Advanced numerical methods for solving the forward problem in EEG

Electroencephalography (EEG) is a technique that measures the electric potential originating from the brain using electrodes located on the scalp. Its main purpose is to characterise the neural sources that give rise to such potentials. To this end, it is necessary to build approximation models of the head and the brain sources involved, which allow us to study electrical propagation through the head tissues. This is done by computing the electric potential on the sensing positions due to a predefined set of neural sources, usually referred to as the EEG forward problem (EEG-FP).

Several numerical methods exist that have been used to solve the EEG-FP in individualised head models. Within them, the finite element method (FEM) stands above the rest because of its flexibility and versatility. In recent years, the FEM has been used for solving the EEG-FP in highly detailed models of the head, providing insights on the impact that different tissue compartments may have on the corresponding potential distribution. However, such increase in the precision comes at the expense of computational resources, which may become prohibitive without highly-specialised equipment.

In this project, the student will tackle the computational constraints found in standard FEM formulations by proposing a domain decomposition (DD) framework for solving the EEG-FP. DD techniques allow us to reduce the complexity involved in solving partial differential equations (PDEs) in highly detailed models by partitioning the domain into several subdomains, to then solve the corresponding PDE in each of them individually. In this context, the student will develop a DD framework for solving the EEG-FP, and compare it to different existing approaches. The impact of the technique will be shown in real, personalised head models, highlighting the advantages over regular methodologies. The implementation in the graphical processing unit will be pursued to speed up the computing time.

Please be aware that Cardiff University reserves the right to close this vacancy early should sufficient applications be received.