Data were collected from 185 auditory nerve fibers in 12 guinea pigs although other data reported elsewhere were also collected from higher CF fibers. For the present study, we specifically targeted fibers with CFs within the range of phase locking of the guinea pig (up to about 3.5 kHz; see Palmer and Russell 1986), and therefore, the CF range in our sample was from 0.071 to 3.227 kHz. We collected the half-octave spaced, 50-repetition data for 134 fibers and the data with finer frequency steps, but only five repetitions for 125 fibers. Both sets of data were collected for 74 fibers.
An example of the data from a single fiber which was held for long enough to obtain a comprehensive data set is shown in Figure 1. There is clear evidence of good phase locking in the period histograms taken at half-octave spacing around the CF (Fig. 1C). Figure 1D shows the mean phase derived from the histograms as a function of stimulus frequency, after unwrapping the phase. The curves for all sound levels are very similar and the slope of the curve indicates the fixed delay to this recording place (see Palmer and Russell 1986 for discussion). Frequency response areas showing the discharge rate as a function of stimulus frequency at a range of different sound levels, as in Figure 1E, have been published many times before (see for example Anderson et al. 1971; and the extensive data in Geisler et al. 1974). The phase versus stimulus frequency curves derived from these data are shown in Figure 1F and, not surprisingly, look very like those in Figure 1D with extra frequency resolution. Finally, in Figure 1B, we show the deviation in the phase compensated for the linear regression fit at 90 dB SPL as a function of sound level for both sets of data. The large symbols represent the half-octave data and these clearly give similar phase estimates to those from Figure 1F.
Estimation of characteristic frequency
Figure 1A shows the full frequency level response area for an example fiber and illustrates one issue with our data collection that needs to be taken into account when considering effects of sound level. Our estimate of the audiovisual CF was 0.717 kHz and the response area was constructed around this frequency (1 octave above and 3 octaves below CF). It is clear from this plot, however, that a better estimate of CF would have been slightly higher in frequency. An alternative measure of the CF would be the frequency of a definite peak at the lowest sound level in the FRA (Fig. 1E), called the BF here for convenience. This frequency is shown by the arrows on the response area (Fig. 1A), the FRA (Fig. 1E), and the corrected phase versus frequency plots (Fig. 1B). The difference between the two estimates of CF is shown in Figure 2 along with a histogram of the difference. The dashed lines show the 95% limits of agreement (Bland and Altman 1999). In many instances, the CF estimates were the same, but the BF could vary symmetrically above and below the audiovisual CF. The measurements were not significantly different (paired t test, t = 1.57, p = 0.12, df = 90; two-sample Kolmogorov–Smirnov goodness of fit test D = 0.059, p = 0.999). To homogenize variance in this test, we transformed the frequencies into equivalent rectangular bandwidth (ERB) rate (a measure of frequency in units of filter bandwidth, Moore and Glasberg 1983) by integrating the ERB function for the guinea pig derived from behavioral and physiological measurements (Evans 2001). In later sections, we compare the position of the null frequency with the CF. In principle, the pattern of results could be different depending upon which definition of CF was used. However, there was no difference in the patterns of these results depending upon the definition of CF, so we only show the results plotted relative to the audiovisual CF.
Variation of the mean phase along the basilar membrane
From plots of phase as a function of frequency and level such as those in Figure 1D, F, we extracted the mean phase at a series of individual frequencies. These are shown over 3 octaves of stimulus frequency from 250–2,000 Hz in half-octave steps as a function of the fiber CF (i.e., basilar membrane position) in Figure 3. The data for different signal frequencies are shown as alternating black and white circles, with the signal frequencies marked by superimposed large triangles in a contrasting color. For all stimulus frequencies, the general trend is a gradually decreasing phase lag, as CF increases, of maximally about 1.5 to two cycles beyond which the curves become flat. As the stimulus frequency increases, the phase lag at any CF increases, and the slope of the function increases (c.f. Kim et al. 1980).
In Figure 3, the data were pooled over sound level to emphasize the major effects of CF and signal frequency. However, there is also a smaller but systematic effect of signal level which is revealed by plotting the mean phase as a function of CF separately for each signal frequency with signal level as parameter in Figure 4 (separated by one cycle for clarity). In this format, it is clear that the transition between the sloping part of the function and the flat portion is quite abrupt, as previously demonstrated by van der Heijden and Joris (2006). A “knee point” and slope were determined by “broken stick” fits to the data (comprising a linear portion of variable slope at low CFs breaking to a flat portion at a variable CF knee point; fit by “nlinfit” in MATLAB, Mathworks) as shown by the superimposed lines. At each stimulus frequency, this “knee-point” shifts to higher CFs with increasing sound level and the low-CF slope becomes shallower. Unfortunately, there are insufficient data at higher CFs to be able to properly delineate the shape of the function for higher stimulus frequencies, but if a knee point exists for stimulus frequencies of 2,000 Hz, it is above CFs of 3,000. Figure 5 shows the variation in the knee-point CF and in the low-CF slope of the data from the first three panels of Figure 4. The variation in knee-point CF and slope with level are clear as are the variations with stimulus frequency. The knee point in response to 250 Hz stimulation, for example, starts off at about 500 Hz at 50 dB SPL and ends up at almost 1,250 Hz at 90 dB SPL.
Figure 6 shows the variation in the discharge rate over the same range of frequencies and levels. We show here normalized driven rates between spontaneous and saturation. At low stimulus levels (40 dB SPL; bottom row in Fig. 6), the locus of activity at each of the four frequencies is relatively well defined and centered at the stimulus frequency (vertical line in all panels of Fig. 6). This locus widens with level due to broadening of the tuning and saturation effects, and the frequency at which it is maximal shifts upward away from low stimulus frequencies or downwards from high stimulus frequencies (as has been demonstrated before, see Palmer 1995, Figure 4). At the highest levels, most of this population of low-frequency fibers is active and firing at near saturation rates. The phase versus characteristic frequency pattern shown in Figure 3 is similar at all sound levels despite the fact that at 90 dB SPL, the firing rates are saturated and at 40–60 dB SPL, the majority of fibers are firing within their spike dynamic range. The phase measured is therefore largely independent of the firing rate provided sufficient spikes are evoked to determine the phase and is little affected by saturation.
Estimates of delay from the phase frequency plots
Figure 7A shows selected examples of phase versus frequency plots at the highest level used in each fiber (usually about 90 dB SPL). The plots are approximately straight lines, showing a nearly constant group delay. Taking the slopes of these plots for all fibers, at each SPL, gives the mean group delay to the recording electrode shown in Figure 7B (open symbols in Fig. 8 taken from Palmer and Russell 1986). On Figure 7B, we also plot the function from Siegel et al. (2005, Figure 7) that they used to summarize the group delays in the guinea pig data of Evans (1972). The function they used was of the same form as that they used to model their more comprehensive chinchilla data but fitted to isolated measurements at low (400 Hz) and high (18–40 kHz) frequencies in the guinea pig data. The close match of this function to our present, much more finely sampled, delay data validates this fit and allows us to infer that the present data set is likely to be very representative of mammals in general.
Variation in phase with sound level
Figure 8 shows examples for individual AN fibers of the variation with stimulus frequency and level of firing rate (Fig. 8A, C, E) and phase (Fig. 8B, D, F) after compensating for the regression fit to the data at 90 dB SPL. On the left (Fig. 8A, C, E) is the FRA from which the phase data shown on the right (Fig. 8B, D, F) were derived. For these three fibers, both the limited frequency resolution data with 50 repeats and the data at the higher frequency resolution were obtained. Phase data from the former one are shown by large symbols. The phase values obtained from both data sets are extremely consistent in all cases giving confidence to conclusions based solely upon the smaller number of repeats. The data are consistent with similar plots that have been previously published in several species including the classical study of Anderson et al. (1971) in the squirrel monkey. The arrows on the phase plots in each case show the audiovisual CF (thick arrow) and the BF estimated from the FRA (thin arrows on both plots). It is clear that these values are somewhat divergent (but, as shown in Fig. 2, not systematically so). In the central panel (Fig. 8D), the phase shows a progressive lag with sound level at frequencies below CF and a progressive lead for frequencies above CF. This is the pattern shown in the earlier studies. The null frequency in this case was at the CF as estimated from the FRA (Fig. 8C). In the plots shown above and below (Fig. 8B and F), the position of the null frequency does not correspond to the CF derived by either estimate. The null is below the CF in Figure 8B and above the CF in Figure 8F. In every case where we could identify a null frequency, the phase progressively lagged at higher levels for frequencies below the null and lead at higher levels for frequencies above the null. Null frequencies were identified in 152/185 fibers. In cases where we were unable to identify a null frequency, this was because (1) most often the fiber CF was above about 1.4 kHz and the functions at different levels had not converged at the limit of useful phase locking, (2) paucity of data when fibers were lost before sufficient repeats were obtained, or (3) the phase curves did not vary in a systematic fashion with sound level.
In Figure 9, we show the offset of the null frequency from the CF as a function of the CF. Null frequencies that occur at the CF were found throughout the CF range. Null frequencies above the CF are also found throughout the CF range but were more prevalent at CFs above 1,000 Hz. Null frequencies below CF were mostly found at CFs below 1,000 Hz. While the accuracy of the estimate of this offset is limited in resolution by the size of the frequency steps used, values of as much as + 0.5 and −1 octaves can be found.
It is clear from Figure 9 that offsets of different sizes and directions can occur at the same CF. This is not due to pooling across animals, as shown in the left hand column of Figure 10, where data for the three animals with most recordings are shown along with the data for all animals pooled together. It is clear that the individual animals show the same pattern as the pooled data, in particular the null offset can vary at the same CF within the same animal.
It is possible that the offset of the null from the CF shown is due to error in estimating the CF; however, a different method of estimating the CF yields similar results. In the center column of Figure 10, we also show the offset of the nulls from the estimate of the BF derived from the FRA. The patterns of offsets are the same as those obtained from audiovisual CF estimates. The estimate of BF should be largely independent of the estimate of audiovisual CF, so if the null offset were merely due to error in estimating CF, then we would expect the null offsets from the audiovisual CF and the BF to be randomly distributed; however, the right-hand column of Figure 10 shows a clear correlation, indicating that the null offset from CF is a genuine phenomenon and not an artifact of inaccurate measurement of CF.
Variation of the corrected mean phase along the basilar membrane
Finally, in Figure 11, we show the variation in compensated phase across the population as a function of level and stimulus frequency. To obtain this figure, we extracted the phase from plots such as those in Figure 8B, D, F at each of four stimulus frequencies and six sound levels and plotted these against fiber CF. Perhaps surprisingly, given the diversity that we have seen in some of these corrected phase curves, these measures are systematic across the population. The data for the three animals with most data are highlighted. At the highest level shown (90 dB SPL), the phase in nearly all fibers irrespective of CF and stimulus frequency is at zero. This is not surprising since we adjusted the phase for each nerve fiber individually so its mean phase at 90 dB SPL was zero and the best fitting linear function to the fibers’ data at 90 dB was flat. At sound levels below 90 dB SPL, a deviation from the flat zero phase line become apparent. At 40 to 70 dB SPL, these deviations occur for CFs above and below the stimulus frequency, which stays at zero phase. The largest deviation occurs at the lowest levels, where the phase transition is the sharpest. The transition is sharper for high stimulus frequencies than for low stimulus frequencies. These deviations reach a maximum of ±0.2 cycles, matching the stereotypical maximum deviations shown in individual fibers. In all cases, phase lags occur for fibers with CFs below stimulus frequency, while phase leads occur for fibers with CFs above the stimulus frequency mirroring in the population the pattern seen in individual fibers