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Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design

S. Bagwell, Paul Ledger, Antonio Gil Orcid Logo, M. Mallett

International Journal for Numerical Methods in Engineering, Volume: 115, Issue: 2, Pages: 209 - 237

Swansea University Authors: Paul Ledger , Antonio Gil Orcid Logo

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DOI (Published version): 10.1002/nme.5802

Abstract

In this work, we simulate the coupled physics describing a Magnetic Resonance Imaging (MRI) scanner by using a higher order finite element discretisation and a Newton‐Raphson algorithm. To apply the latter, a linearisation of the non‐linear system of equations is necessary and we consider two altern...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39052
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spelling 2021-01-14T13:29:23.2228181 v2 39052 2018-03-13 Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design 068dd31af167bcda33878951b2a01e97 Paul Ledger Paul Ledger true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2018-03-13 FGSEN In this work, we simulate the coupled physics describing a Magnetic Resonance Imaging (MRI) scanner by using a higher order finite element discretisation and a Newton‐Raphson algorithm. To apply the latter, a linearisation of the non‐linear system of equations is necessary and we consider two alternative approaches. In the first, the non‐linear approach, there is no approximation from a physical standpoint and the linearisation is performed about the current solution. In the second, the linearised approach, we realise that the MRI problem can be described by small dynamic fluctuations about a dominant static solution and linearise about the latter. The linearised approach permits solutions in the frequency domain and provides a computationally efficient way to solve this challenging problem, as it allows the tangent stiffness matrix to be inverted independently of time or frequency. We focus on transient solutions to the coupled system of equations and address the following two important questions; 1) How good is the agreement between the computationally efficient linearised approach compared with the intensive non‐linear approach? and 2) Over what range of MRI operating conditions can the linearised approach be expected to provide acceptable results for outputs of interest in an industrial context for MRI scanner design? We include a set of academic and industrially relevant examples to benchmark and illustrate our approach. Journal Article International Journal for Numerical Methods in Engineering 115 2 209 237 0029-5981 Multified systems, Finite element methods, Newton methods, Time integration implicit, Linearisation, Acousto‐magneto‐mechanical coupling, MRI Scanner 13 7 2018 2018-07-13 10.1002/nme.5802 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University EPSRC, EP/R002134/1, EP/L505699/1 2021-01-14T13:29:23.2228181 2018-03-13T09:35:00.6472470 S. Bagwell 1 Paul Ledger 2 Antonio Gil 0000-0001-7753-1414 3 M. Mallett 4 0039052-19042018092548.pdf Bagwell_et_al-2017-International_Journal_for_Numerical_Methods_in_Engineeringv3.pdf 2018-04-19T09:25:48.0630000 Output 2158584 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License 4.0 (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
spellingShingle Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
Paul, Ledger
Antonio, Gil
title_short Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
title_full Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
title_fullStr Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
title_full_unstemmed Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
title_sort Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
author_id_str_mv 068dd31af167bcda33878951b2a01e97
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 068dd31af167bcda33878951b2a01e97_***_Paul, Ledger_***_
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil_***_0000-0001-7753-1414
author Paul, Ledger
Antonio, Gil
author2 S. Bagwell
Paul Ledger
Antonio Gil
M. Mallett
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 115
container_issue 2
container_start_page 209
publishDate 2018
institution Swansea University
issn 0029-5981
doi_str_mv 10.1002/nme.5802
document_store_str 1
active_str 0
description In this work, we simulate the coupled physics describing a Magnetic Resonance Imaging (MRI) scanner by using a higher order finite element discretisation and a Newton‐Raphson algorithm. To apply the latter, a linearisation of the non‐linear system of equations is necessary and we consider two alternative approaches. In the first, the non‐linear approach, there is no approximation from a physical standpoint and the linearisation is performed about the current solution. In the second, the linearised approach, we realise that the MRI problem can be described by small dynamic fluctuations about a dominant static solution and linearise about the latter. The linearised approach permits solutions in the frequency domain and provides a computationally efficient way to solve this challenging problem, as it allows the tangent stiffness matrix to be inverted independently of time or frequency. We focus on transient solutions to the coupled system of equations and address the following two important questions; 1) How good is the agreement between the computationally efficient linearised approach compared with the intensive non‐linear approach? and 2) Over what range of MRI operating conditions can the linearised approach be expected to provide acceptable results for outputs of interest in an industrial context for MRI scanner design? We include a set of academic and industrially relevant examples to benchmark and illustrate our approach.
published_date 2018-07-13T04:01:29Z
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