Nonlinear dipole inversion (NDI) enables robust quantitative susceptibility mapping (QSM)

Abstract

Abbreviations:• CNN: convolutional neural network • MEDI: morphology enabled dipole inversion • NDI: nonlinear dipole inversion • QSM: quantitative susceptibility mapping • SMV: spherical mean value • TGV: total generalized variation • TKD: truncated k-space division • TV: total variation • VaNDI: variational nonlinear dipole inversion • VN: variational network • w.r.t: with respect to Abstract We propose Nonlinear Dipole Inversion (NDI) for high-quality Quantitative Susceptibility Mapping (QSM) without regularization tuning, while matching the image quality of state-of-the-art reconstruction techniques. In addition to avoiding over-smoothing that these techniques often suffer from, we also obviate the need for parameter selection. NDI is flexible enough to allow for reconstruction from an arbitrary number of head orientations, and outperforms COSMOS even when using as few as 1-direction data. This is made possible by a nonlinear forward-model that uses the magnitude as an effective prior, for which we derived a simple gradient descent update rule. We synergistically combine this physics-model with a Variational Network (VN) to leverage the power of deep learning in the VaNDI algorithm. This technique adopts the simple gradient descent rule from NDI and learns the network parameters during training, hence requires no additional parameter tuning. Further, we evaluate NDI at 7T using highly accelerated Wave-CAIPI acquisitions at 0.5 mm isotropic resolution and demonstrate high-quality QSM from as few as 2-direction data.

Improved depiction of subthalamic nucleus and globus pallidus internus with optimized high‐resolution quantitative susceptibility mapping at 7 T

“…Furthermore, recent advances in deep learning have dramatically expanded its utility in various MRI studies, and QSM reconstruction could benefit from these advances. For example, in the nonlinear dipole inversion 38 technique, the network parameters can be learned during training rather than during additional parameter tuning. Another limitation is that this study was performed on young healthy adults.…”

Overview of quantitative susceptibility mapping using deep learning: Current status, challenges and opportunities

“…The idea of utilizing synthetic data was further extended by generating susceptibility distributions that mimic the spatial frequency of in-vivo brain 58 and by combining synthetic data and simulated data. 59 Other studies suggested to use variational networks 60,61 and generative adversarial networks 62 for dipole inversion. map (gold standard QSM map using multiple orientation data), two different deep learning-based QSM maps (QSMnet + trained using in-vivo and simulated data, and DeepQSM trained using synthetic data; single orientation field map is used as input for both methods), and three different conventional QSM maps (TKD, iLSQR, and MEDI; single orientation field map is used as input) are shown.…”

SEPIA - SuscEptibility mapping PIpeline tool for phAse images

“…Another focus will be to explore the possibility to incorporate processing methods that are not developed in MATLAB. Emerging techniques using deep learning have already shown very promising results with further improvement in QSM artefact reduction (Bollmann et al, 2019;Chen et al, 2019;Jung et al, 2020;Polak et al, 2020;Wei et al, 2019;Yoon et al, 2018;Zhang et al, 2020). As the implementations of these methods are primarily in Python, while there are rich resources already available in MATLAB and supported in SEPIA to perform tasks such as phase unwrapping and background field removal, it would be valuable for SEPIA to connect the two.…”

“…SEPIA is a QSM processing pipeline tool developed in MATLAB providing with both graphical and command-based operations that allows easy access to various processing algorithms in a unified platform, both for less-experienced users and advanced researchers. et al, 2007;Bilgic et al, 2014a;Li et al, 2011;Polak et al, 2020;Schweser et al, 2011;Sun and Wilman, 2014;Wharton et al, 2010).…”

“…This task can be done on k-space or image space and a variety of methods is available in the QSM panel: (1) a thresholded k-space method (Shmueli et al, 2009;Wharton et al, 2010), (2) a closed-form solution with an L2-regularisation method (Bilgic et al, 2014a), (3) an iterative LSQR approach (Li et al, 2011), (4) Star-QSM (Wei et al, 2017(Wei et al, , 2016(Wei et al, , 2015, (5) MEDI+0 (J. Liu et al, 2011bLiu et al, , 2018, (6) FANSI with the weak-harmonic regularisation (Bilgic et al, 2015(Bilgic et al, , 2014bMilovic et al, 2019Milovic et al, , 2018 and 7a non-linear dipole inversion (NDI) method (Polak et al, 2020). Some algorithms utilise prior information such as magnitude images to constraint the resulting susceptibility map.…”