Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay

Axel Hutt and Fatihcan M. Atay

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Submission date: 06. Nov. 2003 (revised version: January 2006)
published in: Chaos, solitons and fractals, 32 (2007) 2, p. 547-560 
DOI number (of the published article): 10.1016/j.chaos.2005.10.091
Bibtex
PACS-Numbers: 02.30.Rz, 87.18.Hf
Keywords and phrases: neuronal ensemble, synaptic connectivity kernel, bifurcation, stimulus response

Abstract:
This work studies dynamical properties of spatially extended neuronal ensembles. We first derive an evolution equation from temporal properties and statistical distributions of synapses and somata. The obtained integro-differential equation considers both synaptic and axonal propagation delay, while spatial synaptic connectivities exhibit gamma-distributed distributions. This familiy of connectivity kernels also covers the cases of divergent, finite, and negligible self-connections. The work derives conditions for both stationary and nonstationary instabilities for gamma-distributed kernels. It turns out that the stability conditions can be formulated in terms of the mean spatial interaction ranges and the mean spatial interaction times. In addition, a numerical study examines the evoked spatiotemporal response activity caused by short local stimuli and reveals maximum response activity after the mean interaction time at a distance from stimulus offset location equal to the mean interaction range. These findings propose new insights to neuronal mechanisms of experimentally observed evoked brain activity.