title: 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 the solution of 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 whilst 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 three-dimensional echo planar imaging (3D EPI) and Wave-CAIPI (controlled aliasing in parallel imaging) trajectories for signal-to-noise ratio-efficient whole-brain imaging. Herein, we also demonstrate the multi-echo capability of the Wave-CAIPI sequence for the first time, and introduce an automated, phase-sensitive coil sensitivity estimation scheme based on a 4-s calibration acquisition. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
authors.forename: Itthi
authors.initials: I
authors.lastname: Chatnuntawech
authors.affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
authors.forename: Patrick
authors.initials: P
authors.lastname: McDaniel
authors.affiliation: A. A. Martinos Center for Biomedical Imaging, Department of Radiology; Massachusetts General Hospital, Charlestown, MA, USA.|Harvard Medical School, Boston, MA, USA.
authors.forename: Stephen F
authors.initials: SF
authors.lastname: Cauley
authors.affiliation: Harvard Medical School, Boston, MA, USA.|Fetal-Neonatal Neuroimaging & Developmental Science Center, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA.
authors.forename: Borjan A
authors.initials: BA
authors.lastname: Gagoski
authors.affiliation: Department of Neurology, Medical University of Graz, Graz, Austria.
authors.forename: Christian
authors.initials: C
authors.lastname: Langkammer
authors.affiliation: Applied Mathematics, Universidad Rey Juan Carlos, Mostoles, Madrid, Spain.
authors.forename: Adrian
authors.initials: A
authors.lastname: Martin
authors.affiliation: Harvard Medical School, Boston, MA, USA.|Fetal-Neonatal Neuroimaging & Developmental Science Center, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA.
authors.forename: P Ellen
authors.initials: PE
authors.lastname: Grant
authors.affiliation: A. A. Martinos Center for Biomedical Imaging, Department of Radiology; Massachusetts General Hospital, Charlestown, MA, USA.|Harvard Medical School, Boston, MA, USA.|Harvard-MIT Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, USA.
authors.forename: Lawrence L
authors.initials: LL
authors.lastname: Wald
authors.affiliation: A. A. Martinos Center for Biomedical Imaging, Department of Radiology; Massachusetts General Hospital, Charlestown, MA, USA.|Harvard Medical School, Boston, MA, USA.
authors.forename: Kawin
authors.initials: K
authors.lastname: Setsompop
authors.affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.|Harvard-MIT Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, USA.
authors.forename: Elfar
authors.initials: E
authors.lastname: Adalsteinsson
authors.affiliation: A. A. Martinos Center for Biomedical Imaging, Department of Radiology; Massachusetts General Hospital, Charlestown, MA, USA.|Harvard Medical School, Boston, MA, USA.
authors.forename: Berkin
authors.initials: B
authors.lastname: Bilgic
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D038524:Diffusion Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D017352:Echo-Planar Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Wave-CAIPI; alternating direction method of multipliers (ADMM); quantitative susceptibility mapping (QSM); total generalized variation (TGV); total variation (TV)