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

Bagwell, S.; Ledger, P.D.; Gil, A.J.; Mallett, M.

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 nonlinear system of equations is necessary, and we consider two alternative approaches. In the first approach, ie, the nonlinear approach, there is no approximation from a physical standpoint, and the linearisation is performed about the current solution. In the second approach, ie, 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: (i) how good is the agreement between the computationally efficient linearised approach compared with the intensive nonlinear approach and (ii) 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.

Citation

Bagwell, S., Ledger, P., Gil, A., & Mallett, M. (2018). Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design: Transient nonlinear acousto-magneto-mechanical coupling in MRI. International Journal for Numerical Methods in Engineering, 115(2), 209-237. https://doi.org/10.1002/nme.5802

• Journal Article Type: Article
• Acceptance Date: Mar 9, 2018
• Online Publication Date: Apr 17, 2018
• Publication Date: Jul 13, 2018
• Deposit Date: Jun 12, 2023
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 115
• Issue: 2
• Pages: 209-237
• DOI: https://doi.org/10.1002/nme.5802
• Keywords: Applied Mathematics; General Engineering; Numerical Analysis