Stochastic Qualifiers of Epileptic Brain Dynamics

Prusseit, Jens; Lehnertz, Klaus

doi:10.1103/physrevlett.98.138103

Cited by 60 publications

(32 citation statements)

References 28 publications

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“…An example for the numerical implementation procedure is included in appendix B (procedure parBinMLE ). Results for optimizing the drift and diffusion functions (13) for synthetic data obtained from sampling an Ornstein-Uhlenbeck process are listed in table III (case BIN-MLE, last row).…”

Section: Estimation At Small Time Increment and Stepwise Constantmentioning

confidence: 99%

Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Kleinhans

2012

Phys. Rev. E

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Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters. * david.kleinhans@gu.se 2

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Section: Estimation At Small Time Increment and Stepwise Constantmentioning

confidence: 99%

Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Kleinhans

2012

Phys. Rev. E

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“…Very often, however, the dynamics of the epileptic process in between seizures must be regarded as high-dimensional and nonstationary, which might prevent its detailed characterization when using these techniques. Addressing this issue, we recently [105] evaluated the merit of previously proposed data-driven analysis techniques that allow one to estimate drift and diffusion terms of a corresponding Fokker-Planck equation [106][107][108][109]. With these techniques, deterministic laws and fluctuating forces of EEG dynamics can be identified.…”

Section: Value Of Nonlinear Eeg Analysis In the Presurgical Evaluatiomentioning

confidence: 99%

Epilepsy and Nonlinear Dynamics

Lehnertz

2008

J Biol Phys

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107

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This overview summarizes findings obtained from analyzing electroencephalographic (EEG) recordings from epilepsy patients with methods from the theory of nonlinear dynamical systems. The last two decades have shown that nonlinear time series analysis techniques allow an improved characterization of epileptic brain states and help to gain deeper insights into the spatial and temporal dynamics of the epileptic process. Nonlinear EEG analyses can help to improve the evaluation of patients prior to neurosurgery, and with an unequivocal identification of precursors of seizures, they can be of great value in the development of seizure warning and prevention techniques.

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“…To our knowledge, the existing applications are limited to epileptic electrocorticograms (Lamouroux and Lehnertz, 2009;Prusseit and Lehnertz, 2007), intracellular recordings in rat auditory cortex (Deco et al, 2009), and in vitro field potential recordings in mouse hippocampus (Hindriks et al, submitted for publication). All models mentioned above however, have one-dimensional state-variables (and have no delays) and are therefore unable to display oscillatory behavior.…”

Section: Introductionmentioning

confidence: 98%