766 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 27, NO. 6, JUNE 2008 A Dynamic Vector Model of Microstrip RF Resonators for High-Field MR Imaging A. Vukovic*, P. Sewell, D. McKirdy, D. Thomas, T. M. Benson, C. Christopoulos,and P. Glover Abstract—This paper describes a dynamic vector model for modelling the electromagnetic characteristics of microstrip radio-frequency (RF) resonators for high field magnetic resonance imaging (MRI). A biological tissue-equivalent load having a cir- cular cross section is assumed in the analysis. The dynamic model uses the well-known Green’s function for cylindrically stratified media to characterize all six components of the electromagnetic field excited by the microstrip lines. The accuracy of the method as a function of its parameters is assessed and the results compared with those obtained from the quasi-static method often used at low frequencies. The limits of the quasi-static assumption are investigated by comparing values for the modal propagation constant and the terminating capacitances required to tune the cavity resonance over a frequency range of 100 MHz–1 GHz. The dynamic method is further used to analyse the modal content of a microstrip head resonator. Finally, a variational approach is used to assess the impact of the intermodal coupling for the case of small perturbations in the shape and the position of the cylindrical phantom. Index Terms—Green’s functions, magnetic resonance imaging (MRI), radio-frequency (RF) resonators. I. INTRODUCTION A FUNDAMENTAL component of magnetic resonance imaging (MRI) systems is the radio-frequency (RF) resonator; a resonant device that generates and receives an oscillating transverse magnetic field within a sample being imaged. Desirable features of RF coils are high signal-to-noise ratio (SNR), high- factor, and uniformity of the transverse magnetic field across the biological sample. Demand for ever higher image resolution and SNRs are increasing the magnetic field strengths employed by MRI systems. Current clinical scanners are usually between 1 T and 3 T while research based systems have higher magnetic field strengths of 7 T and 11 T [1]–[3]. The operating frequency is directly governed by the Larmor frequency of the proton at a particular magnetic field Manuscript received April 11, 2007; revised November 5, 2007. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) under Grant GR/S80950/01. Asterisk indicates corresponding author. *A. Vukovic is with the George Green Institute for Electromagnetics Research, School of Electrical and Electronic Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K. (e-mail: Ana.Vukovic@nottingham.ac.uk). P. Sewell, D. McKirdy, D. Thomas, T. M. Benson, and C. Christopoulos are with the George Green Institute for Electromagnetics Research, School of Elec- trical and Electronic Engineering, University of Nottingham, Nottingham, NG7 2RD, U.K. P. Glover is with The Sir Peter Mansfield Magnetic Resonance Centre, School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, U.K. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMI.2007.913120 strength. Hence, to image water in tissue at 7 T a frequency of 300 MHz is used. At these frequencies, the electromagnetic wavelength in the biological sample becomes comparable to its size, resulting in so-called “dielectric resonance” effects [4] and a nonuniform transverse magnetic field. Practically this leads to inhomogeneous -fields producing—MRI images with a bright and faded regions and also significant radiation losses. Several approaches have been taken to improve the per- formance of the RF coils for higher field strengths. First, the design of RF resonators is typically moving away from low-frequency birdcage coils towards cavity-like resonators that employ microwave transmission lines such as microstrip or strip-line. This change is motivated by the fact that more uniform fields and improved, sensitivity, and -factor can be obtained [1], [6]–[8]. Second, more accurate characterization of RF resonators is being undertaken with a shift away from simple lumped element equivalent circuit models that neglect the wave-like nature of the electromagnetic fields at higher frequencies. To date, two classes of techniques have been re- ported for modelling MRI RF resonators. Full-wave numerical methods such as the finite difference time domain (FDTD) and method of lines (MoLs) techniques have been used to model microstrip and coaxial line RF coils [9], [10]. In particular, the FDTD method has received significant interest due to its ease of implementation and the opportunity for parallelization to improve run times. However, FDTD and MoL techniques both typically employ a uniform square discretization of the geometry resulting in step-like approximations of the more circularly shaped RF resonator, resonant rods, and biological load. Furthermore, the necessity to adequately model both the large and small features of the RF coil demands the use of finely graded grid which inevitably results in a computationally expensive simulation. As a number of papers have already reported that at higher frequencies optimization of the coil, in terms of its structure and excitation, will become ever more important [10], [11], it is clear that the use of slow numerical methods are not ideal simulation tools in this context. Analytical method based upon transverse electromagnetic wave (TEM) approximations in which the axial electric and magnetic field components are assumed to be of negligible importance has also been reported [12]. Although this approach has been successfully employed to simulate small microstrip RF coils at 200 and 300 MHz [12], increasing magnetic field strengths require higher operating frequencies in which case the TEM approximation becomes less valid. Furthermore, the standard analysis of MRI resonators assumes a cylindrical phantom for a human head which in centrally located in the resonator. Although this is a good first approximation for the head, small, but practical, discrepancies in the cross sectional 0278-0062/$25.00 © 2008 IEEE