Primal-dual and forward gradient implementation for quantitative susceptibility mapping

Automated adaptive preconditioner for quantitative susceptibility mapping

PURPOSE

To develop an automated adaptive preconditioner for QSM reconstruction with improved susceptibility quantification accuracy and increased image quality.

THEORY AND METHODS

The total field was used to rapidly produce an approximate susceptibility map, which was then averaged and trended over R 2 ∗ binning to generate a spatially varying distribution of preconditioning values. This automated adaptive preconditioner was used to reconstruct QSM via total field inversion and was compared with its empirical counterparts in a numerical simulation, a brain experiment with 5 healthy subjects and 5 patients with intracerebral hemorrhage, and a cardiac experiment with 3 healthy subjects.

RESULTS

Among evaluated preconditioners, the automated adaptive preconditioner achieved the fastest convergence in reducing the RMSE of the QSM in the simulation, suppressed hemorrhage-associated artifacts while preserving surrounding brain tissue contrasts, and provided cardiac chamber oxygenation values consistent with those reported in the literature.

CONCLUSION

An automated adaptive preconditioner allows high-quality QSM from the total field in imaging various anatomies with dynamic susceptibility ranges.

Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies the magnetic susceptibility distribution within biological tissues. QSM calculates the underlying magnetic susceptibility by deconvolving the tissue magnetic field map with a unit dipole kernel. However, this deconvolution problem is ill-posed. The morphology enabled dipole inversion (MEDI) introduces total variation (TV) to regularize the susceptibility reconstruction. However, MEDI results still contain artifacts near tissue boundaries because MEDI only imposes TV constraint on voxels inside smooth regions. We introduce a Morphology-Adaptive TV (MATV) for improving TV-regularized QSM. The MATV method first classifies imaging target into smooth and nonsmooth regions by thresholding magnitude gradients. In the dipole inversion for QSM, the TV regularization weights are a monotonically decreasing function of magnitude gradients. Thus, voxels inside smooth regions are assigned with larger weights than those in nonsmooth regions. Using phantom and in vivo datasets, we compared the performance of MATV with that of MEDI. MATV results had better visual quality than MEDI results, especially near tissue boundaries. Preliminary brain imaging results illustrated that MATV has potential to improve the reconstruction of regions near tissue boundaries.

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.

Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge

PURPOSE

The aim of the 2016 quantitative susceptibility mapping (QSM) reconstruction challenge was to test the ability of various QSM algorithms to recover the underlying susceptibility from phase data faithfully.

METHODS

Gradient-echo images of a healthy volunteer acquired at 3T in a single orientation with 1.06 mm isotropic resolution. A reference susceptibility map was provided, which was computed using the susceptibility tensor imaging algorithm on data acquired at 12 head orientations. Susceptibility maps calculated from the single orientation data were compared against the reference susceptibility map. Deviations were quantified using the following metrics: root mean squared error (RMSE), structure similarity index (SSIM), high-frequency error norm (HFEN), and the error in selected white and gray matter regions.

RESULTS

Twenty-seven submissions were evaluated. Most of the best scoring approaches estimated the spatial frequency content in the ill-conditioned domain of the dipole kernel using compressed sensing strategies. The top 10 maps in each category had similar error metrics but substantially different visual appearance.

CONCLUSION

Because QSM algorithms were optimized to minimize error metrics, the resulting susceptibility maps suffered from over-smoothing and conspicuity loss in fine features such as vessels. As such, the challenge highlighted the need for better numerical image quality criteria. Magn Reson Med 79:1661-1673, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.