On the Motion of Spikes: Turbulent-Like Neuronal Activity in the Human Basal Ganglia.

Daniela Andres

doi:10.3389/fnhum.2018.00429

Abstract

Neuronal signals are usually characterized in terms of their discharge rate, a description inadequate to account for the complex temporal organization of spike trains. Complex temporal properties, which are characteristic of neuronal systems, can only be described with the appropriate, complex mathematical tools. Here, I apply high order structure functions to the analysis of neuronal signals recorded from parkinsonian patients during functional neurosurgery, recovering multifractal properties. To achieve an accurate model of such multifractality is critical for understanding the basal ganglia, since other non-linear properties, such as entropy, depend on the fractal properties of complex systems. I propose a new approach to the study of neuronal signals: to study spiking activity in terms of the velocity of spikes, defining it as the inverse function of the instantaneous frequency. I introduce a neural field model that includes a non-linear gradient field, representing neuronal excitability, and a diffusive term to consider the physical properties of the electric field. Multifractality is present in the model for a range of diffusion coefficients, and multifractal temporal properties are mirrored into space. The model reproduces the behavior of human basal ganglia neurons and shows that it is like that of turbulent fluids. The results obtained from the model predict that passive electric properties of neuronal activity, including ephaptic coupling, are far more relevant to the human brain than what is usually considered: passive electric properties determine the temporal and spatial organization of neuronal activity in the neural tissue.

Highlights

The basal ganglia are a circuit of densely interconnected subcortical nuclei, whose disease is related to human movement disorders (Obeso et al, 2008)
In the neural field studied, complex geometrical properties arise from a combination of diffusive properties, a gradient field and a stochastic drive, in a manner similar to that of fluids undergoing turbulence
The model provides a mechanism for the generation of the complex patterns observed in parkinsonian neuronal activity, i.e., that high-pass filtering of turbulent-like velocity signals produces intermittent bursts in non-linear systems with stochastic drive, such as the present one (Frisch and Morf, 1981)

Summary

Introduction

The basal ganglia are a circuit of densely interconnected subcortical nuclei, whose disease is related to human movement disorders (Obeso et al, 2008). Time series of a length of thousands of data points have been analyzed with high order structure functions in different fields, and it was shown that this is a suitable method to look for non-linearity in the exponent function, i.e., to distinguish monofractality from multifractality (Yu et al, 2003; Huang et al, 2011). First it is shown that multifractality can be measured in neuronal signals from the GPi analyzing structure functions of increasing order.

Results

Conclusion