In this thesis we present two mathematical methods for the detection of the epileptic seizure onset zone based on the analysis of ECoG data. We give a step by step introduction to epilepsy and provide the background information for our methods. The two methods are discussed in detail followed by an application to real world data.
Epilepsy is a common neurological disease which is characterized by recurring unprovoked seizures. A common sub-type of this disease is temporal lobe epilepsy. In this special case the epileptic seizures emanate from a circumscribed area in the temporal lobe, the so called focus or seizure onset zone. A surgical removal of the seizure onset zone should render the patient seizure-free. The clinicians determine the exact area of this focus by a visual inspection of EEG or preferably ECoG data (which are recorded directly from the cortex).
The main aim of the two presented methods is to assist the clinicians in this visual analysis in order to increase the chance of a seizure-free surgical outcome.
The first presented methodology is based on the casual analysis of the ECoG data, it is also described in Flamm et al. (2012a). The causality concept we will use for this analysis is Granger causality, which is based on the predictability of the data. The particularity of the proposed method is the application of Granger causality to factor models. This model class is used because it is well-fit for the ECoG data which show co-movement.
We give an introduction to factor models and graphical models as well as an introduction to causality, which is also described in Flamm et al.
(2012b). Based on these mathematical topics we propose our methodology, called influence analysis, and thoroughly discuss its mathematical properties. Then we apply the influence analysis to real ECoG data of a patient. The seizure onset zone is found as the area comprising the most influential electrodes.
The resulting seizure onset zone matches the result of the visual analysis performed by clinical experts.
The influence analysis is the main contribution of this thesis.
The second presented methodology is more practical in nature as it is based on the segmentation of the data. The methodology is also described in Graef et al. (2012a). The ECoG data are non-stationary, that means the data's properties change over time. We partition the data into segments where the data have the same properties. For this purpose we use a measure based on the physiological frequency bands of the human brain, this measure is called band power measure. After this first step we classify each segment with respect to its epileptic character.
Segments showing rhythmic #-activity (which is characteristic for temporal lobe seizures) are classified as epileptic. Combining the segmentation and the classification we are able to derive the start of the epileptic activity per channel as the beginning of the earliest epileptic segment. The seizure onset zone is found as the area comprising the channels showing the first epileptic activity.
The application of this methodology to the aforementioned ECoG data also yields a result that correlates very well with the visual inspection of the clinicians. The band power measure is the second major contribution of this thesis.
Summing up, both presented methods show promising first results as they both detect the seizure onset zone matching the visual analysis of the clinicians.