Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping

A robust multi-scale approach to quantitative susceptibility mapping

Quantitative Susceptibility Mapping (QSM), best known as a surrogate for tissue iron content, is becoming a highly relevant MRI contrast for monitoring cellular and vascular status in aging, addiction, traumatic brain injury and, in general, a wide range of neurological disorders. In this study we present a new Bayesian QSM algorithm, named Multi-Scale Dipole Inversion (MSDI), which builds on the nonlinear Morphology-Enabled Dipole Inversion (nMEDI) framework, incorporating three additional features: (i) improved implementation of Laplace's equation to reduce the influence of background fields through variable harmonic filtering and subsequent deconvolution, (ii) improved error control through dynamic phase-reliability compensation across spatial scales, and (iii) scalewise use of the morphological prior. More generally, this new pre-conditioned QSM formalism aims to reduce the impact of dipole-incompatible fields and measurement errors such as flow effects, poor signal-to-noise ratio or other data inconsistencies that can lead to streaking and shadowing artefacts. In terms of performance, MSDI is the first algorithm to rank in the top-10 for all metrics evaluated in the 2016 QSM Reconstruction Challenge. It also demonstrated lower variance than nMEDI and more stable behaviour in scan-rescan reproducibility experiments for different MRI acquisitions at 3 and 7 Tesla. In the present work, we also explored new forms of susceptibility MRI contrast making explicit use of the differential information across spatial scales. Specifically, we show MSDI-derived examples of: (i) enhanced anatomical detail with susceptibility inversions from short-range dipole fields (hereby referred to as High-Pass Susceptibility Mapping or HPSM), (ii) high specificity to venous-blood susceptibilities for highly regularised HPSM (making a case for MSDI-based Venography or VenoMSDI), (iii) improved tissue specificity (and possibly statistical conditioning) for Macroscopic-Vessel Suppressed Susceptibility Mapping (MVSSM), and (iv) high spatial specificity and definition for HPSM-based Susceptibility-Weighted Imaging (HPSM-SWI) and related intensity projections.

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

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.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.

Coherence enhancement in quantitative susceptibility mapping by means of anisotropic weighting in morphology enabled dipole inversion

PURPOSE

To investigate an anisotropic structural prior in morphology enabled dipole inversion (MEDI) for improving accuracy in quantitative susceptibility mapping (QSM).

THEORY AND METHODS

Anisotropic weighting (AW) was devised and implemented to incorporate orientation information into the edge agreement in the MEDI method. AW performance was compared with isotropic weighting by testing and validating on in vivo brain multiple orientation MRI data using COSMOS and the (33) component of the susceptibility tensor as reference.

RESULTS

Suppressing streaking artifacts, AW improved not only QSM image quality but also accuracy in terms of RMSE (root mean square error), HFEN (high frequency error norm), SSIM (structural similarity index), and GDA (gradient direction agreement). In addition, it outperformed isotropic weighting in region of interest-based analysis. From a computational perspective, AW was as fast as isotropic weighting, taking approximately the same central processing unit times.

CONCLUSION

Using AW in MEDI improves QSM accuracy compared with isotropic weighting. Magn Reson Med 79:1172-1180, 2018. © 2017 International Society for Magnetic Resonance in Medicine.