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.

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.