improved temporal coding of sinusoids in electric stimulation of the

Improved temporal coding of sinusoids in electricstimulation of the auditory nerve using desynchronizingpulse trainsa)

Leonid M. Litvakb)

Eaton-Peabody Laboratory and Cochlear Implant Research Laboratory, Massachusetts Eye and EarInfirmary, 243 Charles Street, Boston, Massachusetts 02114 and Speech and Hearing Bioscienceand Technology Program, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,Massachusetts 02139

Bertrand DelgutteEaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston,Massachusetts 02114 and Research Laboratory of Electronics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Donald K. EddingtonCochlear Implant Research Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston,Massachusetts 02114 and Research Laboratory of Electronics and Neural Prosthesis Research Center,Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

~Received 13 March 2003; accepted for publication 4 August 2003!

Rubinsteinet al. @Hearing Res.127, 108–118~1999!# suggested that the representation of electricstimulus waveforms in the temporal discharge patterns of auditory-nerve fiber~ANF! might beimproved by introducing an ongoing, high-rate, desynchronizing pulse train~DPT!. To test thishypothesis, activity of ANFs was studied in acutely deafened, anesthetized cats in response to10-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 onlyresponded transiently to the unmodulated DPT showed hyper synchronization and narrow dynamicranges 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 depthsas 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 andsynchronization index. This range is much wider than the dynamic range typically found withelectrical 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 largeDPT to encode sounds may evoke temporal discharge patterns in some ANFs that resembleresponses to sound in a healthy ear. ©2003 Acoustical Society of America.@DOI: 10.1121/1.1612493#

PACS numbers: 43.64.Me, 43.64.Nf, 43.64.Pg@WPS#

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I. INTRODUCTION

Speech and other sound stimuli contain informationboth their slowly varying envelope and their rapidly varyinfine-time structure~Rosen, 1992!. Yet, many processingstrategies used in today’s cochlear implants only delivervelope information and discard the temporal fine structuFor example, continuous interleaved sampling~CIS! strate-gies ~Wilson et al., 1991! use an envelope detector in eafrequency channel to derive waveforms used to moducarrier pulse trains. These envelope detectors discard thformation available in the fine-time structure. The SPEAstrategy used with Nucleus implants~Seligman and McDer-mott, 1995! also discards the fine structure in each stimulachannel.

a!Portions of this work were presented as a poster at the ARO MidwiMeeting in St. Petersburg Beach, FL, 2001 and the CIAP ConferencMonterey, CA, 2001.

b!Electronic mail: [email protected]

J. Acoust. Soc. Am. 114 (4), Pt. 1, October 20030001-4966/2003/114(4)/2

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Smith et al. ~2002! evaluated the relative importance oenvelope and fine-time structure information in auditory pception using acoustic stimuli called ‘‘auditory chimerasThe chimeras are sounds which, in each frequency bahave the fine-time structure of one sound, and the enveof another. Smithet al. found that, with four to eight fre-quency bands, speech comprehension is better using thevelope information than the information in the fine-timstructure. However, for the same number of analysis chnels, subjects performed melody identification and soundcalization tasks better with the fine-time structure than wthe envelope information. These results suggest that moding cochlear implant processing strategies to include fitime structure information might improve pitch perceptioThe fine structure may also be essential for taking full avantage of binaural cues delivered by bilateral implants.

Fine structure information might be delivered to cchlear implants in several ways. The simplest method,ready used in some processing strategies, is to delive

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analog representation of the stimulus waveform in eachquency channel. Alternatively, the frequency of a periostimulus might be encoded by the rate of a pulse train.though this method has the disadvantage that signals hadifferent waveforms cannot be distinguished if they havesame fundamental frequency, it was used in early Nuclprocessors to encode the fundamental frequency of v~Tong et al., 1980!. Finally, fine structure information mighbe introduced in a CIS strategy by increasing the cutoff fquency of the envelope detector, or even eliminating it agether. The rate of the carrier pulse trains would also havbe increased so as to sample the resulting high-frequemodulation waveforms without aliasing.

Both single-unit studies in animals and evoked potenstudies in implanted human subjects suggest that neithethe above strategies for delivering fine structure informatwould, by itself, produce temporal discharge patterns in tauditory nerve resembling those evoked by acoustic stimin a normal ear. Auditory-nerve fibers~ANF! encode thefine-time structure of acoustic stimuli in their temporal dcharge patterns for frequencies up to 5 kHz~Rose et al.,1967; Johnson, 1980!. For example, in response to a putone, neurons fire at random multiples of the stimulus perin that there may be one, two or more cycles between scessive spikes~Rose et al., 1967!. The stimulus period isthus represented in the ensemble activity of a populationneurons by a stochastic form of Wever’s volley principeven when the stimulus period is shorter than the neurafractory period. This coding scheme is made possible byongoing stochastic release of neurotransmitter at inner-hcell synapses, and the modulation of this neurotransmrelease by the receptor potential which tracks each cyclthe stimulus waveform.

Because hair cells and their synapses are missing inears, temporal discharge patterns produced by electric stlation are very different from normal acoustic responses.prathreshold responses to electric pulse trains or sinuswith frequencies below 500–800 Hz behave nearly deministically, typically showing one spike discharge on evestimulus cycle~Moxon, 1967; Hartmannet al., 1984, 1990;van den Honert and Stypulkowski, 1987; Parkins, 19Javelet al., 1987; Javel, 1990; Javel and Shepherd, 200!.Such entrainment also occurs for sinusoidally modulaelectric pulse trains similar to stimuli produced by CIS prcessors~Litvak et al., 2001!. Moreover, the temporal precision of discharges evoked by such low-frequency elecstimuli is much higher than with acoustic stimulation~Hart-mann et al., 1984, 1990; Javel, 1990; Javel and Shephe2000!. For example, whereas spikes are distributed omost of one-half cycle in response to a pure tone, they ooccupy a small fraction of the stimulus cycle for electsinusoids, thereby inadequately representing the sinusowave shape~Hartmannet al., 1984; van den Honert and Stypulkowski, 1987!. In fact, temporal discharge patterns felectric sinusoidal, triangular and square waves of the sfrequency are surprisingly similar considering that thestimuli have very different spectra~van den Honert and Stypulkowski, 1987; Parkins, 1989!.

Further issues arise at higher frequencies~.500–800

2080 J. Acoust. Soc. Am., Vol. 114, No. 4, Pt. 1, October 2003

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Hz! where neural refractoriness prevents fibers from dcharging on every cycle of the electric stimulus. With bosinusoidal and pulse train stimuli, refractoriness can cahistory-dependent changes in response latency, resultingneuron discharging at two distinct phases within a stimucycle ~Parkins, 1989; Javel, 1990; Javel and Shephe2000!. Such double-peaked period histograms are notserved for acoustic stimulation above 1000 Hz~Johnson,1980!. Interval histograms are also highly abnormal, demostrating a tendency for spikes to occur at regular interveven for high-frequency~.1000 Hz! stimulation ~Parkins,1989; Dynes and Delgutte, 1992!. In some cases, ANFs fireexactly on every other cycle or even at higher multiplesthe stimulus period~Javel, 1990; Javel and Shepherd, 200!.This tendency is also apparent in measurements of elecompound action potentials~ECAPs! from cochlear implantusers ~Wilson et al., 1997!. Specifically, in response to1-kpps electric pulse train, ECAPs alternate between strand weak responses to each pulse for up to 100–200 msstimulus onset. This alternation suggests that, while mANFs respond to the first pulse, they are in a refractory sduring the second pulse and only respond again to the tpulse. If most fibers fire together on every other cycle, ththe auditory nerve population represents half the stimufrequency rather than the actual frequency. In summary, nral refractoriness, the narrow dynamic ranges, excessihigh discharge rates, and exaggerated synchrony combinmake the temporal coding of electric stimuli highly unnatucompared to normal acoustic stimulation, particularly for frquencies above 500 Hz.

Rubinstein et al. ~1999b! proposed that the temporacoding of stimulus waveforms in cochlear implants mightimproved by introducing an ongoing, high-frequency, deschronizing pulse train~DPT! in addition to the signal pro-duced by the speech processor. The purpose of a DPTamplify noise in sodium channels so as to produce mstochastic responses similar to those of spontaneously afibers. In a companion paper~Litvak et al., 2003b!, we re-corded ANF responses to a 10-min, 5-kpps DPT. We fouthat, after 1–2 min of continuous stimulation, the DPT prduced activity that, in many fibers, resembled spontaneactivity in a healthy ear. Several types of responses toDPT were identified. Some fibers~roughly 50%! only re-sponded transiently to the DPT, while the others showesustained response throughout 10 min of DPT stimulatiFor the sustained responders, the ‘‘pseudo-spontaneoustivity evoked by the DPT had broadly distributed interspiinterval distributions and appeared to be uncorrelated frfiber to fiber. Some interval histograms~25%! had an expo-nential shape, as does normal spontaneous activity; howethe majority of sustained responses had nonexponentiaterval histograms, particularly if they discharged at very hirates.

In this paper, we directly test the hypothesis that a Dimproves the representation of the fine-time structure intemporal discharge patterns of ANFs for sinusoidal stimThere are at least three ways in which a DPT could mresponses to electric stimuli better resemble acousticsponses in a healthy ear. First, a DPT could desynchro

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stimulus-evoked activity across-fibers. For higher-freque~.500 Hz! stimuli, desynchronization may allow differenneurons to discharge on different stimulus cycles, therallowing volley coding of frequency. By simultaneously rcording from pairs of fibers, we showed that such desynchnization does in fact occur after a few seconds of DPT stimlation ~Litvak et al., 2003b!.

Second, a DPT may allow small electric signals toencoded as modulation of ongoing DPT-evoked pseuspontaneous activity, much as normal acoustic responsemost ANFs are effectively modulations of ongoing spontaous activity. Such modulations of random activity allofaithful transmission of the stimulus waveform in neural dcharges by a process akin to stochastic resonance~Yu andLewis, 1989; Collinset al., 1995; Wiesenfeld and Moss1995!. If the stochastic nature of the responses could bestored by the DPT, then a similar mechanism may alsoprove the coding of the stimulus fine-time structure in eltric stimulation.

Finally, computer simulations of auditory-nerve fibesuggest that a DPT may lower the threshold and increasedynamic range to electric stimulation~Rubinstein et al.,1999a!. The increased dynamic range is particularly signcant when one considers complex stimuli such as vowThese waveforms contain peaks of widely different heigin each period. A wide dynamic range might allow fibersrepresent all of the waveform peaks in their temporal dcharge patterns rather than just the largest peak.

Previous tests of the ideas underlying the DPT~Rubin-steinet al., 1999b; Wilsonet al., 1998! were based on electric compound auditory potential~ECAP! responses, whichprovide only indirect evidence of single-unit activity. In adition, these studies used short pulse trains~30 ms!, whichare a poor model of an ongoing DPT. We found thatsponses to a DPT only reach a near steady state aftermin of DPT stimulation~Litvak et al., 2003b!. In this paper,we directly test the hypotheses underlying the DPT bycording from single fibers from the auditory nerve of deened cats. We focus on responses that occurred after adtion to a DPT presented for 10 min. We compare tempodischarge patterns of ANFs for sinusoidal modulations oDPT with normal acoustic responses to pure tones. Wetest the hypothesis that the DPT increases the dynamic rby studying responses to sinusoidally modulated DPTs ovrange of modulation depths.

Our scheme for encoding acoustic signals into elecwaveforms differs somewhat from that used by Rubinstet al. ~1999b! in their original formulation of the DPT ideaIn that paper, an analog electric sinusoid was directly suimposed upon a DPT; here we encode the sinusoid as a smodulation of a DPT. This coding scheme assumes that nral responses to a high-rate pulse train with low modulatdepth are similar to those elicited by the superposition olarge, unmodulated DPT and a small, highly modulated putrain as might be produced by a CIS processor~Fig. 1!. Thisassumption is a mathematical identity if the same pulse tis used for both the DPT and the CIS carrier. It may homore generally if the time constant of the neural membris large compared to the intervals between pulses. In

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scheme, modulation depth is proportional to the amplituof the sinusoidal stimulus for small modulations. The diffeences between the present scheme and the Rubinsteinet al.~1999b! original strategy will be further considered iSec. IV.

II. METHODS

The animal preparation, electrical stimulation, andcording methods are described in the companion paper~Lit-vak et al., 2003b!. Briefly, cats were anesthetized with dialurethane~75 mg/kg!, then deafened by co-administrationkanamycin~subcutaneous, 300 mg/kg! and ethacrinic acid~intravenous, 25 mg/kg! ~Xu et al., 1993!. As described indetail in the companion paper~Litvak et al., 2003b!, most ofthe animals had some residual hearing in the nonimplanear. To minimize the effect of residual hair cells in thepreparations, we only report responses from neurons withspontaneous activity in the absence of a DPT. Two intrachlear stimulating electrodes~400 mm Pt/Ir balls! were in-serted into the cochlea through the round window. One etrode was inserted approximately 8 mm and was used asstimulating electrode. The other electrode was insertedinside the round window and served as the return electro

Standard techniques were used to expose the audnerve via a dorsal approach~Kiang et al., 1965!. We re-corded from single units in the auditory nerve using glamicropipettes filled with 3M KCl. For small modulationdepths, most of the stimulus artifact could be removed onusing a digital signal processor implementing a movingerage filter whose length matched the 0.2-ms pulse perNeural responses were also recorded digitally with a sapling rate of 20 kHz for off-line analysis. Methods usedremove the stimulus artifact from these records are descrin Appendix A.

A. Stimuli

We conducted a neural population study by investigatresponses to a single DPT level for each animal. To ensthat a large fraction of fibers would respond to the DPT,DPT level was set at 8–10 dB above ECAP threshold,described in detail in the companion paper~Litvak et al.,2003b!.

We studied responses to small~modulation depth<15%! sinusoidal modulations of the DPT. Figure 3~top!schematizes the envelope of the electric stimuli. The carwas a 5-kpps train of biphasic pulses~cathodic/anodic, 25msper phase!. In order to acquire responses to both the unmo

FIG. 1. The stimuli used in our experiments are pulse trains with low molation depths~right!. These stimuli can be thought of as the superpositiona large, unmodulated DPT~bottom left! and a small, fully modulated pulsetrain ~top left! similar to the signals produced by CIS processors.

2081Litvak et al.: Improved temporal coding of electric sinusoids

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lated DPT and modulations of the DPT for several modution depths and frequencies, the stimulus was composealternating modulated~400 ms! and unmodulated~600 ms!segments.1 Modulation depth and, in some cases, modulatfrequency was changed on each successive segment. Mlation depth was varied from 0.5% to 15%, while modulatifrequency was either 104, 417 or 833 Hz. The entirequence of modulated and unmodulated segments ha5–12-s period, and was repeated continuously for 10 minuntil contact with the fiber was lost.

Modulation was applied such that the mean amplitudethe carrier pulses was the same during modulated andmodulated segments. Specifically, during modulation, thevelope was defined asA•(11m•sin(2pfmt)), wheref m is themodulation frequency,A is the amplitude of the unmodulateDPT, andm is the modulation depth. The modulation periowas always an integer multiple of the 0.2-ms carrier perto avoid beating, and the modulation phase was chosethat the peak of the modulation waveform always coincidwith a carrier pulse.

B. Analysis

Responses collected during the unmodulated DPT sments were used to classify each fiber using the same schas in the companion paper~Litvak et al., 2003b!. Some fibersexhibited only a transient response to the DPT, and adato near zero~,5 spikes/s! discharge rate after 100 s of DPstimulation. We will refer to these fibers as ‘‘transient DPresponders.’’ Fibers that responded to the unmodulatedments over the entire stimulus duration will be referred to‘‘sustained responders.’’

Litvak et al. ~2003b! further used interval histograms tcharacterize the temporal discharge patterns of sustainesponders. We found that, while some responses had neexponential interval histograms, others had strongly nonponential interval histograms. The degree of ‘‘exponentity’’ of the histogram was quantified using an Interval Histgram Exponential Shape Factor~IH-ExpSF! ~Litvak et al.,2001!. The IH-ExpSF is computed by first fitting the intervhistogram with both a single exponential and, piecewise,three exponentials. The root mean squared~rms! error ofeach fit to the data is then determined, and the IH-Expdefined as the ratio of the rms error for the piecewise fitthat for the single exponential fit. The IH-ExpSF for sampfrom a stationary Poisson process is approximately 1.

C. Stochastic threshold model

As a concise way of summarizing the data, we devoped a simple functional model of responses of ANFsmodulations of a DPT~Fig. 2!. The model takes as input thmodulation waveformm(t). For a sinusoidal modulatorm(t)5m•sin(2pfmt), wheref m is modulation frequency, andm is modulation depth. A spike is produced by the modwheneverm(t) crosses a noisy threshold. The thresholdthe sum of a deterministic term and a noise term. To accofor the refractory properties of ANFs, the deterministic co


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The threshold recovery functionr (t) was chosen to fit theabsolute and relative refractory periods of electrically stimlated ANFs ~Dynes, 1995!. For the noise term, we usecomputer-generated zero-mean, white Gaussian noisestandard deviations. Because the model was simulated uing 0.2-ms time steps, the noise bandwidth was effectiv2500 Hz. Because the noisy threshold is the critical elemof the model, we refer to this model as the stochastic threold model~STM!.

We computed responses of the STM to sinusoidal molators of different frequencies and modulation depths. Tconditional probability that a model neuron fires at timetgiven that the last spike occurred att i is

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whereG is the cumulative Gaussian distribution, andr (t) isthe recovery function described by Eq.~1!. For an unmodu-lated DPT (m50), the pseudo-spontaneous discharge r~the discharge rate during the unmodulated DPT! is entirelydetermined by the threshold-to-noise ratiou0 /s. For non-zero values ofm, the discharge rate depends on the ratiom/sas well. These two ratios entirely determine the modelsponse to sinusoids.

III. RESULTS

A. Basic response characteristics

Our results are based on 68 responses recorded fromauditory-nerve fibers in five cats to sinusoidally modulatelectric pulse trains. Each record included responses

FIG. 2. Stochastic threshold model~STM! of ANF responses to modulationof a DPT. The model takes as input the modulation waveformm(t) andproduces a spike whenever the input crosses a noisy threshold. The outthe model is a set of spike times$t i%. The threshold is the sum of a Gaussianoise termn(t) and a deterministic termun(t) which depends on the timesince the previous spike. The only free parameters in the model areresting thresholdu0 and the noise amplitudes.


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FIG. 3. The top panel shows one cycle of the electpulse train stimulus~5 kpps, 2.5 mA 0-p! to which a417-Hz sinusoidal modulation was applied every seond for 400 ms. Modulation depth ranged from 0.5%11%, and the entire sequence of modulations waspeated every 5 s for 10 min. The left panel of themiddle row shows a period histogram~bin width 2.4ms! locked to the 5-s modulation cycle for onauditory-nerve fiber. For comparison, the right two paels of the middle row show the response pattern ofANF (CF5650 Hz) from a healthy ear to a 440-Hpure tone at 5 and 45 dB above threshold. The bottpanels show the period histograms computed fromsponses during the electric modulations~left! and theacoustic pure tone~right!. The gray line shows a sinusoidal waveform for comparison.

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series of modulated segments with different modulatdepths and, in some cases, different modulation frequenFor 28 of these records, the fiber responded to the unmolated DPT segments at a discharge rate above 5 spikthroughout the stimulus duration. For the other 40 recothe fiber stopped responding to the unmodulated DPT a1–2 min of stimulation, although it still responded to somof the modulated segments. The percentage of transiensponders in the present data sample is somewhat larger~59%vs 46%! than in the larger sample from ten cats describedthe companion paper~Litvak et al., 2003b!, and the differ-ence is statistically significant (p50.0247, binomial exactest!. We attribute this difference to a combination of biasin data collection~the silent responses of transient responers to unmodulated DPTs were sometimes discarded! andindividual differences among animals~some animals had ahigh proportion of transient responses!. In the following, wedescribe only the responses that occurred after 50 s of stlation so that the data would reflect the effects of adaptato the DPT.

Figure 3 shows the response of an auditory-nerve fito a DPT that was sinusoidally modulated at 417 Hz for 4ms every second. Modulation depth was increased fr0.5% to 11% on each successive modulated segment.entire 5-s cycle of five modulation depths was repeated10 min. During the unmodulated segments, the pseuspontaneous discharge rate was 48 spikes/s, and thespike interval distribution was nearly exponential (I2ExpSF50.99).

The left panel in the middle row shows the discharrate as a function of time from the onset of the 5-s stimucycle. Average discharge rate grows monotonically withcreasing modulation depth. For modulation depths betw0.5% and 5%, the discharge rate stays below 300 spikes/the range appropriate for responses to tones in a healthy~Kiang et al., 1965; Liberman, 1978!. At the largest modula-tion depth~11%!, the discharge rate exceeds the rates seeLiberman’s data.


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The right two panels in the middle row show the rsponse patterns of a high spontaneous-rate fiber in a heear to 440-Hz tone bursts at 5 and 45 dB above thresh~McKinney and Delgutte, 1999!. Consistent with classic descriptions~Westerman and Smith, 1984!, the discharge ratedecreases rapidly during the first 10 ms of tone-burst stimlation, and this rapid adaptation is followed by slower adatation with a time constant near 100 ms. In contrast,responses to modulations of the DPT~left! show a form ofslow adaptation, but no sign of rapid adaptation.

The bottom left panel in Fig. 3 shows period histogramlocked to the modulator frequency computed from responduring the modulated DPT segments. The period histogfor a modulation depth of 0.5% is already almost fully modlated, indicating exquisite sensitivity to modulation. At thmodulation depth, there is little or no increase in discharate over that evoked by the unmodulated DPT. Thus, schrony to the stimulus is already large at a modulation dethat evokes no noticeable increase in average rate overesponse to the unmodulated DPT. Similar behavior is fouin responses of high-spontaneous ANFs to pure to~Johnson, 1980!.

As the modulation depth increases, responses becmore precisely phase locked. For a modulation depth of 1the period histogram approaches a half-wave rectified ssoid, suggesting that the modulator waveform is accurarepresented in the temporal discharge patterns. Formodulation depth, the period histogram resembles thosresponse to a pure tone in a healthy ear~Fig. 3, bottom right!.For modulation depths above 2.5%, however, the periodtogram consists of a very sharp mode restricted to a smfraction of the stimulus cycle, and does not resembleresponse to a pure tone at any level. These hypsynchronized responses resemble responses to sinuselectric stimulation without a DPT~Hartmannet al., 1984;van den Honert and Stypulkowski, 1987!.


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B. Temporal discharge patterns for exponential fibers

Figure 4 shows period histograms computed fromsponses to 104, 417, and 833 Hz sinusoidal modulationthe DPT for another ANF. Modulation depth was varied fro0.5% to 10%. During the unmodulated segments, this fihad a pseudo-spontaneous discharge rate of 54 spikes/an exponential interspike interval distribution.

For all modulation frequencies, stimuli with modulatiodepths below 5% evoked average discharge rates belowspikes/s, in the range reported for ANFs in normal earspure-tone stimulation~Liberman, 1978!. In addition, the syn-chronization index was always below 0.9, consistent wacoustic responses to pure tones. The nearly sinusoidal sof the period histograms for modulation depths below 2.suggests that the modulation waveform is accurately resented for all three modulation frequencies.

At 10% modulation depth, the discharge rates in

FIG. 4. Period histograms~bin width 0.2 ms! computed from the responsof an auditory-nerve fiber to sinusoidally modulated pulse trains at thdifferent frequencies~columns! and five modulation depths~rows!. Duringthe unmodulated segments of the DPT, this fiber had a pseudo-spontadischarge rate of 54 spikes/s, and its interval histogram had a nearly enential shape (IH2ExpSF50.97). Numbers in each panel are the averadischarge rate~in spikes/s! and the synchronization index to the modulatioThe vertical axis is in spikes/s.


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sponses to 417- and 833-Hz modulators exceed those sea normal ear. At this high modulation depth, the period htogram for the 104-Hz modulator reveals multiple peakseach cycle, and this is seen for 5% modulation as well. Ulike the ‘‘peak splitting’’ observed in responses of ANFslow-frequency tones~Johnson, 1980; Kiang and Moxon1972! which always occurs on opposite phases, both peof the responses to the electric stimulus occur duringsame half-cycle of the modulator. Similar double-peakedsponses have been reported for sinusoidal electric stimtion without a DPT~Hartmannet al., 1984; van den Honerand Stypulkowski, 1987!.

Interspike interval histograms were also examined totermine whether they resemble those evoked by pure tonea healthy ear. Figure 5 shows the interval histogramscorrespond to the period histograms in Fig. 4. Interval hisgrams for a 440-Hz pure tone in a normal ear are also shfor comparison. Phase locking to the stimulus can be seethese histograms as the clustering of intervals around intemultiples of the stimulus period~dashed lines!.

For modulation depths below 5%, interval histogramfor the modulated DPT resemble acoustic responses inthey have exponential envelopes, and show several modmultiples of the modulation period. One exception is thesponse to the 417-Hz modulator at 2.5% modulation dewhere the sharp interval mode at twice the stimulus permeans that spikes occur on every other stimulus cycle. Hever, this response pattern is unusual for this modulationquency and depth. Detailed examination of the interval htograms for modulation depths below 2.5% revealsadditional difference between DPT responses and normasponses to pure tones. Interval histograms for pure tstimuli always show a mode at the tone’s period for frequcies below 1000 Hz~Rose et al., 1967!. In contrast, re-sponses to the 417-Hz modulated electric pulse train showmode at the modulation period; instead, the earliest moccurs at twice the period. Such lack of a mode at the pehas also been observed in response to both electric sinusand sinusoidally-modulated pulse trains presented withoDPT ~van den Honert and Stypulkowski, 1987; Litvaket al.,2001!.

For 10% modulation depth, the interval histograms

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FIG. 5. The first three columns show the interval hitograms corresponding to the period histograms in F4. The numbers in each panel are the average dischrates in spikes/s. Vertical dashed lines mark multiplesthe stimulus period. The vertical axis represents tnumber of intervals per bin. For comparison, the righmost column shows interval histograms of an AN(CF5650 Hz) from a healthy ear for a 440-Hz purtone at 5 and 45 dB above threshold.


atforn

FIG. 6. Period histograms of responses of a fiber thgave a transient response to the unmodulated DPTthree modulation frequencies and four modulatiodepths. Same format as in Fig. 4.

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responses to electric stimulation differ strongly from normresponses to tones. In response to the 104-Hz modulatorfiber fired twice on each modulation cycle, so that the intval histogram had just two modes, one at 2.3 ms andother one at 7.3 ms. The sum of these two mode locatequals the 9.6-ms modulation period. For 417-Hz modution, the interval histogram had a single mode at the molation period, meaning that a spike occurred exactly oncemodulation cycle. Such entrainment is not seen in normANF responses to pure tones~Roseet al., 1967!, but is com-mon in electric responses without a DPT. For the 833-modulator, the histogram showed a dominant mode at twthe modulation period, indicating that a spike occurrednearly every other cycle. This distortion is particularly dturbing, because, if it occurs in many fibers, and these fibfire in synchrony, then the response of the ANF populatwould represent a signal at half the actual modulationquency. A tendency for spikes to occur at integer multiplesthe stimulus period for frequencies above 500 Hz has abeen observed for pulsatile electric stimulation withouDPT ~Javel, 1990; Javel and Shepherd, 2000!.

Responses of transient responders, a representativeample of which is shown in Fig. 6, contrast sharply wthose of sustained responders illustrated in Figs. 3–5. Tfiber did respond to modulations of the DPT, even thouafter adaptation, it showed no spike discharges to themodulated DPT~zero pseudo-spontaneous rate!. However,the modulation depth necessary to evoke a significantsponse exceeded 5%, larger than that for any of the sustaresponders. In addition, for the 104- and 417-Hz modulatthe synchronization index was invariably higher than thatpure tone responses in a healthy ear. Regardless of motion depth, the period histogram poorly represented the ssoidal modulation waveform. Overall, these responsessemble responses to electric sinusoids presented withoDPT ~Hartmann et al., 1984; van den Honert and Stypulkowski, 1987!.


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C. Temporal discharge patterns for nonexponentialfibers

For the most part, fibers with nonexponential intervhistograms during the unmodulated DPT~Litvak et al., 2001,2003b! responded to modulations of the DPT in a mannsimilar to the exponential, sustained responders illustrateFig. 3–5, but they also showed some unique features,ticularly for very small modulations. For example, the toleft panel of Fig. 7 shows the interspike interval computfrom responses of a fiber to an unmodulated DPT. The inval histogram is clearly nonexponential and shows a pnounced mode at 3.3 ms. We refer to the location of tmode as thepreferred interval. We found that preferred in-tervals systematically influenced the temporal dischargeterns for small modulations of a DPT. The middle panelsFig. 3 shows the interval~left! and period~right! histogramfor responses to 417-Hz modulation of the DPT at 0.5modulation depth. The period histogram shows that the

FIG. 7. Interval~left! and period~right! histograms of a fiber’s responses t417-Hz modulations of the DPT at two modulation depths~0.5% and 2.5%!.The nonexponential interval histogram (IH2ExpSF50.51) computed fromresponses during the unmodulated DPT segments is shown on top.vertical axis represents number of intervals per bin for the interval hisgrams, and discharge rate in spikes/s for the period histograms.


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sponse is phase locked to the modulator, yet the first mod
the interval histogram is systematically offset from tmodulation period~dotted lines!. We refer to the shift of thelargest mode in the interval histogram as themode offset. Thedirection of the mode offset is towards the preferred interfor the unmodulated DPT. A mode offset is also detectabl2.5% modulation depth~lower left panel!, although it is lesspronounced than for 0.5% modulation.

The mode offsets in interspike intervals of nonexpontial units are accompanied by decreased phase locking tomodulator, when compared to exponential units. At 0.5modulation depth, responses of the nonexponential fibeFig. 7 were weakly phase locked to the modulator~synchro-nization index of 0.24!. In contrast, at the same modulatiodepth, the response of the exponential unit in Fig. 4 walready nearly fully modulated (SI50.53). The nonexponential unit also shows reduced phase locking at the 2.5% molation depth.

Reduced phase locking to a 417-Hz modulator as in F7 was observed in some, but not all nonexponential fibFigure 8 shows the synchronization index to a 417-Hz sisoidal modulator~0.5% modulation depth! against the inter-val histogram exponential shape factor~IH-ExpSF! for theunmodulated DPT. For units with IH-ExpSF above 0.8, tsynchronization index was uniformly high~between 0.3 and0.6!. In contrast, for units with IH-ExpSF below 0.8, thsynchronization index varied widely~from 0.1 to 0.5!, andcould be as high as those of exponential units in some cabut much lower in others. The correlation between IH-Expand synchronization index was highly significantp50.007, permutation test!.2

The variability in phase locking among nonexponentneurons can be understood from the relationship betweenmodulation period and the preferred interval for unmodlated DPTs. When the preferred interval is close to the molation period, synchrony to the modulator is high~Fig. 8,upper inset!. In contrast, when the preferred interval does nmatch the modulation period, synchrony to the modulatolow ~lower inset in Fig. 8; see also Fig. 7!. This observation

FIG. 8. The left panel shows the synchronization index to a 417-Hz molator ~0.5% modulation depth! as a function of the interval histogram exponential shape factor~IH-ExpSF! for 25 fibers from four cats. The IH-ExpSFwas computed based on responses during the unmodulated segmentsDPT. The right panels show interval histograms of responses to the unmlated DPT for two units with low IH-ExpSF. The vertical dashed lines mamultiples of the modulation period.


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suggests that the responses to small modulations of ashow an interaction between the stimulus drive and thetrinsic dynamics of the neural membrane giving rise to pferred intervals.

D. Threshold and dynamic range

Because discharge rates in response to sinusoidal mlations increase monotonically with modulation depth, tsound pressure level of acoustic stimuli could in principleencoded by changes in modulation depth in a DPT-enhanstimulation strategy~Fig. 1!. To evaluate the feasibility ofsuch a scheme, we methodically investigated how averdischarge rate and synchronization index to sinusoidal molations vary with the depth of modulation of the DPT, andetermined the range of modulation depths for which thmeasures lie within the normal acoustic range.

Figure 9 shows the average discharge rate and thechronization index as a function of modulation depth for fiauditory-nerve fibers in response to three modulationquencies. The left most point in each curve representsresponse to the unmodulated DPT. The two fibers havinglowest pseudo-spontaneous rates are transient respo~dashed lines!, while the other three are sustained respond~solid lines!. Gray shading indicates the approximate normrange of responses to low-frequency pure tones in a heaear: average discharge rate below 300 spikes/s~Liberman,1978!, and synchronization index below 0.9~Johnson, 1980!.

For the three sustained DPT responders in Fig. 9, bthe average discharge rate and the synchronization ingrow over a wide range of modulation depths. With one eception, both response measures are within the noracoustic range for modulation depths below 5%. At highmodulation depths, most fibers had discharge rates exceethose of acoustically stimulated fibers. Synchrony for tsustained responders grew rapidly with modulation de

-

f theu-FIG. 9. Average discharge rate~left! and synchronization index~right! offive fibers as a function of modulation depth for three modulation frequcies~rows!. Each symbol represents data from one fiber. Transient respers are represented by dashed lines, sustained responders by solid linesynchronization index is only plotted if the response includes at leastspikes. Shading indicates the range of normal acoustic responses tofrequency pure tones.


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FIG. 10. Modulation detection thresholds based on average discharge ra~left! and synchronized rate~right! as afunction of pseudo-spontaneous ratethe DPT for three modulation frequencies. Each point shows data from onfiber. Symbols code modulation frequencies. The straight lines are leassquares fits to the data for each frequency~see Table I!. For the average-rate thresholds, the slopes of thregression lines were constrained to bthe same for all three frequencies.

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from 0.5 to 2.5%, while average rate remained close topseudo-spontaneous rate in this range. This behaviorsembles that of high-spontaneous fibers in response totones in an intact ear~Johnson, 1980!. However, for the104-Hz modulator, synchrony varied nonmonotonically wmodulation depth for two fibers, first increasing then dcreasing somewhat. This decrease is due to the appearanmultiple peaks in the period histogram, as shown in Figfor the largest modulation depth.

For the two transient DPT responders in Fig. 9, tmodulation depths necessary to evoke responses were hthan for the sustained responders. In addition, the dischrates of transient responders grew more rapidly on the lorithmic scale than did those of sustained responders, suging that the dynamic ranges are narrower for transientsponders. For transient responders, the synchronization ireaches its maximum value as soon as there is a sufficnumber of spikes to estimate it reliably, as is the caselow-spontaneous fibers with pure-tone stimulation~Johnson,1980!.

Two criteria were used to define modulation depthresholds for individual fibers. The average rate threshol


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the modulation depth for which the average dischargeduring the 400-ms modulation exceeds the rate duringfollowing 400-ms unmodulated segment for 75% of tstimulus presentations. Similarly, the synchronized rthreshold is the modulation depth for which the synchronizdischarge rate~synchronization index times average rat!during the modulation exceeds the synchronized rate duthe following unmodulated segment for 75% of the stimupresentations. This 75% criterion is similar to that attainby adaptive two-alternative choice procedures commoused in psychophysics for threshold estimation~e.g., Levitt,1971!. Thresholds estimated by our method can thereforedirectly compared to psychophysical thresholds. Becausesampling of modulation depths was rather coarse, and mmodulation depths tested were above threshold, threshwere estimated using a special algorithm described inpendix B.

Figure 10 shows modulation thresholds based on aage discharge rate and synchronized rate against the psespontaneous discharge rate to the unmodulated DPT. Resion lines were fit to the data at each frequency on doulogarithmic coordinates~Table I!. Confidence intervals for

pseudo-n

s of thesionte slopes

TABLE I. Dependence of modulation thresholds based on average rate and synchronized rate onspontaneous rate~PSR! and modulation frequency (Fm). Thresholds were fit by the equatiolog10(Threshold)5A1B log10(PSR). The table shows means and 95% confidence intervals for the slopeB andthe value of the fitted line at 50 spikes/s. Confidence intervals are based on 5000 bootstrap replicationregression line~Efron and Tibshirani, 1993, Chap. 7!. For average-rate thresholds, the slopes of the regreslines were constrained to be the same at all three modulation frequencies because a model with separadid not significantly improve the fit.

Fm

~Hz!

Slope Threshold at 50 spikes/s

Mean 95% C.I. Mean 95% C.I.

Average rate 104 20.270 20.31–0.22 N/A N/A417 same same 0.62 0.53–0.73833 same same 0.93 0.76–1.14

Synchronized rate 104 20.260 20.32–0.20 0.78 0.63–0.91417 20.402 20.46–0.35 0.36 0.31–0.42833 20.318 20.39–0.23 0.59 0.59–1.10


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the regression parameters were determined using bootreplications of the data~Efron and Tibshirani, 1993!. For theaverage-rate thresholds, the slopes of the regressionwere constrained to be the same at all three frequenciescause using separate slopes did not significantly improvemean square error (p50.33).

Both average-rate and synchronized-rate thresholdscrease with increasing pseudo-spontaneous rate for all tfrequencies. The slopes of the regression lines range f20.40 to20.26~Table I!, meaning that a tenfold increasepseudo-spontaneous rate results in a 45%–60% drothreshold. Confidence intervals for the slopes comprise onegative values, indicating that the falling trend is statiscally significant. However, for the 104-Hz modulation frquency, average rate thresholds deviate from this trendpseudo-spontaneous rates above 25 spikes/s; these higdata were not included in the regression analysis. Thesepoints may represent a different response regime sincetiple spikes per cycle become increasingly common asdischarge rate approaches the stimulus frequency.

A second trend apparent in Fig. 10 is the existencecross-frequency differences in thresholds. On the averthresholds are lower for the 417-Hz modulator than forother two frequencies. This effect is most apparent for stained DPT responders~pseudo-spontaneous rates abovespikes/s!. The difference in mean thresholds between 1and 417 Hz is highly significant for both average and schronized rate@p,0.001, two-sided permutation test for location~Good, 2000, p. 37!#, and so is the difference betwee833 and 417 Hz (p,0.002). Twelve out of 13 sustaineresponders have lower synchronized rate thresholds for417-Hz modulator than for the other two frequencies. Crofrequency threshold differences are less obvious for transDPT responders. Regression lines for the synchronizedthresholds in Fig. 10 tend to come together at low pseuspontaneous rates. Permutation tests confirm that tranresponders do not show preferred sensitivity to the 417modulator; in fact, 14 out of 27 fibers are more sensitivethe 104-Hz modulator. Thus, threshold sensitivity appearbe band-pass for sustained DPT responders, and low-pastransient DPT responders.

A final observation from Fig. 10 is that synchronizerate thresholds are significantly lower than average-thresholds for sustained responders (p50.003, two-sidedpermutation test!, but not for transient responders (p50.64). In this respect, pseudo-spontaneous activity insponse to the DPT behaves similarly as true spontaneactivity in that synchronized rate thresholds to pure tonea healthy ear are lower than average-rate thresholds for hspontaneous fibers, but not low-spontaneous fibers~Johnson,1980!.

Synchronized rate thresholds of sustained respondeFig. 10 could be as low as 0.2% modulation depth for417-Hz modulator. Because the median DPT level in thexperiments was 6 dBre: 1 mA ~see Table I in Litvaket al.,2003b!, the peak amplitude of the modulation waveform wtypically only 4 mA at threshold. This is much lower thasingle-unit thresholds reported for low-frequency sinusoielectric stimulation, which are typically tens or hundreds


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mA ~Parkins and Colombo, 1987; Hartmannet al., 1990;Dynes and Delgutte, 1992!. Thus the introduction of a DPTis highly effective in improving thresholds for sustained rsponders.

We define the ‘‘useful dynamic range’’ of a fiber as thrange of modulation depths for which both average discharates and synchronization indices resemble those seenpure-tone stimuli in a healthy ear. The lower limit of thuseful range is the modulation threshold based on syncnized discharge rate. The upper limit is the modulation dethat evokes a discharge rate of 300 spikes/s. As shown in9, for these discharge rates, most sustained DPT responhave synchronization indices below 0.9, and are therewithin the normal range of synchrony for low-frequencpure tones~Johnson, 1980!. The modulation depth that produced a 300 spikes/s discharge rate was estimated by fittisigmoid function to the rate versus modulation depth curThis analysis was not carried out for responses to the 104modulator because these responses rarely reachedspikes/s, and did not resemble normal acoustic responshigh discharge rates in that discharges often occurred at mthan one phase of the modulator~e.g., Fig. 4, lower leftpanel!.

Figure 11 shows the useful dynamic range as a funcof pseudo-spontaneous discharge rate for the 417-833-Hz modulators. Regression lines were fit to the dynarange at each frequency against the logarithm of the psespontaneous rate~Table II!. The slopes of the regression line

FIG. 11. Useful dynamic range to sinusoidal modulations of a DPT afunction of pseudo-spontaneous rate for modulation frequencies of 417833 Hz. The useful dynamic range is the ratio of the modulation depthevokes a discharge rate of 300 spikes/s to the synchronized rate thresEach point shows data from one fiber. Symbols code modulation freqcies. The straight lines are least-squares fits to the data for each frequwith the constraint that the slopes be the same for both frequencies~seeTable II!.


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were constrained to be the same at both frequencies beca regression with separate slopes did not significantly redthe mean square error (p50.21). The slope of the regressioline is 2.3 dB/decade, meaning that a tenfold increasepseudo-spontaneous rate increases the dynamic range bdB. The statistical significance of this trend is confirmedthe entirely positive 95% confidence intervals for the slopeTable II.

The average useful dynamic range of sustained respers is 23 dB for the 417-Hz modulator, and 17 dB for t833-Hz modulator. The difference between the two meanhighly significant (p,0.001, two-sided permutation test fodifference in means!. These values of dynamic range acomparable to those observed with pure-tone stimulationnormal ear~Sachs and Abbas, 1974!, and considerably largethan the dynamic ranges observed with sinusoidal elecstimulation without a DPT~van den Honert and Stypulkovsky, 1987; Hartmannet al., 1990; Dynes and Delgutte1992!. In contrast, transient DPT responders have usefulnamic ranges as low as 10 dB, more in line with electdynamic ranges reported in the literature. However, Fig.may not give a completely representative picture of thenamic range of transient responders because it does noclude data from the fibers~primarily transient responders!whose discharge rates failed to reach the 300 spikes/s ulimit of the useful dynamic range at the highest modulatdepth tested.

While the DPT-induced increase in dynamic rangesustained responders is encouraging, a key question isfraction of the population of auditory-nerve fibers wouldlikely to benefit from a DPT at a given level. To address tquestion, solid lines in Fig. 12 shows the percentage of fibthat gave ‘‘acoustic-like’’ responses to the 417- and 833-sinusoidal modulators as a function of modulation depth.‘‘acousticlike,’’ we mean that the response is above the schronized rate threshold and the average rate is belowspikes/s. Percentages are computed separately for sustand transient DPT responders. Dotted curves indicatepercentage of fibers that have sustained discharge rates a300 spikes/s, and are therefore above the normal acorange. For modulation depths between 1% and 5%, msustained responders have responses within the acorange at both frequencies. For modulation depths of 10%

TABLE II. Dependence of useful dynamic range on pseudo-spontanerate ~PSR! and modulation frequency (Fm). The dynamic range DR in dBwas fit by the equation DR5A1B log10(PSR). The table shows means an95% confidence intervals for the slopeB and the value of the fitted line at 50spikes/s. Confidence intervals are based on 5000 bootstrap replicatiothe regression line~Efron and Tibshirani, 1993, Chap. 7!. The slopes of theregression lines were constrained to be the same at both modulation frecies because a model with separate slopes did not significantly improvfit.

Fm

~Hz!

Slope~dB/decade!Dynamic range at 50

spikes/s~dB!

Mean 95% C.I. Mean 95% C.I.

417 2.32 1.21–3.43 22.7 20.9–24.6833 same same 18.3 16.7–19.9


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above, most sustained DPT responders have dischargeabove the normal acoustic range. On the other hand, molation depth has to exceed 5% for a majority of transieDPT responders to respond to the modulation. Becauseproximately 50% of the fibers in our entire sample from tanimals were transient responders~Litvak et al., 2003b!, thepercentage of acoustic-like responses for this sample~notshown! would be nearly the mean of that for the sustainand transient responders. Overall, a substantial frac~40%–55%! of the fibers would exhibit acoustic-like responses for modulation depths between 1% and 5%.course, these estimates are likely depend on the choicDPT amplitude.

E. Responses of the stochastic threshold model

Several key features of ANF responses to sinusoidmodulated DPTs are predicted by an extremely simplechastic threshold model~STM!. The STM produces a spikewhenever the modulation waveformm(t) crosses a noisythreshold~Fig. 2!. The response of the model is entirely dtermined by two dimensionless parameters:m/s andu0 /s.The input-to-noise ratiom/s determines the effective stimulus level~modulation depth!, while the threshold-to-noise ratio u0 /s determines the pseudo-spontaneous dischargein the absence of modulation. We will show that the relatioship between the STM’s pseudo-spontaneous rate and itsponses to sinusoidal modulators is similar to that seen indata.

Figure 13 shows the average discharge rate and syncnization index as a function ofm/s for model fibers withdifferent pseudo-spontaneous discharge rates~different val-ues ofu0 /s). The model predicts several features of the d

FIG. 12. This figure shows, as a function of modulation depth, the percage of fibers whose responses to a modulated DPT are within the udynamic range~solid lines!, as well as the percentage of fibers that excethe maximal acoustic rate of 300 spikes/s~dashed lines! for modulationfrequencies of 417 Hz~left! and 833 Hz~right!. Percentages are showseparately for sustained and transient DPT responders. Only responsewere recorded at the standard DPT level in each animal~Table I in Litvaket al., 2003b! are included.

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shown in Fig. 9:~1! Both average rate and synchrony groover a wide range of modulation depths.~2! Both model andneural fibers with low~,5 spikes/s! pseudo-spontaneourates have higher modulation thresholds than fibers with hpseudo-spontaneous rates.~3! For both model and neural fibers with high pseudo-spontaneous rates, synchrony grrapidly at low modulation depths, while the average ratemains near pseudo-spontaneous. In contrast, fibers withpseudo-spontaneous rates show high synchrony as soothe modulation depth reaches threshold.~4! For both modeland data, synchrony grows nonmonotonically with modution depth at 104 Hz due to the occurrence of multiple spiin each stimulus cycle at high levels. However, the maximdischarge rates exhibited by the model are larger than thseen in the data. In addition, while neural synchrony gromonotonically with modulation depth at 417 Hz, synchrois somewhat nonmonotonic in the model responses athigh discharge rates.

Figure 14 shows the model average and synchronrate thresholds as a function of pseudo-spontaneous ratthree modulation frequencies. These predictions can berectly compared to the neural thresholds in Fig. 10. Nohowever, that while the neural pseudo-spontaneous dischrates are always below 200 spikes/s, the model rates wextended to 600 spikes/s. For both model and data, averate thresholds decrease nearly linearly with the logarithmpseudo-spontaneous rate at relatively low rates for all thmodulation frequencies. The model thresholds behave nmonotonically, increasing steeply once the pseuspontaneous rate exceeds the modulation frequency. Snonmonotonic dependence of detectability on noise amtude~which controls the pseudo-spontaneous rate! is a defin-ing characteristic of stochastic resonance~Wiesenfeld andMoss, 1995!. Some evidence for a nonmonotonicity can abe discerned in the neural data of Fig. 10 for the 104-

FIG. 13. Average discharge rate~left! and synchronization index~right! ofthe stochastic threshold model as a function of the normalized moduladepth m/s for three modulations frequencies~rows!. Each curve corre-sponds to one value of the threshold to noise ratiou0 /s: 1.4 ~dot-dash!, 1.8~dash!, 2.4 ~dot!, and 4~solid!. The corresponding pseudo-spontaneous dcharge rates are 210, 119, 30, and 0.2 spikes/s, respectively.


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modulator in that thresholds for pseudo-spontaneous rabove 40 spikes/s lie above the regression line fit to the dat lower pseudo-spontaneous rates. However, the data sno nonmonotonicity at 417 and 833 Hz, presumably becathe pseudo-spontaneous rates always remain well belowmodulation frequency.

The model synchronized rate thresholds decrease nelinearly with the logarithm of pseudo-spontaneous rate forthree modulation frequencies. The synchronized rate threolds decrease more rapidly than the average rate threshThe same trends are apparent in the data for the 417modulator~Fig. 10!. However, only the data show a depedence of thresholds on modulation frequency, with the loest thresholds at 417 Hz.

Figure 15 shows the model useful dynamic range afunction of pseudo-spontaneous rate for 417- and 833

n

-

FIG. 14. Normalized modulation depth thresholdsm/s based on averagerate~left! and synchronized rate~right! as a function of pseudo-spontaneourate for the stochastic threshold model. Symbols code modulation freqcies.

FIG. 15. Useful dynamic range of the stochastic threshold model as a ftion of pseudo-spontaneous rate for two modulation frequencies. Thenition of useful dynamic range is the same as in Fig. 11.


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modulators. As for the data, the useful dynamic range isratio of the modulation depth that evokes a discharge rat300 spikes/s to the synchronized rate threshold. Becausdynamic range is a ratio of modulation depths, there arefree parameters in this plot. The model dynamic rangecreases linearly with the logarithm of pseudo-spontanerate up to 50 spikes/s, then flattens out at about 19 dBboth frequencies. The increase in dynamic range atpseudo-spontaneous rates is apparent in the data of Figbut the plateau at high rates is less obvious. The modplateau dynamic range~19 dB! is intermediate between thmean 23-dB dynamic range in the data for the 417-Hz molator and the 17 dB observed for the 833-Hz modulaHowever, the model does not predict the difference innamic ranges between the two modulation frequencies.

Overall, the stochastic threshold model does a goodof predicting the relationship between the pseudspontaneous discharge rates of ANFs and their responssinusoidal modulators at a given frequency. However,version of the model cannot account for the frequencypendence of neural sensitivity to modulation.

IV. DISCUSSION

A. Representation of sinusoid in temporal dischargepatterns

All auditory-nerve fibers in our study responded to sinsoidal modulations of the DPT. Neurons that had sustairesponses to the DPT were the most sensitive to modulatiThese neurons showed strong phase locking to the modufor modulation depths as low as 0.5%. In these neurons,average discharge rate grew monotonically with modulatdepth over a range of 17–23 dB before reaching 3spikes/s, the upper limit of discharge rates for pure-tostimulation. The temporal discharge patterns to moduladepths below 2.5%–5% resembled acoustic responsepure tones. These responses were stochastic, with intersintervals occurring at random at multiples of the modulaperiod. The period histograms of these responses were slar to those seen in responses to pure tones, and providgood representation of the sinusoidal stimulus waveform

For modulation depths above 5%–10%, sustained Dresponders exhibited higher discharge rates than thosefor acoustic stimulation. For 417-Hz modulation, dischargtended to entrain~occur once per stimulus cycle! while, for833-Hz modulation, some neurons fired exactly on evother stimulus cycle. These responses were more precphase locked than acoustic responses. In most respectsponses to large modulations of the DPT resemble suprreshold responses to sinusoidal electric stimulation withoDPT ~Hartmann et al., 1984; van den Honert and Stypulkowski, 1987!.

Fibers that only responded transiently to the unmolated DPT nevertheless responded with phase-locked sdischarges to sinusoidal modulations. However, larger molation depths were needed to produce a response in tfibers than in sustained responders. Thus, the introductioa DPT qualitatively mimics the threshold differences b


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tween high-spontaneous and low-spontaneous fibersserved in normal ears~Liberman, 1978!. At these largemodulation depths, the responses of transient DPT respers were more synchronized than responses to tonesnormal ear, and poorly represented the stimulus wavefoIn addition, transient DPT responders had a smaller dynarange than sustained responders. In this respect, transiensponders differ from low spontaneous-rate ANFs in a heaear, which have wider dynamic ranges than high spontanefibers ~Schalk and Sachs, 1980!.

The deafening protocol in these experiments was opartly successful in that some animals had residual hearinthe nonimplanted ear~Litvak et al., 2003b!. This observationraises the possibility that the acoustic-like responses oftained responders may reflect hair-cell mediated activity.though we cannot rule out this possibility in every case,did observe acoustic-like responses to modulations ofDPT in animals with no residual hearing as well as in amals with substantial hearing. Our measure of residual hing was very conservative in that it did not take into accouany additional hearing loss caused by insertion of the stimlating electrodes into the implanted cochlea.

While the temporal discharge patterns of sustainedsponders to small sinusoidal modulations of a DPT resemresponses to pure tones in a healthy ear, there are neveless differences in the interspike interval distributions btween the two modes of stimulation. While the interspidistributions in response to a pure tone always show a mat the tone period for frequencies below 1 kHz, this mowas often lacking in responses to 417-Hz electric modutions. This lack of a mode at the stimulus period has abeen observed for 500-Hz sinusoidal electric stimulatwithout a DPT~van de Honert and Stypulkowski, 1987!. Inaddition, for neurons having nonexponential interspike intval distributions in responses to unmodulated DPTs, moin the interval histogram for sinusoidal modulators wereten systematically shifted away from multiples of the stimlus period, particularly for very low modulation depthThese shifts are considerably larger than the small, buttematic offsets seen in interspike interval distributionspure tones in a healthy ear~McKinney and Delgutte, 1999!.The mode offsets seen with modulated DPTs seem to rean interaction between the stimulus period and the intrindynamics of the neural membrane leading to preferred invals in response to the unmodulated DPT. Preferred interhave also been noted for electric stimulation with higfrequency~.1 kHz! sinusoids without a DPT, and found tdistort phase locking to the stimulus~Parkins, 1989!.

Although interspike interval distributions of sustaineDPT responders for small sinusoidal modulations difsomewhat from responses to pure tones in a healthythese distortions may not severely interfere with neural rresentation of the stimulus frequency. Because there isevidence for cross-fiber correlation in responses to unmolated DPTs~Litvak et al., 2003b!, responses to small modulations of a DPT may be conditionally uncorrelated from ofiber to the next. By ‘‘conditionally uncorrelated,’’ we meathat the occurrence of a spike on a particular stimulus cyfor one fiber does not alter the probability that a spike occ


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on the same cycle in another fiber. By integrating synapinputs from several conditionally uncorrelated auditonerve fibers, some central auditory neurons might shomode at the stimulus period in their interval histograms eif such a mode is lacking in their ANF inputs. Similarlbecause mode offsets in interspike intervals differ from ofiber to the next and can be either positive or negative~Fig.8!, these offsets might average out in the responses of igrating central neurons so as to produce a mode centerthe stimulus period. Nevertheless, both distortions couldgrade somewhat the accuracy of frequency representaDirect recordings from central neurons~e.g., cochlearnucleus! in response to a modulated DPT stimulus would twhether synaptic integration suffices to overcome the distions in the coding of the modulation frequency observedthe auditory nerve.

B. Dynamic range

A major finding of the present study is the relativewide dynamic range~17–23 dB! for sustained DPT responders. In studies of electric stimulation, dynamic range is nmally measured by the varying the amplitude of a stimuwithout changing its waveform, and determining the rangeamplitudes over which the discharge rate changes. Herevaried the depth of sinusoidal modulations of a DPT, adetermined the range of modulation depths over which eiaverage rate or synchronized rate varied~with an upper limitof 300 spikes/s for average rate!. As shown in Fig. 1, thismethod is equivalent to varying the amplitude of a 100modulated stimulus superimposed upon a fixed, unmodulDPT, which is not considered part of the information-bearstimulus since its function is to evoke pseudo-spontaneactivity. Because modulation depth in percent can be tralated into stimulus amplitude in mA by simple multiplicatioby the DPT amplitude in mA, a modulation-depth dynamrange in dB is numerically equivalent to a conventional dnamic range for the information-bearing part of the stimu~excluding the fixed DPT!.

The most detailed information on dynamic rangeelectric stimulation comes from the example of rate-lefunctions for periodic trains of biphasic pulses shownJavel and his colleagues~Javel et al., 1987; Javel, 1990Shepherd and Javel, 1997; Javel and Shepherd, 2000!. Al-though no formal statistics are provided, the dynamic ranfor the highest pulse rate tested~800 pps! range from 3 to 12dB in the examples shown, with a median near 6 dB. Tdischarge rates of the fibers studied by Javelet al. typicallyapproached the 800/s pulse rate at high stimulus amplituTherefore, the dynamic ranges would only be about hallarge if a 300 spikes/s upper limit was imposed, as we didthe present study. These values are consistent with thosported for sinusoidal electric stimulation at frequencies okHz and above~van den Honert and Stypulkowski, 198Hartmannet al., 1990; Dynes and Delgutte, 1992!. They arealso consistent with the 2–4 dB conventional dynamranges measured in our earlier study~Litvak et al., 2001! for4.8-kpps pulse trains sinusoidally modulated at 400 Hz wa 10% depth. The modulation dynamic ranges observed


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transient DPT responders~as low as 10 dB! overlap with thevalues given in the literature for sinusoidal or pulsatstimuli. However, the 17–23 dB dynamic ranges of sustainDPT responders are clearly higher than any of the valreported in the literature.

The improvement in dynamic range resulting from tintroduction of a DPT in sustained responders arises fromleast two distinct effects. First, the pseudo-spontaneoustivity evoked by the DPT allows synchronized rate thresolds to be about 10 dB lower than the average rate threolds. In this range of modulation depths, the stimusinusoidally modulates the pseudo-spontaneous actwithout causing an increase in average rate, as is the caa spontaneously active fiber with acoustic stimulation.

The second effect giving rise to improved dynamrange with a DPT is that, because rate-level functionsexpansive near threshold, the response to the superposof two stimuli is always greater than the sum of the rsponses to each of the stimuli. The presence of a DPT thfore allows the superimposed modulated stimulus to evan increment in discharge rate over background, even ifitself, this stimulus would be below threshold. Because ralevel functions become compressive rather than expannear their saturation, this mechanism is likely to be effectover only a limited range of pseudo-spontaneous rates. Scifically, if the pseudo-spontaneous rate approached theper limit imposed by neural refractoriness, the thresholdsuperimposed stimuli would be expected to increase rathan decrease. Such an increase in rate thresholds is obsfor the stochastic threshold model at high pseudspontaneous rates~Fig. 14!. However, this condition did nooccur in our data~Fig. 10!, presumably because pronouncadaptation over the course of the DPT always keptpseudo-spontaneous rates well below saturation~Litvaket al., 2003b!. Adaptation to the continuous DPT is thulikely to play an indirect role in improving the dynamirange. Whether it also plays a more direct role, for examby decreasing the slopes of rate-level functions, cannodetermined from our data.

The above reasoning suggests that the effectivenessDPT in lowering threshold and increasing dynamic randoes not depend on either the exact parameters of the Dor the particular scheme used for encoding the sinusostimulus, so long as the pseudo-spontaneous rate evokethe DPT lies in the appropriate range. Thus, a DPT miremain effective if an analog sinusoidal stimulus was simadded to the DPT, as originally proposed by Rubinsteinet al.~1999b!, rather than encoded as a modulation of the DPTother words, a DPT may be as effective with an anastimulation strategy as with the CIS-type strategy used inpaper. Similarly, a lower-rate pulse train~e.g., 1 kpps! mightbe equally effective as our 5-kpps DPT in improving tdynamic range. However, since ANFs adapt less to low-rpulse trains than to high-rate trains~Moxon, 1967; van denHonert and Stypulkowski, 1987!, more fibers might be neasaturation of the input–output function with a low-rate DPA low-rate DPT would have the further disadvantage thphase locking to the pulse rate might give rise to pitch ssations that would bear no relation to the sinusoidal stimu


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In addition, if sinusoidal stimuli are encoded as modulatioof the DPT, the low rate of a 1-kpps pulse train would pvent all but very low frequency signals to be encoded wiout aliasing the modulation waveform. Thus, a 5-kpps Dseems to be preferable over a lower-rate DPT, particulwith a CIS-type strategy.

C. Comparison with models of electrically stimulatedfibers

1. The stochastic threshold model

We presented a stochastic threshold model of ANFsponses to modulations of a DPT. Despite its simplicity,STM accounts for the dependence of both threshold andnamic range on the pseudo-spontaneous dischargeevoked by the unmodulated DPT. In addition, the STM qutitatively predicts~within 2–4 dB! the average useful dynamic range of sustained DPT responders. However, thependence of threshold and dynamic range on modulafrequency is not predicted by the STM. A parsimonious wto account for that dependence would be to introduce a bapass filter at the input to the model, so as to amplify molation frequencies near 400 Hz. We show in a companpaper~Litvak et al., 2003a! that such a filter is also necessato account for ANF responses to complex modulations oDPT.

It may seem at first sight surprising that the dependeof threshold and dynamic range on pseudo-spontaneousis predicted by the very simple stochastic threshold moWe believe that the agreement is not accidental. Many bphysically realistic neural models can be approximated bdriving function, which depends only on the stimulus, aanother~possibly noisy! function describing threshold dynamics, which depends only on previous activity~e.g., Hill,1936!. In general, the driving function may depend on tstimulus in a complex, nonlinear way. However, becausestimuli in our study are composed of a large signal~the DPT!perturbed by small modulators, the driving function maylinearized around the operating point imposed by the DThus, to the extent that the threshold component ofmodel captures the complex dynamics of neural refractness, the stochastic threshold model can be considereapproximation of a more realistic neural model for smmodulation depths.

It is worth emphasizing that the DPT is not explicitrepresented in the STM because the input to the model ismodulation waveform without a pulse-train carrier. Thefect of a DPT is simulated in the model by varying ththreshold-to-noise ratiou0 /s ~Fig. 2!, which controls thepseudo-spontaneous rate. The pseudo-spontaneous ratbe increased by either decreasing the resting thresholdu0 or,equivalently, increasing the neural noise. That the STMnevertheless predict the effects of a DPT on neural respoto modulations bolsters the argument made in the prevsection that the effectiveness of a DPT in improving dynamrange and temporal discharge patterns is not likely to depon the exact characteristics of the DPT such as its pulse


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2. The Rubinstein biophysical model

In many respects, ANF responses to a modulated Dalso resemble the responses of a biophysical model to etric sinusoids in the presence of a 5-kpps conditioner~Rubin-stein et al., 1998!. At low levels of the electric sinusoidperiod histograms for this model resemble the sinusostimulus waveform. We obtained a similar result for rsponses to small modulations of the DPT. The usefulnamic range of the biophysical model responses was neadB, and changed little with DPT level, so long as the DPevoked discharge rates between 10 and 250 spikes/s.measured responses to the modulated DPT showed a sitrend, with no systematic relationship between the pseuspontaneous rate and useful dynamic range for dischrates above 5 spikes/s~Fig. 11!. Because Rubinsteinet al.did not report interval histograms of model responses tosinusoid, it is unclear whether their model captures the mshifts, and the missing first mode observed in the data.though responses of the biophysical model of Rubinstet al. ~1999b! to a modulated DPT remain to be studieddetail, the results so far suggest that this model capturesessential features of responses of ANFs to sinusoidal elestimulation.

D. Function of spontaneous activity

Spontaneous activity in sensory neurons is often conered as noise that imposes fundamental limitations onperformance achievable by an ideal observer in any detecor discrimination task based on the neural discharge patt~Barlow and Levick, 1969; Siebert, 1965; Werner aMountcastle, 1965!. While this point of view is certainlyvalid, it does not specify a functional advantage of sponneous activity that might account for its nearly ubiquitopresence in primary sensory neurons~Retinal ganglion cells:Kuffler, 1953; Rodieck, 1967; Somatosensory afferenWerner and Mountcastle, 1965; Auditory nerve: Kianget al.,1965; Vestibular nerve: Goldberg and Fernandez, 19Walshet al., 1972; Olfactory receptors: Chaput and Holle1979; Rosparsetet al., 1994; Gustatory receptors: Pfafmann, 1955!. Our physiological and modeling results, awell as those of others~Yu and Lewis, 1989; Schneidmaet al., 1998; Rubinsteinet al., 1999a, b! suggest such an advantage.

Spontaneous activity helps to faithfully encode stimuwaveforms in the temporal discharge patterns of sensneurons by allowing these waveforms to be representedsmall modulations of ongoing activity. Such modulation coing lowers threshold and mitigates the distortions causedrefractoriness in single neurons. Spontaneous activity malso desynchronize stimulus-driven activity across neurin a population, thereby allowing a volley principle to opeate when the stimulus period is shorter than the neuralfractory period. In this view, noise resulting from randospontaneous activity is the price paid for the lower threshoand improved temporal representation of waveforms inneural population. The performance limitations imposednoise can, in principle, be reduced by averaging respon


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E. Comparison with psychophysical modulationdetection thresholds

It is of interest to compare our single-fiber modulatidetection thresholds with psychophysical thresholds forman cochlear implant listeners~Shannon, 1992!. In thatstudy, subjects were stimulated continuously with 502000-Hz sinusoids. Beats were produced by presentingother sinusoid differing slightly in frequency. Because oneural threshold criterion closely parallels that used in pchophysics, direct comparison of threshold values is apppriate.

Shannon found that subjects were most sensitive100-Hz beats. At these frequencies, a modulation depth1% could be detected. These modulation depths are comrable to the most sensitive rate modulation detection threolds that we observed for 104-Hz modulators, and are cto the mean synchronized rate thresholds. Unlike the nedata, however, sensitivity of human subjects to beats droprapidly with increasing beat frequency. The best psycphysical modulation detection thresholds for a 400-modulator were near 3%. In contrast, our rate-based nedetection thresholds were lower for 417- than for 104-modulation, and could be as low as 0.4%.

Shannon~1992! suggested that the drop in the subjecability to detect modulations with increasing beat frequenmay reflect a central limitation in sensitivity to highfrequency modulations. Because the peripheral neuronscode 400-Hz modulations at least as well as 100-Hz molations, our data are consistent with this view. However,differences between our neural data and Shannon’s~1992!psychophysical thresholds might also be accounted fordifferences in stimuli~sinusoidal modulations of a 5-kpppulse train versus beats of a 0.5–2 kHz sinusoid!. Psycho-physical studies with stimuli more similar to those usedthis study are needed to determine how well highfrequency modulations of a DPT can be detected by humlisteners.

F. Implications for cochlear implant processors

Our results strongly suggest that a high-rate, ongoDPT can enhance the representation of the temporalstructure of sinusoids in auditory nerve responses forquencies up to at least 800 Hz. The enhancement is maxfor small ~,5%! modulations of the DPT and is most appaent in fibers that have sustained responses to the DPT.cifically, responses of sustained DPT responders to smmodulations resemble responses to sound in a healthy eat least four respects:~1! the dynamic range is near 20 dB~2! interspike intervals occur randomly at multiples of tstimulus period;~3! spikes are distributed over most of onhalf cycle, thereby giving a faithful representation of tstimulus waveform; and~4! there is a range of stimulus levels over which synchrony grows rapidly with little or nincrease in average rate. No other strategy for electric sti


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lation has been shown to exhibit any of these properties oa wide range of levels and frequencies. These observatsuggest that a processing strategy that incorporates a Dand that preserves temporal fine structure information insignals delivered to the stimulating electrodes, may improperformance of cochlear implant users. In particular, iproved coding of the sound fine-time structure may leadimproved perception of musical pitch, and to more effectutilization of binaural cues in bilateral implants~Smithet al.,2002!.

One stimulation strategy that does preserve the fine-tstructure of the signals delivered to the stimulating eltrodes is the continuous analog~CA! strategy. Because aDPT may allow for better encoding of the fine-time structuperformance with a CA strategy may be substantiallyhanced by a DPT. In current implementations, the CIS stegy discards the fine-time structure at the envelope detestage. One function of the envelope detector is to producstrictly positive modulation waveform that can be usedmodulate a carrier pulse train. Because negative wavefocan be represented as decreases in DPT amplitude, it mapossible to entirely eliminate the envelope detector stagDPT-enhanced CIS strategies. The rate of the pulse-trainrier would also have to be increased in order to samplehigher modulation frequencies without aliasing. Thus, a Dmay be beneficial with CIS as well as with CA strategies,long that the information-bearing signals are small compato the ongoing DPT.

We found that sustained DPT responders are best atresenting the sinusoidal stimuli in their temporal dischapatterns. A comfortable majority of the sustained respondin our data gave acousticlike responses for modulatdepths below 5%~Fig. 12!. A key question is what fractionof the auditory-nerve population has a sustained responsa given DPT level. In the companion paper~Litvak et al.,2003b!, we showed that the DPT needs to be at least 4above ECAP threshold to evoke a sustained responsesizeable fraction of the neurons, but that DPT levels mthan 8 dB above ECAP threshold can evoke long-lastchanges in neural excitability, and may therefore be harmto the nerve. To stimulate a large number of fibers, whsimultaneously meeting the safety constraint, it may bevantageous to present a DPT at a low~4 dB above ECAPthreshold! level on several electrodes. Further researchneeded to work out the best trade-off between the safetDPT stimulation and its effectiveness.

The transient responders comprised roughly 50% ofneurons that we recorded from in our sample from ten anals. Even though a strategy that uses only small moduladepths may stimulate only half of the neurons that arecited electrically, it may still produce substantial benefitmimicking some aspects of normal ANF responses inneurons that it does stimulate. On the other hand, evena large number of fibers showing fairly natural temporal dcharge patterns, the central nervous system might not beto make use of this information if temporal processing dpends critically on factors that were not considered here sas phase relationships between response of fibers innerv


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FIG. 16. Algorithm for removing the stimulus artifacfrom contaminated recordings. The top row shows twaveform ~left! and the spectrum~right! of the signalrecorded from a microelectrode after it has been pasthrough a 0.2-ms moving-average filter. The stimulusa sinusoidally modulated pulse train~modulation fre-quency: 417 Hz; modulation depth: 5%!. The insetshows the spike waveform for an unmodulated putrain. The middle row shows the waveform and spetrum after low-pass filtering the signal at 3 kHz. Thbottom row shows the waveform and spectrum afeight steps of the iterative artifact rejection algorithdescribed in Appendix A.

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Our results suggest that a DPT would decrease throlds to electric stimulation. In the case of CIS, if the Ccarrier and the DPT are in phase, then our results suggesthere would be sufficient information in the auditory nervedetect modulations as small as 0.5% for 417-Hz modulatand near 1 to 2% for 104- and 833-Hz modulators. FoDPT level of 2 mA and a modulation depth of 0.5%, tamplitude of the modulation waveform is only 10mA, whichis considerably lower than typical single-unit thresholdsported for sinusoidal electric stimulation. While these resuare promising, the improvements in single-fiber threshomay not necessarily translate into improvements in psycphysical dynamic range because the latter is determinedthe distribution of ANF thresholds as well as by the dynamrange of individual fibers. Because a DPT is expectedmodify the threshold distribution, its effect on the psychphysical dynamic range is unclear.

V. GENERAL CONCLUSION

We showed that, using a DPT, it may be possibledesign strategies for cochlear implants that would realically code the fine-time structure of sound stimuli in ttemporal discharge patterns of electrically stimulaauditory-nerve fibers. If the central nervous system can muse of this information, then these strategies may substially improve the quality of auditory experience enjoyedcochlear implant users.

ACKNOWLEDGMENT

The authors thank M. F. McKinney for providing thacoustic data used in this study, Z. M. Smith for help wthe physiological experiments, and K. M. Brinsko for asstance in figure preparation. We would also like to acknowedge the tireless efforts of Leslie Liberman without whosurgical skills this work would be impossible. This work w


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APPENDIX A: METHOD FOR ARTIFACT REJECTION

Single-unit recordings in response to electric stimulatare contaminated by two distinct signals with can interfewith detection of action potentials:~1! the stimulus artifactproper, representing the voltage drop between the recorelectrodes directly due to the stimulating current, and~2!evoked potentials reflecting the summed activity of maneurons recorded in the far field. For convenience, we reto the superposition of these interfering signals as ‘‘the afact.’’

To remove the artifact from responses off-line, we fifiltered the recorded signal using a moving average filterlength equal to the carrier period~0.2 ms!. This filter re-moved the 5-kpps periodic component from the artifact. Fmodulation depths below 2.5%, the remaining artifact wsmaller than the noise in the recording for nearly all of trecords. For modulation depths between 2.5% and 1however, the artifact was often comparable in amplitudethe spikes. The top row of Fig. 16 shows a typical wavefoand spectrum of the recorded signal after processing bymoving-average filter. This signal, which we denote byy(t),is the sum of~1! the artifact waveforma(t), ~2! the spiketrain x(t), and~3! noisen(t). In this example, the modulatofrequency is 417 Hz. As expected, the spectrum has its lest peaks at the two components present in the stimu50002417 Hz and 50001417 Hz. In addition, there arepeaks at the 417-Hz modulation frequency and its harmo834 and 1251 Hz. These peaks are distortion products ofmodulator waveform, and indicate the nonlinear nature ofartifact ~including evoked responses!. While the higher-frequency components at 50006417 Hz can easily be removed by low-pass filtering~Fig. 16, second row!, the low-frequency distortion products occur in the region whespikes have significant energy, and therefore cannot beply filtered out.


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We developed an iterative algorithm to remove thelow-frequency components of the artifact. The algorithmbased on two assumptions:~1! that the artifacta(t) can berepresented by a low-order Fourier series of the modulfrequency, and~2! that the spike trainx(t) is composed ofspikes whose waveform is known within an overall gain. Tprinciple of the algorithm is to refine an estimate ofa(t)until the spikes in the estimated neural responsey(t)2a(t)maximally resemble spikes recorded during the unmodulaDPT ~Fig. 16, upper left panel, inset!. While the artifact isalways a low-order Fourier series, the spikes, which hrapid rise times and occur with some jitter relative to tmodulator, are poorly represented by this Fourier serThus, it is unlikely that spikes would be erroneously intrduced or removed by this algorithm.

As an initial guessa0(t) for the artifact waveform, weuse the first three Fourier components of the minimum ofrecorded signaly(t) over all modulator periods. The rationale is that, because spikes are mostly positive,y(t) is likelyto have smaller amplitude during a modulation cycle whcontains no spikes than during cycles in which a spike doccur. Nevertheless, the algorithm works even if spikescur on every cycle, so long as they show sufficient time jit

At stepn, the algorithm first estimates the noisy neuresponsexn(t) using the equationxn(t)5y(t)2an21(t),wherean21(t) is the artifact estimate at stepn21. Next, thisnoisy response is fit by a model neural responsex̂n(t), whichis defined as

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wherej is spike number,s(t) is the known spike waveformwhile gj andt j are the spike gains and spike times, resptively. Thegj ’s andt j ’s are determined by cross-correlatinxn(t) with the spike waveforms(t). Spikes are assumed toccur whenever the correlation coefficient is larger thathreshold, which was normally set at 20%, but was increafor particularly noisy recordings. Whenever a spike is dtected, its gaingj is determined from the local maximum othe correlation, while the location of the maximum is takas spike timet j . Finally, the artifact waveforman(t) at stepn is estimated from the first three Fourier componentsy(t)2 x̂n(t).

The algorithm is stopped whenever the differencetween an(t) and an21(t) is less than 0.1% of the spikheight. The bottom row of Fig. 16 shows the estimated nral responsex(t) after eight iterations. The dotted line is thestimated artifacta(t). In this case, the estimated spikmatch those that would be picked by an experienced ey

The algorithm was tested using synthetic neural recoings in response to 100-, 400-, and 800-Hz modulators.synthetic recordings were composed of stereotyped spsimilar to those recorded from ANFs, and additive whnoise.3 For the 100- and 400-Hz stimuli, one synthetic spioccurred on every stimulus cycle with uniformly distributetime jitter. For 800 Hz, a spike occurred on every othcycle. Time jitter and noise amplitude were systematicavaried from 50 to 400ms and from 0% to 30% of spikeamplitude, respectively. The algorithm was applied to s


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thetic spike trains comprising responses to 25 respocycles. For each noise and jitter condition, the procedurerepeated 100 times, and the maximum deviation betweenestimated and the actual artifact waveforms was compuFor all conditions, this deviation was less than 10% of spheight. The largest deviations were seen for responses to800-Hz modulator.

The results of the algorithm were also monitored for reneural recordings, and a record was rejected if the estimneural signal did not resemble spikes. This occurred in oabout 2% of the records and only at the largest moduladepths.

APPENDIX B: METHOD FOR ESTIMATINGMODULATION THRESHOLD

Single-fiber modulation threshold was defined in thstudy as the modulation depth at which either the averdischarge rate or the synchronized rate during the sinusomodulation exceeded the discharge rate during a followunmodulated DPT segment on 75% of stimulus trials. Tmost direct method to determine threshold would rely onpercentage ofhit trials, those in which the rate during thmodulation exceeds the rate during the unmodulated DPTreliably estimate threshold by this method, the data woneed to span the 75% criterion over the range of moduladepths tested. This condition was rarely met, particulawhen measuring the very low synchronized rate threshofor a 417-Hz modulator. A common pattern in the data wahit percentage between 75% and 95% for the smallest msured modulation depth, and 100% for all larger modulatdepths. Examples of this pattern are shown for three offour fibers in the left panel of Fig. 17. In such cases, it is npossible to reliably fit a curve to the data so as to extrapothe hit percentage to the 75% threshold criterion.

We therefore developed an alternative method for demining threshold which does not directly depend on hit pcentages. The method seeks to utilize data points for whthe hit percentage is 100%. To this end, we developemeasure, calledquartile rate difference, which continues togrow with modulation depth even when the hit percentareaches 100%. For each modulation depthm, and each triali,let r m(m,i ) denote the rate during the modulation~rate canbe either synchronized or average discharge rate!, and letr u(m,i ) denote the rate during the corresponding unmolated segment. The quantityr d(m,i )5r m(m,i )2r u(m,i ) isthe rate difference. The quartile rate differencer d

q(m) is the25th percentile ofr d(m,i ) over all stimulus trials~modulatedsegments!. By definition, at modulation threshold, the radifference is positive on 75% of the trials~i.e., the rate dur-ing the modulation exceeds the rate during the corresponunmodulated segment!, and negative on the other 25% of thtrials, sor d

q(m) must be zero. Thus, to determine threshowe need to find the modulation depthmthr such thatr d

q(mthr)50.4

The middle panel of Fig. 17 shows the quartile rate dference as a function of modulation depth for the same dset as in the left panel. The threshold criterion of 0 is shoas a dotted line. Theoretically, asm approaches 0,r d

q(m)approaches a negative valuer 0 , which is the 25% percentile


z forrminatiosholdhe

FIG. 17. Method for estimating modulation depth thresholds. The left panel shows the percentage of hit trials against depth of modulation at 417 Hfoursustained DPT responders. For three of these fibers, the hit percentage was below 100% for only one modulation depth, preventing a direct deten ofthreshold. The middle panel plots the quartile rate differencer d

q(m) against modulation depth for the same four fibers. The dotted line indicates the threcriterion. The right panel shows the same data plotted on an inverted Gaussian vertical scale defined by Eq.~B2!. Gray shading indicates the region where tdata grow approximately linearly. Circled symbols show the estimated thresholds.

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of r u(m,i )2r u(m, j ) for all pairs of trials~i,j!. This valuewas estimated directly from responses to the unmodulaDPT segments. For 55% of the synchronized rate recor d

q(m) crossed zero, and threshold was estimated by linefitting r d

q(m) over a range of modulation depths spannizero. However, for many records from the more sensitsustained DPT responders~including three of the four shownin Fig. 17!, r d

q(m) was above 0 even for the smallest modlation depth tested. We were still able to estimate thresholthese sensitive fibers by applying a nonlinear transformato the data. Specifically, we found thatr d

q(m) could usuallybe described by the expression

r dq~m!5r 01gG•G~a• ln~m!1T0!, ~B1!

whereG(x) is a cumulative Gaussian distribution,gG is themaximum discharge rate, anda and T0 are free parameterfit to the data. The maximum rategG was set to the modulation frequency for 104- and 417-Hz modulators~when spikestend to occur on every stimulus cycle at high modulatdepths!, and to half the modulation frequency for 833 H~when spikes tend to occur on every other cycle!.

This equation implies that

G21S r dq~m!2r 0

gGD ~B2!

and ln(m) are linearly related. The right panel of Fig. 1showsr d

q(m)2r 0 against ln(m) for the same data set as in thother panels. The ordinate uses the inverse Gaussiandefined by Eq.~B2!. In the shaded region~between 3 and300 spikes/s!, the data grow nearly linearly, as predictedthe model. Outside the shaded region, the data deviatelinearity, perhaps because of difficulties in accurately emating a cumulative Gaussian near its saturation. Incase, for most fibers, at least 3–4 data points are locinside the linear, shaded region. This sharply contrasts wthe hit percentage~left panel!, which, typically, providesonly one useful point for estimating threshold.

This method assumes that, over a range of moduladepths, the rate of growth of discharge rate near threshfollows the same cumulative Gaussian function as the ratgrowth well above threshold. This assumption was direcverified for all cases when the data did cross the threshcriterion so that extrapolation was unnecessary.


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This threshold estimation procedure was applied to 4of the data records. The free parametersa andT0 were esti-mated using nonlinear least squares. For 34% of the tnumber of records, the fit was sufficiently close so ththreshold could be determined by inverting Eq.~B1! for thefitted curve. However, for the remaining 11% of the recorthreshold could not be determined by this method becausa poor fit, or lack of data. These records are not includedFig. 10. Most of these~9% of total! were transient responderwhose thresholds were higher than the highest moduladepth tested. For the other 2%,r d

q(m) was above criterion forall modulation depths; therefore, these fibers’ thresholdslikely to be at least as low as those of the more sensifibers.

1To expedite data collection in the later experiments, we shortened theration of the unmodulated segments to 300 ms when the preceding mlated segment had a modulation depth below 2.5%.

2We showed in the companion paper~Litvak et al., 2003b! that nonexpo-nential units respond to the DPT with higher discharge rates, so theserved correlation might simply reflect these rate differences. Howeversynchronization index was not correlated with discharge rate duringunmodulated DPT~correlation coefficient—0.02,p50.54, permutationtest!.

3Mathematical analysis shows that, with our choice of an initial guess,output of the algorithm is independent of the artifact. Thus, no artifact wadded to the model responses.

4This problem is ill-defined for transient responders, becauser dq(m) is zero

for small m. To resolve this ambiguity, a small random number~at mostcorresponding to half a spike! was arbitrarily added to eachr m(m,i ) andr u(m,i ) that equaled 0. Because thresholds of transient responders arecally well above the smallest modulation depth tested, this additiononly a minor effect on the estimate of modulation threshold.

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improved temporal coding of sinusoids in electric stimulation of the

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