Magnetic susceptibility is an important physical property of tissues, and can be used as a contrast mechanism in magnetic resonance imaging. Recently, targeting contrast agents by conjugation with signaling molecules and labeling stem cells with contrast agents have become feasible. These contrast agents are strongly paramagnetic, and the ability to quantify magnetic susceptibility could allow accurate measurement of signaling and cell localization. Presented here is a technique to estimate arbitrary magnetic susceptibility distributions by solving an ill-posed inversion problem from field maps obtained in an MRI scanner. Two regularization strategies are considered, conventional Tikhonov regularization, and a sparsity promoting nonlinear regularization using the ℓ1 norm. Proof of concept is demonstrated using numerical simulations, phantoms, and in a stroke model mouse. Initial experience indicates that the nonlinear regularization better suppresses noise and streaking artifacts common in susceptibility estimation.

Purpose:To assess quantitative susceptibility mapping (QSM) for reducing the inconsistency of standard magnetic resonance (MR) imaging sequences in measurements of cerebral microbleed burden. Materials and Methods:This retrospective study was HIPAA compliant and institutional review board approved. Ten patients (5.6%) were selected from among 178 consecutive patients suspected of having experienced a stroke who were imaged with a multiecho gradient-echo sequence at 3.0 T and who had cerebral microbleeds on T2*-weighted images. QSM was performed for various ranges of echo time by using both the magnitude and phase components in the morphologyenabled dipole inversion method. Cerebral microbleed size was measured by two neuroradiologists on QSM images, T2*-weighted images, susceptibility-weighted (SW) images, and R2* maps calculated by using different echo times. The sum of susceptibility over a region containing a cerebral microbleed was also estimated on QSM images as its total susceptibility. Measurement differences were assessed by using the Student t test and the F test; P , .05 was considered to indicate a statistically signifi cant difference. Results:When echo time was increased from approximately 20 to 40 msec, the measured cerebral microbleed volume increased by mean factors of 1 .49 6 0.86 (standard deviation), 1.64 6 0.84, 2.30 6 1.20, and 2.30 6 1.19 for QSM, R2*, T2*-weighted, and SW images, respectively ( P , .01). However, the measured total susceptibility with QSM did not show signifi cant change over echo time ( P = .31), and the variation was signifi cantly smaller than any of the volume increases ( P , .01 for each). Conclusion:The total susceptibility of a cerebral microbleed measured by using QSM is a physical property that is independent of echo time.q RSNA, 2011

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A new method is proposed to determine the timefrequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a theoretical analysis are presented to assess its effectiveness.