An external reference to enable quantitative susceptibility mapping (QSM) in absolute terms: theoretical considerations, simulations, and experimental evaluation.

OBJECTIVE: Quantitative susceptibility mapping (QSM) is a semi-quantitative method, i.e., only differences in magnetic susceptibility can be quantified. The lack of a stable internal reference hampers longitudinal and systematic comparisons among subjects. In this study, a phase-based approach, enabling the use of an external reference, is proposed. MATERIALS AND METHODS: By modeling the object geometry and analyzing the object-induced magnetic field distortion in the external reference, a relationship between the manifested phase and susceptibility was established. The proposed theoretical framework was validated using a numerical head phantom and 3 T MRI measurements, investigating five phantoms with different concentrations of gadolinium and one healthy volunteer. The derived theoretical relationship, together with accurate phase measurements, provided the absolute mean magnetic susceptibility of the object of interest. RESULTS: Excellent accuracy was demonstrated in the numerical head phantom. Encouraging, although somewhat underestimated, susceptibility results were obtained for the MRI phantom measurements. The relationship between measured and theoretical susceptibility values showed excellent correlation (r = 0.98, p = 0.004). The in vivo measurement yielded an absolute mean susceptibility of 0.02 ppm (relative to water). DISCUSSION: Feasibility and proof of concept were demonstrated, and the approach, in combination with conventional QSM, offers an alternative reference solution with potential to facilitate absolute QSM maps.