Direct water and fat determination in two-point Dixon imaging with flexible echo times.

PURPOSE Identifying water and fat unambiguously in multipoint Dixon imaging often requires phase correction, which can be challenging and may fail. The purpose of this work is to present a geometric interpretation of the two-point Dixon method with flexible echo times (TEs) and to investigate the conditions under which water and fat can be determined directly without phase correction. METHODS Geometrically, the equation for the magnitude of the acquired signal at a given TE represents an ellipse in the water-fat plane centered at the origin. Determining water and fat in two-point Dixon imaging thus amounts to finding the correct intercept between two ellipses from the signals at two TEs. At the right TE combinations, the physicality requirement that water and fat be non-negative can be used to select a unique water and fat solution. Systematic computer simulations were conducted to examine the ranges of the TEs for which this approach is feasible and how different noise levels impact the feasibility. Phantom and in vivo experiments on a 1.5-T whole-body MRI scanner were used to validate the computer simulations. RESULTS In simulation and phantom experiments, nearly all pixels of pure water or pure fat were reliably identified based on the physicality requirement alone for a range of practically useful TE combinations (e.g., around 3 ms/6 ms at 1.5 T) and at moderate to high SNR levels (≥ 25). At other TE combinations, finding the correct solution based on the physicality requirement alone was not feasible or became sensitive to noise. In vivo findings were in overall agreement with the simulation and phantom studies, although the percentage of pixels that were correctly determined was lower. CONCLUSIONS The problem of direct water and fat determination without phase correction can be understood geometrically. Using the physicality requirement, it is possible to identify the different TE combinations and imaging conditions under which water and fat imaging can be performed either completely without phase correction or by generating a first-pass solution that can be used to improve the processing reliability of a phase-correction based method.