Optimization of Planar Stream Functions for Gradient Coil Design

This work presents the Fast Simulated Annealing method for the design of self-shielded gradient coils with biplanar geometry. This method is based on the stochastic optimization of parameterized stream functions, which can be modeled by a few free parameters and can be used for coil designs with different (a) size or (b) number of turns. Gradient coils designed by this method produce magnetic fields with larger homogeneous gradient volumes than those designed by previous methods. Furthermore, they present similar gradient efficiency and lower inductance than previous self-shielded gradient coils in the literature. INTRODUCTION MRI systems with transverse access, like those based on electromagnets or permanent magnets, frequently use gradient coils with biplanar geometry. In these systems, the gap between magnet pole tips is minimized in order to increase the magnetic field strength, Bo, and gradient coils need to be accommodated in restricted volumes and very close to the pole tips. For iron magnets, the proximity between gradient coils and pole tips may results in eddy currents requiring the use of self-shielded gradient sets [ 11. Recently the Fast Simulated Annealing (FSA) method for the design of self-shielded gradients coils with cylindrical geometry was presented [2]. This hybrid method combines the Simulated Annealing (SA) and the Target Field (TF) techniques to optimize standard stream functions used for gradient coil design. The main advantages of this method are its ability to enlarge the homogeneous gradient volume (HGV) and simultaneously reduce coil inductance. Furthermore, versatility for the design of very short and non-standard gradient coils is another quality of this method [3]. In this work, the FSA method for stream function optimization has been extended to the biplanar geometry. METHOD To obtain optimized gradient coils with biplanar geometry, the following procedure was applied: 1. Parameterized stream functions (SF) were used to optimize the design of gradient coils by FSA [l]. 2. Primary current densities were obtained from SF by using the continuity equation [ 11. 3. Shielding current densities were obtained from SF by using the TF shielding condition [2]. 4. To make current distribution discrete, circular and straight wires were used for the longitudinal and transverse gradients, respectively. 5 . The magnetic field produced by the coils was calculated in the region-of-interest by using the BiotSavart law. 6. To increase gradient homogeneity the stream function parameters were adjusted step-by-step by the FSA method [ 11. RESULTS Only 6 stream function parameters were necessary to obtain large homogeneous gradient volumes (HGV) for both longitudinal and transverse gradient coils. As an example, curves in Fig. 1 are contour plots showing the limits of the 95% HGV produced by typical longitudinal (solid line) and transverse (dashed line) gradient coils designed by this method. The calculated inductance of these coils is 20% lower than previous self-shielded designs. Coils designed by this method, present similar shielding and gradient efficiency as other biplanar gradient coils. 1.0, . I . I . I . I -1.01 ' ' ' ' ' ' ' 1 -1.0 -0.5 0.0 0.5 1.0 z l a CONCLUSIONS The FSA method for the design of self-shielded gradient coils with cylindrical geometry has been extended to the planar geometry in this work. Gradient coils designed by this method present low inductance, low gradient efficiency and excellent shielding efficiency. Furthermore, these kind biplanar gradient coils are torque-free and should produce low acoustic noise. Optimized stream functions can be used for easy coil design of different biplanar gradient coils, with the same aspect ratio, but with (a) larger number of turns to linearly (quadratic) increase gradient efficiency (coil inductance); or (b) shorter distances between planes to get a quadratic increase in gradient efficiency and linearly reduce coil inductance. The optimization of planar stream functions results in coils producing larger HGV than those designed by ourprevious method. A hybrid C++ Visual Basic code was developed forPC platforms running under MS Windows to perform thestream function optimization. The computing timenecessary to achieve the optimized parameter was only 3minutes, even in a standard Pentium I1 400 MHz.REFERENCES[1] Tomasi, D, MRM 45505-512, (2001).[2] Tomasi, D et al. JMR 140: 325-339 (1999).[3] Tomasi, D et al. 9" ISMRM annual meeting (2001). I acknowledge financial support form Consejo Nacional deInvestigaciones Cientificas y Tecnologicas (CONICET ) de ArgentinaFig 1.95% HGV produced by the proposed biuplanar self-shielded gradients