Evidence of coupled oscillator to wave packet dynamics in human brain

Abstract

Clear evidence of oscillator dynamics to wave packet collapse and revival in the brain EEG signals is demonstrated for the first time, 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 bi-stability, 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 the boundary of alpha and beta waves of 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.

Unstable periodic orbits are faithful biomarker for the onset of epileptic seizure

“…Similarly, with use of SINDy model for set B 40-45Hz region reconstructed data and the derived governing system equation in Fourier domain is: Whereas system equation for set E 40-45Hz region phase space structure is: From the above 40-45Hz phase space plots as in Fig 6, it can be concluded the occurrence of the energy transfer phenomenon [19] with conservation of energy states here. In this 40-45 Hz region the coherence phenomenon gets more intense and in case of the epileptic patient plot (epileptogenic zone and during seizure) the potential energy is seen to be more dominant (thus the kinetic energy decrease) than in the case of the healthy subjects.…”

“…Phase space plotting is a novel way for the study of the EEG data, with the trajectories revealing periodic motion, UPO and sudden changes quite transparently [40]. From the existence of distinct oscillatory patterns of the recorded EEG data, the different brain states can be clearly distinguished [19-20]. Akin to the observations in well studied electrical potential generating circuits, harmonic motion characterized by the following ordinary differential equation, is clearly discernible in phase-space dynamics: The above is augmented with damping and driving terms, as also non-linear anharmonic terms for appropriate descriptions of diverse physical systems.…”

“…The classical particle dynamics is described by Newtonian mechanics in terms of phase space by considering the coordinate and their instantaneous changes. The wave behavior manifests through coherence effects leading to collapse and revival [19-20]. In the present case, this may arise due to synchronization amongst the neuronal firings.…”

Activation-Inhibition dynamics of the oscillatory bursts of the human EEG during resting state. The macroscopic temporal range of few seconds

“…It has been proposed that these oscillation bursts are the primary ingredients of oscillatory activity that can be observed over the scalp (Feingold et al 2015;Shin et al 2017). The oscillatory bursts have been recently characterized as wave packets (Pal and Panigrahi 2020). The common procedure of averaging power would be obscuring the natural neurodynamics of oscillatory bursts.…”