modulated and unmodulated pulse trains

ANF RESPONSES TO ELECTRIC STIMULATION, MANUSCRIPT 01/20/00

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A U D I T O R Y N E R V E F I B E R R E S P O N S E S T O E L E C T R I C S T I M U L A T I O N :

M O D U L A T E D A N D U N M O D U L A T E D P U L S E T R A I N S

LITVAK, L.M.

DELGUTTE , B.

EDDINGTON, D.K

MANUSCRIPT IN PREPARATION, TO BE SUBMITTED TO JOURNAL OF THE ACOUSTICAL SOCIETY

INTRODUCTION

In continuous interleaved sampling (CIS) strategies, temporal information about incoming

sounds is encoded in the modulations of pulse trains (Wilson, Finley et al. 1991). Proper

representation of modulation in temporal discharge patterns of the auditory nerve is an important

goal in these strategies.

Despite the popularity of CIS schemes, the responses of auditory nerve fibers to a sinusoidal

modulation of an electric pulse train can be very different from responses to a pure tone in a healthy

ear. For modulation frequencies below 500 Hz, virtually every stimulated neuron is likely to entrain

to the modulator (i.e. to produce a spike discharge for every modulator cycle) (van den Honert and

Stypulkowski 1987). In contrast, in response to a pure tone, neurons fire at random multiples of the

stimulus period. For example, there may be 1, 2, 3 or more cycles between successive spikes (Rose,

Brugge et al. 1967). The situation is even worse at higher frequencies, because, with electric

stimulation, neurons may fire on every other cycle or even higher multiples of the modulation period.


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If most stimulated neurons fire together, then the population of auditory neurons would code a

submultiple of the modulator frequency rather than the actual frequency (Wilson, Finley et al. 1997).

Rubinstein et al. (Rubinstein, Wilson et al. 1999) proposed that naturalness in coding of

modulation waveform might be improved by introducing a sustained, high-frequency,

"desynchronizing" pulse train (DPT) in addition to the modulated pulse train (MPT). The rationale

for the DPT is that across-fiber differences in refractory, sensitivity and other properties, as well as

noise present in the membrane will result in the responses across fibers being desynchronized after

the first few hundred milliseconds of DPT stimulation. Such desynchronization would lead to

improved representation of the modulator in temporal discharge patterns. It might also allow an

ensemble of neurons to encode the true modulator frequency rather than a submultiple.

We studied responses of auditory nerve fibers to both modulated and unmodulated electric pulse

trains to physiologically test the ideas underlying the DPT. We focused on two specific questions:

1. Do the responses to a sustained high-frequency pulse train resemble spontaneous

activity? Specifically, we characterized interval histograms (IH) for pulse trains and compared them

to the nearly exponential histograms observed for spontaneous activity in an intact ear (Kiang,

Watanabe et al. 1965). We also quantified the variability in the spike count from presentation to

presentation, and compared it to the variability expected for normal spontaneous activity.

2. Does a high-frequency DPT help encode modulation frequency? We used modulated

high-frequency pulse trains with low modulation depths (≤ 0.2) to imitate the effect of a DPT. We

assumed that neural responses to a high-frequency pulse train with a low modulation depth are

similar to responses elicited by a stimulus that is a sum of a sustained DPT and a highly modulated

pulse train (Figure 1). This assumption may hold if the membrane time constant is large compared to


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the intervals between pulses. We compared period and interval histograms of responses to electric,

modulated pulse trains with acoustic responses to pure tones.

METHODS

We recorded from single units in 5 acutely deafened, anaesthetized cats (total: 106 units). Cats

were first anesthetized using dial. Co-administration of kanamycin (subcutaneous, 300 mg/kg) and

ethacrinic acid (intravenous, 25 mg/kg) was then used to deafen the animals (Xu, Shepherd et al.

1993). An intracochlear stimulating electrode was inserted about 10 mm into the cochlea through

the round window. The electrode was a 400 um Pl/Ir ball. A second electrode was inserted into the

base of the cochlea for compound auditory potential (CAP) recordings. The opening was then sealed

using connective tissue.

In order to verify that the animal was deafened, we measured a CAP in response to acoustic

clicks. In all cases, no CAP was noted for the highest click levels (~90 dB SPL) investigated.

Electrically evoked CAP was measured as a function of level for a single cathodic-anodic (CA)

electric pulse (phase duration of 20.8 usec). The levels at which CAP was roughly 50% of the

maximum varied from roughly -2 dB to 5 dB re 1 mA 0-p across different animals.

Figure 1. When carrier frequencies of the modulated signal and of the DPT are sufficiently high, the net signal is similar to the modulated pulse train. See text.


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Stimuli were delivered through an isolated current source. Our stimuli were either (1)

unmodulated pulse trains (150 msec or 250 msec duration) of pulse rates of 1.2, 2.4, 4.8 or 24 kpps

or (2) "modulated" 4.8 kpps pulse trains (first 50 msec or 150 msec unmodulated, last 100 msec

modulated, modulation frequency 400 Hz) of varying modulation depth. In all cases, pulse trains

consisted of CA pulses (20.8 usec per phase). Modulated stimuli were modulated "down" such that

the peak level was equal in the modulated and the unmodulated portion of the stimulus. Stimuli were

presented at a repetition rate of 1 per second. Stimulus level was adjusted to obtain discharge rates of

50 to 400 spikes/sec. All levels reported in this study are zero to peak.

Standard techniques were used to expose the auditory nerve via a dorsal approach (Kiang,

Watanabe et al. 1965). We measured from single units in the auditory nerve using glass micropipettes

filled with 3M KCl (impedance: 10M). A digital signal processor (DSP) algorithm was used to

separate neural responses from stimulus artifact (voltage excursions recorded at the micropipette as a

result of current flow between the stimulating electrode and the measurement site). First, we

recorded the "artifact" at a subthreshold stimulus level. Then, a scaled version of the recorded

"artifact" was subtracted from the incoming waveform in real time. The gain on the recorded

waveform was adjusted to optimally match the incoming waveform. Using this technique, we were

able to reduce the artifact to approximately 5% of the spike height. The operation of recording the

artifact was repeated for different neurons and for different stimuli for a single neuron. Another

important limitation of this technique is that non-linearities in the conducting medium, stimulation

system or the recording equipment limit the effectiveness of the cancellation. In a beaker our system

could cancel the stimulus artifact effectively at up to 6 dB above the recorded level. In an actual

experiment, however, time constraints in finding the highest level at which there are no spikes, as

well as possibly greater non-linearity of biological tissue limited the effective range to around 2.5 dB

above the neural threshold for any given stimulus.


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Spike times were recorded with a 1 usec precision and used to compute histograms (PST, IH,

Period, PND). Because the remaining artifact was largest in the first 6 msec after the onset of the

pulse train, we discarded spikes that were reported in that time window.


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RESULTS

UNMODULATED PULSE TRAINS

In Figure 2, we show responses of a fiber to two unmodulated pulse trains of similar levels with

pulse rates of 1.2 kpps (A, left) and 4.8 kpps (A, right). At this overall level, both stimuli evoke

sustained responses from the unit. However, there is more accommodation in response to the

higher-rate stimulus (B). This is a common finding in our data. For both pulse rates, responses are

initially synchronized across trials, and become desynchronized over the course of the stimulus (C).

This can be seen in the scatter of the response times from trial to trial in the dot raster histogram.

Figure 2. Response of a fiber to two unmodulated pulse trains of similar levels with pulse rates of 1.2 kpps (left) and 4.8 kpps (right). See text for description.


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Interval histograms (IH, panel D) for the 1.2 kpps pulse train exhibit phase locking to the pulses, and

a roughly exponential envelope. In contrast, IH for the 4.8 kpps pulse train has a non-exponential

envelope, with a pronounced mode at 5 msec. This mode is not related to the stimulus period, but is

inversely related to the average discharge rate.

ADAPTATION

As used here, adaptation refers to a slow (on the order of 30 to 100 msec) change in the response

discharge rate over the course of the stimulus. We found that adaptation is a function of pulse rate.

In Figure 3 we plot the final rate (the discharge rate in the 10 msec window centered at 145 msec

after the onset of the stimulus) versus the initial rate (the rate in a 10 msec window centered at 15

msec from stimulus onset). Each point is an average of these rates over approximately 40 stimulus

Figure 3. Adaptation as a function of pulse rate. See text.


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presentations. Solid black line indicates where the initial and the final rates are equal. Records that fall

on this line would show no adaptation.

The scatter in the points indicates that adaptation varies greatly across units. Such variability in

adaptation has been reported in previous studies (Dynes and Delgutte 1992; Killian 1994). This

variability is large even when comparing adaptation across levels that give similar initial response

rates.

The dashed lines indicate the regression lines for 1.2, 4.8, and 24 kpps data. Despite the scatter,

the degree of adaptation is clearly significantly different between the 1.2 and the 4.8 kpps data (P <

0.001, permutation test). The 1.2 kpps data lies closer (on average) to the "no-adaptation" curve.

Therefore, for levels that evoke the same initial discharge rate, response adapts less for a pulse train

with a lower pulse rate.

Variability

When stimulated with acoustic stimuli, auditory nerve responses show pronounced variability in

the number of spikes elicited from trial to trial. Similarly, spontaneous activity shows variability in the

spike count from one time interval to another (Teich and Khanna 1985; Kelly, Johnson et al. 1993).

The variability was quantified by the Fano Factor:

][

][

i

i

NMean

NVarianceFF ≡ , where Ni represents the number of spikes on Trial i.


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For short (<100 msec) time intervals, FF for normal spontaneous activity is consistent with a

Poisson model with dead time of 2 msec (Kelly, Johnson et al. 1996). A minimum requirement for

responses to the DPT to resemble spontaneous activity is that the Fano Factor should be in the

range for spontaneous activity. Figure 4 plots FF for responses to unmodulated pulse trains of 1.2,

4.8 and 24 kpps as a function of average discharge rate for a 50 msec time interval. For rates below

180 spikes/sec, most points fall within 95% confidence interval for a Poisson model with dead time

of 2.5 msec. Thus, for low and moderate discharge rates, variability in spike count from trial to trial is

comparable with that for spontaneous activity.

Interval Histograms

As indicated in Figure 2, the shape of the interval histogram (IH) can depend on pulse rate. For

the low pulse rate (1.2 kpps), IHs have an exponential envelope (Figure 5, upper inset). An

exponential shape is expected for Poisson discharges and is consistent with the IHs for spontaneous

Figure 4. Fano Factor (which characterizes variability in the stimulus from presentation to presentation) as a function of discharge rate. Measurement is taken in 50 msec window 100 msec after the stimulus onset. The filled area represents the 95% confidence interval for the distribution expected if the spikes were a Poisson process, and is therefore consistent with fano distribution expected for spontaneous activity in a healthy ear.


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activity in an intact ear. For high pulse rates, some but not all IH envelopes are clearly non-

exponential and are characterized by a sharp mode and a long tail (Figure 5, middle inset). To

quantify the shape of the interval histogram, we fit the interval histogram with both a single

exponential (red line in the insets) and piecewise, with three exponentials (green line in the insets).

We measured the root mean squared error of each fit to the data, and defined an IH exponential

shape factor (IH-ExpSF) as the ratio of the error of the piecewise fit to that of the exponential fit.

The IH-ExpSF for samples from a Poisson process is approximately 1.


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The scatter plot shows IH-ExpSF versus average discharge rate for measurements made with

pulse rates of 1.2 (triangles), 4.8 (stars) and 24 (squares) kpps. For pulse rate of 1.2 kpps, virtually all

points fall in the region expected for a Poisson model (shaded area). For higher pulse rates, fewer

than 20% of the data points are in the range expected for Poisson. Thus, only lower pulse rates

produce IHs that resemble spontaneous activity in intact ears.

Figure 5. Distribution of the exponential shape factor as a function of stimulus pulse rate and average discharge rate in the steady-state portion of the response period. The filled area in the main panel shows the distribution expected for spikes generated by a Poisson process. See text for the full description.


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MODULATED PULSE TRAIN

Figure 6 shows responses from a single unit to a sinusoidally amplitude modulated (400 Hz)

pulse train (4.8 kpps) for modulation depths of 0.02 (left) and 0.2 (middle). Pulse trains were

modulated in the last 100 msec of the 150 msec train duration (A). For both stimuli, the response

accommodates over the first 50 msec while the pulse train is unmodulated. At the onset of

modulation, average discharge rate increases for the modulation depth of 0.2 (B-middle; also, panel

4b). This increase in rate is interesting because RMS current is lower (by 0.9 dB for the 0.2

modulation depth) during the modulated portion of the stimulus. Panel (C) shows period and interval

histograms computed from the responses measured during the modulated portion of the stimulus.

For comparison, the right column shows both the interval and the period histogram computed from

responses to a 440 Hz pure tone at a moderate level. For both modulation depths, the period

histograms show pronounced modulation, although spikes are more precisely phase locked for the

higher modulation depth. Even when the modulation depth is only 0.02, the response is nearly fully

modulated; thus, modulation gain for this unit is approximately 50. Furthermore for this modulation

depth, the period histogram is nearly sinusoidal in shape. This suggests that the responses may be

representing the details of the sinusoidal modulator waveform (thin curve).

Figure 6. Response of a neuron to a modulated pulse train of different modulation depths. See text.


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Phase locking can be seen in the interval histogram as the clustering of intervals around multiples

of the stimulus period, which are shown here as dashed lines. For both modulation depths, the mode

distribution is broadly similar to that for pure tones. Close examination reveals several differences.

First, a pronounced mode at the modulation period is absent in the electrical case (arrow). The

magnitude of the first mode is related to the refractory period. Thus, effective refractory period is

longer for electric stimulation than for acoustic stimulation. This is surprising in light of the fact that,

in both cases, the effective refractory period is limited by the neural membrane. Secondly, the mode

at twice the modulator period is strongly exaggerated for the smaller modulation depth. The

exaggeration may be related to the preferred interval found for unmodulated pulse trains.

Large Modulation Depth: Entrainment

Figure 7. Response of a fiber to a stimulus with a large modulation depth at a near-threshold (left panel) and supra-threshold level (right panel). See text.


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Figure 7 shows the response of another unit to two different levels of a pulse train modulated at

a depth of 0.2. The pulse train was 250 msec long, and was modulated only in the last 100 msec. The

increase in rate at the onset of modulation is more pronounced for this unit than for the unit in

Figure 5. The increase is noticeable at both levels shown. For this modulation depth, we observed

similar increases in rate at the onset of modulation in 80% of the units studied.

At the lower level, the distribution of the modes in the interval histogram is similar to that for

acoustic responses to a pure tone. However, at the higher level, responses entrain to the modulator

frequency, as indicated by a single mode at the modulation period. Such entrainment is never seen in

the responses of auditory nerve fibers to pure tones. Thus, similarity between electrically-evoked

responses to a moderately modulated pulse train and acoustic responses to tones holds only over a

limited range of stimulus levels.

Small Modulation Depths

Figure 8 shows average discharge rate

and response modulation depth (which is

a measure of modulation of the period

histogram) for a single unit as a function

of level. The stimulus was a 250 msec

pulse train that was modulated in the last

100 msec (modulation depth 0.02).

Average discharge rate increased 3-fold

over the 1.5 dB range of levels. In

contrast, response modulation depth was nearly independent of level, indicating robust phase locking

at all levels. The insets show the interval histogram for three levels. The first mode in the interval

Figure 8. Responses of a unit to a stimulus with modulation depth of 0.02 at several levels. See text.


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histogram shifts left as the level increased. At the intermediate level of 4.5 dB re 1 mA, the first mode

fell nearly halfway between the first and the second multiple of modulator period (arrow). This result

suggests that the first mode is not related to the modulator frequency for this modulation depth. We

hypothesize that the first mode is related to the preferred firing period demonstrated earlier for high-

frequency unmodulated stimuli. Thus, for very low modulation depths, interval histograms only

partially resemble those evoked by acoustic tones.

DISCUSSION AND CONCLUSIONS

DOES RESPONSE TO A DESYNCHRONIZING PULSE TRAIN (DPT) RESEMBLE

SPONTANEOUS ACTIVITY?

Rubinstein et al. (Rubinstein, Wilson et al. 1999) suggested introducing a continuos pulse train

into CI strategies to produce neural responses resembling normal spontaneous activity. Our results

indicate that responses to sustained high-frequency pulse trains resemble spontaneous activity in

some, but not all respects. The variability across stimulus presentations is comparable with that

expected for spontaneous activity. For a relatively low pulse rate (1.2 kpps) the envelope of interval

histograms resembles those for spontaneous activity. However, for higher rates (4.8 kpps and above)

interval histograms can clearly deviate from those for spontaneous activity, showing a sharp mode

around 5 msec followed by a long tail. Such a preferred firing interval may be interpreted by the

central nervous system as presence of a sound at a frequency of 200 Hz. Thus, lower pulse rates

(below 1.2 kHz) may be better for imitating spontaneous activity if reproducing the exact shape of

the interval histogram is essential.

DOES A HIGH FREQUENCY DPT HELP ENCODE MODULATION FREQUENCY?

We showed that a modulated pulse train with low (<0.2) modulation depth can produce

interspike and period histograms resembling responses to pure tones in intact ears. If we interpret


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those stimuli as consisting of a DPT plus a highly-modulated signal, this result suggests that realistic

responses to sinusoidal stimuli might be obtained with a DPT. However, the realistic, tone-like

responses are only observed over a narrow range of stimulus levels. Furthermore, for very low

(<0.02) modulation depths, there can be preferred intervals unrelated to the modulation frequency

which may be confusing to the central processor. Interestingly, these intervals may co-exist with a

high level of phase locking to the modulator frequency.

IMPLICATIONS FOR THE COCHLEAR IMPLANT PROCESSOR

The purpose for introducing a DPT is to improve the coding of modulation in auditory nerve

responses. Some aspects of our data appear promising in that respect. A DPT can produce responses

that are desynchronized across trials, suggesting that the responses may also be desynchronized

across different fibers, as occurs for normal spontaneous activity (Johnson and Kiang 1976).

Desynchronization of auditory nerve responses may lead to an improved temporal coding of stimuli

with rapid onsets and high frequencies. At least for low pulse rates, responses to a DPT imitate some

characteristics of spontaneous activity. Over some range of parameters, a DPT can help provide

temporal discharge patterns for amplitude modulated stimuli that resemble responses to tones. Other

aspects of the data are less promising. For example, we found that DPTs that accurately encode

sinusoidal waveforms can help produce modes in the interval histogram that are not related to the

modulator frequency. It appears, therefore, that successful use of a DPT depends on what exact

aspects of the temporal discharge pattern (e.g. intervals versus cross-fiber synchrony) are actually

used by the central processor to extract information about the stimulus. Because these mechanisms

are not known, it is difficult to predict whether adding the DPT will result in an overall improvement

in perception of speech by cochlear implant users.


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DPT VERSUS NOISE

Morse and Evans (Morse and Evans 1996) proposed that the representation of complex stimuli

might be improved by introducing additive, wide-band noise. As pointed out by Rubinstein et al.

(Rubinstein, Wilson et al. 1999), DPT might accomplish the same goal. Although we did not directly

test the effect that a DPT might have on complex modulators, our data suggests that it may improve

details of waveform representation. Unlike noise, DPT may produce activity that is uncorrelated

across fibers. Both the DPT and the noise may improve temporal coding for a limited parameter

range. More work needs to be done to determine precise limits of the benefits of DPT stimulation,

and on the effect that noise has on the interspike interval distribution before the two schemes can be

compared.

IMPLICATIONS FOR MECHANISMS

Our results with unmodulated and modulated stimuli also pose important questions for models

of auditory nerve fiber responses to electric stimulation. Published reports based on biophysical

models have not described the complex interval histogram shape (a pronounced mode with a long

tail) which we observed in responses to high-frequency pulse trains (e.g. (Rubinstein, Wilson et al.

1999)). In deciding which mechanisms may account for this discrepancy it is important to determine

whether the relevant processes occur on interval-per-interval basis or on a slower time scale (e.g.

bursting). In a limited number of units for which sufficient data were available, we failed to detect

correlation between the previous and the next interval. Thus, the relevant processes appear to occur

on an interval to interval basis.


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A possible mechanism that may be

responsible for the unusual IH shape

may be related to the mechanism that

governs responses of neural

membranes to steady current

injections. As shown in Figure 9, under

certain conditions, dynamics that

govern responses of a membrane

model to a high-frequency stimulus

can resemble the dynamics observed in

response to a steady injection. The

similarity suggests that one can

understand responses to high

frequency stimuli using techniques

developed for constant currents.

Responses of neural membranes to DC currents have been investigated in detail in both

physiological preparations and in theoretical studies. In an early paper, Huxley computed responses

of the Hodgkin-Huxley (HH) model to steady injections (Huxley 1959). He predicted that for some

levels of current injections, the HH model would respond either by firing repetitively or with damped

subthreshold oscillations. The mode of the response depended on the initial conditions. Because the

range of initial conditions for which oscillations are observed is small, Huxley hypothesized that

subthreshold oscillations are unlikely to be observed experimentally. However, both experimental

(Guttman and Barnhill 1970; Guttman, Lewis et al. 1980) and recent theoretical (Schneidman,

Freedman et al. 1998) work has shown that both subthreshold oscillations and repetitive firing

Figure 9. Response of Hodgkin-Huxley model to a high-frequency sinusoid (A) and to a sustained current injection (B). The model was implemented in MATLAB (provided by Dr. Weiss) and simulated numerically using a 5 usec step. The stimulus was presented in current clamp condition. For panel (A), the stimulus was a 2 kHz sinusoid (400 uA/cm2 0-peak) that was turned on at time 0. The course of the membrane voltage (dashed line) and the course of the same voltage averaged over a period of the sinusoid is shown. In panel (B), steady DC (300 uA/cm2) voltage is applied at time 0. In both cases, the membrane “spikes” initially. The response after the initial spike can be characterized by damped subthreshold oscillations, which settle to a DC value. Note that the high-frequency response does not qualitatively resemble the observed responses.


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should be readily observable in the same response when the excitable area is small. This is the case at

the nodes of Ranvier of small myelinated fibers. Schneidman and colleagues showed by adding noise

to the HH model, one could produce random switches of the model between the firing and the

oscillating states. Such responses to steady

current have been demonstrated directly

for the membrane patches of the squid

axon (Guttman and Barnhill 1970;

Guttman, Lewis et al. 1980).

To determine whether a presence of

such an oscillating, non-firing state can

account for complicated IH shape

observed for high frequency stimuli, we

developed the following model (Figure 10).

We assumed that the model has three

"states" (where each state is in reality an

attractor). One state is "rest," another is "firing," and the third is the "non-firing" oscillatory state. At

rest, in response to a stimulus pulse the state of the membrane can change to either firing state (in

which case we observe a spike) or to a non-firing state (in which case no spike is seen) with preset

probability after each pulse. Alternatively, the model may remain at rest. We assume that once the

membrane switches to one of the dynamic states, it stays in that state for a fixed time and then

returns to rest. For a large range of the three free parameters (Pfiring, Pnon-firing and Tosc), the IHs

produced by model spike trains have interval histograms that are very similar to those observed in

single unit responses (Figure 11). Furthermore, for some choice of parameters, the model indicates a

Figure 10. Simplified stochastic model of neural responses to pulsatile stimulation. See text.


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broad third mode in the IH that is related

to the time course of the oscillation. Such

a third mode is observed in some of the

data.

Another intriguing observation is the

increase in average discharge rate after the

"down" modulation is turned on. The

increase in the average discharge rate is

surprising because the RMS current

actually decreases at the onset of the

modulator. To our knowledge, such

increased response to modulation has not

been reported in biophysical models. Our

simulations using the HH model indicate that although HH model does not mimic the data

quantitatively, an increased response rate can be observed at the onset of the “down” modulations

(personal observations, later: figure). By establishing a better connection between responses of HH

and the simplified models to high frequency stimuli, we hope to provide a heuristic explanation for

the observed rate increases.

BIBLIOGRAPHY

Dynes, S. B. and B. Delgutte (1992). “Phase-locking of auditory-nerve discharges to sinusoidal electric stimulation of the cochlea.” Hear Res 58(1): 79-90.

Guttman, R. and R. Barnhill (1970). “Oscillation and repetitive firing in squid axons. Comparison of experiments with computations.” J Gen Physiol 55(1): 104-18.

Guttman, R., S. Lewis, et al. (1980). “Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator.” J Physiol (Lond) 305: 377-95.

Figure 10. Interval histogram computed from responses of a model described by Figure 9. Parameters used are Pfire=0.05, Posc=0.05, Trefr=2.4 msec, Tosc=5 msec. The output of the model was evaluated every 0.2 msec, corresponding to stimulating the model with a 5 kpps pulse train. For this choice of parameters, the model IH mimics the structure of responses of some ANFs to high-rate electric stimulation. In particular, both exhibit a strongly non-poisson shape, with a mode at around 5 msec, and a second mode around 7.4 msec. There is also a broader third mode that is apparent at around 17 msec. Such a mode is occasionally observed in our data.


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Huxley, A. F. (1959). “Ion movements during nerve activity.” Annals of the N.Y. Academy of. Science 81: 221-246.

Johnson, D. H. and N. Y. S. Kiang (1976). “Analysis of discharges recorded simultaneously from pairs of auditory nerve fibers.” Biophysical Journal 16: 719-734.

Kelly, O. E., D. H. Johnson, et al. (1993). Factors affecting the fractal character of auditory nerve activity. ARO MidWinter Meeting.

Kelly, O. E., D. H. Johnson, et al. (1996). “Fractal noise strength in auditory-nerve fiber recordings.” J Acoust Soc Am 99(4 Pt 1): 2210-20.

Kiang, N. Y. S., T. Watanabe, et al. (1965). Discharge Patterns of Single FIbers in the Cat's Auditory Nerve. Cambridge, MA, The MIT Press.

Killian, M. J. P. (1994). Excitability of the Electrically Stimulated Auditory Nerve. Utrecht, University of Utrecht.

Morse, R. P. and E. F. Evans (1996). “Enhancement of vowel coding for cochlear implants by addition of noise.” Nat Med 2(8): 928-32.

Rose, J. E., J. R. Brugge, et al. (1967). “Phase-locked response to low-frequency tones in single auditory nerve fibers of the squirrel monkey.” J. Neurophysiol. 30: 769-793.

Rubinstein, J. T., B. S. Wilson, et al. (1999). “Pseudospontaneous activity: stochastic independence of auditory nerve fibers with electrical stimulation.” Hear Res 127(1-2): 108-18.

Schneidman, E., B. Freedman, et al. (1998). “Ion channel stochasticity may be critical in determining the reliability and precision of spike timing.” Neural Comput 10(7): 1679-703.

Teich, M. C. and S. M. Khanna (1985). “Pulse-number distribution for the neural spike train in the cat's auditory nerve.” J. Acoust. Soc. Am. 77(3): 1110-1128.

van den Honert, C. and P. H. Stypulkowski (1987). “Temporal response patterns of single auditory nerve fibers elicited by periodic electrical stimuli.” Hear Res 29(2-3): 207-22.

Wilson, B., C. C. Finley, et al. (1997). “Temporal Representations With Cochlear Implants.” American Journal of Otology 18, Suppl. 6: S30-S34.

Wilson, B. S., C. C. Finley, et al. (1991). “Better speech recognition with cochlear implants.” Nature 352: 236-238.

Xu, S. A., R. K. Shepherd, et al. (1993). “Profound hearing loss in the cat following the single co-administration of kanamycin and ethacrynic acid.” Hear Res 70(2): 205-15.

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modulated and unmodulated pulse trains