Finite element method based simulation, desing, and resonant mode analysis of radio frequency birdcage coils used in magnetic resonance imaging

Abstract

Radio Frequency (RF) birdcage coils are widely used in Magnetic Resonance Imaging (MRI) since they can generate very homogeneous RF magnetic field inside the coil and have high signal-to-noise ratio (SNR). In practice, designing a birdcage coil is a time-consuming and difficult task. Calculating the capacitance value, which is necessary for the coil to resonate at the desired frequency, is the starting point of the design process. Additionally, it is also important to know the complete resonance frequency spectrum (or resonant modes) of the birdcage coil that helps the coil designers to be sure that working mode is far away from the other modes and so that tuning and matching procedures of the coil can be done without interfering with the other modes. For this purpose, several studies have been presented in the literature to calculate the capacitance value and the resonant modes of the birdcage coil. Among these studies, lumped circuit element model is the most used technique in capacitance and resonant modes calculations. However, this method heavily depends on the inductance calculations which are made under quasi-static assumptions. As a consequence of this assumption, error in the calculations increases as the frequency increases to a point at which the wavelengths are comparable with the coil dimensions. Additionally, modeling the birdcage coil in a 3D simulation environment and making electromagnetic analysis in the volume of interest is also important in terms of observing the electromagnetic field distributions inside the coil. In this thesis, we have proposed three different Finite Element Method (FEM) based simulation methods which are performed using the developed low-pass and high-pass birdcage coil models in COMSOL Multiphysics. One of these methods is the FEM based optimization method in which magnitude of the port impedance or variance of H+ is used as the objective function and the capacitance value is used as the control variable. This is a new method proposed for calculating the capacitance value of the birdcage coils. The other method is the eigenfrequency analysis which is used to determine not only the resonant modes of the birdcage coil but also the electromagnetic fields distributions inside the coil at these resonant modes. To the best of our knowledge, FEM based eigenfrequency analysis of a birdcage coil is also a new study in the field of MRI. The last method is the frequency domain analysis which is used solve for the electromagnetic fields of a birdcage coil for the specified frequency (or frequencies). One can also use this method to estimate Specific Absorption Rate (SAR) at any object inside the coil. To make these three simulation methods easily and according to the user-specified parameters, we have developed two software tools using MATLAB which have also graphical user interface (GUI). In order to compare the results of the proposed methods and the results of the methods that use lumped circuit element model with the experimental results, we have constructed two handmade birdcage coils and made measurements for different capacitance values. Then, we have compared the measured resonant modes with the calculated resonant modes; used capacitance values with the calculated capacitance values. For the worst case (in which the frequency is the highest), proposed FEM based eigenfrequency analysis method calculates the resonant modes with a maximum of 10% error; proposed FEM based optimization method calculates the necessary capacitance values with 20-25% error. Methods which use lumped circuit element model, on the other hand, calculate the resonant modes and capacitance values with 50-55% error for the worst case.