Fractional dynamic models for MRI to probe tissue microstructure

Project dates: 01/01/2010 - Ongoing

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 herein will be used to generate new magnetic resonance image-based maps to convey information on tissue microstructure changes in the human brain.

 


Funding / Grants

  • ARC DP190101889 (2019 - 2022)

Chief Investigators

Team

Other Team Members

Viktor  VeghMagin Richard

Partners

Publications

  • S. Qin, F. Liu* and Ian Turner (2018) A two-dimensional multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements. Communications in Nonlinear Science and Numerical Simulation, 56, pp.270-286.
  • S. Qin, F. Liu*, I. Turner, V. Vegh, Q. Yu and Q. Yang (2017) Multi-term time-fractional Bloch equations and application in magnetic resonance imaging. Journal of Computational and Applied Mathematics, .
  • S. Qin, F. Liu*, I. Turner, Q. Yang and Q. Yu (2017) Modelling anomalous diffusion using fractional Bloch-Torrey equations on two-dimensional approximate irregular domains. Computers and Mathematics with Applications, .
  • Q. Yu, , F. Liu*, I. Turner and K. Burrage (2014) Numerical simulation of the fractional Bloch equations. Journal of Computational and Applied Mathematics, .
  • J. Song, Q. Yu,F. Liu*, and I. Turner (2014) A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation. Numerical Algorithms, .
  • , , , & (2013) Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1990), pp. 1-18.
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  • , , , & (2013) Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D. Open Physics, 11(6), pp. 646-665.
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  • , , , , & Vegh, V. (2012) The use of a Riesz fractional differential-based approach for texture enhancement in image processing. In Turner, Ian (Chair) (Ed.) The 16th Biennial Computational Techniques and Applications Conference, 23 - 26 September, 2012, Brisbane, Queensland.
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  • , , , & (2012) A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D. Applied Mathematics and Computation, 219(8), pp. 4082-4095.
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