Integral Equation Approach to Modeling RF Fields in Human Body in MRI Systems for Safety

This article discusses the MR modeling of electromagnetic fields generated by the RF coil within a phantom or the human head or body, termed the scatterer, using integral equations. There are two variations in MRI modeling, which are discussed in broad outline. In the first, the scatterer is assumed to be homogeneous, and the known electric and magnetic surface currents generated by the incident RF coil fields are calculated. From these currents, it would be possible to calculate the fields in the interior even if the scatterer is inhomogeneous and average complex permittivity was used. In the second volumetric approach, the inhomogeneous dielectric scatterer is replaced by a polarizable current density, and the scattering fields are calculated in terms of the electric flux density from which the electric and magnetic fields are calculated. The weak formulation is used, and fast Fourier transform is applied to speed up the calculations. The volumetric results obtained in 7 min of a head excited by a plane wave compare very well with the finite difference time domain results which take typically a couple of hours.