Analysis of Wave Behavior in Lossy Dielectric Samples at High Field Qing X. Yang, 1 * Jinghua Wang, 1 Xiaoliang Zhang, 2 Christopher M. Collins, 1 Michael B. Smith, 1 Haiying Liu, 2 Xiao-Hong Zhu, 2 J. Thomas Vaughan, 1 Kamil Ugurbil, 2 and Wei Chen 2 Radiofrequency (RF) ﬁeld wave behavior and associated non- uniform image intensity at high magnetic ﬁeld strengths are examined experimentally and numerically. The RF ﬁeld pro- duced by a 10-cm-diameter surface coil at 300 MHz is evaluated in a 16-cm-diameter spherical phantom with variable salinity, and in the human head. Temporal progression of the RF ﬁeld indicates that the standing wave and associated dielectric res- onance occurring in a pure water phantom near 300 MHz is greatly dampened in the human head due to the strong decay of the electromagnetic wave. The characteristic image intensity distribution in the human head is the result of spatial phase distribution and amplitude modulation by the interference of the RF traveling waves determined by a given sample-coil conﬁg- uration. The numerical calculation method is validated with experimental results. The general behavior of the RF ﬁeld with respect to the average brain electrical properties in a frequency range of 42–350 MHz is also analyzed. Magn Reson Med 47: 982–989, 2002. © 2002 Wiley-Liss, Inc. Key words: calculations; B 1 ; high ﬁeld; MRI; radiofrequency Enhancements in signal-to-noise ratio (SNR) and T * 2 con- trast arising from high static magnetic ﬁeld strengths are desirable for in vivo MR applications. Thus, the number of high-ﬁeld human MRI systems has increased rapidly in recent years (1–10). The advent of high-ﬁeld human imag- ing systems introduces new challenges in radiofrequency (RF) engineering (11,12). Because at high frequencies the wavelength of the RF ﬁeld is comparable to or less than that of the dimension of the human body, the RF magnetic ﬁeld (B 1 ) inside a sample exhibits prominent wave behav- ior (13–16). Additionally, the homogeneity of the B 1 ﬁeld and source currents in the RF coil are strongly perturbed by sample loading (17–19). The B 1 ﬁeld distribution inside a sample is important for both speciﬁc absorption rate (SAR) assessment and RF coil engineering at high fre- quency. However, mathematical treatment of the RF ﬁeld in such systems can be extremely complicated because 1) the quasi-static approximations are no longer valid, and Max- well’s wave equation must be employed; and 2) the geom- etry of the human body is irregular, and electromagnetic properties of tissues are heterogeneous. Thus, computer numerical calculation becomes an effective and indispens- able tool for studying interactions of the RF ﬁeld with the human body at high ﬁeld (20 –24). Associated with the RF ﬁeld wave behavior, the distributions of the B 1 ﬁeld and its circularly polarized components B + and B – , which are directly responsible for the MR image intensity distribu- tion, become distinctively different from one another. Con- sequently, the relationship of RF ﬁeld polarization to coil conﬁguration and sample electric properties needs to be analyzed in order to understand the resultant image inten- sity distribution. Computer modeling provides an effective way to study this problem, and may provide insight into complex RF ﬁeld wave behavior and its dependence on the electrical properties of the sample. In this report, we present a study speciﬁcally devised to analyze high-fre- quency wave behavior of the RF ﬁeld with the aid of numerical calculation and parallel experimental measure- ments. METHODS The study was carried out using water and saline phan- toms with a 10-cm-diameter surface coil made from copper foil (Fig. 1). The phantoms consisted of 16-cm-diameter spherical bottles ﬁlled with either deionized water or sa- line solution. The water phantom exhibits a strong, two- lobe dielectric resonance at approximately the Larmor fre- quency. Conductivity () of the phantom was adjusted by changing the saline concentration. Computer models of the experimental phantom were generated on a rectilinear grid with 2-mm resolution in each dimension. The region for calculation of the phantom model was deﬁned as a 34  34  24 cm rectangular space in the x, y, and z directions. The sample was assigned a relative electric permittivity ( r ) of 78, and conductivities () of 0.0, 0.26, 0.67, and 1.9 S/m corresponding to 0.0, 20, 50, and 150 mM salinity, respectively. The conductivity value 0.67 S/m is hereafter referred to as the average brain tissue conductivity, since it is equal to the averaged value of the conductivity of gray and white matter at 300 MHz. The conductivity of deionized water at 300 MHz is insigniﬁ- cant (0.002 S/m) and is considered to be zero in the cal- culations (25). In the computer model the coil was driven with four voltage sources with identical magnitude and phase. The voltage sources were spaced evenly about the coil. In vivo experimental imaging and computer modeling were also performed with a human head. The 3D head model was created using images from the National Library of Medicine’s Visual Human Project in a space of 62  1 Center for NMR Research, Department of Radiology, Pennsylvania State University College of Medicine, Hershey, Pennsylvania. 2 Center for MR Research, Department of Radiology, School of Medicine, University of Minnesota, Minneapolis, Minnesota. Grant sponsor: Whitaker Foundation; Grant number: RG-99-0157; Grant sponsor: NIH; Grant numbers: NS38070; NS39043; P41 RR08079; Grant sponsors: Keck Foundation; National Foundation for Functional Brain Imag- ing; U.S. Department of Energy. *Correspondence to: Qing X. Yang, Center for NMR Research, NMR/MRI Building, Department of Radiology H066, Pennsylvania State University Col- lege of Medicine, 500 University Drive, Hershey, PA 17033. E-mail: qyang@psu.edu Received 18 April 2001; revised 3 January 2002; accepted 3 January 2002. Magnetic Resonance in Medicine 47:982–989 (2002) DOI 10.1002/mrm.10137 © 2002 Wiley-Liss, Inc. 982