  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.
