Introduction

Quantitative susceptibility mapping (QSM) may enable accurate assessment of liver iron content^1-3. Historically developed for brain imaging, QSM performs dipole inversion of the local susceptibility-induced field map, with regularization needed due to ill-posed nature of the inverse problem⁴. QSM techniques in body imaging face additional challenges, including more complex anatomy, presence of fat, rapid signal decay (especially for severe iron overload), and respiratory motion. These lead to errors in the measured field map, complicate QSM preprocessing (background field removal) and dipole inversion, creating errors and artifacts/shading in the resulting susceptibility maps. These challenges are exacerbated by liver iron overload and require specialized techniques^5,6. In this work, we capitalize on the fact that chemical-shift-encoded (CSE) imaging⁷ used for field mapping in the liver provides additional information that can be exploited to improve dipole inversion. In particular, acquisition of multi-echo data enables estimation not only of the B0 field map but also fat and water images, $$$R_2^*$$$, and fat fraction (FF) maps. We describe an optimized method that uses information provided by CSE to improve accuracy and repeatability of liver QSM.

Theory

Prior Work:
We follow the formulation⁵ of simultaneous background field removal and susceptibility distribution estimation from multi-echo data collected in a single breath-hold:
$$\chi=\arg\min_\chi\left(||WL(\psi-D\ast\chi)||_2^2+\lambda||P\chi||_2^2\right),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad(1)$$
where $$$\chi$$$ is magnetic susceptibility, $$$D$$$ dipole kernel, $$$\psi$$$ measured field map, $$$L$$$ the Laplace operator for background field removal, $$$W$$$ a weighting matrix accounting for spatial noise variations, $$$P$$$ regularization operator with parameter $$$\lambda$$$. Previously⁵, $$$W$$$ was selected to be sum-of-squares of image intensities across all echoes as a measure of SNR in the field map data, while $$$P$$$ combined edge mask and smoothness constraints.
Proposed Method:
The first feature of the proposed method hinges on the fact that the quality of the field map is crucial for the performance of QSM. In practice, the field map may contain errors ranging from phase wraps to areas of poor fit (e.g., due to high iron content, motion, etc.), which can be detected by analyzing residuals of the multi-echo CSE fit⁸. To account for field map estimation uncertainties and to counteract amplification and propagation of these errors by the iterative inversion, we propose modulating the weighting matrix by the residual fit error:
$$W(r)=\left(\sum_{n=1}^{N_{TE}}|s(r,t_n)|^2\right)^{1/2}/\left(\sum_{n=1}^{N_{TE}}\left|s(r,t_n)-\left(s_{water}(r)+s_{fat}(r)\sum_{j=1}^6\rho_je^{-2{\pi}i{\Delta}f_jt_n}\right)\right|^2\right)^{1/2},\qquad(2)$$
where $$$s(r,t_n)$$$ are source images at pixel location $$$r$$$ at echo time $$$t_n$$$, $$$s_{water}$$$ and $$$s_{fat}$$$ are water and fat images, respectively, $$${\Delta}f_j$$$ and $$$\rho_j$$$ are frequency shifts of fat species relative to water and their relative amplitudes.
The second feature of the method is incorporation of susceptibility priors $$$\chi_0$$$ that can be learned with sufficient confidence from the CSE fat/water (F/W) separation in spatial locations defined by a mask M, included into formulation as follows:
$$\chi=\arg\min_\chi\left(||WL(\psi-D\ast\chi)||_2^2+\lambda||P\chi||_2^2+\mu||M(\chi-\chi_0)||_2^2\right).\qquad\qquad\qquad\qquad\qquad\qquad(3)$$
In this work, we exploit the availability of FF map and the assumption of uniform susceptibility in fat since the adipose tissue does not accumulate iron^2,5. As QSM allows only relative quantification of susceptibility (e.g., using fat as the reference), we impose a soft ($$$l_2$$$) constraint of $$$\chi_{fat}\approx0$$$ within the fat mask.

Methods

With IRB approval and informed written consent, 15 human subjects with known or suspected iron overload were scanned in a single 8s breath-hold at 3.0T (MR750 or Premier, GE Healthcare) using multi-echo 3D SGRE sequence (axial orientation, FOV=40x32cm²,slice=8mm,TR=8.0ms,FA=3°,six TEs: TE₁=1.2ms,ΔTE=1.0ms). To evaluate repeatability, MRI table was removed from the scanner, coil array was removed, the subject was asked to sit up and lie back down, coil was replaced, table was returned into the scanner, and the same acquisition was repeated. The collected data were processed with graph-cut approach for CSE F/W separation⁹ to estimate the field map, used as input for QSM. The mapping was performed using the original liver QSM (Eq.1) and the proposed (Eqs.2-3) method with fat mask $$$M_{fat}$$$ comprising pixels with $$$\rm{FF}>0.9$$$. For both methods, susceptibility values were quantified relative to the average susceptibility in fat. We tested correlations between $$$R_2^*$$$ and the obtained susceptibility values averaged in ROIs placed in the right liver lobe and assessed repeatability using Spearman’s rank correlation and Bland-Altman analysis¹⁰.

Results

The impact of regions with poor signal/high residual error in the multi-echo CSE fit (Fig.1a-b) is reduced by the proposed adaptive weighting (Fig.1c-d), which, combined with soft fat constraint, leads to reduced shading in the susceptibility maps (Fig.2). The linear modeling of relationship between $$$R_2^*$$$ and $$$\chi$$$ (Fig.3) is consistent across test/re-test and also with previously reported values⁵. Importantly, inclusion of fat constraint and adaptive weighting leads to lower sensitivity to field map errors, which are especially likely for high liver iron due to low SNR in field map, which results in improved repeatability as illustrated in Figs.4-5.

Discussion and Conclusions

Abdominal QSM faces a number of unique challenges due to large variations in susceptibility, presence of fat, and motion, which further confound an ill-posed inverse problem. We proposed an approach to optimize the use of additional information provided by CSE imaging to regularize the QSM inversion problem. This approach resulted in significantly reduced shading artifact, improved quality of susceptibility maps, and higher repeatability of measurements. Additional validation using reference measurements of liver iron concentration, or liver susceptibility (e.g., from SQUID liver biosusceptometry) is highly desirable and remains a future work.

Acknowledgements

The authors wish to acknowledge support from the NIH (R01 DK117354, R01 DK100651, R01 DK088925, R01EB027087). Also, GE Healthcare provides research support to the University of Wisconsin. Dr. Reeder is a Romnes Faculty Fellow and has received an award provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation.