Estimating and detecting slow wave events in EEG

Slow-wave activity (SWA) is an electroencephalogram (EEG) pattern commonly occurring during anesthesia and deep sleep, and is hence a candidate biomarker to quantify such states and understand their connection to related phenotypes. SWA consists of individual slow waves (ISWs), high-amplitude deflections lasting for approximately 0.5 to 1 second, and occurring quasi-periodically. This latter fact poses a challenge for conventional power spectral density EEG analysis methods that perform best when there is persistent oscillatory activity. In this brief paper, we explore a time-domain detection framework for identifying and quantifying ISWs as a metric for SWA. Our method operates by quantifying the extent to which an EEG signal conforms to a canonical ISW morphology. To do this, we formulate a given univariate EEG signal in two dimensions by means of time-delay embedding. Candidate ISWs are defined as waveform segments between every two zero crossings. In the delay embedded space (DES) we define an admissible region whose traversal by a candidate wave is defined as a slow-wave occurrence. The result of this detection procedure is a binary time series indicating the occurrence of ISWs as a function of time. Once ISWs are detected, we apply a state-space estimation technique based on Kalman filtering to convert this time series into an estimate of the probability of ISW occurrence, which we term the SWA probability. The latter is posed as an instantaneous measure of SWA. We apply this method to EEG data from general anesthesia and deep sleep, establishing that it detects and tracks elevated SWA in both cases.