Exploring linearity of deep neural network trained QSM: QSMnet⁺

Recently, deep neural network-powered quantitative susceptibility mapping (QSM), QSMnet, successfully performed ill-conditioned dipole inversion in QSM and generated high-quality susceptibility maps. In this paper, the network, which was trained by healthy volunteer data, is evaluated for hemorrhagic lesions that have substantially higher susceptibility than healthy tissues in order to test “linearity” of QSMnet for susceptibility. The results show that QSMnet underestimates susceptibility in hemorrhagic lesions, revealing degraded linearity of the network for the untrained susceptibility range. To overcome this limitation, a data augmentation method is proposed to generalize the network for a wider range of susceptibility. The newly trained network, which is referred to as QSMnet⁺, is assessed in computer-simulated lesions with an extended susceptibility range (−1.4 ​ppm to +1.4 ​ppm) and also in twelve hemorrhagic patients. The simulation results demonstrate improved linearity of QSMnet⁺ over QSMnet (root mean square error of QSMnet⁺: 0.04 ​ppm vs. QSMnet: 0.36 ​ppm). When applied to patient data, QSMnet⁺ maps show less noticeable artifacts to those of conventional QSM maps. Moreover, the susceptibility values of QSMnet⁺ in hemorrhagic lesions are better matched to those of the conventional QSM method than those of QSMnet when analyzed using linear regression (QSMnet⁺: slope ​= ​1.05, intercept ​= ​−0.03, R² ​= ​0.93; QSMnet: slope ​= ​0.68, intercept ​= ​0.06, R² ​= ​0.86), consolidating improved linearity in QSMnet⁺. This study demonstrates the importance of the trained data range in deep neural network-powered parametric mapping and suggests the data augmentation approach for generalization of network. The new network can be applicable for a wide range of susceptibility quantification.