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Dynamic streaking artifact regularization for QSM
Yongquan Ye1, Xueping Li2, Qinglei Zhang2, Fei Zhou2, Ming Li2, Zhao Qing2, Bing Zhang2, Shuheng Zhang3, Yanling Chen3, and Jinguang Zong3

1UIH America, Inc., Houston, TX, United States, 2Radiology, The affiliated Drum Tower hospital of Nanjing university medical school, Nanjing, China, 3United Imaging of Healthcare, Shanghai, China

### Synopsis

We propose dynamically estimate, formulate and update the field components that are responsible for causing streaking artifact, as an additional regularization term for solving the QSM optimization problem. As a result, streaking artifacts arising from regions with highly disrupted local fields can be well suppressed, preventing them from spatially extending and affecting other regions of interest. The proposed method can maintain the accuracy of QSM results, and has the potential to be integrated into most QSM optimization algorithms.

### Introduction

A major challenge for quantitative susceptibility mapping (QSM) is the streaking artifacts. Mathematically, streaking artifacts are caused by the ill-posedness of the inverted dipole kernel, and to date, regularization based optimization methods are most popular for their satisfying performance on accuracy and artifact control. On the other hand, although regularization with spatial constraints can reduce streaking artifacts from well-defined local fields, streaking artifacts originating from regions with highly inconsistent or disrupted fields remain a challenge. Such regions usually associate with low SNR, strong and inconsistent susceptibility distribution and/or complex morphology, such as large hemorrhagic sites with significant hemosiderin deposition, post-surgical scars in cerebral tissues, or nucleus with high concentration of iron, etc. Several attempts have been proposed to tackle this challenge, such as evaluating the streaking artifacts for subtraction from QSM results2, or via isolating strong susceptibility sources3. However, subtracting the estimated artifacts can lead to underestimation on the susceptibility values2, and the accuracy of isolation and ROI selection would affect the artifact estimation for strong sources3. In this work, we introduce an additional regularization term to the QSM solution, to dynamically estimate and remove streaking artifacts associated with non-dipole field components.

### Methods

Generally, regularization approaches are solved iteratively for optimized solution. During each iteration, an intermediate QSM solution χiter is obtained and used as input for subsequent iteration. With χiter, the corresponding local field map, Φiter , can be generated using the forward dipole function D, i.e. $\phi _{iter}=F^{-1}DF\chi _{iter}$. Thus the regularization term describing the streaking artifacts can be formulated as $||F^{-1}D'F\Delta\phi||_{2}^{2}$, where D’ is a partial dipole kernel obtained by posing a threshold on D, and ΔΦ is the difference between Φiter and the original local field map Φ. The complete regularization solvers thus were:

$argmin_{\chi }||F^{-1}DF\chi -\phi ||_{2}^{2}+\alpha ||P\bigtriangledown \chi ||_{1}+||F^{-1}D'F\Delta \phi||_{2}^{2}$ [1]

We solve this minimization problem using preconditioned conjugate gradient method4. To evaluate the effectiveness of the streaking artifact regularization term, computer simulation and in vivo data were tested. For simulation, a susceptibility brain model was used to generate a field map as the input for Eq.1, which was solved with and without the artifact regularization term. With IRB approval, 16 patients with history of brain surgery were scanned on 3T (uMR770, UIH, Shanghai), using a 4-echo high resolution GRE sequence. Local field map was calculated as previously described5, and QSM results with and without artifact regularization were calculated and compared.

### Results

Fig.1 compares simulated QSM results with and without the artifact control regularization term. Fig.2 shows similar comparison on a representative brain surgery patient, as well as the corresponding field maps and the visualized artifact regularization term.

### Discussion & Conclusion

We have proposed and demonstrated the feasibility of using an additional regularization term for QSM streaking artifact reduction. The artifact regularization term is obtained from a partial dipole kernel and a difference field map, and is dynamically updated when iteratively solving the QSM minimization problem. In contrary to previous works where streaking artifacts were independently estimated and subtracted from the final QSM results2, our method of modeling the artifact as a regularization term does not underestimate the QSM values, as evidenced by the simulation results in Fig.1. Currently, most available QSM minimization algorithms are competent in controlling the level of streaking artifacts, provided that the local fields are reasonably continuous. However, abrupt changes in the local field will violate the dipole model and cause mismatch on boundary conditions, thus will lead to streaking artifacts that cannot be ‘correctly’ suppressed by using morphologic regularization. Few literature have reported successful results on such scenarios. Our method was demonstrated with a representative case of post brain surgery patient, who had highly abrupt field changes in the surgery region (field maps in Fig.2). Without artifact regularization, which was equivalent to using morphologic regularization only, very strong and spatially extensive streaking artifacts were present, making the QSM results of a whole hemisphere useless. Such streaking artifacts cannot be removed by incorporating morphologic regularization, as the underlying field distribution was disrupted by the lesion as a result of the surgery, thus neither correlate with tissue boundaries nor mathematically satisfy the dipole model. Therefore, dynamically estimating the streaking artifact and using it as an additional regularization terms has the potential to minimize the artifacts, as confirmed in Fig.2. For such extremely disrupted scenarios, complete removal of streaking artifacts is not possible. However, our method is shown to be able to significantly suppress such streaking artifacts to reduce their overlap with other regions. Furthermore, our artifact regularization term can be integrated with most QSM optimization solvers. For tissues with well defined fields, it will not affect the accuracy of QSM results.

### Acknowledgements

No acknowledgement found.

### References

1. Wang, Y. and T. Liu. "Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker." Magn Reson Med, 2015. 73(1): 82-101.

2. Li, W., N. Wang, F. Yu, H. Han, W. Cao, R. Romero, B. Tantiwongkosi, T. Q. Duong and C. Liu. A method for estimating and removing streaking artifacts in quantitative susceptibility mapping. Neuroimage, 2015. 108: p. 111-22.

3. Wei H, Dibb R, Zhou Y, Sun Y, Xu J, Wang N, Liu C. Streaking artifact reduction for quantitative susceptibility mapping of sources with large dynamic range. NMR Biomed 2015;28:1294–1303

4. Bilgic, B., A. P. Fan, J. R. Polimeni, S. F. Cauley, M. Bianciardi, E. Adalsteinsson, L. L. Wald and K. Setsompop. "Fast quantitative susceptibility mapping with L1-regularization and automatic parameter selection." Magn Reson Med, 2014. 72(5): 1444-1459.

5. Yongquan Ye, Jinguang Zong, Jingyuan Lyu, and Weiguo Zhang. SWI+: A robust artifact-free SWI procedure with improved contrast. Proceedings 26th Scientific Meeting, International Society for Magnetic Resonance in Medicine, Paris, 2018(4135).

### Figures

Fig.1 Computer simulation results. a) is the reference susceptibility distribution map, which was used to generate the field map based on which Eq.1 was solved. The resultant QSM maps with (b) and without (c) artifact regularization term are shown, as well as their corresponding difference maps (d & e) with the reference. When calculated with artifact regularization term, the RMSE and SSIM of the results were 23.35 (for d) and 0.963 (for b) respectively, and when calculated without artifact regularization term, the RMSE and SSIM were 26.35 (for e) and 0.967 (for c).

Fig.2 In vivo QSM results comparison between with and without using artifact regularization term, on a representative patient with a history of brain surgery. The field map and an example of the artifact regularization term of the same image planes are also shown.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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