Abstract
Objective
Quantitative susceptibility mapping (QSM) provides an estimate of the magnetic susceptibility of tissue using magnetic resonance (MR) phase measurements. The tissue magnetic susceptibility (source) from the measured magnetic field distribution/local tissue field (effect) inherent in the MR phase images is estimated by numerically solving the inverse source-effect problem. This study aims to develop an effective model-based deep-learning framework to solve the inverse problem of QSM.
Materials and methods
This work proposes a Schatten \(\textit{p}\)-norm-driven model-based deep learning framework for QSM with a learnable norm parameter \(\textit{p}\) to adapt to the data. In contrast to other model-based architectures that enforce the l\(_{\text {2}}\)-norm or l\(_{\text {1}}\)-norm for the denoiser, the proposed approach can enforce any \(\textit{p}\)-norm (\(\text {0}<\textit{p}\le \text {2}\)) on a trainable regulariser.
Results
The proposed method was compared with deep learning-based approaches, such as QSMnet, and model-based deep learning approaches, such as learned proximal convolutional neural network (LPCNN). Reconstructions performed using 77 imaging volumes with different acquisition protocols and clinical conditions, such as hemorrhage and multiple sclerosis, showed that the proposed approach outperformed existing state-of-the-art methods by a significant margin in terms of quantitative merits.
Conclusion
The proposed SpiNet-QSM showed a consistent improvement of at least 5% in terms of the high-frequency error norm (HFEN) and normalized root mean squared error (NRMSE) over other QSM reconstruction methods with limited training data.
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Data/code availability
SNU dataset was made available to the authors by Prof. Lee (e-mail: jonghoyi@snu.ac.kr) of Seoul National University. LPCNN dataset is publicly available at https://github.com/Sulam-Group[16]. QSM 2016 reconstruction challenge (RC-1) dataset is publicly available at http://www.neuroimaging.at/pages/qsm.php[18]. QSM reconstruction challenge 2.0 (RC-2) dataset is publicly available at https://doi.org/10.5281/zenodo.4559541[19]. The developed codes of this manuscript are publicly shared at https://github.com/venkateshvaddadi/SpiNet-QSM.
References
Deistung A, Schweser F, Reichenbach JR (2017) Overview of quantitative susceptibility mapping. NMR Biomed 30(4):e3569
Schweser F, Deistung A, Reichenbach JR (2016) Foundations of MRI phase imaging and processing for Quantitative Susceptibility Mapping (QSM). Z Med Phys 26(1):6–34
Liu C, Wei H, Gong NJ, Cronin M, Dibb R, Decker K (2015) Quantitative susceptibility mapping: contrast mechanisms and clinical applications. Tomography. 1(1):3–17
Reichenbach J, Schweser F, Serres B, Deistung A (2015) Quantitative susceptibility mapping: concepts and applications. Clin Neuroradiol 25(2):225–230
Schweser F, Lehr BW, Andreas D, Rainer RJ (2010) Sophisticated harmonic artifact reduction for phase data (SHARP). Proceeding Proc GC Intl Soc Mag Reson Med
Sun H, Wilman AH (2014) Background field removal using spherical mean value filtering and Tikhonov regularization. Magn Reson Med 71(3):1151–1157
Liu T, Khalidov I, de Rochefort L, Spincemaille P, Liu J, Tsiouris AJ et al (2011) A novel background field removal method for MRI using projection onto dipole fields. NMR Biomed 24(9):1129–1136
Wen Y, Zhou D, Liu T, Spincemaille P, Wang Y (2014) An iterative spherical mean value method for background field removal in MRI. Magn Reson Med 72(4):1065–1071
Zhou D, Liu T, Spincemaille P, Wang Y (2014) Background field removal by solving the Laplacian boundary value problem. NMR Biomed 27(3):312–319
Yoon J, Gong E, Chatnuntawech I, Bilgic B, Lee J, Jung W et al (2018) Quantitative susceptibility mapping using deep neural network: QSMnet. Neuroimage 179:199–206. https://doi.org/10.1016/j.neuroimage.2018.06.030
Rasmussen KGB, Kristensen M, Blendal RG, Østergaard LR, Plocharski M, O’Brien K et al (2018) DeepQSM-using deep learning to solve the dipole inversion for MRI susceptibility mapping. BioRxiv. p. 278036
Gao Y, Zhu X, Moffat BA, Glarin R, Wilman AH, Pike GB et al (2021) xQSM: quantitative susceptibility mapping with octave convolutional and noise-regularized neural networks. NMR Biomed. https://doi.org/10.1002/nbm.4461. (Cited by: 15; All Open Access, Green Open Access)
Liu T, Spincemaille P, De Rochefort L, Kressler B, Wang Y (2009) Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magn Reson Med 61(1):196–204
Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention. Springer; pp 234–241
Aggarwal HK, Mani MP, Jacob M (2019) MoDL: model-based deep learning architecture for inverse problems. IEEE Trans Med Imaging 38(2):394–405. https://doi.org/10.1109/TMI.2018.2865356
Lai KW, Aggarwal M, van Zijl P, Li X, Sulam J (2020) Learned proximal networks for quantitative susceptibility mapping. In: Medical Image Computing and Computer Assisted Intervention–MICCAI 2020: 23rd International Conference, Lima, Peru, October 4–8, 2020, Proceedings, Part II 23. Springer; pp 125–135
Feng R, Zhao J, Wang H, Yang B, Feng J, Shi Y et al (2021) MoDL-QSM: model-based deep learning for quantitative susceptibility mapping. Neuroimage 240:118376. https://doi.org/10.1016/j.neuroimage.2021.118376
Langkammer C, Schweser F, Shmueli K, Kames C, Li X, Guo L et al (2018) Quantitative susceptibility mapping: report from the 2016 reconstruction challenge. Magn Reson Med 79(3):1661–1673
Marques JP, Meineke J, Milovic C, Bilgic B, Ks Chan, Hedouin R et al (2021) QSM reconstruction challenge 2.0: a realistic in silico head phantom for MRI data simulation and evaluation of susceptibility mapping procedures. Magne Reson Med 86(1):526–542
Rastogi A, Yalavarthy PK (2021) SpiNet: a deep neural network for Schatten p-norm regularized medical image reconstruction. Med Phys 48(5):2214–2229. https://doi.org/10.1002/mp.14744
He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition; p. 770–778
Committee QCO, Bilgic B, Langkammer C, Marques JP, Meineke J, Milovic C et al (2021) QSM reconstruction challenge 2.0: design and report of results. Magn Reson Med 86(3):1241–1255
Polak D, Chatnuntawech I, Yoon J, Iyer SS, Milovic C, Lee J et al (2020) Nonlinear dipole inversion (NDI) enables robust quantitative susceptibility mapping (QSM). NMR Biomed 33(12):e4271
Milovic C, Bilgic B, Zhao B, Acosta-Cabronero J, Tejos C (2018) Fast nonlinear susceptibility inversion with variational regularization. Magn Reson Med 80(2):814–821
Nguyen TD, Wen Y, Du J, Liu Z, Gillen K, Spincemaille P et al (2020) Quantitative susceptibility mapping of carotid plaques using nonlinear total field inversion: initial experience in patients with significant carotid stenosis. Magn Reson Med 84(3):1501–1509
Yushkevich PA, Gao Y, Gerig G (2016) ITK-SNAP: an interactive tool for semi-automatic segmentation of multi-modality biomedical images. In: 38th annual international conference of the IEEE engineering in medicine and biology society (EMBC). IEEE 2016:3342–3345
Wei H, Dibb R, Zhou Y, Sun Y, Xu J, Wang N et al (2015) Streaking artifact reduction for quantitative susceptibility mapping of sources with large dynamic range. NMR Biomed 28(10):1294–1303
Milovic C, Tejos C, Acosta-Cabronero J, Özbay PS, Schwesser F, Marques JP et al (2020) The 2016 QSM Challenge: lessons learned and considerations for a future challenge design. Magn Reson Med 84(3):1624–1637
Lange K (2013) Optimization, vol 95. Springer Science & Business Media
Nocedal J, Wright SJ (1999) Numerical optimization. Springer
Li W, Liu C, Duong TQ, van Zijl PC, Li X (2017) Susceptibility tensor imaging (STI) of the brain. NMR Biomed 30(4):e3540
Milovic C, Lambert M, Langkammer C, Bredies K, Irarrazaval P, Tejos C (2022) Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM). Magn Reson Med 87(1):457–473
Cognolato F, O’Brien K, Jin J, Robinson S, Laun FB, Barth M et al (2023) NeXtQSM-a complete deep learning pipeline for data-consistent Quantitative Susceptibility Mapping trained with hybrid data. Med Image Anal 84:102700
Acknowledgements
This work was supported by S. Ramachandran-National Bioscience Award for Career Development awarded by Department of Biotechnology, Govt. of India. The authors are thankful to Dr. Jongho Lee, Laboratory for Imaging Science and Technology, Department of Electrical and Computer Engineering, Seoul National University, Seoul, South Korea, for providing the data. The authors are also thankful to Dr. Jeremias Sulam, Biomedical Engineering Department, Johns Hopkins University for making their data [16] publicly available. The authors are also thankful to Naveen Paluru and Aditya Rastogi, Indian Institute of Science, Bangalore for their input on this work.
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Venkatesh, V., Mathew, R.S. & Yalavarthy, P.K. Spinet-QSM: model-based deep learning with schatten p-norm regularization for improved quantitative susceptibility mapping. Magn Reson Mater Phy (2024). https://doi.org/10.1007/s10334-024-01158-7
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DOI: https://doi.org/10.1007/s10334-024-01158-7