A parametric finite element solution of the generalised Bloch-Torrey equation for arbitrary domains

Journal of Magnetic Resonance
Leandro BeltrachiniAlejandro F Frangi

Abstract

Nuclear magnetic resonance (NMR) has proven of enormous value in the investigation of porous media. Its use allows to study pore size distributions, tortuosity, and permeability as a function of the relaxation time, diffusivity, and flow. This information plays an important role in plenty of applications, ranging from oil industry to medical diagnosis. A complete NMR analysis involves the solution of the Bloch-Torrey (BT) equation. However, solving this equation analytically becomes intractable for all but the simplest geometries. We present an efficient numerical framework for solving the complete BT equation in arbitrarily complex domains. In addition to the standard BT equation, the generalised BT formulation takes into account the flow and relaxation terms, allowing a better representation of the phenomena under scope. The presented framework is flexible enough to deal parametrically with any order of convergence in the spatial domain. The major advantage of such approach is to allow both faster computations and sensitivity analyses over realistic geometries. Moreover, we developed a second-order implicit scheme for the temporal discretisation with similar computational demands as the existing explicit methods. This represe...Continue Reading

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Citations

Jun 19, 2019·Physics in Medicine and Biology·Noel M Naughton, John G Georgiadis
Jun 4, 2019·Journal of Neural Engineering·Leandro Beltrachini
Mar 17, 2020·Magnetic Resonance in Chemistry : MRC·Maria Grazia Concilio
Jul 25, 2019·Science Advances·Ahmed J AllamiIlya Kuprov
Jan 15, 2019·Journal of Magnetic Resonance·Van-Dang NguyenJing-Rebecca Li
Aug 31, 2019·NeuroImage·Jing-Rebecca LiThi Minh Phuong Nguyen
Jul 2, 2021·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Farah N MushtahaAli R Khan
Jul 30, 2019··Noel NaughtonJohn Georgiadis

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