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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.

Magnetic susceptibility varies among brain structures and provides insights into the chemical and molecular composition of brain tissues. However, the determination of an arbitrary susceptibility distribution from the measured MR signal phase is a challenging, ill-conditioned inverse problem. Although a previous method named calculation of susceptibility through multiple orientation sampling (COSMOS) has solved this inverse problem both theoretically and experimentally using multiple angle acquisitions, it is often impractical to carry out on human subjects. Recently, the feasibility of calculating the brain susceptibility distribution from a singleangle acquisition was demonstrated using morphology enabled dipole inversion (MEDI). In this study, we further improved the original MEDI method by sparsifying the edges in the quantitative susceptibility map that do not have a corresponding edge in the magnitude image. Quantitative susceptibility maps generated by the improved MEDI were compared qualitatively and quantitatively with those generated by calculation of susceptibility through multiple orientation sampling. The results show a high degree of agreement between MEDI and calculation of susceptibility through multiple orientation sampling, and the practicality of MEDI allows many potential clinical applications. Magn Reson Med 66:777-783,

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Purpose Venous blood oxygen saturation is an indicator of brain oxygen consumption and can be measured directly from quantitative susceptibility mapping (QSM) by deconvolving the MR phase signal. However, accurate estimation of the susceptibility of blood may be affected by flow induced phase in the presence of imaging gradient and the inhomogeneous susceptibility field gradient. The purpose of this study is to correct the flow induced error in QSM for improved venous oxygenation quantification. Methods Flow compensation is proposed for QSM by using a fully flow compensated multi-echo gradient echo sequence for data acquisition. A quadratic fit of the phase with respect to echo time is employed for the flow phase in the presence of inhomogeneity field gradients. Phantom and in vivo experiments were carried out to validate the proposed method. Results Phantom experiments demonstrated reduced error in the estimated field map and susceptibility map. Initial data in in vivo human imaging demonstrated improvements in the quantitative susceptibility map and in the estimated venous oxygen saturation values. Conclusion Flow compensated multi-echo acquisition and an adaptive-quadratic fit of the phase images improves the quantitative susceptibility map of blood flow. The improved vein susceptibility enables in vivo measurement of venous oxygen saturation throughout the brain.