Modeling binaural responses in the auditory brainstem to electric stimulation of the auditory nerve.

JARO

JARO 16: 135–158 (2015) DOI: 10.1007/s10162-014-0492-6 D 2014 Association for Research in Otolaryngology

Research Article

Journal of the Association for Research in Otolaryngology

Modeling Binaural Responses in the Auditory Brainstem to Electric Stimulation of the Auditory Nerve YOOJIN CHUNG,1 BERTRAND DELGUTTE,2,3

AND

H. STEVEN COLBURN1

1

Biomedical Engineering Department, Hearing Research Center, Boston University, Boston, MA 02215, USA

2

Eaton-Peabody Laboratories, Massachusetts Eye and Ear, Boston, MA 02114, USA

3

Department of Otology and Laryngology, Harvard Medical School, Boston, MA 02115, USA

Received: 7 March 2014; Accepted: 24 September 2014; Online publication: 28 October 2014

ABSTRACT Bilateral cochlear implants (CIs) provide improvements in sound localization and speech perception in noise over unilateral CIs. However, the benefits arise mainly from the perception of interaural level differences, while bilateral CI listeners’ sensitivity to interaural time difference (ITD) is poorer than normal. To help understand this limitation, a set of ITD-sensitive neural models was developed to study binaural responses to electric stimulation. Our working hypothesis was that central auditory processing is normal with bilateral CIs so that the abnormality in the response to electric stimulation at the level of the auditory nerve fibers (ANFs) is the source of the limited ITD sensitivity. A descriptive model of ANF response to both acoustic and electric stimulation was implemented and used to drive a simplified biophysical model of neurons in the medial superior olive (MSO). The model’s ITD sensitivity was found to depend strongly on the specific configurations of membrane and synaptic parameters for different stimulation rates. Specifically, stronger excitatory synaptic inputs and faster membrane responses were required for the model neurons to be ITD-sensitive at high stimulation rates, whereas weaker excitatory synaptic input and slower membrane responses were necessary at low stimulation rates, for both electric and acoustic stimulation. This finding raises the possibility of frequency-dependent differences in neural mechanisms of binaural processing; limitations Correspondence to: Yoojin Chung & Biomedical Engineering Department, Hearing Research Center & Boston University & Boston, MA 02215, USA. Telephone: (617) 573-5592; email: yoojin.chung@ gmail.com

in ITD sensitivity with bilateral CIs may be due to a mismatch between stimulation rate and cell parameters in ITD-sensitive neurons. Keywords: binaural hearing, auditory brainstem model, interaural time difference, cochlear implant, auditory prosthesis

INTRODUCTION Bilateral cochlear implantation is increasingly common as a clinical treatment for severe to profound deafness (American Academy of OtolaryngologyHead and Neck Surgery 2014). Compared to unilateral cochlear implant (CI) users, bilateral CI users show improvements in sound localization and in speech reception in noise. These benefits are based primarily on the acoustic head shadow and the resulting interaural level differences (ILD) (van Hoesel 2012); however, sensitivity to interaural time difference (ITD) remains poorer than normal in bilateral CI users, especially those with prelingual deafness (Litovsky et al. 2010). Using pulsatile stimulation bypassing the clinical processor, bilateral CI users with postlingual deafness can achieve relatively good ITD sensitivity at low pulse rates, but performance rapidly degrades for pulse rates above 200–300 pps in most subjects (van Hoesel 2007; Poon et al. 2009). Similarly, single neurons in the inferior colliculus (IC) of acutely deafened cats can exhibit good ITD sensitivity to electric pulse trains at low pulse rates (G100 pps) for moderate stimulus levels, but their ITD sensitivity degrades at higher 135

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pulse rates where many neurons show only an onset response (Smith and Delgutte 2007, 2008; Hancock et al. 2012). The narrow range of pulse rates yielding good ITD sensitivity with electric stimulation in deaf animals contrasts with the wider range of frequencies over which ITD sensitivity to pure tones is observed in normal hearing animals in both the medial superior olive (MSO) (Yin and Chan 1990) and the IC (Kuwada and Yin 1983; Kuwada et al. 1987). In the modeling reported here, we test the hypothesis that the degradation in ITD processing with bilateral CI is due to limitations in peripheral encoding rather than abnormalities in brainstem circuits specialized for binaural processing. This hypothesis is most relevant to cases of adult-onset deafness of relatively short duration to minimize developmental abnormalities and degenerative changes in the binaural pathways resulting from prolonged deafness (Hancock et al. 2010, 2013; Tillein et al. 2010). Specifically, we hypothesize that the limitations on ITD sensitivity in single cells in acutely deafened animals and postlingually deaf human subjects could be mainly due to the abnormal properties of auditory nerve fiber (ANF) responses to electric stimulation. Some properties of the response patterns to electric stimulation such as precise phase locking (Dynes and Delgutte 1992; Javel and Shepherd 2000) may be of advantage in binaural processing, but it is also possible that these response patterns have unwanted consequences in the central auditory circuits specialized for binaural processing. Low-threshold potassium (KLT) channels are widely expressed in auditory neurons specialized for rapid temporal processing, including neurons in the MSO, where neural sensitivity to ITD first arises (Eatock 2003; Svirskis et al. 2004; Scott et al. 2005; Johnston et al. 2010; Mathews et al. 2010). KLT currents enable neurons to accurately encode temporal information at high frequencies (Manis and Marx 1991; Trussell 1997, 1999; Rothman and Manis 2003a). However, at very high stimulation rates, KLT channels can stay continuously opened and thereby prevent the cell from further discharging by raising the spike threshold. Electric stimulation can produce very high discharge rates (up to 900 spikes/s) in ANFs (Kiang and Moxon 1972; Javel and Shepherd 2000) that may trigger such “KLT shunting” either in the targets of ANFs in the ventral cochlear nucleus (VCN) or in downstream MSO neurons. A previous modeling study (Colburn et al. 2009) showed that such KLT shunting can result in loss of ongoing response to electric pulses at 500 pps in a model MSO neuron and that ITD tuning was highly sensitive to the membrane and synaptic parameters of the model cell. An alternative hypothesis is that the degradation in ITD sensitivity with electric stimulation may be due to

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Modeling binaural responses in the MSO to CI stimulation

a mismatch between the stimulation rate and the biophysical properties of binaural neurons with a given characteristic frequency (CF). It has been suggested that the frequency-dependent differences in binaural performance originate primarily from differences in cochlear processing rather than from intrinsic differences in neural mechanisms in the brainstem (Colburn and Esquissaud 1976; Bernstein and Trahiotis 2002). However, if there is a tonotopic gradient in properties of mammalian binaural circuits (Barnes-Davies et al. 2004; Brew and Forsythe 2005; Baumann et al. 2013), the mismatch between the rate of the electric stimulus and the CF of the binaural neurons could degrade ITD sensitivity. We tested these hypotheses by implementing models of MSO neurons driven by inputs with realistic temporal discharge patterns for both acoustic pure tones and electric pulse trains and examining ITD sensitivity over a wide range of frequencies and levels for models with different biophysical properties. The model’s ITD sensitivity was found to be strongly dependent on the stimulation frequency, the strength of synaptic inputs, and the ionic channel composition of the cell membrane, with each set of model parameters showing a preferred frequency yielding maximal ITD sensitivity.

METHODS Our results are based on a simplified biophysical model of an MSO neuron and its binaural inputs from the auditory periphery. The philosophy was to implement the simplest possible model that would possess the essential features for comparing binaural response to acoustic vs. electric stimulation over a wide range of frequencies. The first stage is a phenomenological model of ANFs that produces realistic temporal discharge patterns to both acoustic pure tones and electric pulse trains (Nourski et al. 2006). MSO neurons receive bilateral excitatory inputs from ANFs via spherical bushy cells (SBCs) in the VCN, as well as bilateral inhibitory inputs originating from globular bushy cells in the VCN (Cant and Casseday 1986; Smith et al. 1993). In our implementation, the SBC stage was omitted because SBC shows little coincidence detection themselves (Wang and Delgutte 2012). The inhibitory inputs were omitted for simplicity as well, so that the MSO neuron model received direct excitatory inputs from ANFs on each side. The exact function of the inhibitory inputs to the MSO is still being debated (for review, see Grothe et al. 2010), and the sharpening of phase locking ascribed to SBCs (Joris et al. 1994) may be of minor importance with the extremely precise phase locking

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already present in ANFs with electric stimuli (see “DISCUSSION”). The ANF model is a modification of a phenomenological model that simulates responses to both acoustic and electric stimulation (Nourski et al. 2006). The model for electric stimulation is based on the integrate-and-fire model of Bruce et al. (1999a, b), while the model for acoustic stimulation additionally incorporates the Schroeder and Hall (1974) model of the synapse between inner hair cells (IHC) and spiral ganglion cells. The MSO neuron model is a single compartment, Hodgkin-Huxley type model with the set of ionic membrane channels described by Rothman et al. (1993, 2003b) for VCN bushy cells. We use a bushy cell membrane model because Rothman et al. provided a detailed, quantitative characterization of the channel dynamics and because the ionic channels incorporated in their model are also found in other cells of the auditory brainstem that are specialized for precise temporal processing, including MSO neurons (Trussell 1999). We studied the effect of membrane and synaptic parameters on ITD sensitivity of the MSO model over a wide range of frequencies (100–1000 Hz) and levels for both acoustic and electric stimuli. In particular, three parameters were varied systematically: the strength of the excitatory synapses, GE; the strength of the low-threshold potassium channel, GKLT; and the number of ANF inputs from each side, NE. The strength of the hyperpolarization-activated cation channel, Ih, always covaried with GKLT to maintain the resting potential constant.

ANF Model The ANF model describes the temporal discharge pattern of an ANF to both acoustic pure tones and electric pulse trains. It consists of three stages: (1) a model of the IHC-ANF synapse (Schroeder and Hall 1974), (2) a model for the ANF membrane potential, and (3) a probabilistic model for spike generation modified from Bruce et al. (1999a, b). Only the last two stages are included in the model for electric stimulation, and these two stages are identical for the acoustic and electric versions of the model. Cochlear filtering is not explicitly included in the acoustic ANF model because we are primarily interested in temporal discharge patterns to pure tones, which are largely unaffected by filtering. We assume that all of the acoustically driven inputs to the MSO are coming from the same place in the cochlea so that there is no spread in best frequencies of these inputs. Likewise, the mean response latencies are assumed to be identical across all ANF inputs for both electric and acoustic stimulation. Outputs of the ANF model are

spike trains that drive the MSO model. The model parameters (Table 1) were chosen to match measured responses to pure tones (Johnson 1980) and electric pulse trains (Javel and Viemeister 2000; Zhang et al. 2007). Model for Electric Stimulation. For electric stimulation, the model receives trains of current pulses as input. The membrane potential ve(t) is computed by convolving the electric current, ie(t), with an exponential impulse response h(t) with time constant τm: v e ðt Þ ¼ i e ðt Þ h ðt Þ ; with

ð1Þ

h ðt Þ ¼ e −t=τ m

ð2Þ

The probabilistic spike generation model is an extension of the model of Bruce et al. (1999a, b) and includes both refractoriness and firing rate adaptation as observed in response to high-rate pulse trains (Zhang et al. 2007). The probability of spike generation, p(t), is derived from the membrane potential by a stochastic model. Specifically, a spike is generated when the membrane potential ve(t) crosses a noisy, time-varying threshold vthr(t): 1 for v e ðt Þ > v thr ðt Þ; p ðt Þ ¼ ð3Þ 0 for v e ðt Þ≤ v thr ðt Þ The average of p(t) over the stimulus duration gives the ANF firing rate. The threshold vthr(t) is defined by: v thr ðt Þ ¼ ½v thr 0 þ v noise ðt Þ⋅r ðt−t m0 Þ=n m ðt Þ

ð4Þ

where vthr0 is the resting threshold, vnoise is the threshold noise, r(t) is the refractory function, and nm(t) is the membrane adaptation function. The random variable vnoise(t) has a normal distribution with zero mean and standard deviation σnoise. The refractory function, r(t), is defined as a function of the time from the last firing time, tm0, as: ( r ðt−t m0 Þ ¼

∞; 1 þ ðr 0 −1Þ⋅ e −ðt−t m0 −t abs Þ=τ rel ;

for 0 ≤ t−t m0 ≤t abs for t−t m0 > t abs

ð5Þ

where tabs is the absolute refractory period, τrel is the relative refractoriness time constant, and r0 defines the amplitude of the refractory function immediately at the end of the absolute refractory period. Our implementation follows the original one in Bruce et al. (1999a, b) rather than its modification by Nourski et al. (2006) because it gave a better representation of the relevant physiological data. The

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TABLE 1

Parameters of the ANF model Λ R ta Ia ρ0 g τm nm0 pm rm tabs τrel r0 vthr0 Relative spread Tm σT

Sampling interval Quanta generation rate Duration of EPSC generated by one vesicle release Amplitude of EPSC generated by one vesicle release Spontaneous quantum release rate Probability of a quantum being released and not causing an event Membrane time constant Activity-dependent membrane adaptation Decrement in excitability produced by each spike Rate of recovery from adaptation Absolute refractory period Relative refractoriness time constant Amplitude of the refractory function immediately after the end of the absolute refractory period Threshold potential of discharge Ratio of standard deviation of threshold noise (σnoise) to vthr0 Mean response latency Standard deviation of response latency

0.01 ms 200/s 100 us 1 mA 25/s 100/s 0.4 ms 1 0.02 10/s 0.7 ms 1.3 ms 1.97 3 0.12 0.5 ms 50 μs

two implementations differ slightly in the amount of relative refractoriness at high stimulation rates. To take into account the adaptation occurring in the cell membrane (as opposed to adaptation caused by synaptic depression) observed with high-rate pulse trains (Zhang et al. 2007), we used the activitydependent membrane adaptation function, nm(t), introduced by Nourski et al. (2006). The value of nm(t) is set to unity at rest and is decreased by a fixed percentage pm immediately after each spike: n m ðt Þ ¼ n m ðt−Δt Þ⋅ 1−p m ð6Þ When there are no spikes, nm(t) recovers gradually with a time constant 1/rm. dn m ¼ r m ⋅½1−n m ðt Þ dt

ð7Þ

To more accurately model the temporal discharge patterns to electric pulse trains, we introduced a new random variable T that adds both a delay and temporal jitter to spike generation after each threshold crossing. This term was not present in the models of Nourski et al. (2006) and Bruce et al. (1999a, b). Specifically, the latency from threshold crossing, T, is a normal random variable with mean Tm and standard deviation σT. This parameter σT defines

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the additional time jitter, added to that resulting from the noisy threshold crossing. This jitter is the main source of latency spread that limits phase locking of model ANFs to electric pulse trains; the standard deviation was set to match physiological observations (Javel and Shepherd 2000). Model for Acoustic Stimulation. The model for acoustic stimulation of ANF (Nourski et al. 2006) includes the same membrane and spike generation modules as the electric model, but also includes an additional, probabilistic first stage describing transmission at the IHC-ANF synapse (Schroeder and Hall 1974). The synapse stage generates excitatory postsynaptic currents (EPSC) that drive the membrane and spike generation stages exactly as the external stimulus current does in the electric model. Other stages of peripheral auditory processing such as middle ear and cochlear filtering are not explicitly modeled here because we are only using pure tone stimuli for which the effect of filtering on temporal response patterns can be largely reproduced by adjusting the stimulus level. The synapse model describes the probability density of vesicle release fa(t) during a brief time interval Δt as the product of a stimulus-dependent permeability pa(t) and the amount of available neurotransmitter quanta na(t): f a ðt Þ ¼ p a ðt Þ⋅n a ðt Þ⋅Δt

ð8Þ

The permeability pa(t) is derived from the sinusoidal stimulus waveform, sa(t) by “soft” half-wave rectification: " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# s a ðt Þ s 2a ðt Þ þ þ1 ; p a ðt Þ ¼ p a0 ⋅ ð9Þ 2 4 where pa0 is the resting permeability which is responsible for spontaneous activity. The number of available neurotransmitter quanta na(t) in the hair cell is governed by the following differential equation: dn a ¼ r a −n a ðt Þ⋅ p a ðt Þ þ g a dt

ð10Þ

ra is the quantum generation rate, and ga is the probability of a quantum being released but not binding to a postsynaptic receptor. Each vesicle release (occurring with probability density fa(t)) generates a rectangular EPSC with a 100 μs width (ta) and 1 mA amplitude (Ia). The summed EPSCs are convolved with the membrane impulse response h(t) to generate an excitatory postsynaptic potential

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(EPSP) waveform that is compared with a noisy threshold as in the electric model (Eqs. 1–4).

MSO Model The MSO neuron model has a single compartment with the membrane properties and the ion channels described by Rothman and Manis (2003b) for VCN bushy cells. This Hodgkin-Huxley type model has the following ion channels: a fast Na+ channel, INa; a noninactivating highthreshold K+ channel, IKHT; a slow-inactivating low-threshold K+ channel, IKLT; a hyperpolarization-activated cation channel, Ih; a leakage current, Ilk; and an excitatory synaptic current, IE. The membrane potential V is described by the following differential equation: Cm

dV ¼ I Na þ I KHT þ I KLT þ I h þ I lk þ I E dt

ð11Þ

where all the currents follow the same kinetics as in Rothman and Manis (2003b). The MSO model parameters are given in Table 2. The model MSO neuron receives NE statistically independent, identically distributed ANF inputs from each side. All the inputs are assumed to have identical CFs, and there are no differences in mean latency between the ANF inputs. Each spike from each ANF generates a time-varying excitatory synaptic conductance gE(t) described by an “α function”: g E ðt Þ ¼ G E ⋅½t=τ E ⋅e ð1−t=τ E Þ

ð12Þ

where GE is the peak conductance and τE is the time constant. The total gE(t) is the sum of the conductance changes produced by all the spikes from all the ANF inputs. These conductances result in an EPSC defined by: I E ðt Þ ¼ g E ðt Þ ⋅ ½V ðt Þ−V E

ð13Þ

where VE is the reversal potential. TABLE 2

Fixed parameters of the MSO model GNa GKHT Glk VNa Vh Vlk VE τE

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Maximum sodium conductance 1000 nS Maximum high-threshold potassium conductance Maximum leakage conductance Reversal potential of INa Reversal potential of Ih −43 mV Reversal potential of Ilk −65 mV Reversal potential of IE Excitatory conductance time constant

150 nS 2 nS 55 mV

0 mV 0.1 ms

Because the focus of this study is on the binaural coincidence detection mechanism rather than on the distribution of best ITDs, no internal delay was incorporated into the model for simplicity. As a result, the model’s nominal best ITD is always zero (although in some conditions, the firing rate may peak for antiphasic ITDs rather than at the nominal best ITD).

Simulations and Data Analysis The response of the MSO model neuron was computed as a function of ITD for both acoustic and electric stimuli of different frequencies (100–1000 Hz) and stimulus levels. Acoustic stimuli were 300 ms pure tones; electric stimuli were 300 ms constant-amplitude, periodic pulse trains (100 μs/phase, cathodic/ anodic). All simulations were done with static ITDs over one stimulus cycle of the stimulus frequency in 0.1 cycle intervals. These simulations were run for MSO models with different parameters to test the effects of these parameters on ITD sensitivity. Specifically, we systematically varied the synaptic strength GE, and the strength of the low-threshold potassium channel, G KLT . The strength of the hyperpolarization-activated cation channel, Ih, always covaried with GKLT so as to maintain a 1:10 ratio between these two conductances; this covariation had the effect of keeping the resting potential constant. The number of ANF inputs from each side, NE, was usually set to 10, but was varied in some simulations (Figs. 8 and 9). Other parameters of the MSO model (Table 2) were held fixed at the same values as in Rothman and Manis (2003b). The ANF model was run with compiled Matlab® (The MathWorks, Natick, MA) scripts on a Sun Grid Engine using a time base of 0.01 ms. MSO models were simulated in the EarLab modeling environment (Mountain et al. 2005) using the same time base. To characterize the ITD sensitivity of the MSO neuron model, we averaged the firing rate over a time widow extending from 30 to 300 ms after stimulus onset. We focused on the sustained response because responses of IC neurons to electric pulse trains are often limited to brief burst of spikes at stimulus onset at high stimulation rates (Smith and Delgutte 2007; Hancock et al. 2012). These electric responses contrast with responses to acoustic pure tones which show sustained response throughout stimulus durations in a majority of IC and MSO neurons (Pecka et al. 2008). Two metrics of ITD sensitivity were derived from rate-ITD curves. The ITD signal-to-total variance ratio (STVR) is a metric based on analysis of variance that has been used to characterize ITD sensitivity of neural data (Hancock et al. 2010). ITD STVR represents the fraction of the variance in neural spike counts due to variation in stimulus ITD, as opposed to random

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variability across stimulus trials (Hancock et al. 2010). It ranges from 0, indicating no ITD sensitivity, to 1, indicating perfectly reliable ITD coding (meaning the spike counts would vary with ITD and be identical on every trial for each ITD). The second metric, the signed ITD modulation depth (sMD), was used to characterize the shapes of ITD tuning curves, specifically to distinguish peakshaped from trough-shaped curves. Since the best ITD of the model MSO neuron is always 0, sMD represents the normalized difference in firing rate between homophasic stimulation (0 ITD) and antiphasic stimulation (ITD = half-period): sMD ¼

ET AL.:


ANF model to pure tones and electric pulse trains and compare their temporal properties and level dependence against physiological data. Next, we characterize responses of the MSO model for membrane parameters that yielded good ITD sensitivity at low frequencies (100 Hz). We then describe a set of parameters that produced good ITD sensitivity at higher frequencies (1000 Hz). Finally, we systematically explore the effect of key model parameters on ITD sensitivity, with a focus of the strength of excitatory synaptic conductance (GE), the density of low-threshold potassium conductances (GKLT), and the number of ANF inputs from each side (NE).

Spike rate at 0 ITD − Spike rate at half‐period ITD maxðSpike rate at 0 ITD; Spike rate at half‐period ITDÞ

ð14Þ When the MSO model shows good binaural coincidence detection with minimum response to monaural inputs, the rate-ITD curve is peak-shaped with a maximum at 0 ITD, so that sMD takes a positive value. On the other hand, if the model responds to monaural coincidences from each side in the antiphasic condition, the spike rate at the halfperiod ITD can be higher than the rate at 0 ITD, resulting in a trough-shaped rate-ITD curve and a negative sMD. In this case, the ITD STVR could still suggest good ITD sensitivity but the sign of sMD would indicate the model’s hypersensitivity to monaural coincidences. Sometimes the model rate-ITD curve changed from peak-shaped to trough-shaped with an increase in synaptic inputs (e.g., caused by an increase in stimulus level), and this was reflected in sMD changing sign.

RESULTS A salient feature of the ITD sensitivity of IC neurons with bilateral electric stimulation of the auditory nerve by constant-amplitude pulse trains is a degradation in sensitivity at pulse rates above 100–300 pps (Smith and Delgutte 2007; Hancock et al. 2012; Chung et al. 2014a), which contrasts with the more robust ITD coding up to 1500–2000 Hz observed with pure-tone acoustic stimulation in normal hearing animals (Yin et al. 1984; Kuwada et al. 1987). To gain insight into this difference, we characterized the ITD sensitivity of an MSO neuron model driven by physiologically realistic ANF inputs using stimulation with both electric pulse trains and acoustic pure tones. The ITD sensitivity for different frequencies clearly depended on the membrane parameters of the model MSO neuron. First, we describe the responses of the

Responses of the ANF Model Figure 1A, B shows histograms describing responses of the ANF model to electric stimulation for two different pulse rates. Figure 1A shows the response to a 100 pps pulse train at −10 dB re 1 mA (2 dB above threshold). Both the peristimulus time (PST) histogram and the period histogram (period histograms are shown by the insets in each panel) show precise phase locking, and the PST histogram also shows some adaptation over the 300 ms stimulus duration. For a 1000 pps pulse train at the same current level (Fig. 1B), adaptation in spike rate is more rapid and more prominent. The distribution of spike times in the period histogram appears wider at 1000 pps than at 100 pps because the constant amount of time jitter σT in the model occupies a larger fraction of the stimulus period at 1000 pps than at 100 pps. The overall pattern of response to pulse trains is consistent with physiological observations (Javel and Shepherd 2000; Javel and Viemeister 2000; Zhang et al. 2007). Figure 1C, D shows responses of the acoustic ANF model to pure tones at 100 and 1000 Hz at 15 dB re threshold (defined as the level where the driven firing rate is 10 % of maximum). The PST histogram for 100 Hz (Fig. 1C) shows a strong modulation at the stimulus period. Such modulation is less obvious in the 1000 Hz PST histogram (Fig. 1D) due to the limited resolution of the histogram, but phase locking is apparent in the period histograms for both frequencies with similar vector strengths. For the 100 Hz tone, the firing rate is higher than the stimulus frequency, indicating multiple spikes per cycle, consistent with physiological observations (e.g., McKinney and Delgutte 1999). Model responses to the 1000 Hz tone also are consistent with physiological observations (Johnson 1980; Javel and Viemeister 2000), although the adaptation produced by the synapse model is somewhat too brief. The acoustic and electric stimulus levels in Figure 1 were used for all subsequent simulations, except for the cases shown in

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Electric

Firing rate (spikes/s)

A 1200

SI=0.9995

53 spikes/sec

800

0

100 Hz

1200

SI=0.76

135.47 spikes/sec

800

10 (ms)

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0

10 (ms)

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0 0

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Acoustic

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100 pps

100

200 Time(msec)

300

D

1000 pps

1200

SI=0.9505

112.27 spikes/sec

0

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100

200 Time(msec)

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1200

SI=0.73

164.13 spikes/sec

800 0

1 (ms)

0

400

1 (ms)

400

0

0 0

100 200 Time(msec)

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0

100 200 Time(msec)

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FIG. 1.

Temporal patterns of model ANF response to electric pulse trains at 100 pps (A) and 1000 pps (B) and acoustic pure tones at 100 Hz (C) and 1000 Hz (D). PST histograms for 50 repetitions based on a 1 ms bin width are plotted with vertical bars, while open circles show histograms based on

progressively wider bins (5 ms for 0–20 ms, 10 ms for 20– 50 ms, and 25 ms for 50–300 ms after stimulus onset). The insets in each panel are period histograms constructed using 100 bins per cycle.

Figures 2, 8, and 9, where the effect of stimulus level was systematically investigated. Figure 2A, B shows model rate-level functions for electric and acoustic stimulation at four frequencies ranging from 100 to 1000 Hz. The firing rate was averaged over the stimulus duration excluding the first 30 ms after stimulus onset in order to focus on the sustained response. For electric stimulation, the firing rate saturates at the stimulation rate (i.e., there is perfect entrainment at high stimulus levels) so that the rate-level curves are clearly distinct from each other. This is consistent with physiological data (Javel and Shepherd 2000; Javel and Viemeister 2000). The 2–3 dB dynamic range for low pulse rates is also consistent with ANF data (Shepherd and Javel 1997; Javel and Viemeister 2000). The dynamic range increases with increasing pulse rate, an effect that has been attributed to relative refractoriness (Bruce et al. 1999a). Variability in firing rate across stimulus trials (as shown by error bars) is minimal both near threshold and in the saturation range, reaching a maximum at the point of maximum slope (Bruce et al. 1999a). In contrast to electric responses, rate-level functions for acoustic stimulation have similar sigmoid shapes for all frequencies (Fig. 2B). The sigmoid shape and ~15 dB dynamic range are appropriate for an ANF fiber with a high spontaneous firing rate, 40 spikes/s in this case (Sachs and Abbas 1974). The threshold for the model ANF is the same for all frequencies due to the lack of cochlear filtering in the

model. Thus, it is more appropriate to think of these curves as representing the responses of different ANFs, each tuned to a different frequency and stimulated at its characteristic frequency. Variability in firing rate across trials is much larger than for electric stimulation and increases approximately in proportion to the mean firing rate. The additional variability in acoustic responses is due to the stochastic release of neurotransmitter vesicles at the synaptic stage (Eq. 8). The degree of phase locking of the ANF responses was quantified by the vector strength (Goldberg and Brown 1969). Vector strengths for electric stimulation (Fig. 2C) are very high (90.94) for all stimulation rates, although they drop slightly at the higher rates (inset in Fig. 2C). The vector strength is nearly independent of stimulus level, as observed in physiology and consistent with the lack of spontaneous activity in deaf ears (Javel and Shepherd 2000). In contrast, vector strengths for acoustic stimulation (Fig. 2D) increase monotonically with sound level up to a maximum of ~0.8 but do not depend on tone frequency over the range tested. As in the physiological data (Johnson 1980), the threshold for vector strength is about 10 dB lower than that for firing rate. Overall, model responses to both acoustic and electric stimulation capture the essential features of the neural data (Johnson 1980; Javel and Shepherd 2000). The firing rates and temporal patterns of the ANF model responses to electric stimulation are clearly distinct from responses to acoustic stimulation.

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ElectricAcoustic Electric

A

100Hz 200Hz 500Hz 1000Hz

800 600

Acoustic 200

400 200

160 120

0

40

−8 −4 0 4 Current level (dB re 1mA)

1

D

0.8 1

0.6 0.95

0.4 −10

−5

0

5

Vector strength

Vector strength

80

0 −12

C


B Firing rate (spikes/s)


1000

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20

30 40 50 Sound level (dB SPL)

60

20

30 40 50 Sound level (dB SPL)

60

1 0.8 0.6 0.4 0.2

0.2 0

0 −12

−8 −4 0 4 Current level (dB re 1mA)

FIG. 2. Rate-level function (top) and degree of phase locking (vector strength) of ANF model responses to electric (A, C) and acoustic (B, D) stimulation at different frequencies. Error bars in A and B represent standard deviation of firing rates across 50 trials. Inset in C shows vector strength over smaller range.

In the following, we test whether these unnatural patterns of ANF activity produced by electric stimulation result in degraded ITD sensitivity for the MSO model.

Effect of Stimulation Frequency on ITD Sensitivity of MSO Neuron Model with Weak Synaptic Inputs and Slow Membrane Response We first tested an MSO model with relatively weak synaptic inputs (GE =1.5 nS, NE =10) and weak K+ conductance GKLT (50 nS) and studied the temporal discharge patterns and rate-ITD curves for different stimulation rates at constant stimulus levels. As in Figure 1, stimulus levels were set at 2 dB above threshold of the ANF model for electric stimulation and at 15 dB above threshold for acoustic stimulation. Figure 3A shows the MSO model response to electric pulse trains at 100–1000 pps. The top row of panels shows responses to five repetitions of each ITD presented as dot-raster plots. At 100 and 200 pps, the MSO model shows a precisely timed response to each pulse for 0 ITD and a much weaker response (often limited to the onset) for other ITDs. At 500 and 1000 pps, discharges become concentrated near stimulus onset for all ITDs and there is no activity after the first 50 ms. The ITD sensitivity for each pulse rate was quantified by the ITD signal-to-total variance ratio (ITD STVR) based on the firing rate over a time

window of 30–300 ms (Fig. 3A, bottom row). As explained in the “METHODS,” the ITD STVR is a number between 0 and 1 indicating the fraction of the variance in neural spike counts accounted for by the variation in ITD. ITD STVRs are near unity at 100 and 200 pps, meaning highly reliable ITD sensitivity. The STVR decreases sharply at 500 pps and is 0 at 1000 pps, reflecting the lack of ongoing activity. The response patterns in Figure 3A are consistent with physiological observations from the IC in anesthetized preparations with bilateral electric stimulation (Smith and Delgutte 2007; Hancock et al. 2012). To our knowledge, physiological data from the MSO are unavailable for electric stimulation. We used the same model parameters to simulate responses to acoustic stimulation. Since good ITD sensitivity to pure tones is observed at least up to 1500–2000 Hz in both MSO (Yin and Chan 1990; Scott et al. 2007) and IC (Kuwada and Yin 1983; Kuwada et al. 1987), we expected the model to show good ITD sensitivity over the frequency range tested. However, as with electric stimulation, the MSO model showed good ITD sensitivity to low-frequency tones, but onset-like responses at high frequencies (Fig. 3B). Compared to electric responses, acoustic responses showed lower firing rates at the best ITD as well as slightly lower ITD STVRs at 100 and 200 Hz. Despite these relatively minor differences, the overall patterns of ITD sensitivity were very similar for both modes of

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ITD (ms)

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2.5

1

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0

0

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−5 0 Firing rate (spikes/sec)

500 pps

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100

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−1 0 300 Time (ms) STVR=0.96 sMD=1

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300

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B: Acoustic

ITD (ms)

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0 Firing rate (spikes/sec)

200 Hz

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Time (ms) 100

STVR=0.92 sMD=1

STVR=0.78 sMD=1

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FIG. 3. ITD tuning of a “slow” MSO model neuron for four different electric pulse rates (A) and pure tone frequencies (B). The model has weak synaptic inputs (GE =1.5 nS) and weak GKLT (50 nS). The top row of each panel shows dot rasters of model response to five presentations of each ITD. Alternating shades of gray distinguish

responses to different ITDs. Bottom row shows rate-ITD curves for each frequency with error bars of ±1 SD. Each panel shows ITD tuning over exactly one cycle of the stimulus frequency. The onset response (first 30 ms) is excluded from the computation of firing rate.

simulation. Thus, an MSO model with parameters that yield good coincidence detection and good ITD sensitivity for low frequencies performs poorly at higher frequencies with both modes of stimulation. To better understand the mechanisms underlying the strong frequency dependence of ITD sensitivity in this model, the waveforms of membrane potentials and synaptic and IKLT conductances were examined in detail (Fig. 4). For homophasic stimulation (ITD=0) with 100 pps pulse trains (Fig. 4A), the membrane potential Vmem(t) showed a spike in response to each pulse, and the excitatory synaptic conductance gE(t) also showed clear pulse locking. In the antiphasic case (ITD = half-period, Fig. 4E), gE(t) showed a peak in

response to each stimulus pulse from each side, resulting in a doubling of the peak rate compared to the homophasic case, but these conductance peaks were too small to elicit spikes in the MSO model. For 1000 pps stimulation in both homophasic and antiphasic conditions (Fig. 4B, F), the fluctuations in gE(t) were both smaller in amplitude and less obviously periodic than for 100 pps stimulation, and the fluctuations were too weak to elicit spikes, except at the onset. In addition, gKLT(t) showed an increase in DC amplitude relative to its resting value, which contributes to the lack of spike activity for both phase conditions. Thus, the neuronal parameters that allow good differentiation between homophasic and

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100 Hz

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D

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gE (nS)

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gKLT (nS)

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gE (nS)

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ITD = half-period

Time (ms)

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Time (ms)

FIG. 4. Membrane potential and synaptic and KLT conductance waveforms of slow MSO model with weak synaptic inputs (GE = 1.5 nS) and weak GKLT (50 nS). Red lines in the panels for KLT conductance represent resting level. Membrane responses are shown for pulse trains at 100 pps (A, E) and 1000 pps (B, F) and for pure

antiphasic inputs at 100 pps are not adequate for the 1000 pps input. The overall pattern of membrane potentials, gE(t) and IKLT conductance waveforms for acoustic stimulation at 100 and 1000 Hz (Fig. 4C, D, G, H), is similar to the electric responses at the same frequencies, consistent with the similar ITD tuning curves in Figure 3A, B. Again, the model allows differentiation between homophasic and antiphasic conditions at 100 Hz (Fig. 4C, G) but not at 1000 Hz (Fig. 4D, H). One difference with the electric case is that, at 100 Hz, the model does not fire on every tone cycle in the homophasic condition. The synaptic conductance fluctuates more for the 100 Hz tone than for the 100 pps pulse train, with only the largest synaptic peaks eliciting a spike. This lower responsiveness of the MSO model for acoustic stimulation occurs despite the firing rate of the ANF model being higher (135 vs. 53 spikes/s, Fig. 1) for the 100 Hz pure tone than for the 100 pps pulse train. The greater dispersion in the ANF temporal patterns for acoustic stimulation (Fig. 1) results in fewer binaural coincidences.

tones at 100 Hz (C, G) and 1000 Hz (D, H). A–D Membrane responses in the homophasic condition (ITD=0), E–H responses in the antiphasic condition (ITD = half-period). Insets show the waveform detail over smaller range in the y-axis.

Good ITD Sensitivity at High Frequencies Requires Both Strong Synapses and Fast Membrane Response Since an MSO model with low synaptic strength and weak GKLT did not produce adequate responses to highfrequency stimulation, we studied the effect of the strengths of synaptic inputs and the IKLT conductance (which affects membrane response time) on rate-ITD curves at 1000 pps (Fig. 5). We tested two different values of GKLT (50 and 200 nS) and two values of synaptic strength GE to compare four versions of the model. Because the model with stronger GKLT required a larger GE to trigger a spike (Table 3), different sets of GE were used with each GKLT to keep the firing rate in a similar range (GE =1.5 and 6 nS for GKLT =50 nS, and GE =3 and 12 nS for GKLT =200 nS). Figure 5A shows the results for electric stimulation with a 1000 pps pulse train. The baseline condition in Figures 3 and 4 is the model with weak synapses (GE =1.5 nS) and slow membrane response (GKLT =50 nS), which produced 0 ongoing firing rate for all ITDs. An ongoing response was also not observed with a

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A 250

G

=50nS, G =6nS

G

=200nS, G =3nS

KLT KLT


200

B

Acoustic

−0.5

0 ITD (ms)

Electric 250

GKLT=50nS, GE=1.5nS E

E

200

GKLT=200nS, GE=12nS

150

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100

100

50

50

0

0 −0.5

0 ITD (ms)

0.5

0.5

FIG. 5. Rate-ITD curves of four different versions of MSO model in response to 1000 pps electric pulse trains (A) and 1000 Hz pure tones (B). The four models differ in strengths of synaptic inputs (GE) and GKLT (see legend).

faster membrane response (GKLT = 200 nS, GE = 3 nS). Increasing synaptic strength alone (GKLT = 50 nS, GE =6 nS) restored ongoing activity, but the tuning curve was only weakly modulated with relatively large firing rates in the antiphasic condition (ITD STVR = 0.80, sMD = 0.40). Finally, the combination of faster membrane response and stronger synaptic inputs (GKLT =200 nS, GE =12 nS) produced good ITD tuning to the 1000 pps pulse train (ITD STVR=0.93, sMD=0.77). The overall effect of model parameters for a 1000 Hz tone was similar to that for the 1000 pps electric pulse train (cf., Fig. 5B). Again, there was no ongoing response with weak synaptic inputs for either value of G KLT . Increasing synaptic strength without changing G KLT increased the firing rate, but the resulting ITD selectivity was relatively poor (ITD STVR = 0.86, sMD = 0.44). Good ITD sensitivity at 1000 Hz (ITD STVR = 0.95, sMD = 0.85) required both a fast membrane response and strong synaptic inputs (G KLT = 200 nS, G E = 12 nS). Thus, fast membrane response and strong synaptic inputs are both necessary for good ITD sensitivity at high frequencies in both modes of stimulation.

Effect of Stimulation Frequency on ITD Sensitivity in the MSO Model with Strong Synaptic Inputs and Fast Membrane Response We systematically investigated the effect of stimulation frequency on temporal response patterns and ITD sensitivity for the model with strong synaptic inputs and fast membrane response (GKLT =200 nS, GE = 12 nS), which gave good ITD tuning at high frequencies as seen above. Figure 6A shows the responses to electric pulse trains for four different pulse rates. Importantly, this model neuron fires in a sustained manner throughout the 300 ms stimulus duration for all pulse rates, unlike the model with weak synaptic inputs in Figure 3 which fired only to the onset of high-rate pulse trains. At 100 and 200 pps, the response is perfectly entrained (one spike per pulse) for homophasic stimulation (ITD=0) so that there is minimal variability in the firing rate. However, the firing rate in the antiphasic condition is even higher than the homophasic rate for these two pulse rates. For antiphasic stimulation at 100 pps, each current pulse from each side elicits a spike so that the model fires at twice the 100 pps pulse rate with good entrainment to inputs from each ear. As a result, the

TABLE 3

Range of values for variable parameters of the MSO model GKLT Gh Vrest GEθ

Peak low-threshold potassium conductance (nS) Peak hyperpolarization-activated cation conductance (nS) Resting potential (mV) Threshold GE to trigger a spike at rest (nS)

50 5 −63.8 14.5

100 10 −63.6 20

200 20 −63.5 30.5

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ITD (ms)

100 pps

500 pps

1000 pps

5

2.5

1

0.5

0

0

0

0

−2.5 300 0


200 pps

400

STVR=0.98 sMD=−0.46

−1 300 0 Time (ms)

−0.5 300 0 STVR=0.98 sMD=0.65

STVR=0.97 sMD=−0.31

300

STVR=0.93 sMD=0.77

200

0 −5

0

5

−2.5

0

2.5 −1 ITD (ms)

0

1

−0.5

0

0.5

B: Acoustic

ITD (ms)

100 Hz

200 Hz

1000 Hz

2.5

1

0.5

0

0

0

0

−1

−2.5


500 Hz

5

400

300

0

STVR=0.35 sMD=0.19

−0.5 300 0

300 0 Time (ms)

STVR=0.97 sMD=0.83

STVR=0.9 sMD=0.6

300

STVR=0.95 sMD=0.85

200

0 −5

0

5

−2.5

0

2.5 −1 ITD (ms)

0

1

−0.5

0

0.5

FIG. 6. ITD sensitivity of a “fast” MSO model for electric (A) and acoustic stimulation (B) at four different frequencies. The model has strong synaptic inputs (GE =12 nS) and high GKLT (200 nS). Same layout as in Figure 3.

ITD tuning curves are trough-shaped, with negative sMDs and ITD STVRs near 1 reflecting the low response variability. Such trough-shaped ITD tuning curves are occasionally observed from IC neurons with electric pulse trains at high stimulus levels (Smith and Delgutte 2007). At higher pulse rates (500 and 1000 pps), the model ITD tuning curves become peak-shaped, with large ITD STVRs and positive sMDs. At these high pulse rates, refractoriness and the sustained activation of IKLT prevent the model from firing on every cycle, especially in the antiphasic condition. Figure 6B shows the model response to acoustic tones as a function of frequency. At 500 and 1000 Hz, the ITD tuning curves are very similar to those for electric stimulation at the same frequencies, with comparable STVRs and sMDs. However, the ITD tuning curves for pure-tone stimulation at 200 Hz is

peak-shaped, contrasting with the trough-shaped curve observed with 200 pps electric pulse trains. For both acoustic and electric stimulation, the responses at 100 and 200 Hz/pps are almost perfect entrained in the homophasic condition, but the two modes of stimulation differ in the antiphasic condition in that there is no entrainment to pulses from each side with acoustic stimulation. Overall, ITD sensitivity to pure tones is very good from 200 to 1000 Hz, with clear peaks at the best ITD and low activity in the antiphasic condition. The membrane potential and conductance traces in Figure 7 provide insight into the behavior of the responses shown in Figure 6. The response to 100 pps homophasic (ITD=0) electric pulse trains (Fig. 7A) is similar to the response of the slower model (Fig. 4A), with perfectly entrained spikes in both cases. However, in the antiphasic condition (Fig. 7E), the

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100 Hz

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C

D

0 −50

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V mem (mV)

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ITD = half-period

Time (ms)

300 200 100 0 0

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Time (ms)

FIG. 7. Membrane potential and conductance waveforms of fast MSO model with strong synaptic inputs (GE =12 nS) and high GKLT (200 nS). Same layout as in Figure 4.

smaller peaks in gE(t) are now strong enough to elicit spikes. Spikes and peaks in gE(t) occur at intervals of 5 ms (half the stimulus period), which indicates that the coincident arrival of ANF spikes from each side suffices to generate a spike in the MSO model. Thus, the firing rate is larger in the antiphasic condition than in the homophasic condition for this model, contrary to expectations for a coincidence detector. The responses to 1000 pps pulse trains (Fig. 7B, F) are more consistent with the expected behavior of a binaural coincidence detector. The larger fluctuations in gE(t) compared to the slower model in Figure 4 enable the fast model to generate more spikes for both homophasic and antiphasic conditions. Although the mean g E (t) amplitudes for the homophasic and antiphasic conditions are not strikingly different, the fluctuations are larger in the homophasic case, resulting in more threshold crossings and more spikes. Furthermore, the KLT conductance has more time to decay in the intervals between the incoming ANF spikes in the homophasic condition (1 ms intervals) than in the antiphasic condition (0.5 ms intervals). Thus, the model shows a clear distinction between homophasic and antiphasic conditions with 1000 pps pulse trains.

The overall pattern of membrane potentials and conductances for 1000 Hz acoustic tones (Fig. 7D, H) are similar to the 1000 pps electric response, consistent with the similar ITD tuning curves in Figure 6A, B. However, there are notable differences between acoustic and electric responses at 100 Hz, especially in the antiphasic condition. Specifically, the smaller fluctuations in gE(t) for the 100 Hz tone in the antiphasic condition do not consistently elicit a spike (Fig. 7G), contrary to the 100 pps pulse train. Thus, for this model, there is clear differentiation between homophasic and antiphasic stimulation at 1000 Hz but less so at 100 Hz.

Effect of Stimulus Level on ITD Sensitivity All simulations presented so far were run at the standard levels of Figure 1, −10 dB re 1 mA for electric stimuli, and 50 dB sound pressure level (SPL) for acoustic stimuli, which produced moderate firing rates in the ANF model. We tested the robustness of ITD coding by MSO models with different parameters to variations in stimulus level. Specifically, we compared the effect of stimulus level in the “slow model” in Figures 3 and 4 (GKLT =50 nS, GE =1.5 nS, NE =10)

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200

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C 25 20

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D -11 dB -10 dB -9 dB -5 dB

400 300

15 200

10 5

100

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0.5

Time (ms) FIG. 8. Effect of stimulus level on ITD sensitivity for electric pulse trains. Rate-ITD curves of slow (A, C; GKLT =50 nS, GE =1.5 nS, NE =10) and fast (B, D; GKLT =200 nS, GE =12 nS, NE =10) MSO models to 100 pps (A, B) and 1000 pps (C, D) electric pulse trains at three to four different levels.

and the “fast model” in Figures 6 and 7 (GKLT =200 nS, GE =12 nS, NE =10). Figure 8 shows rate-ITD curves of both the slow (A and C) and the fast (B and D) model for electric stimulation at 100 and 1000 pps over a range of levels. The level of the 100 pps pulse train was varied over the 2 dB range over which the firing rate of the ANF model grows significantly with level (Fig. 2A), so the response patterns obtained should be representative of the MSO model’s behavior. The slow MSO model (Fig. 8A) responds minimally to 100 pps pulse trains at −11 dB and shows good ITD sensitivity at −10 and −9 dB, although there is some sustained firing to offphase ITDs at −9 dB. For the fast model with strong synaptic inputs (Fig. 8B), the rate-ITD curve for 100 pps pulse trains shows little modulation at −11 dB and becomes trough-shaped at higher levels. At −9 dB, the firing rate of 200 spikes/s indicates perfect entrainment to stimulus pulses in each ear in the antiphasic condition. A wider range of stimulus levels was used to test the MSO models for stimulation at 1000 pps because the dynamic range of ANF responses is wider for higher pulse rates (Fig. 2A). The slow MSO model (Fig. 8C) only responds at −5 dB, where the ITD tuning is peakshaped. This level elicits a firing rate of ~300 spikes/s

in the ANF model, which is substantially higher than is possible with acoustic stimulation (Fig. 2). The fast model (Fig. 8D) is more robust, with peaked shaped rate-ITD curves at all four levels tested. The overall pattern of rate-ITD curves as a function of stimulus level is generally similar for acoustic stimulation (Fig. 9) when the sharp difference in dynamic ranges of the ANF response for the two modes of stimulation is taken into account (Fig. 2). Stimulus level was varied from 40 to 60 dB, a range over which the firing rate of the ANF model grows with level at all frequencies (Fig. 2B). The slow model shows good ITD sensitivity to 100 Hz tones at 50 and 60 dB but does not respond to 100 Hz tones at 40 dB (Fig. 9A) or to 1000 Hz tones at any level (Fig. 9C). For the fast model, a 100 Hz tone at 60 dB elicits strong firing in the antiphasic condition as seen in the electric case, while stimulation at 40 dB only produces a weak response with little dependence on ITD (Fig. 9B). The fast model shows robust, peak-shaped ITD tuning curves for 50 and 60 dB with 1000 Hz tones (Fig. 9D). Overall, for both electric and acoustic stimulation, the ITD tuning of the MSO model is relatively robust to variations in stimulus levels over the dynamic range of the ANF model providing the model parameters are matched to the stimulus

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200

200

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50

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C

−5

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5

−0.5

0

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D

200

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40 dB 50 dB 60 dB

150

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0 −0.5

0 0

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Time (ms) FIG. 9. Effect of stimulus level on ITD sensitivity for pure tones. Same layout as in Figure 8.

frequency (i.e., the slow model for 100 Hz and the fast model for 1000 Hz).

Effect of GKLT and GE on ITD Sensitivity The previous sections showed how ITD sensitivity depends on stimulus frequency and level for two models with different values for GKLT and GE. In this section, the separate effects of these two conductances are evaluated systematically at the standard levels, −10 dB re 1 mA for electric stimuli and 50 dB SPL for acoustic stimuli. Figure 10 shows ITD STVRs and sMDs of MSO models with varying GKLT and GE for electric pulse trains at 100 and 1000 pps (A and C) and acoustic tones at 100 and 1000 Hz (B and D). In general, stronger synaptic inputs are required to obtain good ITD sensitivity for models with higher KLT density. For 100 pps pulse trains (Fig. 10A), only a narrow range of slow membrane response and weak synaptic inputs (GKLT =50 nS and GE =1.5–1.75 nS or GKLT = 100 nS and GE =1.75 nS) yields both high ITD STVR and positive sMD. With a faster membrane (GKLT = 200 nS), the ITD STVR at 100 pps remains high but this is due to monaural coincidences producing higher firing rates in the antiphasic condition than in the homophasic condition (Fig. 6), as indicated by the negative sMD. For acoustic stimulation at 100 Hz (Fig. 10B), there is an optimal GE for each GKLT that

produces both high ITD STVR and large positive sMD, and the optimal GE increases with GKLT. For stimulation at 1000 Hz (Fig. 10C, D), the overall dependence of the ITD coding metrics on membrane speed and synaptic inputs is very similar for both modes of stimulation. The ITD STVR increases monotonically with increasing strength of synaptic input and then reaches an asymptote. Faster membranes (higher GKLT) require stronger synaptic inputs as shown by the rightward shift of the ITD STVR curves. However, stronger synaptic inputs and, especially, a slower membrane response (small GKLT) result in lower sMDs. Thus, the combination of a fast membrane and strong synaptic inputs is essential for ITD coding at 1000 Hz for both acoustic and electric stimulation.

Effect of the Number of ANF Inputs on ITD Sensitivity In the preceding simulations, the effect of varying the conductance of the synaptic inputs to the MSO on ITD sensitivity was investigated while the number of ANF inputs from each side, NE, was held constant at 10. An alternative method for changing the strength of synaptic input is to vary the number of inputs while keeping the conductance of each input constant. A larger number of inputs leads to integration of more spikes that have correlated (but not identical) temporal patterns. When

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50 nS 100 nS 200 nS

0.5


100 Hz 1

0.5

0

0 0

2

4

6

8

10

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12

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ITD sMD

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8

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1000 pps

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−1

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0.5

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0 0

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6

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GE(nS)

GE(nS) 1 ITD sMD

1 ITD sMD

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1

1

C

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GE(nS)

0

0

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6

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0

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6

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FIG. 10. Interacting effects of GKLT and GE on ITD sensitivity. ITD STVR and sMD as a function of GE for electric pulse trains of 100 pps (A) and 1000 pps (C) and acoustic tones of 100 Hz (B) and 1000 Hz (D). Colors code the value of GKLT.

the total synaptic strength (the product of the number of synaptic inputs, NE, and the peak synaptic conductance, GE) is kept constant, the fluctuations in the conductance waveform gE(t) tend to decrease with increasing NE, resulting in fewer threshold crossings, even though the mean value of the conductance is unchanged (Rothman

et al. 1993; Reyes et al. 1996; Kalluri and Delgutte 2003). As a result, we find that the ITD STVR and sMD tend to be larger when NE is smaller and GE is larger. This interaction between NE and GE is observed over a wider range of total conductance at high frequencies, and the effect is similar between electric and acoustic stimulation.

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B 1

1

ITD STVR

0.5

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0 5

0 0

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G E = 0.75nS, N E = 8−50 G = 1.5nS, NE = 4−50 E G E = 3nS, N E = 2−50 G = 3−15nS, N E = 10

1

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0 0

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1 G E = 3nS, N E = 10−50 G E = 6nS, N E = 5−25 G = 12nS, N E = 2−12 E G E = 3−15nS, N E = 10

0

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15

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1

ITD sMD

ITD STVR

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0

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0


Fig. 11. Interacting effects of GE and NE on ITD sensitivity. ITD STVR and sMD as a function of total synaptic strength (the product GE ×NE) for electric pulse trains at 100 pps (A) and 1000 pps (C) and pure tones at 100 Hz (B) and 1000 Hz (D). A model with weak GKLT (GKLT =50 nS) was used for stimulation at 100 Hz/pps (A, B), while a model with high GKLT (GKLT =200 nS) was used for stimulation at

1000 Hz/pps (C, D). Total synaptic strength was manipulated by varying the number of inputs NE while holding the synaptic conductance GE at different values coded by colors. Black lines with open markers are reproduced from Figure 10, where GE was varied while NE was held at 10.

Figure 11A, B shows ITD STVR and sMD of an MSO model with weak GKLT (GKLT =50 nS) as a function of total synaptic strength for stimulation with 100 pps pulse trains and 100 Hz pure tones. Total

synaptic strength was manipulated by either varying GE while keeping NE at 10 or varying NE while keeping GE constant at different values (range 0.75 to 3 nS). The overall pattern of ITD STVR and sMD as a

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function of total synaptic strength is similar for both parameter manipulations and both modes of stimulation. However, in the range of low total synaptic strengths (G15 nS) where the ITD STVR increases rapidly (insets in Fig. 11A, B), the STVR is larger when NE is smaller and GE larger, which results in larger fluctuations in the conductance waveform gE(t). While the ITD STVR is high for all but the lowest values of total synaptic strength (where there is little or no ongoing response), large positive sMDs are restricted to a narrower range of low total synaptic strengths. The upper cutoff for sMD is slightly higher for acoustic stimulation than for electric stimulation, i.e., acoustic stimulation yields somewhat more robust ITD tuning in this case. The interaction between NE and GE is more prominent for a model with high GKLT (GKLT = 200 nS) with GE ranging from 3 to 12 nS using stimulation at 1000 Hz (Fig. 11C, D). The ITD STVR increases monotonically with increasing total synaptic strength, but a smaller GE (and therefore larger NE) requires larger total synaptic strength as shown by the rightward shift of the ITD STVR curves. The overall pattern of ITD STVR and sMD as a function of total synaptic conductance is very similar for acoustic and electric stimulation. The interaction of NE and GE is observed over a wider range of total conductance at 1000 Hz than at 100 Hz because the firing efficiency (the number of spikes per stimulus cycle) of the ANF inputs is lower at high frequencies, so that a larger number of ANF inputs is required to produce the same number of binaural coincidences per stimulus cycle. A similar effect was observed at high frequencies for in vitro recordings from avian nucleus laminaris neurons (Reyes et al. 1996), where intracellular current injections were used to simulate binaural synaptic inputs from nucleus magnocellularis.

DISCUSSION We used a simple biophysical model of MSO neurons driven by bilateral inputs with realistic temporal discharge patterns to study ITD sensitivity for both acoustic and electric stimulation over a wide range of frequencies and levels. The model’s ITD sensitivity was found to be dependent on the frequency of the inputs, the strength (GE) and number (NE) of synaptic inputs, and the ionic channel composition (GKLT) of the cell membrane. For each stimulation frequency, there was an optimal range of model parameters for which the ITD sensitivity was maximal. In general, higher frequency inputs, both acoustic tones and electric pulses, required stronger excitatory conductance,

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stronger KLT conductance, and a larger number of synaptic inputs. In contrast, weaker excitatory conductance, weaker KLT conductance, and fewer synaptic inputs were required for lower frequency inputs with both types of stimulation. ITD tuning was fairly robust over a range of stimulus levels when the model parameters were matched to the stimulus frequency. We originally hypothesized that the limitations in neural and psychophysical ITD sensitivity with electric stimulation would be caused by the inability of MSO neurons to achieve good ITD tuning with severely abnormal inputs from the auditory periphery, including higher firing rates, increased vector strengths, and reduced variability. Contrary to this hypothesis, the overall responses of the MSO model neurons did not greatly differ between the two modes of stimulation. The MSO model neurons showed good ITD sensitivity to both acoustic and electric stimulation when the model parameters were appropriate for the stimulation frequency. The main difference was that more responses were observed in the antiphasic condition for electric stimulation due to the higher synchrony of the inputs. In particular, electric responses could perfectly entrain to inputs from each side at low stimulation rates in models with strong synaptic inputs, resulting in trough-shaped ITD tuning curves that were rarely observed with acoustic stimulation.

Frequency Dependence in Biophysical Properties of MSO The clear dependence of ITD sensitivity on stimulus frequency observed for every set of MSO model parameters investigated is inconsistent with the hypothesis that frequency-dependent differences in binaural processing originate solely from differences in cochlear processing and not from differences in biophysical mechanisms in the brainstem (Colburn and Esquissaud 1976). Our modeling results suggest that a gradient of biophysical properties might be required to achieve the good ITD sensitivity across a wide range of frequencies that is observed in physiological experiments from normal hearing animals (Kuwada et al. 1987; Yin and Chan 1990). Since the MSO is tonotopically organized (Guinan et al. 1972; Karino et al. 2011) and MSO neurons have sharp frequency tuning (Yin and Chan 1990), this further suggests that biophysical properties of MSO neurons may be dependent on their location along the tonotopic axis. Baumann et al. (2013) reported a gradient in the hyperpolarization-activated current Ih along the

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tonotopic axis of gerbil MSO, with stronger Ih in the high-frequency region. They suggested that a gradient in IKLT may exist to maintain the resting potential at a similar value across the tonotopic axis as they observed. Such a gradient in IKLT would be in a direction consistent with our model predictions. However, Scott et al. (2007) found no systematic dependence of membrane time constant and current thresholds for action potentials along the tonotopic axis of gerbil MSO, as might be expected if there were a gradient in I KLT . Alternatively, the stronger inward Ih measured in neurons with higher CFs could raise the membrane potential and, thus, increase the KLT conductance via activation of a greater number ion channels, producing qualitatively similar results to those presented in this manuscript, even in the absence of a tonotopic gradient in KLT channel density. A systematic dependence of K+ channel expression on tonotopic location has been reported for nucleus laminaris (NL), the avian homologue of MSO (Kuba et al. 2005, 2006; Hamlet et al. 2014). NL further shows tonotopic gradients in many other cellular properties, including densities of Na+ and I h channels as well as metabotropic glutamate receptors (Ohmori 2014). Gradients in neural parameters including the density of potassium channels have also been reported for other mammalian brainstem auditory nuclei involved in binaural processing, including the lateral superior olive (LSO) and the medial nucleus of the trapezoid body (MNTB). Specifically, a higher density of IKLT channels has been observed in the low-frequency limb of rat LSO (Barnes-Davies et al. 2004). This higher density may improve the ITD sensitivity to pure tones in low-frequency LSO neurons (Batra et al. 1997). Tonotopic gradients in the distribution of both low-threshold (I KLT ) and high-threshold (IKHT) potassium channels have also been reported in rat MNTB (Brew and Forsythe 2005). These gradients are relevant because the MNTB provides precisely timed inhibitory inputs to MSO that influence ITD sensitivity (Brand et al. 2002). Thus, tonotopic gradients in cellular properties are commonly found in binaural circuits of birds and mammals.

Relation to Other Models and Limitations of the Model Few models of binaural coincidence detection by mammalian MSO and avian NL neurons in normal hearing have investigated ITD tuning over a wide range of frequencies (Agmon-Snir et al. 1998; Zhou et al. 2005; Brughera et al. 2013). Zhou et al. (2005)

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and Brughera et al. (2013) investigated ITD tuning to pure tones from 250 to 1500 Hz using multicompartmental MSO models receiving both excitatory and inhibitory inputs. The strengths of the excitatory synaptic conductances increased systematically with frequency in their models in order to ensure that the model neurons continue to fire at high frequencies. This shows that the shunting effect of KLT channels at high frequencies in our simple single compartment model also holds for more detailed multicompartment models. Our results further suggest that the lack of a concomitant increase in IKLT conductances with frequency in the multicompartment models may have contributed to the decrease in ITD modulation they obtained at high frequencies. Good ITD sensitivity to pure tones is observed up to 2 kHz in both the MSO (Yin and Chan 1990) and the IC (Kuwada and Yin 1983; Kuwada et al. 1987), in contrast to the sharp decrease in ITD sensitivity between 1000 and 1500 Hz in the model of Brughera et al. (2013). Although the frequency limit of 1000–1250 Hz is in agreement with perceptual limits in humans, it is clear that good ITD sensitivity is observed at higher frequencies in other mammalian species. The present model is highly simplified, with a single membrane compartment, excitatory inputs with identical statistical properties, no inhibitory inputs, and no explicit bushy cell model. Using a multicompartment model of avian NL, Agmon-Snir et al. (1998) showed that the systematic dependence of dendritic length on tonotopic position observed in chick NL (Smith and Rubel 1979) is essential to obtain good ITD tuning over a wide range of frequencies. While our single compartment model cannot address the effects of cellular morphology on coincidence detection, there is no evidence for a tonotopic gradient in dendritic length or synaptic input strength in mammalian MSO (Henkel and Brunso-Bechtold 1990; Smith 1995). Using a gerbil MSO slice preparation, Mathews et al. (2010) demonstrated that a gradient of GKLT along the dendrites of MSO neurons increased the modulation of rate-ITD curves. Thus, the GKLT gradient along the dendrites might be more effective in sharpening rate-ITD tuning than increasing GKLT in our single compartment model. However, this still leaves the problem of achieving good ITD modulation over a wide range of frequencies. The lack of inhibition in our model may artificially lower the conductance threshold for firing and make ITD tuning less robust to variations in stimulus level. The exact function of inhibitory projections to MSO is a subject of ongoing debate (Grothe et al. 2010). In the absence of sufficient

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data on the timing of inhibition in vivo, it is difficult to incorporate inhibition into an MSO model in a meaningful way. Using both anatomical and functional data, Couchman et al. (2010) estimated that the total excitatory synaptic strength in gerbil MSO neurons (the sum of the synaptic conductances for all inputs) is 180–200 nS. This value is comparable to the 200 nS total synaptic strength used in the “fast” MSO model that gave good ITD sensitivity at 1000 Hz (Fig. 6), but is much higher than the 30 nS used in the “slow” model that worked well at 100 Hz (Fig. 3). The bias toward lower synaptic strength in our MSO model may be due to the omission of inhibitory inputs. Phase locking in bushy cells is enhanced relative to that in ANFs (Joris et al. 1994), and modeling suggests that this enhancement is important for binaural coincidence detection by MSO neurons (Brughera et al. 1996). On the other hand, because the responses of our MSO model were similar for acoustic and electric stimulation despite the much sharper phase locking of the ANF inputs to electric pulse trains (Fig. 1), the smaller enhancement in phase locking produced by bushy cells may not alter the results significantly. While it has been suggested that SBCs might perform across-frequency coincidence detection that would sculpt the temporal response patterns, this seems unlikely given they only receive 1– 3 ANF inputs through endbulbs of Held (Cant and Morest 1979), and careful analysis provides no evidence for coincidence detection in these cells (Wang and Delgutte 2012). All ANF inputs to our MSO model were assumed to be statistically independent and identically distributed. In reality, inputs are likely to differ somewhat in CF, latencies, thresholds, and maximal firing rates. Having ANF inputs with identical CFs may have exaggerated the pronounced frequency dependence of ITD sensitivity in the model and the need for a close match between stimulation frequency and membrane parameters. The identical thresholds of the ANF inputs likely contributed to the sharp effect of intensity in addition to the lack of inhibition in the model. Finally, dispersion in input latencies can reduce the firing rate at antiphasic ITDs and improve ITD tuning when the inputs are highly synchronized (Colburn et al. 2009). In general, the behavior of a more detailed biophysical model of MSO might differ in relevant response properties from that of our simplified model. This simplified model requires varying intrinsic membrane properties to achieve good ITD tuning over a wide range of frequencies. This conclusion may need to be revised when more detailed models are developed. Nevertheless, our results point to difficul-

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ties in achieving ITD tuning over a wide frequency range, an issue that will have to be addressed in future models.

Limit of Temporal Coding and ITD Sensitivity to Electrical Stimulation If there is a tonotopic gradient of biophysical properties in the MSO, a mismatch between the stimulation rate and the best frequency of the neuron might lead to degraded ITD tuning with electric stimulation. With acoustic stimulation in normal hearing animals, the sharp cochlear frequency selectivity ensures that, for the most part, lowfrequency ANFs will phase lock to frequencies near their CF when stimulated with broadband, naturalistic stimuli (de Boer 1969; Young and Sachs 1979). In other words, cochlear frequency selectivity enforces a statistical match between the tonotopic position of an MSO neuron and the predominant temporal patterns of its inputs from the periphery. In contrast, with electric stimulation, the temporal response patterns will rarely match the characteristic frequency of a given ANF. Every ANF responds to a similar wide range of electric pulse rates and sinusoid frequencies (Kiang and Moxon 1972; Javel and Viemeister 2000; Miller et al. 2001). For constantamplitude, single-channel stimulation, peripheral inputs to ITD-sensitive cells in the brainstem will typically phase lock to the pulse rate with CI stimulation regardless of tonotopic location. This case is simplified relative to currently available implants, in which individual nerve fibers are stimulated by modulated pulse trains from multiple stimulating electrodes. In this more complex case, the pattern of stimulus pulses on a single fiber will depend on the clinical mapping of acoustic frequency band and envelope extraction on multiple electrodes, and the temporal discharge patterns in AN fibers will be influenced by both the carrier pulse rate and the interaction of the envelopes on the nonsynchronous stimuli from different electrodes. Even though the realistic patterns are more complicated, the problem of mismatched stimulation rates and MSO cell parameters is still an issue of concern. For MSO cells tuned to very low frequencies (100 Hz), the model predicts that there should be a cutoff rate beyond which electric stimulation produces only an onset response (Fig. 3). On the other hand, low-rate stimulation of an MSO cell tuned to higher frequencies (1000 Hz) is predicted to produce a saturated response with little ITD sensitivity (Fig. 6). Although no data are available from MSO neurons, data from their targets in IC are only in partial agreement with these predictions. While many IC neurons show an upper rate limit near

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200–300 pps beyond which they only give an onset response to electric pulse trains (Snyder et al. 1995; Hancock et al. 2012; Chung et al. 2014b), ITD sensitivity for low-rate pulse trains appears to be largely independent of tonotopic position (Smith and Delgutte 2007; Hancock et al. 2010). Moreover, there is no evidence that higher CF IC neurons show better ITD tuning to higher rate pulse trains, at least in anesthetized preparations (Smith et al. 2007; Hancock et al. 2010). Overall, there is little physiological evidence for a tonotopic dependence in the range of electric pulse rates over which neurons show ITD sensitivity as predicted by our modeling results. This conclusion is tempered by the fact that predictions of an MSO neuron model are compared with data from IC neurons. Additional intervening mechanisms between the two sites (such as inhibitory inputs from the dorsal nucleus of the lateral lemniscus or varying intrinsic properties of IC neurons) could alter or obscure any tonotopic pattern that might exist in the MSO. Furthermore, the IC studies estimated the tonotopic position from the insertion depth of the recording electrode along dorsoventral penetrations. The uncertainty of this method may be too high to differentiate between CFs of 100 and 1000 Hz (the frequency range investigated in the model). Thus, the model prediction of a tonotopic dependence in the range of electric pulse rates for which MSO neurons show good ITD sensitivity cannot be ruled out by the available data.

Comparison of Responses to Electric and Acoustic Stimulation The overall frequency dependence in responsiveness and ITD tuning of the MSO model was similar for electric and acoustic stimulation. A model that was tuned for a certain tone frequency tended to show good tuning to electric pulse trains at the same rate. Nevertheless, there were still differences between acoustic and electric responses that may contribute to the limitations in perceptual ITD sensitivity with bilateral CI. The range of frequencies that could elicit good ITD tuning was slightly larger for acoustic stimulation than for electric stimulation. For example, in the “fast” model neuron of Figure 6, good ITD tuning was observed from 200 to 1000 Hz with acoustic stimulation, but only at 500 and 1000 pps with electric pulse trains. Similarly, in Figures 10 and 11, ITD sensitivity and modulation were robust over a wider range of total synaptic strength for acoustic stimulation than for electric stimulation at low frequencies. The increased response to antiphasic stimuli with increas-

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ing total synaptic strength quickly degraded the modulation depth to electrical stimulation. While our initial hypothesis was that the binaural circuits operate in the same way for acoustic and electric stimulation, changes in the response properties of auditory neurons resulting from deafness-induced plasticity (for review, see Shepherd and Hardie 2001; Butler and Lomber 2013) may also contribute to the degraded perceptual ITD sensitivity in bilateral CI users. For example, the model shows a strong dependence of ITD sensitivity on total synaptic strength, with higher frequency stimulation requiring a greater total synaptic conductance. If deafness is associated with a loss of convergent inputs to the binaural neurons, the expected reduction in synaptic strength could cause a degradation in ITD sensitivity of MSO neurons at high pulse rates, consistent with the decreased perceptual ITD acuity observed above about 300 pps in bilateral CI users (van Hoesel 2007; Poon et al. 2009). In addition, a decrease in inhibitory gain observed in central auditory neurons with both long-term and shortterm deafness (Vale and Sanes 2000; Kotak et al. 2008) could degrade ITD sensitivity by allowing more firings in the antiphasic condition. Long-term deafness has been shown to reduce the temporal precision of ANF firings (Shepherd and Javel 1997), which could contribute to a degradation in ITD sensitivity at high rates. Lastly, disruption of tonotopic gradients of IKHT (Leao et al. 2006) and Ih channels (von Hehn et al. 2004) have been observed in the MNTB of congenitally deaf mice. A similar loss in the putative tonotopic gradient in the MSO, along with the observed degradation in the MNTB, could impair the ITD sensitivity in neonatal deafness. In addition, the loss of cochlear traveling wave delays in deaf animals may alter the distribution of best ITDs in the MSO (Day and Semple 2011) and may also alter the relative latencies of the various inputs to a given MSO neuron, which in turn could degrade ITD tuning (Colburn et al. 2009). In summary, ITD sensitivity to electric and acoustic stimulations was compared for a family of models differing in their biophysical properties. ITD sensitivity was strongly dependent on the strength (GE) and number (NE) of synaptic inputs, the ionic channel composition (GKLT) of the cell membrane, and the frequency of the inputs. Stronger excitatory synaptic inputs and a faster membrane response were required for the model neurons to be ITD-sensitive at high stimulation rates, although these changes degraded ITD sensitivity at lower rates. We suggest that a mismatch between stimulation rate and cell parameters in

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ITD-sensitive neurons may contribute to the degraded perceptual ITD sensitivity in CI users.

ACKNOWLEDGMENTS This work was supported by the National Institutes of Health (Grants R01 DC005775 to B.D. and R01 DC000100 to H.S.C.) and the Hearing Health Foundation (Emerging Research Grant to Y.C.).

Conflict of Interest None of the authors has conflict of interest to declare.

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Binaural interaction in the auditory brainstem response: a normative study.

Functional modeling of the human auditory brainstem response to broadband stimulation.

Maturation of binaural interaction components in auditory brainstem responses of young guinea pigs with monaural or binaural conductive hearing loss.

Phase-locking of auditory-nerve discharges to sinusoidal electric stimulation of the cochlea.

Auditory brainstem responses in congenital heart disease.

Electrically evoked auditory brainstem response monitoring of auditory brainstem implant integrity during facial nerve tumor surgery.

Optogenetic stimulation of the auditory nerve.

[Intracochlear electrical stimulation of the auditory nerve in deaf kittens--brainstem response audiometric and histopathologic studies].

The Physiological Basis and Clinical Use of the Binaural Interaction Component of the Auditory Brainstem Response.

Otoacoustic emissions and auditory brainstem responses in the newborn.

Auditory-evoked brainstem responses in the hibernating woodchuck Marmota monax.

Test-Retest Reliability of the Binaural Interaction Component of the Auditory Brainstem Response.

Binaural analysis in the aging auditory system.

Use of intraoperative auditory brainstem responses to guide prosthesis positioning.

Lateralization and Binaural Interaction of Middle-Latency and Late-Brainstem Components of the Auditory Evoked Response.

Auditory brainstem frequency following responses to waveform envelope periodicity.

Electrically Evoked Auditory Event-Related Responses in Patients with Auditory Brainstem Implants: Morphological Characteristics, Test-Retest Reliability, Effects of Stimulation Level, and Association with Auditory Detection.

Computational modeling of the effects of auditory nerve dysmyelination.

Information processing in the auditory brainstem.

Electromyographic responses in infants after auditory stimulation.

Brainstem auditory evoked responses in infants and children with AIDS.

Spectrotemporal resolution tradeoff in auditory processing as revealed by human auditory brainstem responses and psychophysical indices.

Prolonged auditory brainstem responses in infants with autism.

Auditory brainstem evoked responses in infants and children.