The diagnosis of many neurologic diseases benefits from the ability to quantitatively assess iron in the brain. Paramagnetic iron modifies the magnetic susceptibility causing magnetic field inhomogeneity in MRI. The local field can be mapped using the MR signal phase, which is discarded in a typical image reconstruction. The calculation of the susceptibility from the measured magnetic field is an ill-posed inverse problem. In this work, a bayesian regularization approach that adds spatial priors from the MR magnitude image is formulated for susceptibility imaging. Priors include background regions of known zero susceptibility and edge information from the magnitude image. There is a growing scientific and clinical interest in quantitatively mapping magnetic biomaterials by measuring their susceptibilities using MRI. Quantifying endogenous paramagnetic iron would be useful for assessing blood oxygenation (1-3) and iron overloading in organs such as the liver (4) and the heart (5). The diagnosis and monitoring of vascular and neurodegenerative diseases in the brain would benefit directly from iron quantification (6). Susceptibility quantification may allow exploiting the strong diamagnetism of calciumbased structures to characterize osteoporosis (7,8) or calcifications in the breast and brain. Furthermore, quantitative susceptibility mapping (QSM) would allow robust quantification of paramagnetic and superparamagnetic contrast agents essential to molecular and cellular imaging (9-11) and also be valuable to the characterization of cardiovascular function (12)(13)(14). Recently, an MR reporter gene enabling iron accumulation within the cell was demonstrated (15), and quantifying the induced iron would be very important for investigating in vivo molecular biology.Quantifying the susceptibility from the magnetic field is an inverse problem similar to magnetoencephalography, in which magnetic sources inside the brain must be located and quantified from limited measurements of the field outside the head (16). While quantification based on geometrical models has long been used for specific applications (1,2,4,8,14,(17)(18)(19)(20), the reconstruction of susceptibility maps in which each voxel has an unknown susceptibility is a much more complex problem. While some approaches have been theoretically proposed (6,21,22), the ill-posedness due to limited measurements was dealt with recently by using regularization approaches (8,23) or acquisition strategies (24). Here, a bayesian regularized approach is presented that introduces priors derived from the MR magnitude image. It is shown that imposing values at given locations together with seeking a solution that shares edges with the MR magnitude image is more robust that the previously proposed methods (23). The technique is validated using simulations and phantom experiments. Additionally, in vivo brain susceptibility maps are obtained, introducing a new quantitative contrast that is directly linked to the amount of iron in the brain. MATERIALS AND METHODS Susceptibility an...

The magnetic susceptibility of tissue can be determined in gradient echo MRI by deconvolving the local magnetic field with the magnetic field generated by a unit dipole. This Quantitative Susceptibility Mapping (QSM) problem is unfortunately ill-posed. By transforming the problem to the Fourier domain, the susceptibility appears to be undersampled only at points where the dipole kernel is zero, suggesting that a modest amount of additional information may be sufficient for uniquely resolving susceptibility. A Morphology Enabled Dipole Inversion (MEDI) approach is developed that exploits the structural consistency between the susceptibility map and the magnitude image reconstructed from the same gradient echo MRI. Specifically, voxels that are part of edges in the susceptibility map but not in the edges of the magnitude image are considered to be sparse. In this approach an L1 norm minimization is used to express this sparsity property. Numerical simulations and phantom experiments are performed to demonstrate the superiority of this L1 minimization approach over the previous L2 minimization method. Preliminary brain imaging results in healthy subjects and in patients with intracerebral hemorrhages illustrate that QSM is feasible in practice.