Daniela Sabrina Andres

FINITE DIMENSIONAL STRUCTURE OF THE GPI DISCHARGE IN PATIENTS WITH PARKINSON'S DISEASE

Stochastic systems are infinitely dimensional and deterministic systems are low dimensional, while real systems lie somewhere between these two limit cases. If the calculation of a low (finite) dimension is in fact possible, one could conclude that the system under study is not purely random. In the present work we calculate the maximal Lyapunov exponent from interspike intervals time series recorded from the internal segment of the Globus Pallidusfrom patients with Parkinsons disease. We show the convergence of the maximal Lyapunov exponent at a dimension equal to 7 or 8, which is therefore our estimation of the embedding dimension for the system. For dimensions below 7 the observed behavior is what would be expected from a stochastic system or a complex system projecting onto lower dimensional spaces. The maximal Lyapunov exponent did not show any differences between tremor and akineto-rigid forms of the disease. However, it did decay with the value of motor Unified Parkinsons Disease Rating Scale -OFF scores. Patients with a more severe disease (higher UPDRS-OFF score) showed a lower value of the maximal Lyapunov exponent. Taken together, both indexes (the maximal Lyapunov exponent and the embedding dimension) remark the importance of taking into consideration the systems non-linear properties for a better understanding of the information transmission in the basal ganglia.

Neuronal Entropy Depends on the Level of Alertness in the Parkinsonian Globus Pallidus in vivo

A new working hypothesis of Parkinson’s disease (PD) proposes to focus on the central role of entropy increase in the basal ganglia (BG) in movement disorders. The conditions necessary for entropy increase in vivo are, however, still not fully described. We recorded the activity of single globus pallidus pars interna neurons during the transition from deep anesthesia to full alertness in relaxed, head-restrained, control, and parkinsonian (6-hydroxydopamine-lesioned group-lesioned) rats. We found that during awakening from anesthesia, the variation of neuronal entropy was significantly higher in the parkinsonian than in the control group. This implies in our view that in PD the entropy of the output neurons of the BG varies dynamically with the input to the network, which is determined by the level of alertness. Therefore, entropy needs to be interpreted as a dynamic, emergent property that characterizes the global state of the BG neuronal network, rather than a static property of parkinsonian neurons themselves. Within the framework of the “entropy hypothesis,” this implies the presence of a pathological feedback loop in the parkinsonian BG, where increasing the network input results in a further increase of neuronal entropy and a worsening of akinesia.

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

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.

Editorial: Pathophysiology of the Basal Ganglia and Movement Disorders: Gaining New Insights from Modeling and Experimentation, to Influence the Clinic

Citation: Andres DS, Merello M and Darbin O (2017) Editorial: Pathophysiology of the Basal Ganglia and Movement Disorders: Gaining New Insights from Modeling and Experimentation, to Influence the Clinic. Front. Hum. Neurosci. 11:466. doi: 10.3389/fnhum.2017.00466 Editorial: Pathophysiology of the Basal Ganglia and Movement Disorders: Gaining New Insights from Modeling and Experimentation, to Influence the Clinic