Kalman filtering for EEG source localization : Applying standardized low-resolution brain electromagnetic tomography weighting to Kalman filtering

Abstract

Electroencephalography source localization can be modeled as an inverse problem. That is, find a brain current distribution that describes the electroencephalography measurement data. The inverse problem is an ill-posed problem, which means that there are an infinite amount of solutions and the solution is unstable. Regularization or prior knowledge is needed to find a decent solution. We implement Kalman filtering and introduce a new method, temporal sLORETA weighting to the Kalman filtering. Kalman filtering provides an optimal state estimation for a dynamic system. Introducing the temporal aspect to the system, we expect the source localization to improve.

Implementation is done using Zeffiro Interface. It is a brain imaging toolbox for FEM-based forward and inverse calculation. Simulated electroencephalography data is provided by Zeffiro. We compare Kalman filtering, Kalman sLORETA filtering and sLORETA method together. Somatosensory and slow auditory evoked potentials are simulated using a dipole model. Part of the somatosensory evoked potential dipole configuration is used to test model noise durability. Model noise performance is tested by reconstructing data, where has been added background noise or amplitude noise. Somatosensory evoked potential and slow auditory evoked potential reconstructions are evaluated with brain area activity plots and reconstruction visualization.

Based on the numerical simulations in the thesis, the Kalman sLORETA method finds deep and cortical activity even with high noise levels. Kalman filtering without weighting has difficulty finding deep activity, which means that it is unusable on the brainstem and thalamus reconstruction. On somatosensory evoked potential simulation, we find that Kalman sLORETA can localize the deeper sources. It provides weaker but very local reconstruction at the surface level. When compared to the sLORETA method, Kalman sLORETA provides very competitive results on SEP reconstruction. Reconstructing auditory evoked potentials creates challenges to the temporal model, where dipole activations vary from side to side. Kalman filtering is usable because of the lack of deep sources. Again The Kalman sLORETA filtering provided a very localized reconstruction, but the temporal model causes some artifacts from the previous time steps.

Based on this work, the Kalman sLORETA filter provides a new and comparable method for normalized source localization, where brain activity can be reconstructed at any depth. The method is a straightforward mathematical extension of the traditional sLORETA normalization. The method is simple in operation and improves modeling accuracy compared to traditional standardization. The size of the source space and the calculation time are significant limitations in terms of practical implementation. Optimization of computational efficiency and application of the method in experimental source localization offer opportunities for future research.