Changes across time in spike rate and spike amplitude of auditory nerve fibers stimulated by electric pulse trains

Abstract

We undertook a systematic evaluation of spike rates and spike amplitudes of auditory nerve fiber (ANF) responses to trains of electric current pulses. Measures were obtained from acutely deafened cats to examine time-related changes free from the effects of hair-cell and synaptic adaptation. Such data relate to adaptation that likely occurs in ANFs of cochlear-implant users. A major goal was to determine and compare rate adaptation observed at different pulse rates (primarily 250, 1000, and 5000 pulse/s) and describe them using decaying exponential models similar to those used in acoustic studies. Rate-vs.-time functions were best described by two-exponent models and produced time constants similar to (although slightly greater than) the "rapid" and "short-term" components described in acoustic studies. There was little dependence of these time constants on onset spike rate, but pulse-rate effects were noted. Spike amplitude changes followed a time course different from that of rate adaptation consistent with a process related to ANF interspike intervals. The fact that two time constants governed rate adaptation in electrically stimulated and deafened fibers suggests that future computational models of adaptation should not only include hair cell and synapse components, but also components determined by fiber membrane characteristics.

Figures

FIG. 1

Examples of waveforms recorded in response to pulse trains presented at three rates. In each of the three cases shown, “raw” waveforms (with large electrical stimulus artifacts) are plotted above the processed waveforms. See text for explanations of stimulus artifact reduction schemes. Each of the three sets of “raw” traces and each of the three sets of processed waveforms are plotted to the same scales (indicated by the two calibration bars in the upper plots). Stimulus parameters (pulse rate, stimulus level) are shown at the upper right of each graph.

FIG. 2

Examples of spike-rate adaptation observed in the PSTHs from the responses of two auditory nerve fibers (ANFs) at the four stimulus rates used in this study. Histograms for stimulus rates of 250, 1000, and 5000 pulse/s were provided by one fiber, whereas a second fiber provided the 10,000 pulse/s rate data. Each column contains poststimulus-time histograms (PSTHs) obtained at three stimulus levels. Histograms based on 1-ms bins are plotted with vertical bars, whereas those based on progressively wider bins (defined in the text) are plotted using open circles.

FIG. 3

Rate-level functions for 15 ANFs obtained at multiple stimulus pulse rates, demonstrating greater sensitivity (left-shifted plots) for functions obtained with high-rate stimulation. Abscissa and ordinate scaling is identical for all graphs. Dotted lines indicate cases in which linear regression was used to estimate threshold values. Data for 10,000 pulse/s stimuli (diamond symbols) were available in only three of the fibers.

FIG. 4

Examples of the effect of adaptation on rate-level functions assessed across different temporal analysis windows. (a) Functions obtained from six fibers of this study using three windows to characterize onset response (0- to 1-ms window), the “rapid” response (0- to 12-ms window) and the steady state, or adapted (200–300 ms) response. Stimulus rate was 5000 pulse/s. (b) Normalized ANF rate-level functions obtained in response to pure-tone stimuli. The functions of the left graph are reproduced from those reported by Westerman and Smith (, Fig. 6), whereas the functions in the right graph have been normalized to the maximum value of each function in the left graph. Their data are based on mean values of 19 ANFs. Their “onset” responses are the maxima that occurred within a 1-ms window near stimulus onset. “Rapid”, “short term”, and “steady state” functions were derived from their two-exponential model fits.

FIG. 5

Group ANF data showing the effect of pulse rate and response rate on rate adaptation. Rate decrements (left column) and normalized rate decrements (right column) for each ANF are plotted as a function of onset spike rate for four pulse rates. Normalized data were computed as described in the text. Gray regions indicate normalized decrements greater or equal to 0.9, the criterion used to define an ANF as a “strong adapter” (as defined in the text). The line segments defined by gray circles indicate linear regression trends from Litvak et al. (2001) for stimulus rates of 1000 and 4800 pulse/s. Panel C plots a subset of the data in panel B, with data from 12 fibers selected on the basis that they spanned the greatest ranges of onset spike rate. Those functions confirm the inverted U-shaped function suggested by the general trend seen in panel B.

FIG. 6

Demonstration of correlations in spike-rate decrements (adaptation) observed across different pulse rates. Spike rate decrements caused by 250 pulse/s trains (upper graph) and 1000 pulse/s trains (lower graph) are plotted versus the decrements caused by 5000 pulse/s stimuli. To control for spike onset rate effects, each datum represents x–y pairs obtained from an ANF such that the difference of onset spike rates for the x and y values did not exceed 10%. Regressions indicate that the degree of adaptation observed at one pulse rate is correlated to that observed at other pulse rates. The upper graph contains data from 53 fibers and the lower graph contains data from 35 fibers.

FIG. 7

Across-fiber summary of rate-adaptation time constants obtained using a single-exponent (upper row) and a two-exponent (lower row) model of adaptation for pulse rates of 250, 1000, and 5000 pulse/s. Numbers of data points and contributing fibers are shown in each panel. Results indicate that the rapid and short-term adaptation time constants are generally independent of onset response rate, used here as a correlate to stimulus level. The curved trend seen in the upper-right plot is believed to be an artifact of the limitations of the single-exponent model.

FIG. 8

Results of comparisons of “goodness of fit” of the single-exponent and double-exponent models used to fit PSTH data. Ratios of the Akaike’s information criterion (AIC) computed for the double-exponent model (“Model 2”) and the single-exponent model (“Model 1”) are plotted as a function of different ranges of onset spike rates, with pulse rate as a parameter. Values less than 1 indicate that the double-exponent model was, on average, a better fit than the single-exponent model. The horizontal brackets about each plotted datum indicate the range of onset spike rates used for each AIC computation.

FIG. 9

Rate adaptation time-constants estimated with the two-exponent model. Regression lines are shown by the thick line segments. The correlation coefficient for short-term time constant is statistically significant but that for rapid time constant is not (see text). Median values for each pulse rate are plotted using open symbols.

FIG. 10

Comparisons of ANF thresholds (upper panel) and rate-level slopes (lower panels) for stimulus rates of 250 and 5000 pulse/s. For both rates, the fiber categories of “strong” and “weak” adapters were defined on the basis of data obtained at 5000 pulse/s. Statistically significant differences were found between the strong and weak adapters for both measures and pulse rates (see text). The number of contributing ANFs is indicated immediately below each plotted data set.

FIG. 11

Examples of ANF spike amplitude changes in response to 5000 pulse/s stimuli. The three panels show response waveforms from one ANF stimulated at three levels (italicized numbers). The vertical scale of the three panels is identical. The upper two panels (a) show 30 superimposed traces in response to the high-rate pulses. Reductions in the amplitude of the second spike of each response are evident. The lowest panel (b) shows two response epochs of a single trace (i.e., response to a single pulse train). The number above each spike indicates the spike amplitude relative to the first spike. Note how the amplitude of the second spike of any spike pair is influenced by the ISI.

FIG. 12

Effect of (1) pulse rate, (2) time after train onset, and (3) response rate on spike amplitude. Plotted are the mean normalized amplitudes (computed across fibers) versus time for responses obtained with 250 pulse/s trains (upper panel) and 5000 pulse/s trains (lower panel). For each ANF, amplitudes were normalized to those measured in the first temporal analysis window (i.e., the 0- to 4-ms response epoch). For each graph, data are parsed into three onset spike rate ranges (indicated by different symbols).

FIG. 13

Influence of ISI on the amplitudes of the first and second spikes in response to pulse-train stimuli. Amplitude changes are expressed as the ratio of the second spike amplitude and the first spike amplitude of the recorded response to each train presentation. These ratios are plotted as functions of the time interval between the two spikes. Data were included from all ANFs that contributed data at ISI’s equal to or greater than 20 ms. The number of contributing ANFs is indicated by “n” in each panel. Separate plots are provided for three stimulus pulse rates (panels a, b, and c), with the greatest decrements observed at small ISIs. Median values, plotted for each pulse rate using open symbols, were computed as described in the text. These median values are replotted in panel d for the three pulse rates, showing the similarity of the functions across stimulus rates.