Beltrachini, L., Taylor, Z.A. and Frangi, A.F. (2015) A parametric finite element solution of the generalised Bloch-Torrey equation for arbitrary domains. Journal of Magnetic Resonance , 259. 126 -134. ISSN 1090-7807
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 represents a huge step forward for obtaining reliable results with few iterations. Comparisons with analytical solutions and real data show the flexibility and accuracy of the proposed methodology.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier Inc. All rights reserved. This is an author produced version of a paper subsequently published in Journal of Magnetic Resonance. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Arbitrary geometry; Implicit method; Microstructure; Numerical solution |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Mechanical Engineering (Sheffield) The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Jan 2016 15:11 |
Last Modified: | 21 Aug 2017 01:40 |
Published Version: | http://dx.doi.org/10.1016/j.jmr.2015.08.008 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jmr.2015.08.008 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90964 |