IEEE Access (Jan 2022)
Coupled Oscillator Dynamics in Brain EEG Signals: Manifestation of synchronization and Across Frequency Energy Exchange by Neutral Turbulence
Abstract
Phenomenological models, involving coupled oscillators of both deterministic and stochastic nature, have been invoked to describe the behavior of the EEG signals, with experimental validation. These models derive justification from the fact that the basic electronic unit for potential generation, incorporating capacitive, inductive, and resistive components, as well as the source, is modelled as damped driven oscillator, which can behave independently and may also exhibit synchronized dynamics with others, that can manifest in spatially correlated behavior observed in brain dynamics. Here, using a phase-space approach, we show clear evidence of oscillator dynamics to wave packet collapse and revival in the brain EEG signals, with distinct differences in healthy individuals and epileptic patients. The low frequency components exhibit single oscillator type behavior in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bistability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behavior. Wave behavior with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits that appear at 8-14Hz, centered at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.
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