An accurate and efficient three‐dimensional high‐order finite element methodology for the simulation of magneto‐mechanical coupling in MRI scanners

Abstract

Summary Transient magnetic fields are generated by the gradient coils in an magnetic resonance imaging (MRI) scanner and induce eddy currents in their conducting components, which lead to vibrations, imaging artefacts, noise, and the dissipation of heat. Heat dissipation can boil off the helium used to cool the super conducting magnets and, if left unchecked, will lead to a magnet quench. Understanding the mechanisms involved in the generation of these vibrations, and the heat being deposited in the cryostat, are key for a successful MRI scanner design. This requires the solution of a coupled physics magneto‐mechanical problem, which will be addressed in this work. A novel computational methodology is proposed for the accurate simulation of the magneto‐mechanical problem using a Lagrangian approach, which, with a particular choice of linearisation, leads to a staggered scheme. This is discretised by high‐order finite elements leading to accurate solutions. We demonstrate the success of our scheme by applying it to realistic MRI scanner configurations.

A regularised-adaptive Proper Generalised Decomposition implementation for coupled magneto-mechanical problems with application to MRI scanners

“…In the presence of moving components (within a computational electromagnetic domain), it is customary to establish a reference position X and a time-dependent (t ∈ [0, T ]) mapping φ that links this reference state to the current position φ(X, t). Adopting a Lagrangian viewpoint [44], the Lagrangian electromagnetic fields H 0 , E 0 and B 0 are used, which denote the magnetic field intensity, the electric field intensity and the magnetic flux density, respectively. In addition, the following considerations are made: (1) both the eddy current approximation and the constitutive laws for electromagnetics are applied in the Eulerian setting and, then, the simplified Maxwell equations are transformed to the Lagrangian description; (2) for small displacements u (although not necessarily small velocities or accelerations), Total and Updated Lagrangian descriptions coincide; (3) a vector potential formulation A is used where the gauging of the electromagnetic problem is applied to the already Lagrangian eddy current model; (4) the Cauchy stress tensor is comprised of a mechanical σ m (u) and an electromagnetic interaction Maxwell stress component σ e (A) defined in terms of B 0 .…”

“…For this problem, the user-defined parameters are shown in Table 1. I N and I F P denote the maximum number of PGD modes and fixed-point iterations, respectively; tol N and tol F P are the tolerance values used for the stopping criteria of the greedy and ADS algorithms, respectively, as defined in (45) and (44). As for the spatial domain Ω p , its discretisation is defined by the mesh size h, the number of triangular elements E Ω C p and the polynomial order p. In addition, α denotes the damping coefficient.…”

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

“…These fields excite the protons in the human body generating a signal that is used to construct an image of the body. The transient magnetic field generated by the gradient coils induces eddy currents in the conducting radiation shields, which leads to vibrations and the dissipation of heat [22,4,39]. These vibrations cause a reduction in image quality, while the dissipation of heat can cause helium boil-off and potentially result in a magnet quench 1 .…”

“…This was based on a linearised approach using an AC-DC splitting and assuming small displacements and velocities. This work was then extended in [39] to consider the general three-dimensional (3D) case and assuming small displacements but not necessarily small velocities. In [39] a new Lagrangian formulation was used, which results in an efficient staggered scheme.…”

“…Although the formulation developed in [39] results in an accurate and efficient solver, a bottleneck still arises in the design process of a new MRI configuration due to the need to solve the problem repeatedly for varying frequencies and material properties. These variations affect the system to be solved and therefore cannot be tackled with a simple factorization.…”