A non-homogeneous binomial model for thalamic oscillations

The thalamic ventral posterior lateral neurons (VPL) respond to somatosensory stimulation with a burst of action potentials followed by a periodic oscillation at the spindle frequency. This study aims to build a statistical model to quantify the multi-unit behavior and explain putative underlying mechanisms. Multi-unit data, comprising 4 or 5 different neurons, were collected from anesthetized adult rats (n=2) by positioning a microelectrode in the ventral posterior lateral (VPL) nuclei of the thalamus. Using an observation window of 1 ms and assuming that neuronal firing is uncorrelated within this window, the firing rate of the neurons can be successfully modeled by using a non-homogeneous binomial model with N=1 (with 99.5% confidence). Using maximum likelihood estimator (MLE) of the parameter p, statistically consistent prediction of the parameters of non-homogeneous binomial model was made using a minimum of 50 stimulus-response pairs. The interstimulus interval histograms of the individual neuronal firing indicate a possible stochastic resonance behavior that will model the spindles in thalamus. Our model offers a statistically elegant description of oscillations in neuronal action potential data and can in general, be used to track changes in the neuronal dynamics with function or dysfunction.