Study level

  • Vacation research experience scheme


Topic status

We're looking for students to study this topic.

Research centre


Dr Qianqian Yang
Senior Lecturer
Division / Faculty
Faculty of Science


Mathematical models are becoming increasingly important in magnetic resonance imaging (MRI), as they provide a mechanistic approach for making a link between tissue microstructure and signals acquired using the medical imaging instrument. For example, diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. However, dMRI signal behaviour at high or ultra-high field strengths has shown increased deviation from the classically expected mono-exponential decay. Characterising the underlying mechanism of such anomalous decay can contribute to a better understanding of the interaction of proton spins with their surroundings (ie. tissue microstructure). In recent years, mathematical models based on fractional calculus have been developed and have shown encouraging potential to describe the MRI signal measurements more accurately and provide extra information on healthy and diseased brain tissue [1,2].


[1] Q. Yang, S.Puttick, Z.Bruce, B.W. Day, V.Vegh. (2020) Investigation of Changes in Anomalous Diffusion Parameters in a Mouse Model of Brain Tumour. Computational Diffusion MRI., pp. 161-172.

[2] Q. Yang, V. Vegh. (2021) Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human white matter.

Research activities

In this project, you will:

  • Study the Bloch-Torrey equation that underpins the diffusion MRI
  • utilise recently developed fractional-order diffusion models to fit brain dMRI data on a voxel by voxel basis
  • write MATLAB codes to perform the non-linear least squared parameter fitting
  • generate parameter maps that provide good white-grey matter contrast.


At the end of project, you will:

  • Write a report to document the research activities and findings
  • present your findings to peer students and academics.

Skills and experience

Familiar with differential equations and MATLAB.


You may be eligible to apply for a research scholarship.

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