Abstract

Revealing dynamical mechanisms of the brain in order to understand how it works and processes information has recently stimulated enormous interest in computational neuroscience. Understanding the behavior of a single neuron, the most important building block of the brain, is of core interest in the brain-related sciences. Application of the advanced statistical signal processing methods, e.g., Bayesian methods, in assessing the hidden dynamics and estimating the unknown parameters of a single neuron has been considered recently as of special interest in neuroscience. This thesis attempts to develop robust and efficient computational techniques based on Bayesian signal processing methods to elucidate the hidden dynamics and estimate the unknown parameters of a single neuron.
In the first part of the thesis, Kalman filtering (KF)-based algorithms are derived for the Hodgkin-Huxley (HH) neuronal model, the most detailed biophysical neuronal model, to identify the hidden dynamics and estimate the intrinsic parameters of a single neuron from a single trace of the recorded membrane potential. The unscented KF (UKF) has already been applied to track the dynamics of the HH neuronal model in the literature. We extend the existing KF technique for the HH neuronal model to another version, namely, extended Kalman filtering (EKF). Two estimation strategies of the KF, dual and joint estimation strategies, are employed in conjunction with the EKF and UKF for simultaneously tracking the hidden dynamics and estimating the unknown parameters of a single neuron, leading to four KF algorithms, namely, joint UKF (JUKF), dual UKF (DUKF), joint EKF (JEKF) and dual EKF (DEKF).
In the second part of this thesis, the problem of inferring excitatory and inhibitory synaptic inputs that govern activity of neurons and process information in the brain is investigated. The importance of trial-to-trial variations of synaptic inputs has recently been investigated in neuroscience. Such variations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model. Moreover, a special case of the GMKF when there is only one mixand, the standard KF, is studied for the same problem.
Finally, in the third part of the thesis, inferring the synaptic input of a spiking neuron as well as estimating its dynamics and parameters is considered. The synaptic input underlying a spiking neuron can effectively elucidate the information processing mechanism of a neuron. The concept of blind deconvolution is applied to Hodgkin-Huxley (HH) neuronal model, for the first time in this thesis, to address the problem of reconstructing the hidden dynamics and synaptic input of a single neuron as well as estimating its intrinsic parameters only from a single trace of noisy membrane potential. The blind deconvolution is accomplished via a novel recursive algorithm based on extended Kalman filtering (EKF). EKF is then followed by the expectation-maximization (EM) algorithm which estimates the statistical parameters of the HH neuronal model.
Extensive experiments are performed throughout the thesis to demonstrate the accuracy, effectiveness and usefulness of the proposed algorithms in our investigation. The performance of the proposed algorithms is compared with that of the most recent techniques in the literature. The promising results of the proposed algorithms confirm their robustness and efficiency, and suggest that they can be effectively applied to the challenging problems in neuroscience.