Responses to single tones
Single tone data were collected with the purpose of determining the limits and degree of phase locking in gerbil ANFs. Responses to 70-ms tones were obtained from 163 ANFs, with CF ranging from 88 Hz to 24.71 kHz, presented at intensities of 10–90 dB SPL. Figure 1A shows vector strength as a function of stimulus frequency. For each ANF, vector strength was determined for a wide range of stimulus frequencies and intensities. Each data point represents a single frequency/intensity combination. Different symbols are used for different ranges of CFs as indicated in the figure. The large spread at each frequency is mainly caused by the inclusion of data obtained with arbitrary SPLs, including low and moderate levels which yield relatively poor phase locking. The solid line is a polynomial fit estimating the upper envelope of the data. The derivation of this curve and its use in the correction of amplitude curves extracted from multitone data are described in “Methods”.
Between 50 Hz and 1 kHz, vector strength was typically below 0.9, with a few outliers as high as 0.99 in the 500-Hz region. Vector strength decreased for stimulus frequencies above 1 kHz and just above 4 kHz it had dropped below 0.2. Notice that the data are not limited to near-CF stimulation; for example, the highest vector strengths were found for stimulus frequencies around 500 Hz, presented to ANFs with CF >2 kHz.
For each ANF, the maximum vector strength found for tones in a 0.25-octave band around CF are indicated in Figure 1A (open circles). These values typically fall below the polynomial fit to the upper envelope of the data (solid line). Only two near-CF data points between 500 Hz and 1 kHz show a vector strength slightly exceeding 0.9. The highest near-CF vector strength (R = 0.94) was found around 100 Hz.
Figure 1B compares the upper limit of vector strength in gerbil to three other mammalian species. Both the guinea pig data (Palmer and Russell 1986) and the chinchilla data (Temchin and Ruggero 2009) were obtained using brief tone bursts covering a wide range of frequencies (i.e., both near-CF and off-CF stimulation). In both studies, the vector strengths from all ANFs and animals were pooled to obtain their maximum for each stimulus frequency, similar to our data from gerbil. In chinchilla, the stimulus level was fixed at 70 dB SPL. The data from cat (Johnson 1980) are different in two ways. Firstly, they were obtained using long tonal stimulation. However, this does not strongly affect vector strength (Joris et al. 1994a). Secondly, stimulation was restricted to near-CF tones. For off-CF stimuli, Joris et al. (1994b) reported vector strengths up to 0.95 for cat ANFs with CF >2 kHz stimulated at 500 Hz. Thus, the restriction to near-CF stimulation in the data of the cat (Johnson 1980) tends to underestimate the overall maximum vector strength in that frequency region, similar to our results in Figure 1A. Taking this tendency into account, phase locking in the gerbil is very similar to that in cat, both in terms of maximum vector strength values and of frequency limit. In a final comparison to phase locking in rat (data not shown), gerbil ANFs also show higher vector strengths for off-CF tones as well as for near-CF tones (Paolini et al. 2001).
Responses to tone complexes
Responses to tone complexes were obtained from 157 ANFs, with CFs ranging from 88 Hz to 5 kHz. Fourier analysis of the response to the tone complexes produced linear estimates of amplitude and phase characteristics of the ANF (see “Methods” and Van der Heijden and Joris 2006). Figure 2 (left panel) shows an example of an amplitude curve from a single ANF, computed from the response to a single tone complex. It represents the relative magnitudes (i.e., the relative vector strength, expressed in decibel) of each of the stimulus components in the response. Since we are mainly interested in cochlear frequency selectivity, we corrected the amplitude curves for the overall decline of phase locking with frequency using the frequency response of the vector strength, derived from population data in Figure 1A (solid line). Note that this correction is small (<4 dB) at frequencies up to 3 kHz; at higher frequencies, the amplitude curves have a very limited dynamic range due to poor phase locking. The corrected amplitude curve (Fig. 2) shows a clear peak near CF, which reflects the peripheral frequency selectivity.
The slope of the phase curves, extracted from the multitone responses, reflects overall group delay (∼2.3 ms in the example in Fig. 2, middle panel). This delay combines the contributions from middle-ear transmission, intracochlear propagation, and synaptic and neural transmission. In order to zoom in on the finer details of phase transfer, the curve was advanced in time by 2.1 ms, an amount large enough to compensate most of the overall delay of this ANF response (Fig. 2, right panel; the 2.1-ms compensation is indicated in the graph). The phase compensation revealed deviations from a straight line, i.e., small, frequency-dependent, variations of group delay.
Tuning characteristics at low SPL
For low stimulus intensities (maximally 30 dB above threshold), we observed a gradual, systematic transformation in the amplitude and phase curves with CF. This is illustrated by the examples in Figure 3. Amplitude curves of low-CF ANFs were asymmetric with a steep low-frequency flank and a shallow high-frequency flank (Fig. 3A, left panel). With increasing CF, lower flanks became shallower, while upper flanks became steeper (Fig. 3, left column). Amplitude curves became symmetric (on a logarithmic frequency scale) for CFs near 1 kHz (Fig. 3B). For still higher CFs, the amplitudes became asymmetric again, but now with the lower flanks shallower than the upper flanks (Fig. 3C, D).
The corresponding phase curves also show systematic changes with CF. For ANFs with the lowest CF, phase curves were concave from above: they were steepest at the lowest frequencies (including CF) and contain an extended shallow part above CF. With increasing CF, the phase curves became less bent, turning into almost straight lines (Fig. 3C, right panel). For higher CFs, the curves were concave from below with the steepest gradient around CF and a more shallow tail below CF. In addition, many phase curves of higher-CF (>1 kHz) ANFs exhibited a marked upturn (increased group delay) below 1 kHz (Fig. 3D, right panel).
Figure 4 represents a schematic overview of the gradual transformation of the amplitude and phase curves with CF, based on a qualitative analysis of 446 recordings from 157 ANFs. With increasing CF, the amplitude and phase curves (curves marked d in Fig. 4; see also Fig. 3D) start to resemble the characteristics of mechanical responses to single tones measured in the base of the cochlea (Robles and Ruggero 2001).
To quantify sharpness of tuning, we computed the quality factor (Q
10dB; peak frequency divided by bandwidth at −10 dB) from the amplitude curves. In Figure 5, Q
10dB is plotted against CF, using different symbols for two non-overlapping ranges of SPL. As expected from the amplitude curves (Figs. 3 and 4), Q
10dB increased with CF. Sound intensity also had a clear effect on Q
10dB: The high-SPL values (Fig. 5, triangles) were systematically lower than the low-SPL values (Fig. 5, squares). A comparison with Q
10dB data from gerbil threshold curves (Fig. 5, solid line; adapted from Ohlemiller and Echteler 1990) revealed a good agreement with our low-SPL Q
Near-CF group delays
In most cases, the segment around CF was the steepest part of the phase curve, corresponding to the largest group delay. Consequently, fitting a single straight line to the entire phase curve would underestimate near-CF group delay. We therefore restricted our near-CF group delay estimates to a 0.4-octave-wide band around CF, while pooling data obtained at different SPLs. Near-CF group delay (Fig. 6A, circles) ranged from >10 ms for the lowest CFs (∼100 Hz) down to ∼2 ms for the highest CFs (∼5 kHz). The relation between near-CF group delay and CF was fitted to a power function (Fig. 6A, solid line). The fit describes a lower limit of 2.1 ms for the highest CFs. This is higher than the estimated 1-ms “synaptic delay” for ANFs (Ruggero and Rich 1987), suggesting that for the entire range of CFs covered (<5 kHz), cochlear travel delays of near CF components exceed 1.1 ms. The range of near-CF group delays and their systematic decrease with CF is similar to near-CF group delays reported for squirrel monkey (Anderson et al. 1971), chinchilla (Temchin and Ruggero 2009), guinea pig (Palmer and Russell 1986), and cat (Goldstein et al. 1971), as shown in Figure 6B.
The wide range of stimulus frequencies covered by many phase curves allowed an assessment of group delay for frequencies remote from CF. Motivated by the shapes of phase curves (Fig. 4B), we estimated group delays in three non-CF regions (Fig. 7A–C), which are illustrated in the insets of Figure 7. At very low (<400 Hz) frequencies (Fig. 7A), well-below-CF group delay showed a large variability and little dependence on CF. Large values of group delay in this low-frequency region reflect the upturns in the phase curves mentioned previously (cf. Fig. 3D), which were observed in some, but not all ANFs. Group delays for the frequency region just below CF (∼1.5–0.6 octaves below CF, i.e., 0.3×CF to 0.6×CF) are shown in Figure 7B. These below-CF group delays decreased with CF, but less strongly than the near-CF delays of Figure 6A. Above-CF (>1.6×CF) group delay (Fig. 7C) showed a weak trend to decrease with CF.
We compared the group delays obtained from the different segments of single phase curves by computing the difference of the near-CF group delay and the various off-CF regions of the same curve, when available. This comparison of steepness across segments provides a quantitative analysis of the deviation of phase curves from straight lines (Fig. 7D). The group delay data of Figures 6 and 7 can be summarized as follows: Most of the variation with CF is observed in the near-CF region, with group delay monotonically decreasing with CF (Fig. 6A). The off-CF regions show little, if any, variation of group delay with CF (Fig. 7A–C). In most ANFs, the largest group delays were obtained for near-CF stimulus frequencies, with the exception of some ANFs with CF of 1 to 2 kHz, for which very low stimulus frequencies yielded the largest group delays (Fig. 7D, X’s).
Effect of SPL on amplitude curves
For 92 ANFs, we obtained responses to tone complexes presented at multiple SPLs. If the auditory periphery were linear, the amplitude curves obtained at different SPLs would have the same shape. The broadening of tuning with SPL (Fig. 5), however, indicates that the shape of amplitude curves is SPL dependent. When considering the effect of SPL on amplitude curves, it is important to realize that each curve only represents the relative amplitudes of the different components. They do not yield any information about the absolute amplitude of the response. Therefore, there is no intrinsic way of comparing amplitude curves across SPLs, so the vertical alignment of the curves is arbitrary (Van der Heijden and Joris 2006).
In contrast, mechanical measurements do yield absolute amplitudes and the variation of tuning with SPL is conveniently visualized by normalizing each amplitude curve by the amplitude of the stimulus. When overlaying these “sensitivity curves” obtained from the base of the cochlea, the linear growth well below CF results in complete overlap in the low-frequency tail, while compressive growth around CF results in a sharp peak at low SPLs that declines with increasing SPL (Rhode 2007).
The similarity of our highest-CF data (Fig. 4, curves marked d) with cochlear mechanical data motivated us to align the multiple amplitude curves at their low-frequency tail. Assuming linear growth for below-CF tones, vertical alignment of low-frequency tails of amplitude curves obtained at different stimulus levels converts them into sensitivity curves (this procedure can be viewed as a “wideband version” of Cooper and Yates’ (1994) method to estimate mechanical compression from single-tone rate-level curves.) Three examples of this alignment procedure are shown in Figure 8 (left column). The curves were aligned by minimizing the squared distance of each low-frequency tail (<CF/2) to the averaged curve. With increasing SPL, the relative response at CF (Fig. 8, filled circles) decreased, indicating compressive growth at CF. A similar alignment procedure could be applied to 44 ANFs (CF between 0.4 and 3 kHz). For each ANF, the growth rate (decibel response growth per decibel stimulus increase) was estimated by fitting a straight line to the magnitude at CF as a function of SPL. The growth rate was obtained by converting gain to non-normalized amplitude, i.e., by adding one to the slope of the straight line. This yielded a median compressive growth rate of 0.66 ± 0.22 dB/dB. The absence of distinct below-CF tails in the response curves of low-CF ANFs largely limited the alignment procedure to ANFs with CF above 800 Hz. An exception is shown in Figure 8C for an ANF with CF = 500 Hz, which yielded a compression of 0.87 dB/dB.
Many amplitude curves for which low-tail alignment was not feasible did show clear effects of SPL. Some of these effects were systematic: As shown earlier (Fig. 5), peak width broadened with increasing SPL. In other aspects, however, the SPL-induced changes varied considerably across ANFs (Fig. 9). In some ANFs, the broadening of the curves was accompanied by a downward shift to lower frequencies. For other ANFs, the shape of the amplitude curve changed little (Fig. 9E), although sometimes its position also shifted to lower frequencies (Fig. 9D). In other cases, the lower/higher flank became shallower, while the upper/lower flank and best frequency showed little change (Fig. 9A and B, respectively). In three cases, we also observed the occurrence of secondary peaks at higher SPLs (Fig. 9A). Similar secondary peaks were observed in in vivo intracellular recordings of inner hair cells (Chatterjee and Zwislocki 1997, Fig. 4).
Our data did not reveal a systematic relationship between SPL-dependent peak shifts and CF. Some ANFs showed a clear peak shift, while such a shift was completely absent in other ANFs of comparable CF (compare Fig. 9D, E). We have not been able to link the observed variation in SPL-dependent tuning to any systematic experimental factor such as threshold of the ANF, condition of the animal, or time into the experiment. These findings are in contrast to in vivo, intracellular recordings in gerbil of low-CF (500–2,500 Hz) outer hair cells and Hensen cells (Zhang and Zwislocki 1996) and inner hair cells (Chatterjee and Zwislocki 1997), which showed systematic downward peak shifts (as large as two octaves in some cases) of amplitude-versus-frequency curves with increasing SPL. A potential explanation for this discrepancy is the difference in the auditory stimuli used; wideband stimuli tend to linearize the cochlear response compared to single tones (Recio-Spinoso et al. 2009). The comparison between the two types of data is difficult because little is known about the exact relation between transduction potentials in hair cells and ANF responses.
Effect of SPL on phase curves and group delay
The effect of SPL on phase curves was highly variable. The most consistent effect that we observed was a decline in group delay (downward slope of the phase curve) with increasing SPL, but there were exceptions even to that trend (see below). Examples of phase curves obtained at multiple SPLs are shown in Figures 8 and 9 next to the corresponding amplitude curves. As before (Fig. 2), the phase curves were compensated for overall group delay as indicated in the lower-right corner of the graphs. For optimal across-SPL comparison, the same compensation was applied to all curves obtained from the same ANF.
In the examples in Figure 8A, B, phase lag at CF decreased with SPL and the downward slope around CF became shallower. The example in Figure 8C, which showed an amplitude behavior (left column) similar to that of Figure 8A, B, showed an opposite phase behavior, with both phase lag and near-CF group delay increasing with SPL. In Figure 9B, phase at CF is nearly constant across SPL, whereas the curve becomes shallower (decreasing group delay) with increasing SPL. This “pivoting” of the phase curve around CF was previously observed in squirrel monkey ANFs by Anderson et al. (1971). Other examples, however, show pivoting about a frequency different from CF (below CF: Fig. 8C; above CF: Fig. 9F) as previously observed in guinea pig by Palmer and Shackleton (2009) and in one ANF in the squirrel monkey (Anderson et al. 1971). The phase curves of some ANFs showed nonmonotonic effects of SPL (Fig. 9D); in other ANFs, phase was nearly constant over a large range of SPLs (Fig. 9E). A similar variability in phase curves was reported for squirrel monkey (Anderson et al. 1971) and guinea pig (Palmer and Shackleton 2009). In three ANFs, we found phase anomalies (Fig. 9C) reminiscent of those observed in gerbil by Ronken (1986) and in chinchilla by Temchin and Ruggero (2009).
To quantify the effect of SPL on the group delays, we computed the change in group delay per 10-dB increase of stimulus intensity (Δτ
10dB) for each of the segments of the phase curves described earlier (Figs. 6 and 7). The results of this analysis are shown as a function of CF in Figure 10. In most ANFs, near-CF group delay (Fig. 10A, circles) decreased with sound intensity (Δτ
10dB <0). A subset of ANFs (six of 36), however, showed an increase of near-CF group delay with increasing SPL. The effect of SPL on near-CF group delays has been investigated in several mammalian species, using either single tones or first-order Wiener kernels (Anderson et al. 1971; Møller 1977; Carney and Yin 1988; Rhode and Cooper 1997; Recio-Spinoso et al. 2005; Palmer and Shackleton 2009; Temchin and Ruggero 2009). For comparison, Δτ
10dB values estimated from those studies are displayed in Figure 10A (numbered dots). The different studies show comparable ranges of Δτ
10dB values. Interestingly, some studies report increases of group delay with increasing SPL (positive Δτ
10dB values), in contrast with the widespread “textbook view” that group delay around CF always decreases with stimulus intensity.
As before (cf. Fig. 7), off-CF group delays were split in three sets. Group delay in the 100–400-Hz stimulus range (Fig. 10B, crosses) generally increased with increasing SPL (positive Δτ
10dB), whereas group delay evaluated 1.5–0.6 octaves below CF (Fig. 10B, squares) and >0.6 octaves above CF (Fig. 10B, diamonds) generally decreased with increasing SPL (negative Δτ
10dB). The range of Δτ
10dB values for the latter two regions (Fig. 10B, squares and diamonds) was comparable to that observed in the near-CF region (Fig. 10A, circles).