■ REVIEW : Chaos Theory and Epilepsy

Iasemidis, Leonidas D.; Sackellares, J. Chris

doi:10.1177/107385849600200213

Cited by 173 publications

(92 citation statements)

References 44 publications

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“…Concerning epilepsy, the driving force behind a large number of studies on dimension analysis of EEG is that epileptic seizures are regarded as emergent states with reduced complexity compared to non-epileptic activity (Lai, 2002, and references therein): seizure onset represents a transition from relatively less orderly state to one of more orderly state (Iasemidis and Sackellares, 1996). Figure 4b also reveals that the epoch later in the epileptic seizure is of greater complexity than the early epoch.…”

Section: Remarkmentioning

confidence: 80%

Unified approach to catastrophic events: from the normal state to geological or biological shock in terms of spectral fractal and nonlinear analysis

Eftaxias

Kapiris

Balasis

et al. 2006

Nat. Hazards Earth Syst. Sci.

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Abstract. An important question in geophysics is whether earthquakes (EQs) can be anticipated prior to their occurrence. Pre-seismic electromagnetic (EM) emissions provide a promising window through which the dynamics of EQ preparation can be investigated. However, the existence of precursory features in pre-seismic EM emissions is still debatable: in principle, it is difficult to prove associations between events separated in time, such as EQs and their EM precursors. The scope of this paper is the investigation of the pre-seismic EM activity in terms of complexity. A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. Interestingly, theoretical studies (Hopfield, 1994;Herz and Hopfield 1995;Rundle et al., 1995;Corral et al., 1997) suggest that the EQ dynamics at the final stage and neural seizure dynamics should have many similar features and can be analyzed within similar mathematical frameworks. Motivated by this hypothesis, we evaluate the capability of linear and non-linear techniques to extract common features from brain electrical activities and pre-seismic EM emissions predictive of epileptic seizures and EQs respectively. The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or a large EQ can be studied in terms of "Intermittent Criticality".

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Section: Remarkmentioning

confidence: 80%

Unified approach to catastrophic events: from the normal state to geological or biological shock in terms of spectral fractal and nonlinear analysis

Eftaxias

Kapiris

Balasis

et al. 2006

Nat. Hazards Earth Syst. Sci.

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“…However, time series analysis methods that chose the detection of these statistically significant UPOs as a criterion for establishing deterministic chaos are more recent. A number of different techniques for search of UPOs in time series obtained from both low dimensional and high dimensional systems have been proposed [4,15,24,[34][35][36][37] and subsequently applied to time series from physiological and biological systems [4,9,11,12,18,21,26,29,35,38]. Most of these methods adopt surrogate methods to establish the statistical significance of the detected UPOs.…”

Section: Determinism From Uposmentioning

confidence: 99%

“…Applications of chaos control techniques [2,3] in neural dynamics, mainly due to its possible medical applications in the treatment of epilepsy [4], have also been explored for some time. A number of anticontrol of chaos methods have also been developed for this purpose [4][5][6][7][8][9]. Establishing the occurrence of deterministic chaos in epilepsy is of fundamental importance.…”

Section: Introductionmentioning

confidence: 99%

“…The chaos control experiment on epileptic hippocampal slices has been subsequently repeated by Slutzky et al [21][22][23] adopting more stringent UPOs detection method [9] along with a more robust adaptive chaos control technique [24].…”

Section: Introductionmentioning

confidence: 99%

“…However, recurrent UPOs with similar statistical significance have been reported from IBIs from stochastic neuron models as well [14]. Analysis of biological time series and EEG data for seizure like activity and its suppression have been done using tools other than UPO analysis also [2,9,25].…”

Section: Introductionmentioning

confidence: 99%

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Reliability of unstable periodic orbit based control strategies in biological systems

Mishra

Hasse

Biswal

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information from the detected UPO trajectories are vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics. Unstable periodic orbits (UPOs) analysis has now become an established tool for detecting determinism in biological systems. If the system is truly deterministic, accurate UPO characteristics can be further used for application of control or anti control strategies with potential medical application. However, accurate biological time series analysis for UPOs critically depend on the length of data set, strength of noise, type of geometry, nonstationarity etc. In this work we show that it is possible to establish determinism through UPO analysis in presence of all these factors. However, the inaccuracy in the measured UPO parameters and non-stationarity nature of biological systems mean only adaptive control strategies are useful for successful chaos control in such systems. At the same time, comparable success of adaptive control strategies on a stochastic neural network model of epileptic slices demand more stringent criteria for linking adaptive control success with determinism.

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