Fractional Calculus in Magnetic Resonance

Dear Colleagues,

The applications of fractional calculus in the field of magnetic resonance are widespread and growing. In particular, we can extend the capabilities of nuclear magnetic resonance (NMR), electron spin resonance (ESR), and magnetic resonance imaging (MRI) by the generalization of the integer-order derivatives found in the governing equations (Bloch, and Bloch–Torrey equations). Solutions obtained using fractional calculus illuminate the structure and dynamics of materials at the molecular, cellular, and tissue length scales. In these situations, the space and time-fractional derivatives encode features that are not completely resolved using standard methods. As a consequence, molecular couplings, cell membrane permeability, and imaging biomarkers, for example, can be computed and displayed. These new techniques combine the specificity of fractional calculus with the non-perturbing sensitivity of magnetic resonance. The development of these methods and models requires cooperation between experts in magnetic resonance and applied mathematics; cooperation exhibited by the technical, review, and tutorial papers in this Special Issue.

The purpose of this Special Issue is to gather articles reflecting the latest developments of fractional calculus in the fields of nuclear magnetic resonance (NMR), electron spin resonance (ESR), and magnetic resonance imaging (MRI). Applications employing fractional calculus in the sub-disciplines of NMR/ESR spectroscopy, relaxation, diffusion, and MRI are encouraged.

Prof. Richard L. Magin
Dr. David Reiter
Guest Editors

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