Computational neuronal correlation with enhanced synchronized activity in the basal ganglia and the slowing of thalamic theta and alpha rhythms in Parkinson's disease

Spiking Neural Networks and Mathematical Models

Neural networks are applied in various scientific fields such as medicine, engineering, pharmacology, etc. Investigating operations of neural networks refers to estimating the relationship among single neurons and their contributions to the network as well. Hence, studying a single neuron is an essential process to solve complex brain problems. Mathematical models that simulate neurons and the way they transmit information are proven to be an indispensable tool for neuroscientists. Constructing appropriate mathematical models to simulate information transmission of a biological neural network is a challenge for researchers, as in the real world, identical neurons in terms of their electrophysiological characteristics in different brain regions do not contribute in the same way to information transmission within a neural network due to the intrinsic characteristics. This review highlights four mathematical, single-compartment models: Hodgkin-Huxley, Izhikevich, Leaky Integrate, and Fire and Morris-Lecar, and discusses comparison among them in terms of their biological plausibility, computational complexity, and applications, according to modern literature.

Graph Theory on Brain Cortical Sources in Parkinson's Disease: The Analysis of 'Small World' Organization from EEG

Parkinson’s disease (PD) is the second most common neurodegenerative disease in the elderly population. Similarly to other neurodegenerative diseases, the early diagnosis of PD is quite difficult. The current pilot study aimed to explore the differences in brain connectivity between PD and NOrmal eLDerly (Nold) subjects to evaluate whether connectivity analysis may speed up and support early diagnosis. A total of 26 resting state EEGs were analyzed from 13 PD patients and 13 age-matched Nold subjects, applying to cortical reconstructions the graph theory analyses, a mathematical representation of brain architecture. Results showed that PD patients presented a more ordered structure at slow-frequency EEG rhythms (lower value of SW) than Nold subjects, particularly in the theta band, whereas in the high-frequency alpha, PD patients presented more random organization (higher SW) than Nold subjects. The current results suggest that PD could globally modulate the cortical connectivity of the brain, modifying the functional network organization and resulting in motor and non-motor signs. Future studies could validate whether such an approach, based on a low-cost and non-invasive technique, could be useful for early diagnosis, for the follow-up of PD progression, as well as for evaluating pharmacological and neurorehabilitation treatments.