Nonlinear Dynamic Modeling of Spike Train Transformations for Hippocampal-Cortical Prostheses

Abstract

One of the fundamental principles of cortical brain regions, including the hippocampus, is that information is represented in the ensemble firing of populations of neurons, i.e., spatio-temporal patterns of electrophysiological activity. The hippocampus has long been known to be responsible for the formation of declarative, or fact-based, memories. Damage to the hippocampus disrupts the propagation of spatio-temporal patterns of activity through hippocampal internal circuitry, resulting in a severe anterograde amnesia. Developing a neural prosthesis for the damaged hippocampus requires restoring this multiple-input, multiple-output transformation of spatio-temporal patterns of activity. Because the mechanisms underlying synaptic transmission and generation of electrical activity in neurons are inherently nonlinear, any such prosthesis must be based on a nonlinear multiple-input, multiple-output model. In this paper, we have formulated the transformational process of multi-site propagation of spike activity between two subregions of the hippocampus (CA3 and CA1) as the identification of a multiple-input, multiple-output (MIMO) system, and proposed that it can be decomposed into a series of multiple-input, single-output (MISO) systems. Each MISO system is modeled as a physiologically plausible structure that consists of 1) linear/nonlinear feedforward Volterra kernels modeling synaptic transmission and dendritic integration, 2) a linear feedback Volterra kernel modeling spike-triggered after-potentials, 3) a threshold for spike generation, 4) a summation process for somatic integration, and 5) a noise term representing intrinsic neuronal noise and the contributions of unobserved inputs. Input and output spike trains were recorded from hippocampal CA3 and CA1 regions of rats performing a spatial delayed-nonmatch-to-sample memory task that requires normal hippocampal function. Kernels were expanded with Laguerre basis functions and estimated using a maximum-likelihood method. Complexity of the feedforward kernel was progressively increased to capture higher-order system nonlinear dynamics. Results showed higher prediction accuracies as kernel complexity increased. Self-kernels describe the nonlinearities within each input. Cross-kernels capture the nonlinear interaction between inputs. Second- and third-order nonlinear models were found to successfully predict the CA1 output spike distribution based on CA3 input spike trains. First-order, linear models were shown to be insufficient.

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: computational study

“…In order to facilitate the estimation of the PV kernels from broadband input-output data, we use the Laguerre expansion technique (Watanabe and Stark 1975;Marmarelis 1993;Song et al 2007) which yields better estimates than the conventional kernel estimation technique of cross-correlation (Lee and Schetzen 1965;Sclabassi et al 1988) and allows reliable kernel estimation from short and noisy datasets. This improved performance results from the utilization of the orthonormal basis of discrete-time Laguerre functions to expand the kernels and reduce the number of unknown parameters to be estimated.…”

Identifying and Predicting Rat Behavior Using Neural Networks

“…Damage to the hippocampal region from events, such as a stroke or head trauma, can impair electrophysiological transfer of information and disrupt the spatio-temporal patterns between hippocampal regions possibly causing amnesia or impairing long-term memory formation [8]. Alzheimer's disease and other forms of dementia are typically associated with loss of neurons in the EC region, the region that provides input to the hippocampus [9] Understanding the electrophysiological signal encoding of hippocampal neurons from the EC to CA1 region in a rat hippocampus may provide insight concerning the relation of electrophysiological activity between the EC and CA1 hippocampal regions and rat behavior, which has not been as extensively studied as electrophysiological activity between the CA3 to CA1 region [1], [8].…”

“…Alzheimer's disease and other forms of dementia are typically associated with loss of neurons in the EC region, the region that provides input to the hippocampus [9] Understanding the electrophysiological signal encoding of hippocampal neurons from the EC to CA1 region in a rat hippocampus may provide insight concerning the relation of electrophysiological activity between the EC and CA1 hippocampal regions and rat behavior, which has not been as extensively studied as electrophysiological activity between the CA3 to CA1 region [1], [8]. This thesis aims to use neurological patterns simultaneously recorded from the EC and CA1 region in a rat to identify whether the neurological activity is associated with wheel running, T-maze or open exploration behavior.…”

“…Understanding the mechanisms underlying neural activity and transfer of information in the hippocampus has been a research topic of interest for neural prostheses applications involving sensory input, motor control or cognitive function [8]. Many aspects of neurological activity have been extensively researched, including mechanisms underlying synaptic transmission and generation of electrical activity for individual neurons [8], transfer of information based on spatio-temporal neural activity of neuron ensembles in the CA3 to CA1 region in rats [1], [5], [8], [16], and transfer of information in the prefrontal cortex in nonhuman primates [15].…”

“…Many aspects of neurological activity have been extensively researched, including mechanisms underlying synaptic transmission and generation of electrical activity for individual neurons [8], transfer of information based on spatio-temporal neural activity of neuron ensembles in the CA3 to CA1 region in rats [1], [5], [8], [16], and transfer of information in the prefrontal cortex in nonhuman primates [15]. These studies contribute to modeling dynamic properties of neural activity and behavior associated with neural activity.…”