Учебники / Hearing - From Sensory Processing to Perception Kollmeier 2007

Figure 3 shows the steps in computing an optimum shape. The left column shows the first iteration step. The initial reference q was an RSS stimulus with 0 dB in all bins, shown by the horizontal line in Fig. 3A. The dashed line shows an example of an RSS perturbation δ q. The eigenvector emax is shown in Fig. 3C and the discharge rates for stimuli with spectral shape q + Aemax are shown in Fig. 3E, plotted as a function of A. The open circle shows the rate in response to the 0-dB reference stimulus and the filled circle shows the maximum rate, over the 16-dB range tested. The error bars are the SD of 10 repetitions of each stimulus.

The second column shows the second iteration. The reference in this case (solid line in Fig. 3A) has the shape of emax from the first iteration. emax and

the rates for δ q = Aemax are shown in Fig. 3C,E as before. In this case the maximum rate occurred at the spectral shape shown in Fig. 3B. This stimulus is a

rate maximum for all directions δ q and so terminated the iterations.

Close inspection shows that the maximum rate after the second iteration was slightly smaller than the maximum rate after the first iteration. This occurred because of a systematic rate change in the neuron, sometimes seen in DCN principal cells. Essentially the rate decreased by 18% during the first iteration, as shown by rates in response to a control stimulus (not shown). Thus the rate maximum after the second iteration was indeed an overall rate maximum at this time.

The optimization process only constrains the amplitudes at frequencies to which the neuron is sensitive. The bins marked by asterisks in Fig. 3B account for 80% of the rate change across a set of RSS stimuli. Those are also the bins that changed significantly during the iteration; note that the remaining, nonasterisk, bins stayed near their initial values. Thus the optimal stimulus should be considered to consist of the four asterisked bins.

4The Optimal Stimulus for DCN Neurons

The optimal stimulus for the example neuron in Fig. 3B is a rising spectral slope centered on BF. Figure 3D shows the outcome of the optimization process for a second type IV neuron, whose optimal stimulus is a sharp spectral edge at BF. The results of the optimization process thus correspond to the organization of excitatory and inhibitory inputs in Fig. 1 and the rate peaks observed in Fig. 2. It is important to emphasize that not all DCN principal cells show the notch edge sensitivity of the examples shown here, presumably because of different arrangements of the inhibitory inputs (Reiss and Young 2005).

The method of Sect. 3 provides a general way to find optimal spectral shapes that is applicable to neurons in all parts of the auditory system. It is fast and can be made faster by initiating the search with a reference stimulus that produces the highest discharge rate across an RSS set. Its major limitation is that it does not incorporate temporal aspects of the stimulus.

Acknowledgements. This work was supported by NIH grants DC00115 and DC05211.

7 Psychophysical and Physiological Assessment of the Representation of High-frequency Spectral Notches in the Auditory Nerve

ENRIQUE A. LOPEZ-POVEDA1, ANA ALVES-PINTO1, AND ALAN R. PALMER2

1Introduction

Destructive interference between sound waves within the pinna produces notches in the stimulus spectrum at the eardrum. Some of these notches have a center frequency that depends strongly on the relative vertical angle between the sound source and the listener (e.g. Lopez-Poveda and Meddis 1996). Therefore, it is not surprising that they constitute useful cues for judging sound source elevation (reviewed by Carlile et al. 2005).

The auditory nerve (AN) is the only transmission path of acoustic information to the brain. Single fibers encode the physical characteristics of the sound in at least two ways: in their discharge rate and in the time at which their spikes occur (reviewed by Lopez-Poveda 2005). Because spectral notches due to the pinna occur at frequencies beyond the cut-off of phase locking, the common view is that the AN representation of these notches must be based on the discharge rate alone, i.e. temporal representations do not contribute (Rice et al. 1995). In other words, the brain would infer the stimulus spectrum from a representation of the discharge rate of the population of AN fibers as a function of their characteristic frequencies (CFs). This representation is known as the rate profile.

On the other hand, evidence exists that the apparent quality of the rateprofile representation of high-frequency spectral notches degrades as the sound pressure level (SPL) of the stimulus increases (Rice et al. 1995; LopezPoveda 1996). Almost certainly this is due to the low threshold and the narrow dynamic range of AN fibers with high-spontaneous rate (HSR), which are the majority, and to the progressive broadening of their frequency tuning with increasing SPL. Although low-spontaneous rate (LSR) fibers have higher thresholds and wider dynamic ranges, they are a minority. Furthermore, the broadening of basilar membrane tuning at high levels makes it unlikely that they can convey high-frequency spectral notches in their rate profile equally well at low and high levels (Carlile and Pralong 1994; Lopez-Poveda 1996).

1Instituto de Neurociencias de Castilla y León, Universidad de Salamanca, Avda. Alfonso X El Sabio s/n, 37007 Salamanca, Spain, ealopezpoveda@usal.es, aalvespinto@usal.es

2MRC Institute of Hearing Research, University Park, Nottingham, NG7 2RD, UK, alan@ihr.mrc.ac.uk

Hearing – From Sensory Processing to Perception

B. Kollmeier, G. Klump, V. Hohmann, U. Langemann, M. Mauermann, S. Uppenkamp, and J. Verhey (Eds.) © Springer-Verlag Berlin Heidelberg 2007

where t denotes time, and ri(t, α) the instantaneous discharge rate of the i-th fiber in response to the stimulus with parameter α. In our context, α corresponds to the notch depth. Hence, Eq. (1) allows predicting the threshold notch depth for discriminating between a flat-spectrum noise and a noise with a spectral notch based on the experimental AN responses.

Equation (1) was derived on the assumption that the times at which AN spikes occur follow a Poisson distribution (i.e., that spikes occur at times that are independent of each other). Furthermore, it was derived on the assumption that psychophysical discrimination thresholds reflect optimal use of every bit of information available in the activity of the population of fibers. Neither of these two conditions apply here (see Heinz et al. 2001); thus we do not expect the resulting ∆αJND values to match the psychophysical thresholds directly. However, it is reasonable to assume that the error in using Eq. (1) for predicting the psychophysical thresholds will be similar for all SPLs. Therefore, Eq. (1) remains useful for predicting the shape of the threshold notch depth vs level function, as reported previously by us (Alves-Pinto and Lopez-Poveda 2005).

It is noteworthy that Eq. (1) predicts the threshold notch depth for spectral discrimination using the instantaneous discharge rate of the population of AN fibers. This contrasts with the rate-place model described in the Introduction that only considers the information conveyed in the overall discharge rate of the fibers.

For obvious reasons, in applying Eq. (1) we had to consider a discrete version of the instantaneous discharge rate, ri(∆t, α) rather than the continuoustime ri(t, α). Note that ri(∆t, α) may be interpreted as a mean-rate post-stimulus time histogram for a bin width duration of ∆t. Instead of decid-

ing on an arbitrary value for ∆t, we computed ∆αJND for different bin widths (or sampling periods), ∆t, from 0.333 to 110 ms. Note that in the extreme case

that ∆t equals the stimulus duration, the resulting ∆αJND corresponds to performance based on a rate-place code only.

In Eq. (1), the term between square brackets denotes the change in instantaneous discharge rate for an incremental change in parameter α. It was calculated as the instantaneous difference in discharge rate for the

flat-spectrum, (α = 0 dB) and the notched (α = 3 dB) noises. ∆αJND becomes unrealistically equal to zero when the discharge rate of any fiber is equal to

zero for any bin. To prevent this artifactual result, a small, arbitrary constant of 0.1 spikes/s was added to the measured discharge rate in all bins of all fibers. The actual value of this constant did not alter the results significantly.

3Results

The results are illustrated in Fig. 1. The series denoted by the open circles (left ordinate) illustrates the ∆αJND values based on the experimental AN responses. These will be hereinafter referred to as the physiological JNDs.

processing between human and guinea pig, and/or that humans do not behave as “optimal” spectral discriminators; otherwise the absolute values would match.

The shape of the psychophysical threshold notch depth vs level function varies among listeners (Alves-Pinto and Lopez-Poveda 2005). Similarly, the shape of the physiological-JND vs level function depends on the value of the bin width ∆t (Fig. 1). Kendall’s τ correlation coefficient (Press et al. 1992) was used to quantify the degree of correlation between the shapes of the psychophysical function for each one of five listeners (S1 to S5) considered by Alves-Pinto and Lopez-Poveda (2005) with the physiological-JND vs level functions for different values of ∆t. Figure 2 shows the ∆t values (circles; left ordinate) that yielded the highest correlations for each listener, as well as the corresponding correlation values (squares; right ordinate). The degree of correlation varies considerably across listeners, but the ∆t that yields the highest correlations is similar across listeners (mean ± s.d. =8.66 ± 0.36).

In Fig. 1, the series for ∆t equal to the stimulus duration (110 ms, top trace), shows the predicted physiological-JND values taking only the overall average discharge rate. The shape of this function clearly differs from that of the psychophysical function and matches overall the prediction of the rate-only theory. That is, threshold notch depths are lowest for overall levels around 60 dB SPL (corresponding to a spectrum level of 18 dB SPL) and increase progressively with increasing SPL. The level for which the physiological-JND is

Fig. 2 Binwidths (circles, left ordinate) for which maximum correlation occurred between the shapes of the physiological and the psychophysical threshold notch depth vs level functions for the five listeners considered by Alves-Pinto and Lopez-Poveda (2005). Squares (right ordinate) illustrate the actual degree of correlation. Two asterisks denote highly significant ( p < 0.01) correlations

Our previously suggested interpretation was based on the premise that the spectral notch must be encoded in the AN rate profile. The present results suggest that this premise is almost certainly false.

Indeed, the results of Fig. 1 argue against the view that high-frequency spectral notches must be encoded in the average rate profile of AN fibers and suggest, instead, that the discharge rate over narrow time windows conveys useful information for discriminating between flat-spectrum and notched noise stimuli. The results also suggest that humans somehow sample the discharge rate of AN fibers in non-overlapping time windows of approximately 8.6 ms (Fig. 2).

Three important questions arise now: 1) what is the temporal code in question; 2) how is it generated; and 3) how does it relate to the predicted 8.6-ms sampling period. The answer to these questions requires further analysis of the AN responses and we can only speculate at present.

The effective drive to any AN fiber is a half-wave rectified, low-pass filtered version of the basilar membrane (BM) response waveform at its corresponding place in the cochlea. With broadband noise stimulation, this can be described as a randomly amplitude-modulated carrier with a carrier frequency near the fiber’s CF, where the range of modulation frequencies is limited by the bandwidth of the cochlear filter (Louage et al. 2004) or the cut-off of phase locking. The bandwidth of BM filters, and thus the range of modulation frequencies, increases with increasing the SPL. Similarly, the phase of the BM response waveform depends on the filter bandwidth and thus on the stimulus SPL. AN fibers can phase-lock to the envelope of BM excitation even at high levels, when their discharge rate is at saturation (Cooper et al. 1993). Fibers with CFs near the notch frequency certainly “see” a different level compared with those with CFs well away from it. It is, therefore, possible that spectral discrimination be based on detecting either the range of modulation frequencies or the phase differences implicit in AN spike trains (or both).

On the basis of this conjecture, the psychophysical threshold notch depth vs level functions reported by Alves-Pinto and Lopez-Poveda (2005) would reflect the “dynamic range” of envelope-following rather than of discharge rate of AN fibers.

5Conclusions

High-frequency spectral notches are not encoded in the auditory rate profile, as is commonly thought. Instead, they are encoded by mean rate measures taken over quite short (~8.6 ms) time windows.

Acknowledgments. Work supported by FIS (PI02/203 and G03/203) and PROFIT (CIT-390000- 2005-4). We thank Trevor Shackleton, Ray Meddis, and Gerald Langner for their support and suggestions.