Single‐step quantitative susceptibility mapping with variational penalties

Abstract

Quantitative Susceptibility Mapping (QSM) estimates the underlying tissue magnetic susceptibility from the gradient echo (GRE) phase signal through background phase removal and dipole inversion steps. Each of these steps typically requires solving an ill-posed inverse problem and thus necessitates additional regularization. Recently developed single-step QSM algorithms directly relate the unprocessed GRE phase to the unknown susceptibility distribution, thereby requiring the solution of a single inverse problem. In this work, we show that such a holistic approach provides susceptibility estimation with artifact mitigation and develop efficient algorithms that involve simple analytical solutions for all of the optimization steps. Our methods employ Total Variation (TV) and Total Generalized Variation (TGV) to jointly perform the background removal and dipole inversion in a single step. Using multiple spherical mean value (SMV) kernels of varying radii permits high fidelity background removal while retaining the phase information in the cortex. Using numerical simulations, we demonstrate that the proposed single-step methods reduce the reconstruction error by up to 66% relative to the multi-step methods that involve SMV background filtering with the same number of SMV kernels, followed by TV- or TGV-regularized dipole inversion. In vivo single-step experiments demonstrate a dramatic reduction in dipole streaking artifacts and improved homogeneity of image contrast. These acquisitions employ the rapid 3D-EPI and the Wave-CAIPI trajectories for SNR-efficient whole-brain imaging. Herein, we also demonstrate the Multi-Echo capability of Wave-CAIPI sequence for the first time, and introduce an automated, phase-sensitive coil sensitivity estimation scheme based on a 4-second calibration acquisition.

Simultaneous Time Interleaved MultiSlice (STIMS) for Rapid Susceptibility Weighted acquisition

“…24 channels were selected to ensure that the RMSE (root-mean-squared error) due to compression remained below 1% for the low-resolution calibration data. At 3T, the dominant channel in SVD compression acts as a virtual body coil with smooth phase, allowing high quality coil combination without phase singularities (Chatnuntawech et al, 2016). While SVD compression is a heuristic approach to coil combination, it performs similarly as the Roemer combination (Roemer et al, 1990) that uses an actual body coil acquisition (at 3T, less than 3% difference between virtual- and actual-body coil reference (Bilgic et al, 2016b)).…”

Model‐based iterative reconstruction for single‐shot EPI at 7T

“…In this study, although the standard coil sensitivity estimation provided singularity‐free phase images at 7T equipped with a 32‐channel coil, it may not be guaranteed to work with different coil geometries or at even higher field. To address this challenge, more advanced methods could be applied, for example, 1) birdcage mode reception as reference body coil, if this is a transceive array ; or 2) block coil compression . Second, successful application also depends on the proper selection of regularization parameter (λ) that controls the degree of smoothness imposed on the reconstruction.…”

“…In the absence of a body coil, the eigenvalue‐based coil estimations are usually used to address this problem. In this work, we applied the method introduced in , which employs a virtual body coil concept . The reference channel that can replace the body coil is obtained by applying singular value decomposition (SVD) coil compression.…”

On the sensitivity of quantitative susceptibility mapping for measuring trabecular bone density

“…The most common regularizer used in QSM is total variation (TV), in combinations with or without morphlogical edges weightings and evaluated with the ℓ 1 or ℓ 2 norm . TV promotes piece‐wise constant susceptibility distributions in the QSM reconstructions, whereas the recently proposed total generalized variation (TGV) allows also for more linear susceptibility variations . The question of which regularization scheme is best for the MRI application and clinical question at hand is still subject of ongoing research across body regions and applications.…”

“…40,41 TV promotes piece-wise constant susceptibility distributions in the QSM reconstructions, whereas the recently proposed total generalized variation (TGV) allows also for more linear susceptibility variations. 42,43 The question of which regularization scheme is best for the MRI application and clinical question at hand is still subject of ongoing research 44 across body regions and applications. The purpose of the present study is to develop a methodology for simultaneous R * 2 -mapping and QSM of trabecularized bone marrow and to assess the sensitivity of QSM for measuring trabecular bone density using both numerical simulations and in vivo measurements.…”