Unstable periodic orbits are faithful biomarker for the onset of epileptic seizure
AbstractEEG signals of healthy individuals and epileptic patients, when treated as time series of evolving dynamical systems, are found to display characteristic differences in the behavior of the unstable periodic orbits (UPO), marking the transition from regular periodic variations to self-similar dynamics. The UPO, manifesting as broad resonances in the Fourier power spectra, are quite prominent in their presence in the normal signals and are either absent or considerably weakened with a shift towards lower frequency in the epileptic condition. The weighted average and visibility power computed for the UPO region are found to distinguish epileptic seizure from healthy individuals’ EEG. Remarkably, the unstable periodic motion for healthy ones is well described by damped harmonic motion, the orbits displaying smooth dynamics. In contrast, the epileptic cases show bi-stability and piecewise linear motion for the larger orbits, exhibiting large sudden jumps in the ‘velocity’ (referred to the rate of change of the EEG potentials), characteristically different from the healthy cases, highlighting the efficacy of the UPO as biomarkers. For both the regions, 8-14Hz UPO and 40-45Hz resonance, we used data driven analysis to derive the system dynamics in terms of sinusoidal functions, which reveal the presence of higher harmonics, confirming nonlinearity of the underlying system and leading to quantification of the discernible differences between the healthy and epileptic patients. The gamma wave region in the 40-45Hz range, connecting the conscious and the unconscious states of the brain, reveals well-structured coherence phenomena, in addition to the prominent resonance, which potentially can be used as a biomarker for the epileptic seizure. The wavelet scalogram analysis for both UPO and 40-45Hz region also clearly differentiates the healthy condition from epileptic seizure, confirming the above dynamical picture, depicting the higher harmonic generation, and intermixing of different modes in these two regions of interest.SignificanceUnstable periodic orbits are demonstrated as faithful biomarkers for detecting seizure, being prominently present in the Fourier power spectra of the EEG signals of the healthy individuals and either being absent or significantly suppressed for the epileptic cases, showing distinctly different behavior for the unstable orbits, in the two cases. A phase space study, with EEG potential and its rate of change as coordinate and corresponding velocity, clearly delineates the dynamics in healthy and diseased individuals, demonstrating the absence or weakening of UPO, that can be a reliable bio-signature for the epileptic seizure. The phase-space analysis in the gamma region also shows specific signatures in the form of coherent oscillations and higher harmonic generation, further confirmed through wavelet analysis.
