Mathematical and computational models for diffusion magnetic resonance imaging

Overview

In 1985, the first image of water diffusion in the living human brain came to life. Since then, significant developments have been made and diffusion magnetic resonance imaging (dMRI) has become a pillar of modern neuroimaging.

Over the past decade, combining computational modelling and diffusion MRI has enabled researchers to link millimetre scale diffusion MRI measures with microscale tissue properties, to infer microstructure information, such as diffusion anisotropy in white matter, axon diameters, axon density, intra/extra-cellular volume fractions, and fibre orientation distribution. This microstructure information can provide significant insights on the diagnosis, progress and treatment of diseases, such as stroke, tumour, Alzheimer’s disease, and multiple sclerosis.

However, conventional modelling frameworks were developed assuming Gaussian diffusion of water molecules in the living tissue, which violates what is observed in the diffusion MRI signals. Hence, there is an urgent need for new mathematical frameworks and computational methods that can accurately characterise non-Gaussian diffusion.

Our research addresses this challenge by developing innovative mathematical models and computational techniques that establish more accurate links between diffusion MRI measurements and tissue microstructural properties. Through this work, we aim to advance the field of brain microstructure imaging and improve the ability of diffusion MRI to provide quantitative biomarkers for neuroscience research and clinical applications.

Research activities

In this VRES project, the research activities can be tailored to your background and interests and may include some of the following (but not limited to):

• studying the mathematical models (including both Gaussian and non-Gaussian diffusion models) that underpin the diffusion MRI signals
• analysing diffusion MRI data of human brain
• developing numerical simulation of diffusion MRI signals based on realistic brain tissue microstructure
• performing non-linear least squared parameter fitting of data and proposed models
• generating parameter maps that provide specific brain tissue properties, such as diffusivity, axon diameter, neurite orientation and density,  intra- and extra- cellular volume fractions.

Skills and experience

We are looking for highly motivated students who are passionate about learning and research.

You should be familiar with:

• partial differential equations
• MATLAB, Python or Julia.

Start date

2 November, 2026

End date

19 February, 2027

Location

QUT Gardens Point Campus

Keywords

• diffusion MRI
• tissue microstructure imaging
• computational modelling
• mathematical modelling
• numerical simulations
• parameter estimation

Contact

A/Prof Qianqian Yang

07 3138 2890

q.yang@qut.edu.au