Plenary Talk

Fractional Calculus Models in Magnetic Resonance Imaging

November 23, 9:00-11:00 Am, Central Time 

Richard L. Magin

Distinguished Professor, AIMBE and IEEE Fellow,
Department of Bioengineering,
University of Illinois at Chicago, USA

Abstract: Fractional calculus applications in magnetic resonance imaging (MRI) are needed to capture tissue complexity.  Fractional calculus tools describe the dynamic behavior of proteins, membranes and cells observed using nuclear magnetic resonance (NMR) by incorporating power law convolution kernels into the generalized time and space derivatives appearing in the Bloch-Torrey equations of precession, relaxation and diffusion. Early studies incorporated the fractal dimensions of multi-scale materials in the non-linear growth of the mean squared displacement and assumed power-law behavior of the spectral density; suggesting stretched signal relaxation and non-Gaussian diffusion behavior. Subsequently, fractional order generalization of the Bloch-Torrey equation provided analytical solutions of fractional order equations in time and space. Currently a multifaceted approach using coarse graining, simulation, and accelerated computation is being developed to recover ‘imaging’ biomarkers of disease. This presentation will survey the principal fractional order models used to describe NMR and MRI phenomena, identifies limitations and shortcomings, and finally points to future applications of the approach.