A Method for Accurate Calculation of B1 Fields in Three Dimensions. Effects of Shield Geometry on Field Strength and Homogeneity in the Birdcage Coil

A method for calculating B1 field strength and homogeneity In order to construct an optimal RF system, it is important as functions of radiofrequency shield geometry is presented. The to consider how shield geometry will affect the performance method requires use of three-dimensional finite-element analysis, of the RF system. It is possible to measure B1 field strength birdcage-coil theory, and antenna-array theory. Calculations were and homogeneity experimentally (2, 3) . While this may at performed for a 12-element birdcage coil (19 cm diameter, 21 cm times be more practical than performing three-dimensional length) at 125 MHz. Calculated B1 field strengths and homogene(3D) field calculations, experimental measurements of B1 ities for the coil in 25 different shields and in no shield are given. field magnitude and homogeneity of RF systems require acFor configurations where the shield is longer than the coil, both cess to machining and electronics facilities, and specialized B1 field strength and homogeneity decrease as shield diameter imaging sequences on an available MR system. Many redecreases or as shield length increases. In configurations where searchers have found field calculation to be a desirable alterthe shield is shorter than the coil and has a diameter of 25.6 cm, B1 homogeneity is greater than in an unshielded coil. B1 field native to experimental measurement (4–13) . strength was measured experimentally at 125 MHz in a birdcage Much of the reason B1 field strength and homogeneity coil of the same geometry as the model within shields of four have not been accurately calculated as functions of shield different diameters. Calculated results very closely matched expergeometry before now is due to the complexity of the probimental measurement. q 1997 Academic Press lem. Complete consideration requires both thorough representation of currents and solution of the appropriate portions of Maxwell’s equations in 3D. Two-dimensional calculaINTRODUCTION tions require much less computation than 3D calculations and have proven to be useful in a variety of coil-design In the design of radiofrequency coils and shields, the efapplications (4–6) , but they do not allow for complete, fects of RF shield geometry are little understood and often accurate simulation of shielded 3D coils. Several methods ignored. Because RF shield geometry affects both RF magof calculation have been used to determine the magnetic netic-field (B1) strength and homogeneity, it is an important fields produced by RF imaging coils in 3D (7–13) . At this factor and should be considered. A homogeneous B1 field is time, these methods either have not yet been applied successnecessary for production of good MR images (1, 2) , and fully to solving optimization problems or have shortcomings the signal-to-noise ratio available after a 907 pulse in systems that render them inadequate for thoroughly solving problems where one coil is used to both transmit and receive is directly involving shielded coils in 3D. Ochi et al. have used the proportional to the B1 field strength in the homogeneous moment method of analysis to solve for the impedance of a imaging region of the coil (1) . birdcage coil (7) . Their calculations of impedance as a funcAn RF shield serves to confine the region which is extion of frequency match experiment very well (7, 14) , and posed to RF fields produced by the coil, shield the coil the field plot they present looks reasonable (7) . They have from RF fields produced elsewhere, and permit reproducible used their method to perform calculations of B1 strength as tuning of the coil in a variety of environments. In the devela function of shield length and diameter (14) , but their opment of working MR systems, space constraints place calculations yield some counterintuitive results. They calculimitations on the size and shape of the RF shield. The shield lated that as shield diameter increases, the sensitivities of must be large enough to accompany an RF coil appropriate identical coils within shields of different lengths asymptotifor the study being done, and must fit within the magnet bore and gradient coils. cally approach different values, and the B1 strength in their