International Journal of Neural Systems

Three synchronization measures are applied to scalp electroencephalogram (EEG) data collected from 20 patients diagnosed to have either: (1) no dementia, (2) mild cognitive impairment (MCI), or (3) Alzheimer's disease (AD). We apply the three synchronization measures — the phase synchronization, and two measures of nonlinear interdependency — to the data collected from awake patients resting with eyes closed. We show that the synchronization in potential between electrodes near the left and right occipital lobes provides a statistically significant discriminant between the healthy and AD subjects, and the MCI and AD subjects. None of the three measures appears able to distinguish between the healthy and MCI subjects, although MCI subjects show synchronization values intermediate between healthy subjects (with high synchronization values) and AD subjects (with low synchronization values) on average.

Granger causality is becoming an important tool for determining causal relations between neurobiological time series. For multivariate data, there is often the need to examine causal relations between two blocks of time series, where each block could represent a brain region of interest. Two alternative methods are available. In the pairwise method, bivariate autoregressive models are fit to all pairwise combinations involving one time series from the first block and one from the second. The total Granger causality between the two blocks is then derived by summing pairwise causality values from each of these models. This approach is intuitive but computationally cumbersome. Theoretically, a more concise method can be derived, which we term the blockwise Granger causality method. In this method, a single multivariate model is fit to all the time series, and the causality between the two blocks is then computed from this model. We compare these two methods by applying them to cortical local field potential recordings from monkeys performing a sensorimotor task. The obtained results demonstrate consistency between the two methods and point to the significance potential of utilizing Granger causality analysis in understanding coupled neural systems.

We study the properties of a homoclinic model of neuron by introducing a suitable one-dimensional map. We show that the system is characterized by a response time to external signals which is a decreasing function of the signal strength, in contrast to excitable models whose response time is signal-independent. In a one-dimensional array of these systems with bidirectional coupling, we observe a sudden transition to a synchronized state at a certain value of the coupling strength. The transition occurs when the response time of a site to the signals of the adjacent sites is of the order of refractory time. Near the transition, we find an intermittent behavior due to the competition between a turbulent and a synchronized state. The observed behavior distinguishes homoclinic systems from excitable systems.

Neurons extracted from specific areas of the Central Nervous System (CNS), such as the hippocampus, the cortex and the spinal cord, can be cultured in vitro and coupled with a micro-electrode array (MEA) for months. After a few days, neurons connect each other with functionally active synapses, forming a random network and displaying spontaneous electrophysiological activity. In spite of their simplified level of organization, they represent an useful framework to study general information processing properties and specific basic learning mechanisms in the nervous system. These experimental preparations show patterns of collective rhythmic activity characterized by burst and spike firing. The patterns of electrophysiological activity may change as a consequence of external stimulation (i.e., chemical and/or electrical inputs) and by partly modifying the "randomness" of the network architecture (i.e., confining neuronal sub-populations in clusters with micro-machined barriers). In particular we investigated how the spontaneous rhythmic and synchronous activity can be modulated or drastically changed by focal electrical stimulation, pharmacological manipulation and network segregation. Our results show that burst firing and global synchronization can be enhanced or reduced; and that the degree of synchronous activity in the network can be characterized by simple parameters such as cross-correlation on burst events.

The paper applies biologically plausible models to investigate how noise input to small ensembles of neurons, coupled via the extracellular potassium concentration, can influence their firing patterns. Using the noise intensity and the volume of the extracellular space as control parameters, we show that potassium induced depolarization underlies the formation of noise-induced patterns such as delayed firing and synchronization. These phenomena are associated with the appearance of new time scales in the distribution of interspike intervals that may be significant for the spatio-temporal oscillations in neuronal ensembles.

A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.

We have studied coupled neural populations in an effort to understand basic mechanisms that maintain their normal synchronization level despite changes in the inter-population coupling levels. Towards this goal, we have incorporated coupling and internal feedback structures in a neuron-level population model from the literature. We study two forms of internal feedback — regulation of excitation, and compensation of excessive excitation with inhibition. We show that normal feedback actions quickly regulate/compensate an abnormally high coupling between the neural populations, whereas a pathology in these feedback actions can lead to abnormal synchronization and "seizure"-like high amplitude oscillations. We then develop an external control paradigm, termed feedback decoupling, as a robust synchronization control strategy. The external feedback decoupling controller acts to achieve the operational objective of maintaining normal-level synchronous behavior irrespective of the pathology in the internal feedback mechanisms. Results from such an analysis have an interesting physical interpretation and specific implications for the treatment of diseases such as epilepsy. The proposed remedy is consistent with a variety of recent observations in the human and animal epileptic brain, and with theories from nonlinear systems, adaptive systems, optimization, and neurophysiology.