Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. 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 mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. 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. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Predicting strength of porous materials. This project aims to develop a predictive theory of strength for unflawed, low-ductile porous materials – an unsolved problem in computational solid mechanics. Three-dimensional printing of lightweight, porous materials is used in industry, medicine and science. The project will develop the theory and conduct experiments on porous metallic and polymeric samples made using additive manufacturing, which require understanding and optimisation of the building ....Predicting strength of porous materials. This project aims to develop a predictive theory of strength for unflawed, low-ductile porous materials – an unsolved problem in computational solid mechanics. Three-dimensional printing of lightweight, porous materials is used in industry, medicine and science. The project will develop the theory and conduct experiments on porous metallic and polymeric samples made using additive manufacturing, which require understanding and optimisation of the building of fine scale features. Understanding strength should improve design of stronger materials, by using and extending the capabilities of three-dimensional printing. These advances will further provide a much-needed basis for a fundamental understanding of fracture in other porous materials important to society such as concrete, rocks, porous ceramics and bone implants.Read moreRead less