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

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: http://sites.cardiff.ac.uk/cubric/. 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.

For more information, or if there are any questions, please contact Dr Leandro Beltrachini BeltrachiniL@cardiff.ac.uk

The typical academic requirement is a minimum of a 2:1 physics and astronomy or a relevant discipline.

Applicants whose first language is not English are normally expected to meet the minimum University requirements (e.g. IELTS 6.5 Overall with 5.5 minimum in sub-scores) (https://www.cardiff.ac.uk/study/international/english-language-requirements)

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 (https://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/physics-and-astronomy) including:

• your academic CV
• Your degree certificates and transcripts to date including certified translations if these are not in English
• a personal statement/covering letter
• two references, at least one of which should be academic. Your references can be emailed by the referee to physics-admissions@cardiff.ac.uk

Please note: We are do not contact referees directly for references for each applicant due to the volume of applications we receive.

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

In the funding section, please select that you will be self-funded or include your own sponsorship or scholarship details.

Once your application is submitted, we will review it and advise you within a few weeks if you have been shortlisted for an interview.

Cardiff University and the School of Physics and Astronomy are committed to supporting and promoting equality and diversity. Our inclusive environment welcomes applications from talented people from diverse backgrounds. We strongly welcome female applicants and those from any ethnic minority group, as they are underrepresented in our School. The School of Physics & Astronomy has a Juno Practitioner accreditation that recognises good employment practice and a commitment to develop the careers of women working in science. The University is committed to ensuring that we sustain a positive working environment for all staff to flourish and achieve. As part of this commitment, the University has developed a flexible and responsive framework of procedures to support staff in managing their work and personal commitments wherever possible. Applications are welcome from individuals who wish to work part-time or full time.

Cardiff University is a signatory to the San Francisco Declaration on Research Assessment (DORA), which means that in hiring and promotion decisions we will evaluate applicants on the quality of their research, not publication metrics or the identity of the journal in which the research is published. More information is available at: Responsible research assessment - research – Cardiff University.

Applications may be submitted in Welsh, and an application submitted in Welsh will not be treated less favourably than an application submitted in English. We very much welcome applications in Welsh.

Funding Notes

This project is offered for self-funded students only, or those with their own sponsorship or scholarship award.

References

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.