Rogue bioelectrical waves in the brain: the Hurst exponent as a potential measure for presurgical mapping in epilepsy.

Objective. Brain electromagnetic activity in patients with epilepsy is characterized by abnormal high-amplitude transient events (spikes) and abnormal patterns of synchronization of brain rhythms that accompany epileptic seizures. With the aim of improving methods for identifying epileptogenic sources in magnetoencephalographic (MEG) recordings of brain data, we applied methods previously used in the study of oceanic 'rogue waves' and other freak events in complex systems. Approach. For data from three patients who were awaiting surgical treatment for epilepsy, we used a beamformer source model to produce volumetric maps showing areas with a high proportion of spikes that could be classified as 'rogue waves', and areas with high Hurst exponent (HE). The HE describes the extent to which a system is exhibiting persistent behavior, may predict the likelihood of freak events. These measures were compared with the more standard measure of kurtosis, which has been shown to be a reliable method for localizing interictal spikes. Main results. There was partial concordance between the three different volumetric maps indicating that each measure provides different information about the underlying brain data. The HE, when combined with a simple connectivity analysis based on phase slope index (PSI), was able to identify the probable epileptogenic zone in all three patients, despite very different patterns of abnormal activity. The differences between distributions of high HE and high kurtosis values indicates that while spikes are propagated through cortex from the epileptogenic zone, the persistent dynamical conditions under which the spikes are generated may not be propagated in a similar way. Finally, the patterns of persistent activity, indicating a departure from 'healthy criticality' in brain networks may explain the wide range of social and cognitive impairments that are seen in epilepsy patients. Significance. The HE is a potentially useful addition to the clinician's battery of measures which may be used convergently to guide surgical intervention.