PhD Studentship in Mathematics

Statistical Processing Methods for Diffusion Tensor Imaging

Diffusion tensor imaging (DTI) is an advanced magnetic resonance imaging (MRI) modality which provides a unique insight into biological tissue structure and organisation in vivo. In DTI, displacement of water molecules over time is modelled by a zero-mean trivariate Gaussian distribution with covariance matrix evolving linearly with time and determined by the diffusion tensor (DT), a 3 by 3 symmetric positive-definite matrix. At each location (voxel) of interest, the principal eigenvector of the tensor estimates the dominant fibre orientation whereas various tensor-derived diffusion anisotropy indices measure local anisotropy. Lately,  DTI has been used to study stroke and a wide range of neurological disorders such as multiple sclerosis, Alzheimer's and Parkinson's disease, and schizophrenia. White matter tractography is another promising application of DTI for investigating brain connectivity.

This project will investigate and compare various tensor processing methods for DTI. Due to the symmetric positive-definiteness of the DT, non-Euclidean statistical methods will be imposed to preserve the non-Euclidean property of diffusion tensors. This project will also explore weighted processing methods in which an arbitrary number of tensors can be interpolated or smoothed efficiently with the additional flexibility of controlling their individual contributions. The results of this project will be illustrated through synthetic examples as well as white matter tractographies of real human brains.

How to Apply

The studentship is to run for three years, subject to satisfactory progress, with an expected bursary of £1,000 p.a. To apply, email Mike Thelwall m.thelwall @ wlv.ac.uk with a maximum of 200 words stating why you would like the post and attach a recent C.V. Applicants from outside of the UK are welcome. The deadline for receipt of an email is 30 November, 2011. Candidates selected for further consideration will be sent a reply email within 48 hours of the receipt of their original email. Non-receipt of an email means that you have not been shortlisted.

Statistical Cybermetrics Research Group, University of Wolverhampton, UK

http://cybermetrics.wlv.ac.uk