Mathematical models have continually been developed to improve our understanding of physical and biological processes.
In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking.
We will develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods.
The tools developed will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain.
You'll be working with Professor Fawang Liu and the Fractional dynamical systems and applications team.
You'll be required to:
- conduct a thorough preliminary literature review
- undertake coursework where needed
- attend School Seminars and fractional group meeting
- develop a rigorous theoretical analysis of fractional models.
- derive, design and implement numerical methods for solving fractional differential equations
You'll be expected to write a number of journal papers depending on your study level:
PhD: Write 4-6 Q1 journal papers
Honours or Master of Philosophy: Write 1-2 Q1 journal papers
Skills and experience
We expect you to have significant experience in MATLAB or FORTRAN.
You may be able to apply for a research scholarship in our annual scholarship round.
Contact the supervisor for more information.