On the estimation of the worst-case implant-induced RF-heating in multi-channel MRI

The increasing use of multiple radiofrequency (RF) transmit channels in magnetic resonance imaging (MRI) systems makes it necessary to rigorously assess the risk of RF-induced heating. This risk is especially aggravated with inclusions of medical implants within the body. The worst-case RF-heating scenario is achieved when the local tissue deposition in the at-risk region (generally in the vicinity of the implant electrodes) reaches its maximum value while MRI exposure is compliant with predefined general specific absorption rate (SAR) limits or power requirements. This work first reviews the common approach to estimate the worst-case RF-induced heating in multi-channel MRI environment, based on the maximization of the ratio of two Hermitian forms by solving a generalized eigenvalue problem. It is then shown that the common approach is not rigorous and may lead to an underestimation of the worst-case RF-heating scenario when there is a large number of RF transmit channels and there exist multiple SAR or power constraints to be satisfied. Finally, this work derives a rigorous SAR-based formulation to estimate a preferable worst-case scenario, which is solved by casting a semidefinite programming relaxation of this original non-convex problem, whose solution closely approximates the true worst-case including all SAR constraints. Numerical results for 2, 4, 8, 16, and 32 RF channels in a 3T-MRI volume coil for a patient with a deep-brain stimulator under a head imaging exposure are provided as illustrative examples.