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New Mathematical Models for Longitudinal Perfusion-weighted Imaging Study of Lesion In Stroke

  • Full or part time
  • Application Deadline
    Tuesday, January 01, 2019
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

Project Description

Conventional computed tomogramphy (CT) and magnetic resonance (MR) imaging are not sufficiently sensitive to evaluate acute stroke. More commonly diffusion weighted imaging (DWI), a form of MR imaging based upon measuring the random Brownian motion of water molecules within a voxel of tissue while imposing suitable diffusion restriction to counter the non-randomness of tissues, is used to evaluate lesion evolution and to design ways of helping stroke patients. Perfusion-weighted imaging (PWI) allows us to infer how blood traverses the brain’s vasculature, aiming to obtain absolute cerebral blood flow. DWI and PWI are both useful tools -- the difference between the diffusion and perfusion abnormalities provide a measure of the ischemic penumbra or the brain tissue at risk for infarction. However, this approach poses a formidable challenge and demand due to the risk of errors in such differences giving misleading conclusions. Part of the risks stems from using the established and more standard software which employ simple mathematical models are not capable of delivering the required accuracy and sensitivity.

A recent trend in mathematical imaging is focused on the use of variational models, based on differential geometry, to replace the traditional least square models [1-3] and to deliver the high accuracy needed for biomedical studies. Amongst other benefits, this will provide a more reliable means to maximise the capability of DWI and PWI to study the human brain. These tools will provide a better mismatch map than before between perfusion-weighted and diffusion-weighted imaging in identifying tissue at risk for infarction.

The main aim of this project is exploiting this novel variational approach to create an image analysis pipeline for perfusion weighted imaging to increase our understanding of lesion evaluation and to predict clinical response to early reperfusion. The main objectives / tasks will be:

(1) familiarisation of state of arts techniques and software tools used for imaging study of lesion in stroke; this covers both maths and patient’s data from acquisition to clinics.
(2) development of advanced preprocessing models for input images, since all MR images may contain patient movement, MR slice misalignment, non-uniform noise;
(3) optimization of image registration models to allow nonlocal displacement (rather global ones as wildly used before) while restricted to physically possible displacement;
(4) validation of our image analysis pipeline for realistic patient data and models refinement.

We envisage a three-part programme for this proposal at this international setting involving two Universities. The first part of the project, to be carried out at NTHU (maximum: 12 months), will be devoted to the above task (1). This training period is crucial in clarifying the overall analysis pipeline from input images to clinical interpretations and identifying the specific problems of the current technology, especially in accuracy issues in quantitative measurements. The second part, to be done at Liverpool (maximum: 24 months), aims to develop and optimize new imaging models for image preprocessing and registration, in tasks 2-3, with both new maths and algorithms planned to devise, based on the requirements from task 1 and that set by Prof Yang. In the third and final part 3, the PhD candidate is expected to spend a maximum of 6-12 months at NTHU to test the designed analysis pipeline in a clinical setting and to further refine them according to feedback provided by clinicians and collaborators. The student will also benefit from access to a broad range of on-going imaging projects, expertise, networking activities and multidisciplinary opportunities through the EPSRC Liverpool Centre of Mathematics in Healthcare at the University of Liverpool and its strategic partners.

The work at the University of Liverpool (UoL) will be mostly focused on the design and optimization of the maths models and algorithms, though the modern imaging facilities at CPI will be accessible. The initial training and supply of images will be Prof Yang’s CCMS lab where the student will be based, connecting with the Liverpool team via regular skype meetings and exploiting the extensive expertise. During the periods at NTHU, the starting preliminary tests and final verifications in a clinical setting will be performed. The theoretical and experimental results will be fully exchanged between UoL and NTHU.


Prof Ke Chen: or Prof Gloria Yang Tel. +886-03-574-2706

Application Procedure

1) Complete the online application form:
2) State “UoL-NTHU” position for possible sources of funding and enter this project’s title.
3) Email your skypename or contact phone number to Shirley Farrell via email (or phone +44 (0)151 794 4043) for interview purposes.

This opportunity will remain open until 1 January 2019, unless a suitable candidate is found before this date. We therefore recommend applying early.

Funding Notes

Award Value: Both University of Liverpool and NTHU have agreed to waive the tuition fees for the duration of the project. Moreover, a stipend of TWD 10,000/month will be provided to cover part of the living costs.

Eligibility: Applications are invited from any home or international students with or expecting to gain a first or upper-second class BSc honours degree in Mathematical or Computational Sciences including algorithms, programming skills, or be a highly motivated student from other backgrounds, for this Liverpool-NTHU funded post. A Masters qualification (MSc) is an advantage but not essential.


[1] C Beaulieu et al. “Longitudinal magnetic resonance imaging study of perfusion and diffusion in stroke: Evolution of lesion volume and correlation with clinical outcome”, Annals of Neurology, 46(4):568-78, 1999.
[2] H W Leatham et al. “Early diffusion-weighted imaging and perfusion-weighted imaging lesion volumes forecast final infarct size in DEFUSE 2”, Stroke 44:681-5, 2013
[3] B J Kim et al. “Magnetic Resonance Imaging in Acute Ischemic Stroke Treatment”, J. Stroke, 16(3): 131-145, 2014.

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