PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Application of a computationally efficient coincidence detector
model to simulate auditory brainstem neurons
Go ASHIDA1,2; Mathias DIETZ1,3; Jutta KRETZBERG1,2
1

Cluster of Excellence "Hearing4all", University of Oldenburg, 26129 Oldenburg, Germany.
2

3

Department of Neuroscience, University of Oldenburg, 26129 Oldenburg, Germany.

Department of Medical Physics and Acoustics, University of Oldenburg, 26129 Oldenburg, Germany.

ABSTRACT
Computational modeling plays an important role in the investigation of acoustic information processingalong the auditory system. Recent studies found that a relatively simple neuronal model, which produces
action potentials depending on the count and timing of modeled synaptic inputs, can simulate a number of
response features of auditory brainstem neurons, such as interaural time and intensity difference coding in thelateral superior olive. Here we review this simple coincidence detector model and discuss its possible
applications to several other types of auditory neurons. Our application targets include principal neurons in
the medial superior olive that change their number of action potentials according to interaural timedifferences and globular bushy cells in the anteroventral cochlear nucleus that show enhanced phase-locking
to low frequency tones than auditory nerves. Because of its computational efficiency, the model is also
suitable for large-scale simulations that typically include thousands of neurons to study, for example,
across-frequency integration and the resulting perception of binaural sounds. Further modifications of themodel for better biological plausibility, such as introducing an adaptive threshold, are also discussed.
Keywords: Physiological model, Auditory brainstem, Binaural neurons, Sound localization

1. INTRODUCTION
Modeling is a fundamental tool in theoretical studies of acoustic information processing in thebrain. Models of binaural neurons, for example, allow us to investigate how these neurons integrate
synaptic inputs originating from the two ears to detect binaural cues, such as the interaural time andlevel differences (ITDs/ILDs). A variety of models were created to simulate the functions of binaural
neurons (reviewed in 1, 2).
Previous neuroscientific studies have revealed that mammals have specialized neuronal circuits inthe brainstem to encode ITDs and ILDs (3). Ascending auditory nerve fibers project to spherical andglobular bushy cells (SBCs/GBCs) in the anteroventral cochlear nucleus, which in turn innervate toseveral nuclei of the superior olivary complex (Figure 1A). SBCs send their excitatory inputs
bilaterally to the medial superior olive (MSO) and ipsilaterally to the lateral superior olive (LSO).
GBCs drive neurons in the contralateral medial nucleus of the trapezoid body (MNTB) that makes
inhibitory projections to the ipsilateral MSO and LSO.
Neurophysiological recordings in vivo showed that phase-locking to low frequency tones (<1 kHz)in SBCs and GBCs is better than that of auditory nerves (4). The principal neurons of MSO vary its
spiking output according to ITDs, by detecting the time difference of its ipsi - and contralateral
excitatory synaptic inputs (3, 5). An LSO neuron, which is excited by ipsilateral sound and inhibitedby contralateral sound, changes its spike rate depending on ILD. In addition, the output spike rate of alow-frequency LSO neuron is also affected by ITDs (6).
Depending on the purposes of modeling, neuron models can be simple or complex (7). Our previous
study that compared different types of physiological models of LSO neurons revealed that both
functional shot-noise models and more physiologically complex Hodgkin-Huxley-type models
produce very similar results if they are calibrated with common criteria (8). Based on these results, wehere aim to simulate the physiological functions of MSO, LSO and GBC using a computationallysimple model. The model introduced in this study allows us to focus on the input -output relations ofthese neurons without considering their subneuronal, biophysical details.

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Figure 1 – A. Circuit diagram of the binaural circuit in the auditory brainstem. AN: auditory nerve; GBC:
globular bushy cell; SBC: spherical bushy cell; MNTB: medial nucleus of the trapezoid body; MSO: medialsuperior olive; LSO: lateral superior olive. The inhibitory connection from MNTB to MSO (shown in gray) isnot considered in the model here. B. Schematic description of the coincidence counting model. Each verticalbar represents a spike. Excitatory inputs (blue: ipsilateral; purple: contralateral) are summed in thecoincidence window (vertical gray rectangles). If the number of input counts reaches the threshold (three inthis example), an output spike is generated. The number of inhibitory inputs (red) occurring in the inhibition
window (vertical dotted rectangle) is weighted and subtracted from the excitatory input counts. An output
spike that is too close to a preceding spike is rejected by the refractory period (small black arrow).

2. METHODS
2.1 Coincidence Counting Model
The general structure of the coincidence counting model (8, 9, 10) is shown in Figure 1B. The
model receives multiple excitatory inputs (possibly from various sources: blue and purple) andinhibitory inputs (red). A coincidence window (vertical gray band in Figure 1B) slides along the timeaxis. When the number of excitatory inputs in the coincidence window reaches or exceeds thethreshold, an output spike is generated (green). If multiple threshold crossings occur within therefractory period, then only the first spike is counted, and the others are discarded (small arrow).
Effects of inhibition were modeled as subtraction of excitatory inputs (or, equivalently, as an increasein threshold) for a certain time length (dotted vertical band). Detailed descriptions and analyses of themodel were presented in (8, 9). We apply this model to MSO, LSO and GBC.
2.1.1 MSO Model
The MSO model receives ipsilateral and contralateral excitatory inputs. For simplicity, we here did
not consider inhibitory inputs to MSO as in most previous studies (1, 10). To account for the non-zeropeak position of the rate-ITD tuning curve, an internal (neuronal) delay between the ipsi - andcontralateral inputs was used. Consequently, the parameters of the MSO model are the numbers of ipsi and contralateral inputs, excitatory input threshold, length of the coincidence window, the length of therefractory period, and the size of the internal delay. Ipsilateral and contralateral inputs are assumed toshare the same coincidence window and threshold. In this study, we did not consider monaural
response of MSO neurons. Therefore, we did not use distinct monaural and binaural thresholds thatwere introduced in a previous study (10).
2.1.2 LSO Model
The LSO model receives ipsilateral excitatory inputs and contralater al inhibitory inputs, but notcontralateral excitatory inputs (8, 9). To account for the non-zero trough position of the rate-ITD
tuning curve, an internal (neuronal) delay between the ipsi- and contralateral inputs was used. The664

parameters of the LSO model are the numbers of ipsi- and contralateral inputs, excitatory input
threshold, length of the coincidence window, length of the inhibition window, amplitude of inhibition(i.e., how many excitatory inputs are cancelled by one inhibitory input), the length of the refractory
period, and the size of the internal delay.
2.1.3 GBC Model
The GBC model receives only ipsilateral phase-locked excitatory inputs and no contralateral orinhibitory inputs. Its parameters are the numbers of inputs, excitatory input threshold, length of thecoincidence window, and the length of the refractory period.
2.2 Phase-locked Input Model
We here consider only tone-evoked, sustained responses of MSO/LSO neurons and GBCs. To
simulate phase-locked spike trains of their inputs, we used an inhomogeneous Poisson process
combined with the von-Mises distribution function as its intensity function (9, 11). The degree ofphase-locking, measured as vector strength (VS: 12), is mathematically related to the concentration
parameter of the von-Mises distribution (11). The input model is thus characterized by the frequency,
the average spiking rate, and the degree of phase-locking.

Figure 2 – Simulated ITD tuning of MSO. Model output (blue) is compared with experimental data (gray) byYin and Chan (5). Parameters used are: (A) Frequency: 500 Hz; number of excitatory inputs: 4 (each side);
excitatory input rate: 300 spikes/sec; VS of excitatory inputs: 0.9; binaural coincidence threshold: 2 inputs;
coincidence window: 0.25 ms; refractory period: 1.6 ms; relative input delay: 0.06 ms (ipsilateral input
lagging). (B) Frequency: 1000 Hz; number of excitatory inputs: 6 (each side); excitatory input rate: 300
spikes/sec; VS of excitatory inputs: 0.85; binaural coincidence threshold: 2 inputs; coincidence window: 0.08
ms; refractory period: 1.6 ms; relative input delay: 0.10 ms (ipsilateral input lagging).

3. RESULTS AND DISCUSSION
3.1 MSO Model - ITD Tuning
The model MSO neuron receives ipsi- and contralateral excitatory inputs arriving with timedifferences that depend on ITD and internal delay. Simultaneous arrivals of the inputs from the twosides result in a high output spike rate. The rate-ITD curves of the model (after parameter fitting)resembled those obtained in cat in vivo recordings (Figure 2). The peak position of the model tuning
curve is determined by the internal delay, which is one of the model parameters. Without this delay, themodel always produces a peak at zero ITD, because ipsi- and contralateral inputs are temporally
symmetric with each other.
Previous in vivo recording studies indicated that inhibitory inputs from MNTB to MSO (3) as wellas input history (13) affect the peak location of an ITD-tare tuning curve. Our minimalistic MSO

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model, which does not explicitly simulate these effects, can nevertheless simulate the overall shape ofthe tuning curve (Figure 2), because the effect of peak shifting by various sources (of cochlear, axonal,synaptic, or neuronal origins) was simply incorporated into the relative delay of the inputs from t hetwo sides.

Figure 3 – Simulated binaural tuning of LSO: (A) ITD and (B) ILD. Model output (blue) is compared withexperimental data (gray) by Tollin and Yin (6). Parameters used are: (A and B) Frequency: 566 Hz; number of
excitatory inputs: 18; number of inhibitory inputs: 8; VS of excitatory inputs: 0.9; VS of inhibitory inputs:0.9; coincidence threshold: 12 inputs; coincidence window: 0.4 ms; inhibition weight: 1 excitatory input;
inhibition window: 0.8 ms; refractory period: 1.6 ms; relative input delay: 0.1 ms (contralateral input
lagging). (A) Excitatory input rate: 300 spikes/sec; inhibitory input rate: 300 spikes/sec. (B) Excitatory(ipsilateral) input rate: 250 spikes/sec; ipsilateral level: 40 dB SPL. Inhibitory input rate was defined with asigmoidal function of the sound intensity as 30 + 330/(1+exp(-(Lc-30)/4)) (spikes/sec), with Lc being thecontralateral level in dB SPL.

3.2 LSO Model - ITD and ILD Tuning
The model LSO neuron receives ipsilateral excitatory inputs and contralateral inhibitory inputs.
Because these inputs are phase-locked (if stimulated with low-frequency tones), the LSO modelchange its spike rate in not only an ILD- but also an ITD-dependent manner (Figure 3). Similar
ITD-dependent spike-rate changes were observed in LSO neurons driven by binaural
amplitude-modulated tones and were explained with (anti)coincidence detection between excitatory
and inhibitory inputs (9).
Although the model ITD-tuning curve follows the overall trend of the ITD-dependence of theexperimental data (Figure 3A), not all details could be simulated. First, the simulated ITD -tuning
curve is more symmetric about the trough position than the experimental data, probably because
synaptic input shapes are temporally symmetric in the model but not entirely so in the real system (8).
Second, the two peaks of the cat data (at about -0.7 ms and +0.9 ms) are different in height (Figure 3A,gray), while the model predicted the same heights (Figure 3A, blue). We suspect that the asymmetry in
the reference data is primary due to trail-to-trial variability, because LSO neurons driven by
amplitude-modulated tones usually show more symmetric ITD-tuning curves (14).
Recent in vivo intracellular physiological recordings combined with anatomical characterizations
found that neurons in LSO can be subdivided into several groups (15). Principal cells respond only atthe onset of tonal stimuli, while non-principal cells respond in a more sustained manner, which waslong (and wrongly) regarded as the canonical response pattern of representative LSO neurons. Themodel needs to be re-tuned to be able to simulate the onset-type responses of LSO principal neurons,
which show only marginal dependence on ILDs to sustained tones.

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Figure 4 – Simulated phase-histograms at 500 Hz (A), 1500 Hz (B), and 4500 Hz (C). Inputs from AN are
shown in red and the GBC outputs are shown in blue; corresponding VS values are also shown. Parameters
used are: (A, B, and C) Number of excitatory inputs: 20; excitatory input rate: 250 spikes/sec; coincidence
threshold: 5 inputs; coincidence window: 0.5 ms; refractory period: 1.4 ms.
3.3 GBC Model - Enhancement of Phase-locking
A GBC receives converging inputs from auditory nerves (16), which results in the improvement ofphase-locking compared to auditory nerve inputs (17). This effect can be simulated in our model(Figure 4A). The enhancement of phase-locking is limited at low frequencies (typically 1 kHz orbelow) (Joris et al., 1994). Such frequency dependence is also seen in the model (Figure 4B), although
the degradation of phase-locking at high frequency may not be as severe in the model as in experiments(Figure 4C).
Another prominent response characteristic of the GBC is the so-called "primary-like-with-notch"
peristimulus time histogram, in which an onset peak of spiking activity is followed by a short pause
and a gradual decrease (4, 18). However, since our goal here was to simulate the sustained activity ofauditory neurons, we did not take the onset activity into account. To more faithfully simulate transient
responses of GBCs, the model may need to include additional components such as an adapting
threshold (19).
3.4 Limitations and Possible Modification of the Model
Despite its simplicity, the model we used can simulate fundamental temporal properties of MSO
and LSO neurons and GBCs. The computational time required for the model was below 1% of that fora Hodgkin-Huxley-type model (8). This computational efficiency will allow us to calculate theresponses of thousands of neurons simultaneously in future large-scale simulations, complementing
the existing model framework using more complex models (20). Neurons in the cochlear nucleus
neurons are physiologically and morphologically categorized into several groups (4, 2 1). Applicationof this simple model to neurons other than GBCs will be the topic of a future study.
Comparisons of the model outcome with experimental data obtained in vivo revealed that thesimulated tuning curves are in general more symmetric than empirical tuning curves (Figure 3). In
addition, the model GBC may represent better phase-locking than real neurons at high frequencies(Figure 4C). Several reasons may underlie these discrepancies. First, the modeled synaptic input isrectangular and reaches its maximum instantaneously at the onset, while real synaptic inputs of theseneurons are temporally asymmetric and also subject to jitter (e.g., showing variability in amplitude andarrival time). To make the model more physiologically plausible, modifications of the input shapewould be necessary but at the cost of reducing computational simplicity (7, 8).

4. CONCLUSIONSIn this work, we presented a simple coincidence counting model that can be applied to several types
of auditory brainstem neurons, such as MSO, LSO and GBC. More specifically, ITD tuning of MSO
and LSO, ILD tuning in LSO, and enhancement of phase-locking in GBCs were simulated. Because of
its computational efficiency, the model can complement existing more complex models especiallywhen the input-output function, but not the subneuronal biophysics, is the main focus of the simulation.

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By modifying the shape of synaptic inputs, the model could gain a better physiological plausibility at
the cost of partly losing its computational efficiency.

ACKNOWLEDGEMENTS
This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German ResearchFoundation) under Germany's Excellence Strategy EXC 2177/1, Project ID 390895286 (GA and JK)
and by the European Research Council (ERC) under the European Union's Horizon 2020 Research andInnovation Programme Grant Agreement no. 716800 (ERC Starting Grant to MD).

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