Mathematical models for MRI to probe tissue microstructure

Study level


Master of Philosophy


Topic status

We're looking for students to study this topic.


Dr Qianqian Yang
Senior Research Fellow (DECRA)
Division / Faculty
Science and Engineering Faculty


Magnetic resonance imaging (MRI) can reveal exquisite details about the complex structure and function of human and animal brain tissue. However, magnetic resonance imaging signal behaviour at high or ultra-high field strengths has shown increased deviation from the classically expected mono-exponential relaxation. Characterising the underlying mechanism of anomalous relaxation and diffusion can contribute to a better understanding of the interaction of proton spins with their surroundings.

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. These fractional order models are used to fit the observed magnetisation signal decay on a pixel by pixel basis, hence provide a new contrast mechanism that has the potential to improve our understanding of microstructure in healthy and diseased brain tissue

Research activities

In this project, depending on your level of study and research interests, you will work with Dr Qianqian Yang on all or some of the following research activities:

  • applying fractional order models to diffusion MRI data to estimate the diffusion tensor and the extent of heterogeneity in different parts of the brain (measured by the fractional index);
  • developing sophisticated numerical schemes for parameter estimation and solution of fractional order models;
  • identifying new biomarkers to classify brain diseases such as brain tumour (glioblastoma), based on the fractional index values;
  • developing a mathematical model of brain tumour growth based on diffusion tensor MRI data and estimates of fractional index values from real experimental data providing insights into early onset and anisotropic progression of tumour growth.


You will:

  • develop skills in software such as Mipav and FSL for visualising and managing MRI data, MATLAB for implementing numerical schemes and Latex for mathematical typesetting;
  • receive training in scientific writing and contribute to publishing journal articles in top magnetic resonance imaging, computational mathematics and mathematical biology journals.

Skills and experience

  • Familiar with MATLAB.
  • Sound background in computational mathematics and differential equations.
  • No biology or medical imaging background is required.


You may be able to apply for a research scholarship in our annual scholarship round.

Annual scholarship round



Contact the supervisor for more information.