Reference-Free PRFS MR-Thermometry Using Near-Harmonic 2-D Reconstruction of the Background Phase

Proton resonance frequency shift (PRFS) MR thermometry (MRT) is the generally preferred method for monitoring thermal ablation, typically implemented with gradient-echo (GRE) sequences. Standard PRFS MRT is based on the subtraction of a temporal reference phase map and is, therefore, intrinsically sensitive to tissue motion (including deformation) and to external perturbation of the magnetic field. Reference-free (or reference-less) PRFS MRT has been previously described by Rieke and was based on a 2-D polynomial fit performed on phase data from outside the heated region, to estimate the background phase inside the region of interest. While their approach was undeniably a fundamental progress in terms of robustness against tissue motion and magnetic perturbations, the underlying mathematical formalism requires a thick unheated border and may be subject to numerical instabilities with high order polynomials. A novel method of reference-free PRFS MRT is described here, using a physically consistent formalism, which exploits mathematical properties of the magnetic field in a homogeneous or near-homogeneous medium.