An analytical model for the design of RF resonators for MR body imaging

A closed form, analytical solution describing the RF fields generated by an RF body coil resonator for MR imaging at 1.5 and 4.0 T is presented. This solution extends the results of earlier studies of RF penetration in the body by explicitly including the RF coil, the RF shield, and the field variation along the z axis for high-pass birdcage coils. A salient feature of this treatment is the calculation of the axial propagation constant, k(z), which determines the z dependence of the RF field. We have determined the relative power deposition in the body, the B̄₁ field homogeneity, and coil losses, which are functions of the coil-to-shield separation and body size. The relative power deposition in the body has been calculated to vary as the 1.58 power of the body radius. The calculations have also predicted that the field homogeneity in the z direction exhibits greater degradation at higher frequencies in a high-pass coil than in a low-pass coil. The model predicts an increase in coil losses by a factor of 2.8 as the coil-to-shield separation is reduced from 5 to 2 cm in a standard body resonator. Although the results for only a homogeneous cylindrical object or body are presented, the theory can be extended to a multilayered heterogeneous object of varying permittivity and conductivity.