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Advanced numerical methods for solving the forward problem in E/MEG

   Cardiff School of Physics and Astronomy

About the Project

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.

The PhD project will take place in the Cardiff University Brain Research Imaging Centre (CUBRIC), a pioneer in brain imaging research. CUBRIC recently moved to new purpose-built premises housing up to 200 researchers and a host of state-of-the-art neuroimaging equipment. This is a rare opportunity to join a successful neuroimaging centre in a phase of strong growth and to work in a vibrant and positive research environment. You can learn more about CUBRIC at: The student will also be part of the Brain Imaging Group (BIG), one of the six research groups in the School of Physics and Astronomy.


The typical academic requirement is a minimum of a 2:1 a relevant discipline.

Applicants whose first language is not English are normally expected to meet the minimum University requirements (e.g. 6.5 IELTS) (

How to apply

Applicants should apply to the Doctor of Philosophy in Physics and Astronomy.

Applicants should submit an application for postgraduate study via the Cardiff University webpages ( including:

• your academic CV

• a personal statement/covering letter

• two references, at least one of which should be academic

• Your degree certificates and transcripts to date (with certified translations if these are not in English).

In the "Research Proposal" section of your application, please specify the project title and supervisors of this project.

This project is only available to self-funded students, please can you include your funding source in the "Self-Funding" section.

Funding Notes

Please note that bench fees may be charged in addition to tuition fees for this project. This will be confirmed as part of any formal offer for this project.


L Beltrachini, “The analytical subtraction approach for solving the forward problem in EEG”, Journal of neural engineering 16 (5), 056029, 2019
L Beltrachini, “A finite element solution of the forward problem in EEG for multipolar sources”, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 27: 368-377, 2018.
L Beltrachini, “Sensitivity of the projected subtraction approach to mesh degeneracies and its impact on the forward problem in EEG”, IEEE Transactions on Biomedical Engineering 66 (1), 273-282, 2018.

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