Nonlinear modeling of causal interrelationships in neuronal ensembles.

The increasing availability of multiunit recordings gives new urgency to the need for effective analysis of "multidimensional" time-series data that are derived from the recorded activity of neuronal ensembles in the form of multiple sequences of action potentials--treated mathematically as point-processes and computationally as spike-trains. Whether in conditions of spontaneous activity or under conditions of external stimulation, the objective is the identification and quantification of possible causal links among the neurons generating the observed binary signals. A multiple-input/multiple-output (MIMO) modeling methodology is presented that can be used to quantify the neuronal dynamics of causal interrelationships in neuronal ensembles using spike-train data recorded from individual neurons.

Modeling the nonlinear dynamic interactions of afferent pathways in the dentate gyrus of the hippocampus.

The dentate gyrus is the first region of the hippocampus that receives and integrates sensory information (e.g., visual, auditory, and olfactory) via the perforant path, which is composed of two distinct neuronal pathways: the Lateral Perforant Path (LPP) and the Medial Perforant Path (MPP).

Modeling the nonlinear properties of the in vitro hippocampal perforant path-dentate system using multielectrode array technology.

A modeling approach to characterize the nonlinear dynamic transformations of the dentate gyrus of the hippocampus is presented and experimentally validated. The dentate gyrus is the first region of the hippocampus which receives and integrates sensory information via the perforant path. The perforant path is composed of two distinct pathways: 1) the lateral path and 2) the medial perforant path.

Improving bioassay sensitivity for neurotoxins detection using volterra based third order nonlinear analysis.

Based on a novel analytical method for analyzing short-term plasticity (STP) of the CA1 hippocampal region in vitro, a screening tool for the detection and classification of unknown chemical compounds affecting the nervous system was recently introduced [1], [2]. The recorded signal consisted of evoked population spike in response to Poisson distributed random train impulse stimuli. The developed analytical approach used the first order Volterra kernel and the Laguerre coefficients of the second order Volterra model as classification features [3].

Modeling hippocampal nonlinear dynamic transformations with principal dynamic modes.

A new modeling approach of hippocampal nonlinear dynamics is presented. It is based on Principal Dynamics Modes (PDMs) derived from the Volterra kernels quantifying the hippocampal transformations. The approach is illustrated using data obtained from acute hippocampal slice preparations and from behaving rats performs a memory task.

Modeling the nonlinear dynamic interactions of the lateral and the medial perforant path of the hippocampal dentate gyrus.

We present a new method to characterize the nonlinearities resulting from the co-activity of two pathways that converge on a common postsynaptic element. We investigated the nonlinear dynamic interactions between the lateral perforant pathway (LPP) and the Medial Perforant Pathway (MPP) of the hippocampal dentate gyrus, and the effects of these cross-pathway interactions on granule cell output. A third order Volterra-Poisson modeling approach was implemented to capture the interactions between the two pathways.

A multi-input modeling approach to quantify hippocampal nonlinear dynamic transformations.

A multi-input modeling approach is introduced to quantify hippocampal neural dynamics. It is based on the Volterra modeling approach extended to multiple inputs. The computed Volterra kernels allow quantitative description of hippocampal transformations and define a predictive model that can produce responses to arbitrary input patterns.

VLSI implementation of a nonlinear neuronal model: a "neural prosthesis" to restore hippocampal trisynaptic dynamics.

We are developing a biomimetic electronic neural prosthesis to replace regions of the hippocampal brain area that have been damaged by disease or insult. We have used the hippocampal slice preparation as the first step in developing such a prosthesis. The major intrinsic circuitry of the hippocampus consists of an excitatory cascade involving the dentate gyrus (DG), CA3, and CA1 subregions; this trisynaptic circuit can be maintained in a transverse slice preparation.

Boolean modeling of neural systems with point-process inputs and outputs.

This paper presents a novel modeling approach for neural systems with point-process inputs and outputs (binary time-series of 0's and 1's) that utilizes Boolean operators of modulo-2 multiplication and addition, corresponding to the logical AND and OR operations respectively. The form of the employed mathematical model is akin to a "Boolean-Volterra" model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean model are also binary variables that indicate the presence or absence of the respective term in each specific model/system.

Nonlinear dynamic model of CA1 short-term plasticity using random impulse train stimulation.

A comprehensive, quantitative description of the nonlinear dynamic characteristics of the short-term plasticity (STP) in the CA1 hippocampal region is presented. It is based on the Volterra-Poisson modeling approach using random impulse train (RIT) stimuli. In vitro hippocampal slice preparations were used from adult rats.

Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor.

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener-Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal).

An algorithm for real-time extraction of population EPSP and population spike amplitudes from hippocampal field potential recordings.

A new method is presented for extracting the amplitude of excitatory post synaptic potentials (EPSPs) and spikes in real time. It includes a low pass filter (LPF), a differentiator, a threshold function, and an intelligent integrator. It was applied to EPSP and population spike data recorded in the Dentate Gyrus and the CA1 hippocampus in vitro.

Detection and classification of neurotoxins using a novel short-term plasticity quantification method.

A tissue-based biosensor is described for screening chemical compounds that rapidly affect the nervous system. The proposed sensor is an extension of a previous work on cultured hippocampal slices [Biosens. Bioelectron.

An efficient method for studying short-term plasticity with random impulse train stimuli.

In this article, we introduce an efficient method that models quantitatively nonlinear dynamics associated with short-term plasticity (STP) in biological neural systems. It is based on the Voterra-Wiener modeling approach adapted for special stimulus/response datasets. The stimuli are random impulse trains (RITs) of fixed amplitude and Poisson distributed, variable interimpulse intervals.