64 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 49, NO. 1, JANUARY 2002 A Time-Harmonic Inverse Methodology for the Design of RF Coils in MRI Ben G. Lawrence*, Stuart Crozier, Member, IEEE, Desmond D. Yau, and David M. Doddrell Abstract—An inverse methodology is described to assist in the design of radio-frequency (RF) coils for magnetic resonance imaging (MRI) applications. The time-harmonic electromagnetic Green’s functions are used to calculate current on the coil and shield cylinders that will generate a specified internal magnetic field. Stream function techniques and the method of moments are then used to implement this theoretical current density into an RF coil. A novel asymmetric coil operating for a 4.5 T MRI machine was designed and constructed using this methodology and the results are presented. Index Terms—Electromagnetic, Green’s function, inverse tech- nique, magnetic resonance imaging (MRI), radio-frequency (RF) coil, time-harmonic. I. INTRODUCTION R ADIO-FREQUENCY (RF) coils are used in magnetic res- onance imaging as near-field antennas transmitting RF pulses and receiving the nuclear magnetic resonance (NMR) signal. In transmitter mode, the RF coil’s ideal performance is to generate a homogeneous magnetic field within a speci- fied volume usually described as the diameter of the spherical volume (DSV). This magnetic field is directed tangential to the high static magnetic field that, for cylindrical systems, is parallel to the cylinder axis (denoted as the axis) [1], [2]. This paper outlines a procedure to design an RF coil for magnetic resonance imaging machines using a time-harmonic inverse technique. Recently quasi-static inverse techniques [3]–[5] have successfully lead to RF coils operating at wavelengths con- siderably larger than device dimensions. However, as MRI technology improves, higher operating frequencies are being used such that the coil structure is an appreciable fraction of the operating wavelength [6]. This means that a full-wave time harmonic analysis becomes necessary to correctly predict current density distributions for a desired geometry and a set of target constraints. The technique begins with a specified field within a region of a cylinder (see Fig. 1). The time harmonic Green’s func- tion is then used to calculate the current density distribution on a cylinder necessary to generate such a field within the DSV. Shield currents are included to simulate the RF shield that is usually constructed from metal sheets. With the current den- Manuscript received June 25, 200; revised September 19, 2001. This work was supported by the Flux project coordinators. Asterisk indicates corresponding author. *B. G. Lawrence is with the Centre for Magnetic Resonance, Uni- versity of Queensland, St. Lucia Brisbane 4072, Australia (e-mail: ben.lawrence@cmr.uq.edu.au). S. Crozier, D. D. Yau, and D. M. Doddrell are with the Centre for Magnetic Resonance, University of Queensland, St. Lucia Brisbane 4072, Australia. Publisher Item Identifier S 0018-9294(02)00204-5. Fig. 1. The cylinders for which currents are calculated to generate a specified field within the DSV. sity known, the stream-function can be calculated and the cor- responding conductor patterns found. These patterns are used to design an RF coil that has approximately the same current den- sity distributions as the original theoretical current distribution calculated from the inverse technique. As a test of the methodology, an asymmetric shielded RF coil was designed to operate at 190 MHz with a specified diameter of 20 cm and length of 25 cm with a shield 26 cm in diameter. Designing the coil with an asymmetry furthers the work in pro- ducing a complete asymmetric system [7], [8] and is a difficult test for the methodology. The DSV was specified to be a spher- ical region with a diameter of 10 cm, offset along the axis by 2.5 cm. The coil was designed for and tested in a Bruker 4.5-T narrow-bore (40 cm) MRI machine. The resulting images indi- cate proof of the methodology. II. METHODS A. Basis Functions The current density on the surface of a cylinder with radius and of length can be described by a general Fourier series (1) 0018–9294/02$17.00 © 2002 IEEE