On the motion of spikes: a model of multifractality as observed in the neuronal activity of the human basal ganglia

Abstract

AbstractNeuronal signals are usually characterized in terms of their discharge rate. However, this description is inadequate to account for the complex temporal organization of spike trains. In particular multifractality is a hallmark of the neuronal activity of the human, parkinsonian basal ganglia, which is not accounted for in most models. Here I develop a new conceptualization of neuronal activity, enabling the analysis of spike trains in terms of a velocity field. Firstly, I show that structure functions of increasing order can be used to recover the multifractal spectrum of spike trains obtained from the globus pallidus interna (GPi) of patients with Parkinson’s disease. Further, I propose a neural field model to study the observed multifractality. The model describes the motion of spikes in terms of a velocity field, including a diffusive term to consider the physical properties of the electric field that is associated to neuronal activity. As the model is perturbed with colored noise, the following is observed: 1. multifractality is present for a wide range of diffusion coefficients; and 2. multifractal temporal properties are mirrored into space. These results predict that passive electric properties of neuronal activity are far more relevant to the human brain than what has been usually considered.