Quantitative Susceptibility Mapping (QSM) Algorithms: Mathematical Rationale and Computational Implementations

Youngwook Kee, Zhe Liu, Liangdong Zhou, Alexey Dimov, Junghun Cho, Ludovic De Rochefort, Jin Keun Seo, Yi Wang

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


Quantitative susceptibility mapping (QSM) solves the magnetic field-to-magnetization (tissue susceptibility) inverse problem under conditions of noisy and incomplete field data acquired using magnetic resonance imaging. Therefore, sophisticated algorithms are necessary to treat the ill-posed nature of the problem and are reviewed here. The forward problem is typically presented as an integral form, where the field is the convolution of the dipole kernel and tissue susceptibility distribution. This integral form can be equivalently written as a partial differential equation (PDE). Algorithmic challenges are to reduce streaking and shadow artifacts characterized by the fundamental solution of the PDE. Bayesian maximum a posteriori estimation can be employed to solve the inverse problem, where morphological and relevant biomedical knowledge (specific to the imaging situation) are used as priors. As the cost functions in Bayesian QSM framework are typically convex, solutions can be robustly computed using a gradient-based optimization algorithm. Moreover, one can not only accelerate Bayesian QSM, but also increase its effectiveness at reducing shadows using prior knowledge based preconditioners. Improving the efficiency of QSM is under active development, and a rigorous analysis of preconditioning needs to be carried out for further investigation.

Original languageEnglish
Article number8025796
Pages (from-to)2531-2545
Number of pages15
JournalIEEE Transactions on Biomedical Engineering
Issue number11
Publication statusPublished - 2017 Nov

Bibliographical note

Funding Information:
Manuscript received March 16, 2017; revised June 2, 2017; accepted July 24, 2017. Date of publication September 25, 2017; date of current version October 18, 2017. This work was supported in part by grants from National Institutes of Health (R01 NS095562, R01 NS090464, R01 NS072370, S10 OD021782). The work of J. K. Seo was supported by NRF grant 2015R1A5A1009350. (Corresponding author: Yi Wang.) Y. Kee and L. Zhou are with the Department of Radiology, Weill Cornell Medical College, New York, NY 10065 USA.

Publisher Copyright:
© 1964-2012 IEEE.

All Science Journal Classification (ASJC) codes

  • Biomedical Engineering


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