(a) Schematic of an uncoiled cochlea illustrates the idea of using multiple bandwidths of high-pass noise to systematically limit the region of auditory nerve fibers that can contribute synchronously to CAPs evoked with high-level stimuli. (b) N 1 amplitude (normalized relative to the unmasked N 1 amplitude) would theoretically grow differently for a cochlea with missing auditory nerve fibers (dashed line) than for a normal cochlea (solid line). (c) Derivatives of the respective amplitude growth functions yield density functions that theoretically reveal the distribution of viable nerve fibers contributing to the CAP.
(a) Digital waveform of gerbil-tailored chirp stimulus rising in frequency and amplitude over a duration of 3.06 ms. (b) Instantaneous frequency of chirp stimulus is equivalent to the inverse of cochlear traveling wave delay in gerbil (estimated with gerbil CAP latency data from Earl and Chertoff, 2010). (c) Acoustic spectrum of chirp stimulus shows relatively flat spectral energy between 1 and 60 kHz, spanning nearly the entire range of gerbil hearing. (d) Representative spectra of four of the high-pass masking conditions illustrating the increase in spectrum level to equalize the rms SPL across all conditions.
(a) Representative unmasked and masked CAP waveforms for chirp stimuli at 90 dB pSPL from a normal-hearing gerbil illustrate the trend of decreasing N 1 amplitude and increasing N 1 latency as the high-pass noise masker cutoff frequency decreases. (b) Representative raw data for N 1 amplitude (filled circles, units on right ordinate) and N 1 latency (open circles, units on left ordinate) for all 25 masking conditions. Unmasked values represent the mean of four unmasked CAP recordings.
(a) Representative N 1 amplitude data for CAPs evoked with chirps at 90 dB pSPL (filled circles) plotted as a function of distance from cochlear apex (transformed from high-pass noise cutoff frequency with the frequency-place map for gerbil from Müller, 1996). Fitting the N 1 amplitude data with a four-parameter (a, b, x0, y0) sigmoid function yields a cumulative amplitude function (CAF), shown with thick line along with its corresponding coefficient of determination (R 2). (b) The neural density function (NDF) (thick line) is obtained by using the CAF parameters to solve the analytical derivative of the CAF equation [Eq. (2)] for distance from cochlear apex (x). The peak location is given by parameter x0 and the bandwidth is defined as the distance spanned by the inner 2/3 of the area under the curve (calculated by multiplying peak density by 0.3413 and finding the difference between the corresponding distance values).
A representative CAP evoked with 2 kHz tonebursts at 60 dB pSPL (a) is nearly 10 times smaller in magnitude than a CAP evoked with chirps at the same level (b). (c) Comparison of unmasked N 1 amplitudes illustrates that chirps at 60 dB pSPL produced the largest CAPs. Even chirps as low as 30 dB pSPL generated CAPs that were larger in magnitude than 2 kHz tonebursts at 90 dB pSPL. Error bars represent one standard deviation. The sample size is 9 for each stimulus condition except for the chirp condition at 30 dB pSPL for which the sample size is 4.
Normalized N 1 amplitude growth curves (thin lines) for the nine normal-hearing gerbils (experiment 1) with their corresponding mean CAFs (thick lines) show differences in slope and variability across stimulus type and level. The amplitude growth curve shown with a dashed line in panel (b) was determined to be an outlier (i.e., initial masked amplitude was more than two SD above the mean of initial masked amplitude across all stimulus conditions) and was excluded from further analysis. Mean coefficients of determination (R 2) indicate that the four-parameter sigmoid function accounts for a large majority of the variance in the data.
Individual NDFs (thin lines) and the corresponding mean NDFs (thick lines) for the nine normal-hearing gerbils (experiment 1) illustrate the distribution of neural firing density for each stimulus type and level combination. The individual NDF shown with the dashed line in panel (b) represents the outlier that was described in Fig. 6. Statistical analyses (see Table II) indicated that the mean NDF of chirps at 90 dB pSPL was significantly broader and peaked significantly closer to the base than the mean NDF of 2 kHz tonebursts at 90 dB pSPL. At 60 dB pSPL, the mean NDF of 2 kHz tonebursts was significantly broader than the mean NDF of chirps, although the mean peak location of the chirp NDFs was significantly closer to the base than the mean peak location of the 2 kHz toneburst NDFs.
N 1 latency shift (ms; masked-unmasked latency) plotted as a function of high-pass noise cutoff frequency and distance from cochlear apex for the normal-hearing group of experiment 1. Individual animal data are shown with thin lines and the group means are shown with thick lines. The latency shift functions are generally consistent with the theory suggested by Teas et al. (1962) that the location of synchronous neural firing for moderate and high-level stimuli is shifted toward the apex proportional to the high-pass noise cutoff frequency. The trends in latency shift resemble the inverse of the patterns observed for N 1 amplitude growth (Fig. 6).
(a) Cochlear microphonic (CM) data for the ten gerbils in experiment 2 indicate an exponential decrease in amplitude over a course of 15 min following application of 200 μg of gentamicin to the round window niche. The CM was evoked with 16 kHz tonebursts (10 ms in duration) at 80 dB pSPL. Dose-response curves for lower gentamicin doses (50 and 100 μg) are shown for comparison. (b) Post-gentamicin CAP threshold data show shifts ranging from 10 to 25 dB for chirps and a general trend of increasing threshold shifts for tonebursts as stimulus frequency increases.
(a) and (b) N 1 amplitude functions for ten gentamicin-exposed gerbils (thin lines) fall within the normal range (mean +/− 2SD; gray areas) for chirps at 90 dB pSPL, whereas for chirps at 60 dB pSPL, six out of the ten gentamicin-exposed animals fall outside the normal range. Thick dashed lines in the top panels represent the mean of the post-gentamicin CAFs. Mean R 2 values indicate that the four-parameter sigmoid function accounts for a large majority of the variance in the post-gentamicin data. (c) and (d) Individual NDFs for the ten gentamicin-exposed gerbils (thin lines) with the mean NDFs (thick dashed lines) plotted against the normal ranges (mean +/− 2SD; gray areas) indicate minimal difference between the mean bandwidth and mean peak location for chirps at 90 dB pSPL. For chirps at 60 dB pSPL, mean bandwidth did not differ across groups but the mean peak location for the gentamicin-exposed group was significantly more apical than the mean peak location for the normal-hearing group (open circle). See Table II for statistical analyses.
N 1 latency shift (ms; masked-unmasked latency) plotted as a function of high-pass noise cutoff frequency and distance from cochlear apex for the post-gentamicin group in experiment 2 (thin lines = individual animal data; thick dashed lines = group means). Post-gentamicin latency shifts were approximately half that of the chirp conditions for the normal-hearing group (Fig. 7).
Plotting the post-gentamicin shift in chirp CAP thresholds against the post-gentamicin shift in NDF peak location for chirps at 60 dB pSPL (re: normal mean peak location for chirps at 60 dB pSPL) reveals a significant inverse correlation between the two variables. Negative values for peak shift indicate apical shifts re: normal peak location. Filled circles (n = 10) represent the animals that met the inclusion criteria for experiment 2. Open circles (n = 4) represent animals that were excluded from analysis due to progressive CAP threshold shifts during the course of data collection (two upper circles) or due to minimal chirp CAP threshold shifts following gentamicin application (two lower circles).
An alternative method of analyzing neural firing density involves constructing numeric NDFs by calculating the numerical derivatives of the N 1 amplitude data (instead of taking the analytical derivative of the equations fitted to the data to construct analytic NDFs). These numeric NDFs (thin lines) preserve the “fine-structure” of neural firing density that may be useful for differentiation of normal and pathologic cochleae. However, other than for chirp stimuli at 90 dB pSPL (top left panel), the analytic NDFs (thick lines; mean NDFs from experiment 1) correspond closely with the distributions of neural firing depicted by the numeric NDFs.
Within-animal coefficients of variation (CV) for N 1 amplitude of the four unmasked CAPs recorded from each animal during each stimulus condition.
Descriptive statistics and results of paired samples t-tests comparing NDF bandwidth and peak location across stimulus type at 90 and 60 dB pSPL (experiment 1). Sample size was 8 for 90 dB pSPL conditions [due to exclusion of outlier indicated with dashed line in top right panel (b) of Fig. 6 and 9 for 60 dB pSPL conditions.
Descriptive statistics and results of independent samples t-tests comparing bandwidth and peak location of chirp NDFs for normal to post-gentamicin (post-gent.) groups at 90 and 60 dB pSPL (experiment 2)
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