Epilepsy is a neurological disorder marked by sudden recurrent episodes of sensory disturbance, loss of consciousness, or convulsions, associated with abnormal electrical activity in the brain. Approximately one third of epilepsy patients do not respond to antiepileptic drug treatment and have to revert to surgical removal of the tissues generating seizures in the patient’s brain. Post-operative seizure freedom largely depends the accurate localization and delineation of the seizure-generating sites. Seizure localization is typically based on visual inspection by epileptologists of electroencephalographic (EEG) signals recorded at multiple sites on the scalp or brain of an epilepsy patient. Automated statistical algorithms will improve the chance of surgical success for patients without direct access to epileptologists. Due to the level of noise present in epileptic scalp EEGs, computational algorithms for seizure localization need to stay robust under
amplitude and frequency disturbances. Building on elements of computational topology, we advance a spectral permutation test for comparing single-trial epileptic EEG signals via their topological features in the time domain. We also propose performance criteria via topological invariance to ensure that the exploratory framework stays robust under non-topological changes in signals. Simulation studies and a multichannel data application demonstrate the potential utility oftopological features in seizure localization and beyond. |