A method for estimating and removing streaking artifacts in quantitative susceptibility mapping
Introduction
The signal phase of gradient echo MRI provides much higher gray–white matter contrast than the corresponding magnitude, and contains unique information regarding deoxyhemoglobin, iron, myelin, and tissue microstructure (Duyn et al., 2007, He and Yablonskiy, 2009, Rauscher et al., 2005). Despite these promises, one intrinsic limitation is that phase value at one location depends on both the adjacent magnetic susceptibility distribution and the orientation with respect to the main magnetic field, and thus not suitable for quantitative assessment of tissues. Over the past few years, there have been growing efforts in developing quantitative susceptibility mapping (QSM), a novel MRI technology for solving the ill-posed phase-susceptibility equation to derive the voxel-wise magnetic susceptibility (de Rochefort et al., 2010, Kressler et al., 2010, Li et al., 2011, Liu et al., 2009, Liu et al., 2011b, Schweser et al., 2011b, Shmueli et al., 2009, Wharton et al., 2010, Wu et al., 2012). To date, QSM has been applied in studying cerebral micro-bleeds (Liu et al., 2012b), differentiating iron deposits from calcifications (Deistung et al., 2013), quantifying iron overload in Parkinson's diseases (Lotfipour et al., 2012), assessing the abnormalities in white matter myelination (Liu et al., 2011a), and in many other applications (Duyn, 2013, Reichenbach, 2012).
QSM attempts to solve an ill-posed inverse problem, and many methods have been developed to stabilize the inversion. While threshold-based k-space division or multi-orientation methods have been used in earlier studies (Liu et al., 2009, Shmueli et al., 2009), iterative solutions with regularization and prior information from magnitude or phase are increasingly used for single-orientation reconstruction with reduced streaking artifacts (de Rochefort et al., 2010, Liu et al., 2011b). Although prior information is highly useful in suppressing streaking artifacts around strong susceptibility sources, e.g. cerebral hematoma or large veins, one general concern is that excessive external constraints may alter the spatial frequencies of magnetic susceptibility in an unpredictable manner with degradation of tissue contrast. This is especially problematic for evaluating white matter lesions, whose susceptibility variations are small compared to that of major brain gray and white matter structures. Similar concerns also exist for studying small gray matter structures in the human brain, e.g. subthalamic nucleus, substantia nigra, cerebellar nuclei, which are small in size but have vital functions. Hence, eliminating streaking artifacts while minimizing the regularization-related confounding factors is crucial for evaluating subtle contrast changes in white matter diseases and for delineation of small but functionally important brain structures.
Previously, several methods have been proposed to separate the k-space into different sub-regions and to apply constraints only on ill-posed and ill-conditioned sub-regions (Li et al., 2011, Schweser et al., 2012, Wu et al., 2012). The results suggest that optimization of the ill-conditioned k-space region alone can reduce streaking artifacts. In this study, we propose a general method for estimating streaking artifacts and subtracting them from susceptibility maps. We demonstrate the application of the methodology in reducing streaking artifacts for the LSQR algorithm (Li et al., 2011). We show that, by estimating and subtracting out the streaking artifacts, reproducible QSM can be achieved with negligible streaking artifacts. This method allows for improved delineation of white matter lesions in multiple sclerosis patients and small brain structures in healthy human brains that otherwise would have been obscured by streaking artifacts. The proposed methodology can be extended to other existing QSM algorithms.
Section snippets
A method for estimating streaking artifacts
The normalized phase (ψ = φ/ γμ0H0TE) and magnetic susceptibility (χ) can be related using the following equation (Koch et al., 2006, Marques and Bowtell, 2005, Salomir et al., 2003):where γ, μ0, H0, and TE, are the gyromagnetic ratio, vacuum permeability, applied magnetic field, and echo time, respectively; FT means Fourier transform; and D2 can be calculated from the spatial frequency (k) and the field direction Ĥ as:
For a given initial susceptibility
Overview of the iLSQR method
Fig. 1 illustrates the algorithmic steps of the proposed streaking artifact removal method. The three inputs for streaking artifact estimation are the initial susceptibility estimate χLSQR (Fig. 1A), the binary mask of the ill-conditioned k-space regions MIC (Fig. 1B) and the weighting functions WGi (Fig. 1D). Here, the weighting functions WGi are determined using the susceptibility map by the fast QSM method (Fig. 1C). The susceptibility artifacts χSA (Fig. 1E) are then calculated by solving
Discussion
In this study, we proposed and developed a general method for estimating streaking artifacts and subtracting them from a given susceptibility map. Specifically, this method used an iterative approach to estimate the streaking artifacts from the ill-conditioned k-space regions using the initial susceptibility estimate by the LSQR method and the susceptibility boundaries estimated using a fast QSM method. By estimating and subtracting out the streaking artifacts, an unbiased quantification of
Acknowledgment
This study was supported in part by the National Institutes of Health (NIH) through grants NIBIB P41 EB015897, R21HL122759 and R01 MH096979 and by the National Multiple Sclerosis Society (RG4723) to C.L. W.L. was also supported in part by UL1 TR001119 via the Clinical Translational Science Awards (CTSA).
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