Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

Abstract

In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance.

Annealed Importance Sampling for Neural Mass Models

“…Dynamical models have also been fitted to neuroimaging data using a range of global optimisation methods. For example, mean field models have been fitted to EEG using particle swarm optimisation [ 52 ] and stochastic nonlinear oscillator models have been fitted to EEG using a multi-start algorithm [ 53 ]. Additionally, DCMs have been fitted to fMRI data using a method that combines local search with Gaussian process approximation [ 41 ].…”

Collective almost synchronization-based model to extract and predict features of EEG signals

“…Some studies have considered a stochastic limit cycle oscillator to model EEG signals [21][22][23] . They can also be modeled using networks of stochastic coupled nonlinear oscillators, with the dynamic unit described by the Duffing oscillator 24 or by Jansen's single-column model 25 . It was shown that a stochastic Duffing-van der Pol oscillator network model could capture the key characteristics of EEG signals, such as its time-varying power spectrum, Shannon entropy, and sample entropy of healthy controls and patients with a brain disorder.…”

Discriminant Subspace Low-Rank Representation Algorithm for Electroencephalography-Based Alzheimer’s Disease Recognition

“…More researchers are studying methods that can sensitively and conveniently monitor AD, involving cognitive neuropsychological detection, biochemical detection, neuroimaging detection, and so on. In recent years, electroencephalography (EEG) has become an important tool for studying human brain activity (Ghorbanian et al, 2015). Noninvasive EEG imaging methods are directly related to neural local field potentials and have a high temporal resolution.…”