A Point Process Model for Auditory Neurons Considering Both Their Intrinsic Dynamics and the Spectrotemporal Properties of an Extrinsic Signal

Abstract

We propose a point process model of spiking activity from auditory neurons. The model takes account of the neuron’s intrinsic dynamics as well as the spectro-temporal properties of an input stimulus. A discrete Volterra expansion is used to derive the form of the conditional intensity function. The Volterra expansion models the neuron’s baseline spike rate, its intrinsic dynamics - spiking history - and the stimulus effect which in this case is the analog of the spectro-temporal receptive field (STRF). We performed the model fitting efficiently in a generalized linear model framework using ridge regression to address properly this ill-posed maximum likelihood estimation problem. The model provides an excellent fit to spiking activity from 55 auditory nerve neurons. The STRF-like representation estimated jointly with the neuron’s intrinsic dynamics may offer more accurate characterizations of neural activity in the auditory system than current ones based solely on the STRF.

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“…Using similar techniques, Trevino et al (2010) and Plourde et al (2011) were able to extract a rudimentary refractory function (i.e., low temporal resolution) from the neuron's spiking history given an acoustic stimulus, but this framework could easily be extended for electrical stimulation. Campbell et al (2012) were also able to delineate between the effects of refractoriness and spike rate adaptation using constant and variable pulse train amplitudes.…”

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“…The biophysical properties may include absolute and relative refractory periods, bursting propensity, and network dynamics. We assume that we can express $\log \lambda \left(t\right|H_t)$ in a Volterra series expansion as a function of the signal and the biophysical properties (31). The first-order and second-order terms in the expansion are$\log \lambda \left(t\right|H_t)=true\underset{0}{\overset{t}{\int }}s(t-u){\beta }_S\left(u\right)du+{\displaystyle \underset{0}{\overset{t}{\int }}{\beta }_H}\left(u\right)dN(t-u)+true\underset{0}{\overset{t}{\int }}{\displaystyle \underset{0}{\overset{t}{\int }}s(t-u)s(t-v)h_1(u,v)dudv}+true\underset{0}{\overset{t}{\int }}{\displaystyle \underset{0}{\overset{t}{\int }}{h}_2(u,v)dN(t-u)dN(t-v)}+true\underset{0}{\overset{t}{\int }}{\displaystyle \underset{0}{\overset{t}{\int }}{h}_3(u,v)s(t-u)dN(t-v)+...},$where $s\left(t\right)$ is the signal at time t , $dN\left(t\right)$ is the increment in the counting process, ${\beta }_S\left(u\right)$ is the one-dimensional signal kernel, ${\beta }_H\left(t\right)$ is the one-dimensional temporal or spike history kernel, $h_1(u,v)$ is the 2D signal kernel, $h_2(u,v)$ is the 2D temporal kernel, and $h_3(u,v)$…”

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“…[3], [6], [7]). However, the spectrogram may not be the most efficient representation to study the auditory system since it does not match well the processing performed by the peripheral auditory system.…”