Improved temporal coding of sinusoids in electric stimulation of the auditory nerve using desynchronizing pulse trains

Abstract

Rubinstein et al. [Hearing Res. 127, 108-118 (1999)] suggested that the representation of electric stimulus waveforms in the temporal discharge patterns of auditory-nerve fiber (ANF) might be improved by introducing an ongoing, high-rate, desynchronizing pulse train (DPT). To test this hypothesis, activity of ANFs was studied in acutely deafened, anesthetized cats in response to 10-min-long, 5-kpps electric pulse trains that were sinusoidally modulated for 400 ms every second. Two classes of responses to sinusoidal modulations of the DPT were observed. Fibers that only responded transiently to the unmodulated DPT showed hyper synchronization and narrow dynamic ranges to sinusoidal modulators, much as responses to electric sinusoids presented without a DPT. In contrast, fibers that exhibited sustained responses to the DPT were sensitive to modulation depths as low as 0.25% for a modulation frequency of 417 Hz. Over a 20-dB range of modulation depths, responses of these fibers resembled responses to tones in a healthy ear in both discharge rate and synchronization index. This range is much wider than the dynamic range typically found with electrical stimulation without a DPT, and comparable to the dynamic range for acoustic stimulation. These results suggest that a stimulation strategy that uses small signals superimposed upon a large DPT to encode sounds may evoke temporal discharge patterns in some ANFs that resemble responses to sound in a healthy ear.

FIG. 1

The stimuli used in our experiments are pulse trains with low modulation depths (right). These stimuli can be thought of as the superposition of a large, unmodulated DPT (bottom left) and a small, fully modulated pulse train (top left) similar to the signals produced by CIS processors.

FIG. 2

Stochastic threshold model (STM) of ANF responses to modulations of a DPT. The model takes as input the modulation waveform m(t) and produces a spike whenever the input crosses a noisy threshold. The output of the model is a set of spike times {t_i}. The threshold is the sum of a Gaussian noise term n(t) and a deterministic term θ_n(t) which depends on the time since the previous spike. The only free parameters in the model are the resting threshold θ₀ and the noise amplitude σ.

FIG. 3

The top panel shows one cycle of the electric pulse train stimulus (5 kpps, 2.5 mA 0-p) to which a 417-Hz sinusoidal modulation was applied every second for 400 ms. Modulation depth ranged from 0.5% to 11%, and the entire sequence of modulations was repeated every 5 s for 10 min. The left panel of the middle row shows a period histogram (bin width 2.4 ms) locked to the 5-s modulation cycle for one auditory-nerve fiber. For comparison, the right two panels of the middle row show the response pattern of an ANF (CF=650 Hz) from a healthy ear to a 440-Hz pure tone at 5 and 45 dB above threshold. The bottom panels show the period histograms computed from responses during the electric modulations (left) and the acoustic pure tone (right). The gray line shows a sinusoidal waveform for comparison.

FIG. 4

Period histograms (bin width 0.2 ms) computed from the response of an auditory-nerve fiber to sinusoidally modulated pulse trains at three different frequencies (columns) and five modulation depths (rows). During the unmodulated segments of the DPT, this fiber had a pseudo-spontaneous discharge rate of 54 spikes/s, and its interval histogram had a nearly exponential shape (IH – ExpSF = 0.97). Numbers in each panel are the average discharge rate (in spikes/s) and the synchronization index to the modulation. The vertical axis is in spikes/s.

FIG. 5

The first three columns show the interval histograms corresponding to the period histograms in Fig. 4. The numbers in each panel are the average discharge rates in spikes/s. Vertical dashed lines mark multiples of the stimulus period. The vertical axis represents the number of intervals per bin. For comparison, the rightmost column shows interval histograms of an ANF (CF = 650 Hz) from a healthy ear for a 440-Hz pure tone at 5 and 45 dB above threshold.

FIG. 6

Period histograms of responses of a fiber that gave a transient response to the unmodulated DPT for three modulation frequencies and four modulation depths. Same format as in Fig. 4.

FIG. 7

Interval (left) and period (right) histograms of a fiber's responses to 417-Hz modulations of the DPT at two modulation depths (0.5% and 2.5%). The nonexponential interval histogram (IH – ExpSF = 0.51) computed from responses during the unmodulated DPT segments is shown on top. The vertical axis represents number of intervals per bin for the interval histograms, and discharge rate in spikes/s for the period histograms.

FIG. 8

The left panel shows the synchronization index to a 417-Hz modulator (0.5% modulation depth) as a function of the interval histogram exponential shape factor (IH-ExpSF) for 25 fibers from four cats. The IH-ExpSF was computed based on responses during the unmodulated segments of the DPT. The right panels show interval histograms of responses to the unmodulated DPT for two units with low IH-ExpSF. The vertical dashed lines mark multiples of the modulation period.

FIG. 9

Average discharge rate (left) and synchronization index (right) of five fibers as a function of modulation depth for three modulation frequencies (rows). Each symbol represents data from one fiber. Transient responders are represented by dashed lines, sustained responders by solid lines. The synchronization index is only plotted if the response includes at least 100 spikes. Shading indicates the range of normal acoustic responses to low-frequency pure tones.

FIG. 10

Modulation detection thresholds based on average discharge rate (left) and synchronized rate (right) as a function of pseudo-spontaneous rate to the DPT for three modulation frequencies. Each point shows data from one fiber. Symbols code modulation frequencies. The straight lines are least-squares fits to the data for each frequency (see Table I). For the average-rate thresholds, the slopes of the regression lines were constrained to be the same for all three frequencies.

FIG. 11

Useful dynamic range to sinusoidal modulations of a DPT as a function of pseudo-spontaneous rate for modulation frequencies of 417 and 833 Hz. The useful dynamic range is the ratio of the modulation depth that evokes a discharge rate of 300 spikes/s to the synchronized rate threshold. Each point shows data from one fiber. Symbols code modulation frequencies. The straight lines are least-squares fits to the data for each frequency, with the constraint that the slopes be the same for both frequencies (see Table II).

FIG. 12

This figure shows, as a function of modulation depth, the percentage of fibers whose responses to a modulated DPT are within the useful dynamic range (solid lines), as well as the percentage of fibers that exceed the maximal acoustic rate of 300 spikes/s (dashed lines) for modulation frequencies of 417 Hz (left) and 833 Hz (right). Percentages are shown separately for sustained and transient DPT responders. Only responses that were recorded at the standard DPT level in each animal (Table I in Litvak et al., 2003b) are included.

FIG. 13

Average discharge rate (left) and synchronization index (right) of the stochastic threshold model as a function of the normalized modulation depth m/σ for three modulations frequencies (rows). Each curve corresponds to one value of the threshold to noise ratio θ₀/σ: 1.4 (dot-dash), 1.8 (dash), 2.4 (dot), and 4 (solid). The corresponding pseudo-spontaneous discharge rates are 210, 119, 30, and 0.2 spikes/s, respectively.

FIG. 14

Normalized modulation depth thresholds m/σ based on average rate (left) and synchronized rate (right) as a function of pseudo-spontaneous rate for the stochastic threshold model. Symbols code modulation frequencies.

FIG. 15

Useful dynamic range of the stochastic threshold model as a function of pseudo-spontaneous rate for two modulation frequencies. The definition of useful dynamic range is the same as in Fig. 11.

FIG. 16

Algorithm for removing the stimulus artifact from contaminated recordings. The top row shows the waveform (left) and the spectrum (right) of the signal recorded from a microelectrode after it has been passed through a 0.2-ms moving-average filter. The stimulus is a sinusoidally modulated pulse train (modulation frequency: 417 Hz; modulation depth: 5%). The inset shows the spike waveform for an unmodulated pulse train. The middle row shows the waveform and spectrum after low-pass filtering the signal at 3 kHz. The bottom row shows the waveform and spectrum after eight steps of the iterative artifact rejection algorithm described in Appendix A.

FIG. 17

Method for estimating modulation depth thresholds. The left panel shows the percentage of hit trials against depth of modulation at 417 Hz for four sustained DPT responders. For three of these fibers, the hit percentage was below 100% for only one modulation depth, preventing a direct determination of threshold. The middle panel plots the quartile rate difference ${\text{r}}_d^q(m)$ against modulation depth for the same four fibers. The dotted line indicates the threshold criterion. The right panel shows the same data plotted on an inverted Gaussian vertical scale defined by Eq. (B2). Gray shading indicates the region where the data grow approximately linearly. Circled symbols show the estimated thresholds.