PEAK-SPLITTING IN THE RESPONSE OF THE LEAKY INTEGRATE-AND-FIRE NEURON MODEL TO LOW-FREQUENCY PERIODIC INPUTS Levin Kuhlmann 1,2,* , Anthony Burkitt 2 , and Graeme M. Clark 1,2 1 Department of Otolaryngology, The University of Melbourne, Royal Victorian Eye and Ear Hospital, 32 Gisborne Street, East Melbourne, VIC 3002, Australia 2 The Bionic Ear Institute, 384-388 Albert Street, East Melbourne, VIC 3002, Australia * l.kuhlmann@medoto.unimelb.edu.au Abstract - The cause of peak-splitting in the output phase distribution of the leaky integrate-and-fire single neuron model in re- sponse to low-frequency periodic nerve fibre inputs is analyzed. It is found that peak- splitting largely arises from an increase of the spiking-rate of individual nerve fibre inputs, or from an increase in amplitude of individual input excitatory postsynaptic potentials, or both. These findings add another dimension to the understanding of how peak-splitting arises in the phase histograms of the responses of neurons in the auditory pathway, given that peak-splitting is typically thought to arise as a result of the non-linear dynamics of the basi- lar membrane and the hair cells. This research has implications for the understanding of the temporal code in the auditory pathway. Index Terms - auditory pathway, leaky integrate-and-fire neuron model, peak-splitting, temporal coding I. INTRODUCTION When stimulating auditory nerve (AN) fibres with a low-frequency (≤ 1 kHz) tonic sound stimulus, in most cases there is only a single peak in a phase histogram constructed on the period of the low- frequency tone [1]. In some cases, however, when the stimulus intensity is increased, two or even three peaks can be seen in the phase histogram [1]. Peak- splitting is the term given to this peak multiplication that occurs within a phase histogram when there is an increase in intensity of a low-frequency tonic sound stimulus [1], [2], [3]. The work done on peak-splitting in the auditory pathway has concentrated on inner hair cells (IHCs) of the cochlear [4], [5] and AN fi- bres [1], [2], [3], [4], [6], [7], [8], [9]. An understanding of the causes of peak-splitting in these cell types is slowly being elucidated. Cody and Mountain [5] have demonstrated that peak-splitting in low-frequency responses of IHCs arises from the mechanical input to the IHC, i.e. the vibrations of the basilar membrane (BM) relative to the tectorial membrane. Furthermore, the IHCs provide the in- puts to AN fibres and so it is clear that AN fibre low- frequency responses will show similar peak-splitting to that seen in IHC responses. It is theoretically pos- sible, however, for AN fibres to show peak-splitting in their low-frequency responses even when there is no peak-splitting present in the attached IHC low- frequency responses. If this were to occur, then it is likely to arise as a result of non-linearities asso- ciated with the way in which a AN fibre processes its IHC input. Cai and Geisler [1] demonstrated that peak-splitting in AN fibre responses was unpre- dictable, thus giving strong indication of non-linear effects. Cochlear nucleus (CN) neurons, which re- ceive inputs from AN fibres, are also thought to demonstrate peak-splitting in their response to low- frequency tones. The goal of the present study is to understand how peak-splitting in the low-frequency responses of CN neurons depends on neuronal param- eters, such as the spiking-rate of individual input AN fibres and the amplitude of the input excitatory post- synaptic potentials (EPSPs). To achieve this goal a leaky integrate-and-fire (LIF) single neuron model of a CN neuron receiving stochastic periodic AN fibre inputs was implemented. In this model input EPSPs to the neuron are summed and an action potential (AP or spike) is generated when the membrane po- tential reaches threshold. II. METHODS II.1. Neural Model The analysis presented here considers a single neu- ron with N independent inputs (afferent fibres) as- sumed to have the same synaptic response amplitude, a, and time course, s(t). The time course of an in- put at the site of spike generation is described by the synaptic response function u(t) for the LIF neuron model. The membrane potential is assumed to be re- set to its initial value at time t = 0, V (0) = v 0 , after an AP has been generated. An AP is produced only when the membrane potential exceeds the threshold, V th , which has a potential difference with the reset potential of θ = V th - v 0 . After an AP has been generated there is an absolute refractory period, τ r , during which no APs can be generated. The mem-