EEG source analysis using space mapping techniques

The electroencephalogram (EEG) measures potential differences, generated by electrical activity in brain tissue, between scalp electrodes. The EEG potentials can be calculated by the quasi-static Poisson equation in a certain head model. It is well known that the electrical dipole (source) which best fits the measured EEG potentials is obtained by an inverse problem. The dipole parameters are obtained by finding the global minimum of the relative residual energy (RRE). For the first time, the space mapping technique (SM technique) is used for minimizing the RRE. The SM technique aims at aligning two different simulation models: a fine model, accurate but CPU-time expensive, and a coarse model, computationally fast but less accurate than the fine one. The coarse model is a semi-analytical model, the so-called three-shell concentric sphere model. The fine model numerically solves the Poisson equation in a realistic head model. If we use the aggressive space mapping (ASM) algorithm, the errors on the dipole location are too large. The hybrid aggressive space mapping (HASM) on the other hand has better convergence properties, yielding a reduction in dipole location errors. The computational effort of HASM is greater than ASM but smaller than using direct optimization techniques.