Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map

• Published in: NeuroImage (Orlando, Fla.) Vol. 59; no. 3; pp. 2560 - 2568
• Main Authors: Liu, Jing, Liu, Tian, de Rochefort, Ludovic, Ledoux, James, Khalidov, Ildar, Chen, Weiwei, Tsiouris, A. John, Wisnieff, Cynthia, Spincemaille, Pascal, Prince, Martin R., Wang, Yi
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.02.2012; Elsevier Limited
• Subjects: Adult; Algorithms; Brain Injuries - pathology; Brain Mapping - methods; Computer Simulation; Constraint minimization; Echo-Planar Imaging; Electromagnetic Fields; Fourier Analysis; Gradient echo; Humans; Image Interpretation, Computer-Assisted; Image Processing, Computer-Assisted; Intracranial Hemorrhages - pathology; Inverse problem; L1 norm; L2 norm; Lagrange multiplier; Medical research; Methods; Morphology enabled dipole inversion; Noise; Phantoms, Imaging; Quantitative susceptibility mapping; Reproducibility of Results; Sparsity; Tissue susceptibility; Gradient echo; Constraint minimization; L2 norm; Sparsity; Quantitative susceptibility mapping; L1 norm; Morphology enabled dipole inversion; Tissue susceptibility; Inverse problem
• ISSN: 1053-8119; 1095-9572; 1095-9572
• DOI: 10.1016/j.neuroimage.2011.08.082

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. [Display omitted] ► We present a dipole inversion for quantitative susceptibility mapping (QSM). ► The structural consistency between anatomy and susceptibility is used for inversion. ► We implement the structural consistency in the L1- and L2-norm minimization. ► The L1-norm is superior to the L2-norm for QSM accuracy and quality. ► High quality QSM is feasible for imaging brain structures and hemorrhages.