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A regularized, model‐based approach to phase‐based conductivity mapping using MRI
Author(s) -
Ropella Kathleen M.,
Noll Douglas C.
Publication year - 2017
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.26590
Subject(s) - imaging phantom , gaussian , inverse problem , laplace operator , noise (video) , filter (signal processing) , gaussian noise , inverse , conductivity , algorithm , computer science , mathematics , physics , artificial intelligence , mathematical analysis , optics , computer vision , image (mathematics) , geometry , quantum mechanics
Purpose To develop a novel regularized, model‐based approach to phase‐based conductivity mapping that uses structural information to improve the accuracy of conductivity maps. Theory and Methods The inverse of the three‐dimensional Laplacian operator is used to model the relationship between measured phase maps and the object conductivity in a penalized weighted least‐squares optimization problem. Spatial masks based on structural information are incorporated into the problem to preserve data near boundaries. The proposed Inverse Laplacian method was compared against a restricted Gaussian filter in simulation, phantom, and human experiments. Results The Inverse Laplacian method resulted in lower reconstruction bias and error due to noise in simulations than the Gaussian filter. The Inverse Laplacian method also produced conductivity maps closer to the measured values in a phantom and with reduced noise in the human brain, as compared to the Gaussian filter. Conclusion The Inverse Laplacian method calculates conductivity maps with less noise and more accurate values near boundaries. Improving the accuracy of conductivity maps is integral for advancing the applications of conductivity mapping. Magn Reson Med 78:2011–2021, 2017. © 2016 International Society for Magnetic Resonance in Medicine.