Evaluation of multi-channel phase reconstruction methods for quantitative susceptibility mapping on postmortem human brain

Quantitative Susceptibility Mapping (QSM) is an established Magnetic Resonance Imaging (MRI) technique with high potential in brain iron studies associated to several neurodegenerative diseases. Unlike other MRI techniques, QSM relies on phase images to estimate tissue's relative susceptibility, therefore requiring a reliable phase data. Phase images from a multi-channel acquisition should be reconstructed in a proper way. On this work it was compared the performance of combination of phase matching algorithms (MCPC3D-S and VRC) and phase combination methods based on a complex weighted sum of phases, considering the magnitude at different powers (k = 0 to 4) as the weighting factor. These reconstruction methods were applied in two datasets: a simulated brain dataset for a 4-coil array and data of 22 postmortem subjects acquired at a 7T scanner using a 32 channels coil. For the simulated dataset, differences between the ground truth and the Root Mean Squared Error (RMSE) were evaluated. For both simulated and postmortem data, the mean (MS) and standard deviation (SD) of susceptibility values of five deep gray matter regions were calculated. For the postmortem subjects, MS and SD were statistically compared across all subjects. A qualitative analysis indicated no differences between methods, except for the Adaptive approach on postmortem data, which showed intense artifacts. In the 20% noise level case, the simulated data showed increased noise in central regions. Quantitative analysis showed that both MS and SD were not statistically different when comparing $k=1$ and $k=2$ on postmortem brain images, however visual inspection showed some boundaries artifacts on $k=2$. Furthermore, the RMSE decreased (on regions near the coils) and increased (on central regions and on overall QSM) with increasing $k$. In conclusion, for reconstruction of phase images from multiple coils with no reference available, alternative methods are needed. In this study it was found that overall, the phase combination with $k=1$ is preferred over other powers of $k$.