Modeling event-driven nonlinear dynamics in Biological Neural Networks
Spiros H. Courellis, Vasilis Z. Marmarelis, and Theodore
W. Berger
A new computationally efficient methodology will be introduced for analyzing and modeling event-driven nonlinear dynamics of biological neural systems with multiple inputs and outputs. The new method yields quantitative descriptors of the nonlinear interactive effects of multi-input (impulse) event-sequences, on a system’s response. It also generates a model that allows prediction of the response to arbitrary patterns of multiple impulse-input sequences. The generated model has a form that enables potential implementations of the modeled system.
The new methodology is based on a variant of the Volterra modeling approach, properly adapted for the event-driven case, and characterizes and models nonlinear dynamics by means of kernel functions, using spike input/output data. It can be used as the tool to analyze and model event-driven experimental data from biological neural networks, typically represented as impulse sequences (spike trains). Its efficiency allows for rapid progress in the study of neuronal functions, where thorough analysis of experimental spike-train data has been hindered by the lack of appropriate computational methodologies that can tackle the complexities of the intrinsic nonlinear dynamics, especially in the case of multiple inputs and outputs.
Results from initial testing of the new method on hippocampal neuronal data will be presented to demonstrate this approach for up to two inputs. Based on the new method, an architecture (including more than two inputs) will be also presented, addressing the emerging issue of spatiotemporal data analysis (in vision or elsewhere) whereby the multiple inputs/outputs represent different points in space.