title: Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients.
abstract: To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection ("focal signals") and one set of signals recorded from brain areas that were not involved at seizure onset ("nonfocal signals"). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain.
authors.affiliation: Universitat Pompeu Fabra, Department of Information and Communication Technologies, E-08018 Barcelona, Spain.
authors.forename: Ralph G
authors.initials: RG
authors.lastname: Andrzejak
authors.forename: Kaspar
authors.initials: K
authors.lastname: Schindler
authors.forename: Christian
authors.initials: C
authors.lastname: Rummel
mesh_terms: D000704:Analysis of Variance; D004569:Electroencephalography / Q000379:methods*; D004827:Epilepsy / Q000175:diagnosis*; D006801:Humans; D017711:Nonlinear Dynamics; D011336:Probability; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes