Solving inverse problems in EEG-based source localization by combining parametric and non-parametric methods

C Jareteg, Master thesis, University of Gothenburg, supervisor S Jakobsson, examiner S Larsson, June 2012.

Epilepsy is a worldwide neurological disease that around 50 million people suffer from. For patients with medically intractable epilepsy resective surgery is an important alternative considered. This kind of surgery relies on localization of an epileptic source in the brain. In EEG-based source localization an ill-posed inverse problem must be solved. With a source localization methodology giving medically reasonable solutions, complicated and time-consuming invasive EEG recordings, i.e. where the scalp is opened and electrodes are put directly on the brain, can be avoided.

In this master thesis, a widely used non-parametric EEG source localization method with Tikhonov regularization has been used as basic inverse solution method. By using medical pre-knowledge, the basic non-parametric method has been extended with novel parametric EEG source localization methods. The first aim is to get a more focused source distribution by adding penalty centered at a specific point. Then the location of this point is optimized. The second aim is to constrain the direction of the epileptic source. Two solution methodologies based on these aims are constructed. Both result in a source distribution function, with support only in the grey matter cortex of the brain. These two methodologies are intended to work together as one methodology incorporating three main medical facts, i.e. grey matter restriction, constrained orientation orthogonal to the grey matter surface and restriction to a small region.

The combination of non-parametric and parametric inverse solution methods is done such that we do not need to model the epileptic source as is commonly done in parametric methods. With one of the parameters introduced we are able to vary the strength of the penalty, enabling even without source model, more and more focused solutions.

These solution methodologies have been applied to a clinical test case as well as numerically generated synthetic data. The method based on focusing by penalty gives results which are within a medically reasonable threshold for the clinical test case. The method based on constraining the direction of the source is promising but needs further development.

Photo credits: Nic McPhee