Daniel K. Sodickson1,
2, Leeor Alon1, 2, Cem Murat Deniz, 23,
Noam Ben-Eliezer1, Martijn A. Cloos1, Lester A.
Sodickson4, Christopher Michael Collins1, 2,
Graham C. Wiggins1, Dmitry S. Novikov1
1Bernard
and Irene Schwartz Center for Biomedical Imaging, Department of Radiology,
New York University School of Medicine, New York, NY, United States; 2Sackler
Institute of Graduate Biomedical Sciences, New York University School of
Medicine, New York, NY, United States; 3Bernard and Irene Schwartz
Center for Biomedical Imaging, Department of Radiology, New York University,
New York, NY, United States; 4Cambridge Research Associates,
Newton, MA, United States
At last years ISMRM meeting, we introduced the Local Maxwell Tomography (LMT) method for noninvasive mapping of the electrical properties of tissue or materials. Here, we generalize the theory of LMT to encompass the electrodynamic effects of a) non-vanishing spatial gradients of electrical properties, e.g. at tissue boundaries, and b) structural anisotropies resulting in nontrivial electrical property tensors. We demonstrate that the generalized LMT framework eliminates edge artifacts observed in simpler implementations. We also outline strategies by which tensor structure may be determined if a sufficient number of measurements and coil elements are deployed, potentially enabling electrical property tractography.