Data-driven reconstruction algorithms for Magnetic Resonance Elastography

Modelling and Analytics for Medicine and Life sciences Doctoral Training Centre: PhD Scholarship

Supervisors: Marco Iglesias (School of Mathematical Sciences), Daniele Avitabile (School of Mathematical Sciences) and Deirdre McGrath (School of Medicine)

Project description: Data-driven reconstruction algorithms for Magnetic Resonance Elastography

Magnetic Resonance Elastography (MRE) (1,2) is a powerful diagnostic imaging technique that measures changes in the biomechanical properties of biological tissue caused by disease. MRE research has recently begun at the Sir Peter Mansfield Imaging Centre, University of Nottingham, with the installation of an MRE system on the Philips 3-Tesla Ingenia Magnetic Resonance Imaging (MRI) scanner. MRE works by delivering mechanical waves to the tissue, which are measured using MRI, and these wave measurements are converted into estimated biomechanical properties using specialised reconstruction algorithms.

These algorithms solve an inverse problem: starting from MR imaging data, they estimate tissue biomechanical properties, thereby allowing the differentiation of healthy and diseased tissue. The accurate identification of the disease location and boundaries is a main challenge for current reconstruction algorithms (3), which are required to assimilate a large amount of noisy MRI imaging data.

We aim to develop novel reconstruction algorithms for MRE data, using Bayesian inversion approaches (4,5). These techniques enable one to quantify how uncertainty in the data and in the modelling assumptions affect the quality of the reconstruction of tissue properties. The algorithms will be informed by and validated with data acquired at the Sir Peter Mansfield Imaging Centre.
The development of these methods has the potential to improve significantly MRE-based diagnosis, by assimilating MRI data into a general class of heterogeneous and anisotropic biomechanical models.

References
1. Muthupillai R, Lomas DJ, Rossman PJ, Greenleaf JF, Manduca A, Ehman RL. Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science (New York, NY) 1995;269(5232):1854-1857.
2. Mariappan YK, Glaser KJ, Ehman RL. Magnetic resonance elastography: a review. Clinical anatomy (New York, NY) 2010;23(5):497-511.
3 Doyley MM. Model-based elastography: a survey of approaches to the inverse elasticity problem. Physics in medicine and biology 2012;57(3):R35-73.
4. Iglesias, M, Lu Y, Stuart A, A Bayesian Level Set Method for Geometric Inverse Problems,
Interfaces and Free Boundaries 18 (2016), 181-217
5. Iglesias, M. A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems, Inverse Problems, 32 (2016) 025002
6. McGrath DM, Ravikumar N, Wilkinson ID, Frangi AF, Taylor ZA. Magnetic resonance elastography of the brain: An in silico study to determine the influence of cranial anatomy. Magnetic resonance in medicine 2016;76(2):645-662.


The MAML programme: The MAML doctoral training programme focuses on innovative modelling, simulation and data analysis to study real-world problems in medicine and biology. Maintaining a healthy society creates major challenges in areas including ageing, cancer, drug resistance, chronic disease and mental health. Addressing such challenges necessitates continuing development and implementation of a raft of new mathematical approaches and their integration with experimental and clinical science. Students will apply mathematical approaches (from areas such as dynamic modelling, informatics, network theory, scientific computation and uncertainty quantification) to research projects at the forefront of biomedical and life sciences identified through well-established collaborations with both academic and industrial partners.

MAML students will be provided with an excellent training environment within the Centre for Mathematical Medicine and Biology and collaborating departments. Students will undertake tailored training, complemented by broadening, soft-skills, wet-lab (where appropriate) and student-led activities. There will also be opportunities for training and exchanges with world-leading partners.

Summary: These 3.5 year PhD scholarships start in September 2018. Successful applicants will receive a stipend (£14,553 per annum for 2017/8) for up to 3.5 years, tuition fees and a Research Training Support Grant. Fully funded studentships are available for UK applicants. EU applicants who are able to confirm that they have been resident in the UK for a minimum of 3 years prior to the start date of the programme may be eligible for a full award, and may apply for a fees-only award otherwise

Applications: Please follow the instructions at the MAML website: http://www.nottingham.ac.uk/mathematics/maml Applicants for the MAML programme should have at least a 2:1 degree in mathematics, statistics or a similarly quantitative discipline (such as physics, engineering, or computer science).

Completed applications and references should be submitted by Wednesday 28 February 2018.


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