior colliculus can show parallels between the population's neural output and Steven's power function. This function describes how loudness grows with intensity. We also show that the same neural responses have parallels to intensity discrimination and duration discrimination. We hope our new insights will kindle interest about the topics studied and provide future investigators with “pilot data” and examples of unexpected success that may help them to garner support for their particular endeavors.

The neural data were collected in the inferior colliculus (IC) of awake rabbits7 (see pp. 1309–1310 for methodological details). The “best” frequencies of neurons were determined by delivering tone bursts monaurally at frequencies from 250 Hz to 16 kHz in 1 2-octave steps at moderate intensities (30–50 dB SPL). Then, responses of each neuron at its “best” frequency were recorded to 500 ms–long tone bursts, which covered the range from 85 down to 5 dB SPL.

During data collection, in accord with the original purpose of the first author’s experiment, each tone burst was repeated five times in order to evaluate whether and to what extent post-stimulatory inhibitory effects were present. That was not the goal of the loudness-related analyses reported here. To avoid such inhibitory effects and any mild adaptation occurring from repetition to repetition, only responses from the first repetition at each stimulus level were considered.

Figure 1(A) shows that the bulk of the distribution of best frequencies of the neurons was in the most sensitive region of the rabbit's behavioral audiogram.

Responses of an IC neuron to a single presentation of a 500 ms tone burst at its best frequency (4 kHz) for levels from 5 to 85 dB SPL are shown as raster plots in Fig. 1(B). The vertical lines reflect the durations within which responses were accumulated (500, 250, 125, 62, or 31 ms). Responses within 8 ms from stimulus onset were excluded in order to include only stimulus driven spikes. Spike-count vs level functions at the different durations for the neuron in Fig. 1(B) are displayed in Fig. 1(C).

The responses of our illustrative neuron increased monotonically with level over about the 80-dB range of the stimulus set. Other neurons, however, had more restricted dynamic ranges. Still other neurons displayed either saturating or non-monotonic functions. Figure 2 shows the average functions calculated across neurons for all three types of response functions [Figs. 2(A) and 2(B); n = 240], for those showing only monotonic and saturating response functions [Figs. 2(C) and 2(D); n = 167], and those showing only non-monotonic response functions [Figs. 2(E) and 2(F); n = 73). The left panels contain spike counts plotted on a linear scale; the right panels contain the same data on a logarithmic scale. Note that the patterning of the averaged responses in Figs. 2(A) and 2(C) and in Figs. 2(B) and 2(D) are very similar. The relatively small contribution of the nonmonotonic neurons to the response of the total neural population is no doubt due to their relatively lower averaged activity. When relating the neural responses to behavior, the focus will be on the averaged responses of the whole population.

When the averaged responses of the whole population are viewed on a linear scale, the spike count/level functions increase monotonically over the whole 80-dB range, independent of duration [Fig. 2(A)]. Thus, the limited dynamic ranges that characterize auditory nerve fibers do not, per se, constrain the average population response seen in the IC. A similar observation, also in the IC of the unanesthetized rabbit, has been reported recently by Sivaramakrishnan et al.8 When the responses in Fig. 2(A) are plotted on a logarithmic scale [Fig. 2(B)], the functions become more linear with level and are parallel across duration. Such functional relations are reminiscent of Steven's power law which states that “equal stimulus ratios produce equal sensation (loudness) ratios”. In our neural population, equal stimulus ratios produced equal spike ratios, and, therefore, may provide a neural basis for achieving equal loudness ratios.

These neural data can also be viewed as the substrates for the reciprocity between loudness and duration for tones reported in humans by McFadden.9 Figure 3(A) displays data replotted from McFadden's Fig. 1(A). Note that the SPL necessary for equal judgments of loudness decreases with increases in tonal duration and does so in a parallel manner across different base levels of loudness. A similar relation is seen in the neural data when SPL necessary for equal spike counts is plotted against duration [Fig. 3(B)]. Note that the neural data are parallel across different base levels of neural counts. This suggests that the aggregate activity of our neural population may provide a basis for the temporal integration of loudness.

Next, we consider how the discriminability of differences of intensity changes as a function of increasing base intensity. Figure 3(C) displays the data of Jesteadt et al.10 who measured, in humans, just noticeable differences (ΔI) over several base levels of intensity (I) using tonal stimuli. Note that relative discriminability (viz., ΔI/I) decreases with increasing base intensity. This is a robust finding that McGill and Goldberg11 termed the “near miss to Weber's law” and holds only for tonal stimuli. Figure 3(D) shows the neural responses in Fig. 2(A) re-plotted as the standard deviation of the spike count divided by the mean spike count, as a function of SPL for each tonal duration. This transformation of the data is based on the reasonable assumption, supported by signal detection theory, that the variability of the estimates of the mean base intensity (I) directly limit the resolution of changes in base intensity (ΔI). Note that the neural data, when plotted this way, also show that resolution of differences in intensity improves with increases in base levels of intensity, i.e., they parallel the near miss to Weber's law. Interestingly, these neural functions do not change in a consistent way with changes in duration. This observation is consistent with Henning and Psotka's12 finding in human listeners that resolution of differences in amplitude does not depend on the duration of the tone.

Finally, we consider how the discriminability of differences of duration changes as a function of increasing base duration. Figure 3(E) displays some of the data (1000 and 3500 Hz at 65 and 85 dB SPL) of Abel13 who measured, in humans, just noticeable differences (ΔD) over several base levels of duration using tonal stimuli. The data are plotted in the same way as Abel's, wherein ΔD is plotted as a function of base duration. Here, the just noticable difference is approximately proportionate to base duration, in accord with Weber's law. In Fig. 3(F), our neural data are plotted in a format like that used by Abel. For reasons discussed above, the standard deviation of the spike count, at each duration, is used to reflect sensitivity to changes in base duration. For comparisons with Abel's data, only the neural responses obtained at 65 and 85 dB SPL are plotted. Interestingly, the neural sensitivity to changes in duration is seen to be surprisingly like the behavioral sensitivity to changes in duration.

In summary, we have shown that several important behavioral findings concerning loudness, intensity discrimination, and duration discrimination have counterparts in the overall or population responses recorded from neurons in the IC. We do not mean to imply that the neural responses mimic human behavior in a way that they provide an accurate quantitative model of human performance. Rather, we believe that we have shown that changes in important stimulus dimensions produce similar changes in performance be it evaluated behaviorally or neurally.

We thank Blagoje Filipovic for assistance in data collection and William Loftus for assistance in organizing and collating the neural spikes. The first author, S.K., collected the neural data and then transformed and plotted them as suggested by the second author, C.T. That was done in an “independent, double-blind” manner such that S.K. was unaware of the nature of the behavioral data of interest. C.T. was not involved directly with and did not actively participate in, the analyses of the neurophysiological data. This report was written simultaneously by both authors and represents the culmination of more than four decades of their lively, enthusiastic, and extremely satisfying professional and personal interactions. It is also illustrative of the myriad multi-disciplinary scientific contributions made by S.K. with dozens of his students and colleagues before his untimely death on May 3, 2019. Dr. Leslie R. Bernstein is gratefully acknowledged for cheerfully and with great care doing what was necessary for making the final manuscript suitable for publication in this journal. Two anonymous reviewers deserve thanks for their comments that served to strengthen the presentation.

The authors have no conflicts to disclose.

This study was approved by the University of Connecticut Health Center Animal Care Committee.

Data supporting this study are available upon request from the corresponding author.

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