An improved sub-voxel QSM for susceptibility source separation

Conventional quantitative susceptibility mapping (QSM) reconstruction methods only provide voxel-averaged susceptibility value. We proposed a comprehensive complex signal model that describes the relationship between the 3D GRE signal and the contributions of opposing susceptibility to the frequency shift and $R₂^*$ relaxation. We used an iterative data fitting scheme to alternatively determine the sub-voxel susceptibilities and the voxel-wise proportionality coefficient between $$R₂'$ and absolute susceptibility. Our experiments on in-vivo human brain data compared with histological staining images demonstrate that the proposed method provides more accurate results for quantifying brain iron and myelin than previous QSM separation methods.