Exploring linearity of deep neural network trained QSM: QSMnet+

Recently, deep neural network-powered quantitative susceptibility mapping (QSM), QSMnet, successfully demonstrated to resolve the ill conditioned dipole inversion problem of QSM and generated high quality susceptibility maps. In this paper, the network, which is trained using healthy volunteers, is evaluated for patients with hemorrhage that has substantially higher susceptibility than healthy tissues in order to test the '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 by a computer-simulated lesion with an extended susceptibility range (-1.4 ppm to +1.4 ppm) and twelve hemorrhagic patients. The simulation results demonstrate improved linearity of QSMnet+ over QSMnet (root mean square error of QSMnet: 0.39 ppm vs QSMnet+: 0.03 ppm). When applied to patient data, QSMnet+ maps show superior image quality to those of conventional QSM maps. Moreover, the susceptibility values of QSMnet+ in hemorrhagic lesions better matched to those of the conventional QSM method than those of QSMnet (QSMnet+: slope = 1.04, intercept = -0.02, R2 = 0.93; QSMnet: slope = 0.78 intercept = 0.02, R2 = 0.92), consolidating the improved linearity in QSMnet+. This study demonstrates the importance of the trained data range in deep neural network powered parametric mapping. The new network can be applicable for a wide range of susceptibility quantification.