A New Kind of Permutation Entropy Used to Classify Sleep Stages from Invisible EEG Microstructure

Permutation entropy and order patterns in an EEG signal have been applied by several authors to study sleep, anesthesia, and epileptic absences. Here, we discuss a new version of permutation entropy, which is interpreted as distance to white noise. It has a scale similar to the well-known chi(2) distributions and can be supported by a statistical model. Critical values for significance are provided. Distance to white noise is used as a parameter which measures depth of sleep, where the vigilant awake state of the human EEG is interpreted as almost white noise. Classification of sleep stages from EEG data usually relies on delta waves and graphic elements, which can be seen on a macroscale of several seconds. The distance to white noise can anticipate such emerging waves before they become apparent, evaluating invisible tendencies of variations within 40 milliseconds. Data segments of 30 s of high-resolution EEG provide a reliable classification. Application to the diagnosis of sleep disorders is indicated.