Modeling of movement-related potentials using a fractal approach

Evidence of Chaos in Electroencephalogram Signatures of Human Performance: A Systematic Review

(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.

Non-linear dynamics in parkinsonism

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the “rate hypothesis” and the “oscillatory hypothesis.” In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

An entropy-based model for basal ganglia dysfunctions in movement disorders

During this last decade, nonlinear analyses have been used to characterize the irregularity that exists in the neuronal data stream of the basal ganglia. In comparison to linear parameters for disparity (i.e., rate, standard deviation, and oscillatory activities), nonlinear analyses focus on complex patterns that are composed of groups of interspike intervals with matching lengths but not necessarily contiguous in the data stream. In light of recent animal and clinical studies, we present a review and commentary on the basal ganglia neuronal entropy in the context of movement disorders.