In MRI, the main magnetic field polarizes the electron cloud of a molecule, generating chemical shift for observer protons within the molecule and magnetic susceptibility inhomogeneity field for observer protons outside the molecule. The number of water protons surrounding a molecule for detecting its magnetic susceptibility is vastly greater than the number of protons within the molecule for detecting its chemical shift. However, the study of tissue magnetic susceptibility has been hindered by poor molecular specificities of hitherto used methods based on MRI signal phase and T2* contrast, which depend convolutedly on surrounding susceptibility sources. Deconvolution of the MRI signal phase can determine tissue susceptibility but is challenged by the lack of background signal and by the zeroes in the dipole kernel. Recently, physically meaningful regularizations including the Bayesian approach have been developed to enable accurate quantitative susceptibility mapping (QSM) for studying iron distribution, metabolic oxygen consumption, blood degradation, calcification, demyelination and other pathophysiological susceptibility changes, as well as contrast agent biodistribution in MRI. This paper attempts to summarize the basic physical concepts and essential algorithmic steps in QSM, to describe clinical and technical issues under active development, and to provide references, codes and testing data for readers interested in QSM.

Quantitative susceptibility mapping (QSM) opens the door for measuring tissue magnetic susceptibility properties that may be important biomarkers, and QSM is becoming an increasingly active area of scientific and clinical investigations. In practical applications, there are sources of errors for QSM including noise, phase unwrapping failures, and signal model inaccuracy. To improve the robustness of QSM quality, we propose a nonlinear data fidelity term for frequency map estimation and dipole inversion to reduce noise and effects of phase unwrapping failures, and a method for model error reduction through iterative tuning. Compared with the previous phase based linear QSM method, this nonlinear QSM method reduced salt and pepper noise or checkerboard pattern in high susceptibility regions in healthy subjects and markedly reduced artifacts in patients with intracerebral hemorrhages.

For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). Previous background removal techniques have limited effectiveness depending on the accuracy of model assumptions or information input. In this article, we report an observation that the magnetic field for a dipole outside a given region of interest (ROI) is approximately orthogonal to the magnetic field of a dipole inside the ROI. Accordingly, we propose a nonparametric background field removal technique based on projection onto dipole fields (PDF). In this PDF technique, the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space. This novel PDF background removal technique was validated on a numerical simulation and a phantom experiment and was applied in human brain imaging, demonstrating substantial improvement in background field removal compared with the commonly used high-pass filtering method.

Purpose:To apply quantitative susceptibility mapping (QSM) in the basal ganglia of patients with multiple sclerosis (MS) and relate the findings to R2* mapping with regard to the sensitivity for clinical and morphologic measures of disease severity. Materials and Methods:The local ethics committee approved this study, and all subjects gave written informed consent. Sixty-eight patients (26 with clinically isolated syndrome, 42 with relapsing-remitting MS) and 23 control subjects underwent 3-T magnetic resonance (MR) imaging. Susceptibility and R2* maps were reconstructed from the same three-dimensional multiecho spoiled gradient-echo sequence. Mean susceptibilities and R2* rates were measured in the basal ganglia and were compared between different phenotypes of the disease (clinically isolated syndrome, MS) and the control subjects by using analysis of variance, and regressing analysis was used to identify independent predictors. Results:Compared with control subjects, patients with MS and clinically isolated syndrome had increased (more paramagnetic) magnetic susceptibilities in the basal ganglia. R2* mapping proved less sensitive than QSM regarding group differences. The strongest predictor of magnetic susceptibility was age. Susceptibilities were higher with increasing neurologic deficits (r = 0.34, P , .01) and lower with normalized volumes of gray matter (r = 20.35, P , .005) and the cortex (r = 20.35, P , .005). Conclusion:QSM provides superior sensitivity over R2* mapping in the detection of MS-related tissue changes in the basal ganglia. With QSM but not with R2* mapping, changes were already observed in patients with clinically isolated syndrome, which suggests that QSM can serve as a sensitive measure at the earliest stage of the disease.q RSNA, 2013

Purpose To quantitatively map cerebral metabolic rate of oxygen (CMRO2) and oxygen extraction fraction (OEF) in human brains using quantitative susceptibility mapping (QSM) and arterial spin labeling measured cerebral blood flow (CBF) before and after caffeine vasoconstriction. Methods Using the multiecho 3D gradient echo sequence and an oral bolus of 200 mg caffeine, whole brain CMRO2 and OEF were mapped at 3mm isotropic resolution on 13 healthy subjects. The QSM based CMRO2 was compared with an R2* based CMRO2 to analyze the regional consistency within cortical gray matter (CGM) with the scaling in the R2* method set to provide same total CMRO2 as the QSM method for each subject. Results Compared to pre-caffeine, susceptibility increased (5.1±1.1ppb, p<0.01) and CBF decreased (−23.6±6.7ml/100g/min, p<0.01) at 25min post-caffeine in CGM. This corresponded to a CMRO2 of 153.0±26.4µmol/100g/min with an OEF of 33.9±9.6% and 54.5±13.2% (p<0.01) pre- and post- caffeine respectively at CGM, and a CMRO2 of 58.0±26.6µmol/100g/min at white matter. CMRO2 from both QSM and R2* based methods showed good regional consistency (p>0.05), but quantitation of R2* based CMRO2 required an additional scaling factor. Conclusion QSM can be used with perfusion measurements pre- and post- caffeine vascoconstriction to map CMRO2 and OEF.

Background Parkinson’s disease (PD) is marked pathologically by dopamine neuron loss and iron overload in the substantia nigra pars compacta. Midbrain iron content is reported to be increased in PD based on magnetic resonance imaging (MRI) R2* changes. Because quantitative susceptibility mapping is a novel MRI approach to measure iron content, we compared it with R2* for assessing midbrain changes in PD. Methods Quantitative susceptibility mapping and R2* maps were obtained from 47 PD patients and 47 healthy controls. Midbrain susceptibility and R2* values were analyzed by using both voxel-based and region-of-interest approaches in normalized space, and analyzed along with clinical data, including disease duration, Unified Parkinson’s Disease Rating Scale (UPDRS) I, II, and III sub-scores, and levodopa-equivalent daily dosage. All studies were done while PD patients were “on drug.” Results Compared with controls, PD patients showed significantly increased susceptibility values in both right (cluster size = 106 mm3) and left (164 mm3) midbrain, located ventrolateral to the red nucleus that corresponded to the substantia nigra pars compacta. Susceptibility values in this region were correlated significantly with disease duration, UPDRS II, and levodopa-equivalent daily dosage. Conversely, R2* was increased significantly only in a much smaller region (62 mm3) of the left lateral substantia nigra pars compacta and was not significantly correlated with clinical parameters. Conclusion The use of quantitative susceptibility mapping demonstrated marked nigral changes that correlated with clinical PD status more sensitively than R2*. These data suggest that quantitative susceptibility mapping may be a superior imaging biomarker to R2* for estimating brain iron levels in PD.

Purpose To investigate systematic errors in traditional quantitative susceptibility mapping (QSM) where background field removal and local field inversion (LFI) are performed sequentially, to develop a total field inversion (TFI) QSM method to reduce these errors, and to improve QSM quality in the presence of large susceptibility differences. Theory and Methods The proposed TFI is a single optimization problem which simultaneously estimates the background and local fields, preventing error propagation from background field removal to QSM. To increase the computational speed, a new preconditioner is introduced and analyzed. TFI is compared with the traditional combination of background field removal and LFI in a numerical simulation and in phantom, 5 healthy subjects and 18 patients with intracerebral hemorrhage. Results Compared with the traditional method PDF+LFI, preconditioned TFI substantially reduced error in QSM along the air-tissue boundaries in simulation, generated high-quality in vivo QSM within similar processing time, and suppressed streaking artifacts in intracerebral hemorrhage QSM. Moreover, preconditioned TFI was capable of generating QSM for the entire head including the brain, air-filled sinus, skull, and fat. Conclusion Preconditioned total field inversion improves the accuracy of QSM over the traditional method where background and local fields are separately estimated.

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility. It relies on having a high quality field map, typically acquired with a relatively long echo spacing and long final TE. Applications of QSM outside the brain require the removal of fat contributions to the total signal phase. However, current water/fat separation methods applied on typical data acquired for QSM suffer from three issues: inadequacy when using large echo spacing, over-smoothing of the field maps and high computational cost. In this paper, the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves. This method is referred as simultaneous phase unwrapping and removal of chemical shift (SPURS). The result from SPURS is then used as the initial guess for a voxel-wise iterative decomposition of water and fat with echo asymmetric and least-squares estimation (IDEAL). The estimated 3-D field maps are used to compute QSM in body regions outside of the brain, such as the liver. Experimental results show substantial improvements in field map estimation, water/fat separation and reconstructed QSM compared to two existing water/fat separation methods on 1.5T and 3T magnetic resonance human data with long echo spacing and rapid field map variation.