Forbidden ordinal patterns of periictal intracranial EEG indicate deterministic dynamics in human epileptic seizures

Purpose: Epileptic seizures typically reveal a high degree of stereotypy, that is, for an individual patient they are characterized by an ordered and predictable sequence of symptoms and signs with typically little variability. Stereotypy implies that ictal neuronal dynamics might have deterministic characteristics, presumably most pronounced in the ictogenic parts of the brain, which may provide diagnostically and therapeutically important information. Therefore the goal of our study was to search for indications of determinism in periictal intracranial electroencephalography (EEG) studies recorded from patients with pharmacoresistent epilepsy. Methods: We assessed the number of forbidden ordinal patterns of 110 periictal multichannel intracranial EEG studies of 16 patients. Ordinal patterns are derived from the rank order of short sequences of consecutive EEG values. Ordinal patterns are well suited for analyzing real-world time series, for they have low sensitivity for many forms of noise and are applicable to nonstationary data. Although Gaussian random dynamics generate all possible ordinal patterns for a given sequence length, deterministic dynamics typically manifest with less random and more regular signals that miss a certain number of all the possible ordinal patterns. These missing ordinal patterns are referred to as forbidden ordinal patterns. In this study, the number of forbidden ordinal patterns n(fp) of an EEG signal was interpreted as an indication of determinism, when it was larger than the number of forbidden patterns occurring in amplitude adjusted Fourier transform surrogates. We computed n(fp) for each EEG signal in a time-resolved way by using a moving-window approach. Then we specifically investigated n(fp)(mean) denoting the average number of forbidden patterns across all EEG signals, and n(fp)(max), which represents the number of forbidden patterns occurring in the EEG signal with the largest n(fp) during the seizure-onset period. Key Findings: The average number of forbidden patterns of all EEG signals, n(fp)(mean), typically first increased and then decreased during the seizures. However, these changes were not statistically significant relative to the preseizure time period. In contrast, n(fp)(max) typically increased significantly during the first third of the seizure period and then gradually decreased toward and beyond seizure termination. In those patients who became seizure free following surgery, a larger percentage of the EEG signals containing the maximal number of forbidden patterns during the seizure-onset period tended to be recorded from within the visually identified seizure-onset zones. Significance: Our findings demonstrate a spatiotemporally limited shift of neuronal dynamics toward a more deterministic dynamic regimen, specifically pronounced during the seizure-onset period. Assessing the number of forbidden ordinal patterns of intracranial EEG provides quantitative and observer-independent information. We propose that it is at least partially complementary to classical visual EEG reading and may be diagnostically helpful to better delineate ictogenic parts of the brain.