Magnetic Shielding of an MRI Magnet Using the Thin Plate Boundary Condition

Many electromagnetic simulations include ferrous geometry with extreme aspect ratios. A good example of this is modelling the magnetic shielding in a calculation of the stray field from a shielded room surrounding a representative superconducting coil set of an MRI magnet. It is an important legislative requirement that public areas are only subjected to DC field levels below a limit that is deemed to be not harmful to humans (usually 5 gauss).

However, even though active shielding is used in modern MRI magnets (superconducting coils that oppose the main field of the magnet), most installations also require a steel shield attached to the structural walls, and possibly to the floor and ceiling. The shield designer needs to ensure that it is effective, but also wishes to minimize the weight (and hence cost). The MRI magnet designer is concerned that the magnetization of the shield does not perturb the homogeneous field at the center of the magnet to such an extent that it cannot be corrected on-site using shims.

Opera-3d already has useful features, such as mesh layering and hexahedral / prism elements, which enable these structures to be meshed with high aspect ratio volume elements. But even these tools reach a limit when several plates meet – such as around windows and doors. Either the junction area becomes considerably over-meshed, increasing throughput time for simulations without improving accuracy, or the model building requires considerable effort to create “beveled” edges where the plates join.

Opera has a Thin Plate boundary condition [1], where the three dimensional volume structure of the plate is replaced with a two dimensional surface representation. Hence, any surfaces can meet without introducing extra elements or requiring special modelling.

The data requirements for the boundary condition are very simple. A material label is used to specify from which magnetic material the plate is constructed, and the thickness of the plate is given. The boundary condition can use either magnetically linear or non-linear materials.

Although the Thin Plate boundary condition is applied to a two dimensional surface, the field on the surface is multivalued. For example, if the magnetic flux enters the plate normally and then largely turns to flow in the plate, the normal component will be discontinuous across the plate.

As can be seen, using 4 cm thick mild steel shielding plates, fields exceeding the 5 gauss limit are found above and below the shielded room, at floor and ceiling level just outside the shield and near the viewing window. Consequently, the shield needs to be made more effective, ceiling and floor plates may also be needed, if the installation is in a multi-story building, and the size of the viewing window reviewed. Increasing the shield effectiveness can be accomplished by increasing thickness or by using a better quality magnetic steel. This is simply achieved with the new Thin Plate boundary condition, since, as previously mentioned, its parameters include both thickness and material characteristics.

Script to Generate Shielding Structure Automatically

Opera has produced a COMI script to build the shielding for a set of MRI coils automatically. The script is run from the Modeller. It is interactive and will ask the user to provide a set of coils as .cond file.

The script will then ask some questions about the shielding geometry such as number of walls, wall height, shielding thickness and floor position. It is possible to have different heights for each wall. Positions of each wall are then entered.

When the geometry description is completed, the script prompts the user on whether floor and ceiling plates exist, and if so where they are located. The script then builds the finite element model. A BH curve is required for the Thin Plate approximation, and its definition is read from a .bh file.

The model is then built. It is constructed entirely out of air, with the Thin Plate boundary condition applied to faces of the cells as defined by the user values.  A larger volume of air is created around the shield so that the fields will be correctly modeled. Mesh refinement is performed around the coils and where appropriate.

The COMI script finally gives several options for saving OPC, OP3 and text files storing the model and optionally running the analysis.

If required the model can be modified to add doors or windows before solving.

Reference

1] Christopher S. Biddlecombe and Christopher P. Riley, “Improvements to finite element meshing for magnetic signature simulations”, presented at MARELEC 2015 conference, Philadelphia, PA, USA, June 2015