Magnetic susceptibility is an important physical property of tissues, and can be used as a contrast mechanism in magnetic resonance imaging (MRI). 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 l(1) norm. Proof of concept is demonstrated using numerical simulations, phantoms, and in a stroke model in a rat. Initial experience indicates that the nonlinear regularization better suppresses noise and streaking artifacts common in susceptibility estimation.
