Theoretical Information

Magnetic Resonance Imagining (MRI), an application of Nuclear Magnetic Resonance (NMR), is at the forefront of non-invasive medical visualisation. Utilising the interaction between strong magnetic fields, RF energy, and particular atomic nuclei present in the visualized specimen, MRI can produce very detailed three-dimensional images. There are many efforts to push MRI to higher frequencies, more power, extreme volumes, and with greater resolution. Many researchers have used the popular Finite Difference Time Domain (FDTD) technique to do their designs, but the Method of Moments (MoM) is rapidly becoming the computational technique of choice. Especially suited to the MoM technique are the large free space regions and curved metallic surfaces and wires that are intrinsic in MRI designs. The advantages of an integral equation-based technique such as the MoM is that the discretisation is done in terms of surfaces and not volumes, and therefore free space regions need not be discretised. The MoM is also more suitable to accurately model curved surfaces and wires. No special boundary condition needs to be applied. The metallic structures are modelled as triangular patches and wires as line segments. The currents on these are calculated with the MoM solution.

For treatment of dielectric (lossy or lossless) objects the surface of multiple closed dielectric regions needs to be discretised, using again triangular elements. Applying the Surface Equivalence Principle (SEP), the equivalent electric and magnetic currents are calculated with MoM. Metallic surfaces, wires, and dielectric objects can be combined into one solution with these elements either inside, on the boundary, or external to any dielectric region.

The RF Coil

There is no theoretical restriction on the number of closed dielectric regions that can be treated with the MoM implementation in FEKO. Modelling the RF coil of the MRI system is a perfect example. The design of the RF coil is critical, since its uniform magnetic field is the determining factor in high quality images. Past solutions have used two-dimensional approximations, perfect boundary conditions, and equivalent circuits. But FEKO is well-suited to get more accurate answers than these solutions because the mutual inductances are accounted for through the currents on a meshed and discretised three-dimensional structure. It has been shown that the full wave formulation used by FEKO gives accurate predictions of the coupling, near fields, far fields, radiation patterns, current distributions, impedances, etc.

FEKO can address the complexity of the various components inherent in an MRI system. Like in a real MRI system, the RF coil can be modelled with magnet, shim coils, and gradient coils present to get extremely accurate solutions where asymmetries are accounted for. Furthermore, an arbitrary phantom can be placed inside the RF coil to predict image quality. Of course, as with any computation technique, the larger volume requires the most computing time. But FEKO reduces the volume meshing drastically because the discretisation is done on surfaces (not volumes) and therefore free space regions need not be discretised. Furthermore, FEKO has the unique hybridisation of MoM with FEM (Finite Element Method) so that inhomogeneous or electrically large dielectric bodies can be solved in an efficient and timely manner.

Figure 1: A human phantom is inside the birdcoil of the MRI system

Field cuts of the birdcage RF coil magnetic field are shown in Figures 2 and 3. Drawing circular wires and straight lines that make up the birdcage coil was trivial and can easily be adjusted in size. Capacitors were put in both the ring and rung of the birdcage coil, and their values can be readily tuned for the right resonance frequency using FEKO’s OPTFEKO.

The feed points of the birdcage RF coil were placed in the rings. Requirements on the magnetic field profile and strength determine the number and location of these feed points, and FEKO’s graphical user interface makes the feed design parameters easy to manipulate. As a first approximation, a feed point can be a wire that is a voltage source. FEKO can parameterise the location, magnitude, and phase of these feed points. When greater precision is warranted, various feeds such as BNC, coaxial, microstrip, etc can modelled, and these also can be optimised.

Figure 4 shows the admittance profile of the birdcage RF coil. Since mutual inductances were incorporated in FEKO’s full wave solution, the resonance values in frequency are accurate and complete. Note that unlike 2D approximations, equivalent circuit models, or perfect boundary conditions, resonant frequencies not from the main mode (i.e, higher order modes) are accurately predicted.

Figure 2: The magnetic field of a birdcage RF coil at the main mode (117 MHz). As is expected, uniform magnetic field (coloured green) is present inside of the birdcage, especially in the centre. Spikes in the magnetic field are near the rungs, as confirmed by various publications.

Figure 3: The magnetic field of a birdcage RF coil in Cartesian plot. The x-axis is the cylindrical radial axis of the birdcage coil.

Figure 4: The admittance profile of the birdcage RF coil. As theory predicts, the resonance frequency of the main mode appears (117 MHz). But unlike other calculations that use approximations, higher-order modes are also seen by FEKO (209 and 229 MHz).

Summary

FEKO is especially suited to simulate RF coils for MRI applications. To obtain a specific uniform magnetic field, OPTFEKO can optimise various parameters such as wire size and shape, feed design and location, and three-dimensional coil form. Calculations are accurately performed since the mutual inductances and currents are determined on the entire three-dimensional model with a full wave solution. Furthermore, large objects take less time to simulate in FEKO than other codes because it is the surface that is discretised and not the volume.

Then, with an easy graphical user interface in POSTFEKO, these results are readily viewed in a variety of formats such as contour, colour magnitude and phase, extrusion, Cartesian, etc.