A Green's function approach to local rf heating in interventional MRI

Current safety regulations for local radiofrequency (rf) heating, developed for externally positioned rf coils, may not be suitable for internal rf coils that are being increasingly used in interventional MRI. This work presents a two-step model for rf heating in an interventional MRI setting: (1) the spatial distribution of power in the sample from the rf pulse (Maxwell's equations); and (2) the transformation of that power to temperature change according to thermal conduction and tissue perfusion (tissue bioheat equation). The tissue bioheat equation is approximated as a linear, shift-invariant system in the case of local rf heating and is fully characterized by its Green's function. Expected temperature distributions are calculated by convolving (averaging) transmit coil specific absorption rate (SAR) distributions with the Green's function. When the input SAR distribution is relatively slowly varying in space, as is the case with excitation by external rf coils, the choice of averaging methods makes virtually no difference on the expected heating as measured by temperature change (deltaT). However, for highly localized SAR distributions, such as those encountered with internal coils in interventional MRI, the Green's function method predicts heating that is significantly different from the averaging method in current regulations. In our opinion, the Green's function method is a better predictor since it is based on a physiological model. The Green's function also elicits a time constant and scaling factor between SAR and deltaT that are both functions of the tissue perfusion rate. This emphasizes the critical importance of perfusion in the heating model. The assumptions made in this model are only valid for local rf heating and should not be applied to whole body heating.