A Phase Fitting Algorithm for Multi-Echo Quantitative Susceptibility Mapping

doi:10.11938/cjmr20160410

Abstract

Abstract: A weighted linear least-square (WLS) algorithm is generally applied for multi-echo phase data to estimate the voxel-by-voxel field shift, which is further used for inversion of susceptibility map. The fitting error on the estimated field map, induced from conventional WLS method, may lead to artifacts and low signal-to-noise ratio on the susceptibility map, especially in the regions with inhomogeneous distribution of magnetic susceptibility. To improve the accuracy of the estimated field map, a truncated WLS approach was used to truncate the signal of low signal-to-noise ratio and capture the field information before the signal in a voxel decays to the noise level, which can enhance the contrast of structures in the bottom of the brain on the susceptibility map. Experimental studies demonstrated that susceptibility noise was dramatically reduced by method of truncated WLS.

Key words: quantitative susceptibility mapping(QSM), multi-echo phases fitting, threshold truncation, weighted linear least-square(WLS)

CLC Number:

O482.53

ZHAO Xin-xin, BO Bin-shi, LIU Tian, WANG Yi, LI Jian-qi. A Phase Fitting Algorithm for Multi-Echo Quantitative Susceptibility Mapping[J]. Chinese Journal of Magnetic Resonance, 2016, 33(4): 609-617.

References

[1] Wang Y, Liu T. Quantitative susceptibility mapping (QSM):Decoding MRI data for a tissue magnetic biomarker[J]. Magn Reson Med, 2015, 73(1):82-101.
[2] Li W, Wu B, Liu C. Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition[J]. Neuroimage, 2011, 55(4):1645-1656.
[3] Haacke E M, Liu S, Buch S, et al. Quantitative susceptibility mapping:current status and future directions[J]. Magn Reson Imaging, 2015, 33(1):1-25.
[4] Liu C, Li W, Tong K A, et al. Susceptibility-weighted imaging and quantitative susceptibility mapping in the brain[J]. J Magn Reson Imaging, 2015, 42(1):23-41.
[5] Liu T, Khalidov I, de Rochefort L, et al. A novel background field removal method for MRI using projection onto dipole fields (PDF)[J]. NMR Biomed, 2011, 24(9):1129-1136.
[6] Liu J, Liu T, de Rochefort L, et al. Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map[J]. Neuroimage, 2012, 59(3):2560-2568.
[7] de Rochefort L, Liu T, Kressler B, et al. Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization:validation and application to brain imaging[J]. Magn Reson Med, 2010, 63(1):194-206.
[8] Shmueli K, de Zwart J A, van Gelderen P, et al. Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data[J]. Magn Reson Med, 2009, 62(6):1510-1522.
[9] Wang A-li(王阿莉), Lin Jian-zhong(林建忠), Liu Wei-jun(刘伟俊), et al. Quantitative susceptibility mapping(定量磁化率成像重建方法及其应用)[J]. Chinese J Magn Reson(波谱学杂志), 2014, 31(1):133-154.
[10] Fritzsch D, Reiss-Zimmermann M, Trampel R, et al. Seven-tesla magnetic resonance imaging in Wilson disease using quantitative susceptibility mapping for measurement of copper accumulation[J]. Invest Radiol, 2014, 49(5):299-306.
[11] Li J Q, Chang S X, Liu T, et al. Phase-corrected bipolar gradients in multi-echo gradient-echo sequences for quantitative susceptibility mapping[J]. Magn Reson Mater Phy, 2015, 28(4):347-355.
[12] Gilbert G, Savard G, Bard C, et al. Quantitative comparison between a multiecho sequence and a single-echo sequence for susceptibility-weighted phase imaging[J]. Magn Reson Imaging, 2012, 30(5):722-730.
[13] Wang Y. Quantitative Susceptibility Mapping:Magnetic Resonance Imaging of Tissue Magnetism[M]. Seattle:Createspace, 2013, p228.
[14] Kressler B, de Rochefort L, Liu T, et al. Nonlinear regularization for per voxel estimation of magnetic susceptibility distributions from MRI field maps[J]. IEEE Trans Med Imaging, 2010, 29(2):273-281.
[15] Murakami Y, Kakeda S, Watanabe K, et al. Usefulness of quantitative susceptibility mapping for the diagnosis of Parkinson disease[J]. Am J Neuroradiol, 2015, 36(6):1102-1108.
[16] Barbosa J H, Santos A C, Tumas V, et al. Quantifying brain iron deposition in patients with Parkinson's disease using quantitative susceptibility mapping, R₂ and R₂^*[J]. Magn Reson Imaging, 2015, 33(5):559-565.
[17] Du G, Liu T, Lewis M M, et al. Quantitative susceptibility mapping of the midbrain in Parkinson's disease[J]. Mov Disord, 2016, 31(3):317-324.
[18] He N, Ling H, Ding B, et al. Region-specific disturbed iron distribution in early idiopathic Parkinson's disease measured by quantitative susceptibility mapping[J]. Hum Brain Mapp, 2015, 36(11):4407-4420.
[19] Hung K W, Siu W C. Improved image interpolation using bilateral filter for weighted least square estimation[C]. Hong Kong:Proceedings to IEEE International Conference on Image Processing, 2010:3297-3330.
[20] Yin X, Shah S, Katsaggelos A K, et al. Improved R₂^* measurement accuracy with absolute SNR truncation and optimal coil combination[J]. NMR Biomed, 2010, 23(10):1127-1136.
[21] Lotfipour A K, Wharton S, Schwarz S T, et al. High resolution magnetic susceptibility mapping of the substantia nigra in Parkinson's disease[J]. J Magn Reson Imaging, 2012, 35(1):48-55.
[22] Lv Z, Jiang H, Xu H, et al. Increased iron levels correlate with the selective nigral dopaminergic neuron degeneration in Parkinson's disease[J]. J Neural Transm, 2011, 118(3):361-369.
[23] Liu T, Wisnieff C, Lou M, et al. Nonlinear formulation of the magnetic field to source relationship for robust quantitative susceptibility mapping[J]. Magn Reson Med, 2013, 69(2):467-476.
[24] Ma J F, Son J B, Hazle J D. An improved region growing algorithm for phase correction in MRI[J]. Magn Reson Med, 2015, doi:10.1002/mrm.25892.
[25] Association N E M. Determination of Signal-to-Noise Ratio (SNR) in Diagnostic Magnetic Resonance Imaging[M]. Rosslyn:National Electrical Manufacturers Association, 2008
[26] Haacke E M, Tang J, Neelavalli J, et al. Susceptibility mapping as a means to visualize veins and quantify oxygen saturation[J]. J Magn Reson Imaging, 2010, 32(3):663-676.
[27] Dong Fang(董芳), Pei Meng-chao(裴孟超), Wang Qian-feng(王前锋), et al. Gradient echo imaging of the human brain:Respiratory induved artifacts and navigator echo correction(颅脑梯度回波成像:呼吸伪影和导航回波矫正)[J]. Chinese J Magn Reson(波谱学杂志), 2014, 31(3):321-330.
[28] Groger A, Berg D. Does structural neuroimaging reveal a disturbance of iron metabolism in Parkinson's disease? Implications from MRI and TCS studies[J]. J Neural Transm, 2012, 119(12):1523-1528.
[29] Chan W C, Tejani Z, Budhani F, et al. R₂^* as a surrogate measure of ferriscan iron quantification in thalassemia[J]. J Magn Reson Imaging, 2014, 39(4):1007-1011.