Using max entropy ratio of recurrence plot to measure electrocorticogram changes in epilepsy patients
Introduction
Detection of dynamical changes in complex systems is one of the most important problems in physical, medical, engineering, and economic sciences [1]. Especially in medicine, accurate detection of transitions from a normal state to an abnormal state may improve diagnosis and treatment [2], [3]. Recurrence plot, a two-dimensional graphical plot which shows the recurrences of states [4], is an important method for detecting dynamical changes [5]. It can uncover hidden periodicities in a signal in recurrence domain which are not easily noticeable [6]. The detection of recurrence domains has become increasingly important in recent years in the neurosciences [7], [8]. Except for the recurrence plot, a number of interesting methods have been proposed to detect dynamical changes during the last two decades, including, recurrence quantification analysis [9], [10], recurrence time statistics based approaches [11], [12], space–time separation plots [13], recurrence plots of dynamical systems with nontrivial recurrences [14], recurrence plot statistics [15], base scale entropy [16], and nonlinear cross prediction analysis [17]. Most of these methods are based on quantifying certain aspects of the nearest neighbors in the phase space, and thus are computationally expensive.
Graben et al. proposed a novel algorithm for detecting recurrence domains from measured or simulated time series [18]. This symbolic analysis approach was successfully used for segmentation of event-related potentials into quasi-stationary states and providing an application to human language processing [19]. Its starting point is Eckmann et al.’s recurrence plot (RP) method for visualizing Poincare’s recurrences [4]. Based on that, the authors proposed a maximum entropy ratio (MER) method, which is obtained by transforming the traditional recurrence plot to symbolic recurrence plot. The proposed method is numerically less time-consuming and advantageous especially for high-dimensional data since it simply exploits the recurrence structure of a system’s dynamics. MER is a good estimator for a symbolically encoding for its adaptability, need of only a few parameters and wide application in various complex signals. Moreover, MER-based methods can provide quantified results and facilitate statistical analysis.
In this study, we applied the MER method on multi-dimensional Electrocorticogram (ECoG) data collected from epilepsy patients, to investigate whether MER could be used to detect epileptic seizures from ECoG data. The reminder of the paper is organized as follows. In Section 2, we explain the data acquisition and the computation process of MER. In Section 3, we present the MER results for both interictal and ictal states. The paper closes with a discussion on MER’s potential usage in epilepsy studies.
Section snippets
ECoG data
In this study, ECoG data were retrospectively analyzed from the patients undergoing pre-surgical evaluation for drug-resistant temporal lobe epilepsy. Since the localization of the epileptic focus could not be accomplished by means of noninvasive EEG recordings, intracranial electrodes were chronically implanted for the purpose of identifying the focal seizure origin. Eight patients (age: 15–41, 4 male and 4 female) were chosen for dynamical analysis of their stored pre-surgical ECoG recordings
Application
Graben et al. analyzed event-related EEG data as a proof of the MER method [18]. In our study, we investigate MER’s application in the long-term resting state of ECoG data to explore whether it is able to measure the ECoG changes from the interictal state to the ictal state for epilepsy patients. For the MER analysis, similar with Graben et al. [19], we regard the observation space spanned by the instantaneous ECoG voltages , with as ECoG electrode index and the number of recording
Discussion and conclusions
This work applied maximum entropy ratio that describes complex dynamic systems in ECoG analysis. The underlining method is believed to be suitable for analyzing nonlinear systems like EEG. We tried to explore whether it can be applied in multi-channel ECoG data from epilepsy patients.
First we computed MER for interictal and ictal epochs. The transformed recurrence plot showed many related points compared with the original recurrence plot. MER had a significant change from the interictal state
Acknowledgments
This research was supported by National Natural Science Foundation of China (61025019, 61105027, and 81341042); Beijing Natural Science Foundation (4143063), and the Fundamental Research Funds for the Central Universities.
Contributions
X.L. Li and G.X. Ouyang designed the study; T. Yu collected the ECoG data; J.Q. Yan and G.X. Ouyang analyzed the data; J.Q. Yan, Y.H. Wang and G.X. Ouyang wrote the manuscript.
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