Quantitative susceptibility mapping of the spine using in-phase echoes to initialize inhomogeneous field and R2* for the nonconvex optimization problem of fat-water separation

Quantitative susceptibility mapping (QSM) of human spinal vertebrae from a multi-echo gradient-echo (GRE) sequence is challenging, because comparable amounts of fat and water in the vertebrae make it difficult to solve the nonconvex optimization problem of fat-water separation (R2*-IDEAL) for estimating the magnetic field induced by tissue susceptibility. We present an in-phase (IP) echo initialization of R2*-IDEAL for QSM in the spinal vertebrae. Ten healthy human subjects were recruited for spine MRI. A 3D multi-echo GRE sequence was implemented to acquire out-phase and IP echoes. For the IP method, the R2* and field maps estimated by separately fitting the magnitude and phase of IP echoes were used to initialize gradient search R2*-IDEAL to obtain final R2*, field, water, and fat maps, and the final field map was used to generate QSM. The IP method was compared with the existing Zero method (initializing the field to zero), VARPRO-GC (variable projection using graphcuts but still initializing the field to zero), and SPURS (simultaneous phase unwrapping and removal of chemical shift using graphcuts for initialization) on both simulation and in vivo data. The single peak fat model was also compared with the multi-peak fat model. There was no substantial difference on QSM between the single peak and multi-peak fat models, but there were marked differences among different initialization methods. The simulations demonstrated that IP provided the lowest error in the field map. Compared to Zero, VARPRO-GC and SPURS, the proposed IP method provided substantially improved spine QSM in all 10 subjects.