A method for estimating and removing streaking artifacts in quantitative susceptibility mapping

Abstract

Quantitative susceptibility mapping (QSM) is a novel MRI method for quantifying tissue magnetic property. In the brain, it reflects the molecular composition and microstructure of the local tissue. However, susceptibility maps reconstructed from single-orientation data still suffer from streaking artifacts which obscure structural details and small lesions. We propose and have developed a general method for estimating streaking artifacts and subtracting them from susceptibility maps. Specifically, this method uses a sparse linear equation and least-squares (LSQR)-algorithm-based method to derive an initial estimation of magnetic susceptibility, a fast quantitative susceptibility mapping method to estimate the susceptibility boundaries, and an iterative approach to estimate the susceptibility artifact from ill-conditioned k-space regions only. With a fixed set of parameters for the initial susceptibility estimation and subsequent streaking artifact estimation and removal, the method provides an unbiased estimate of tissue susceptibility with negligible streaking artifacts, as compared to multi-orientation QSM reconstruction. This method allows for improved delineation of white matter lesions in patients with multiple sclerosis and small structures of the human brain with excellent anatomical details. The proposed methodology can be extended to other existing QSM algorithms.

Keywords: High resolution brain imaging; Multiple sclerosis; Quantitative susceptibility mapping; Streaking artifact removal.

Fig. 1

Overview of the streaking artifact removal method. A: Initial susceptibility estimate using LSQR. B: The fraction of k-space for streaking artifact estimation. C: The susceptibility map by fast QSM method for estimation of susceptibility boundaries. D: Weights determined using χ_FS. E: the estimated susceptibility artifacts. F: The final streaking artifact removed susceptibility map.

Fig. 2

Fast QSM method for estimating susceptibility boundaries. A: Tissue phase. B: W_FS determined by Eq. (10). C: Susceptibility estimate determined by the first step of Fast QSM method using Eq. (8). D: The k-space corresponding to (C). Arrow pointed to the discontinuities in k-space. E: the final susceptibility estimate using the Eq. (14). F: The k-space corresponding to (E).

Fig. 3

Dependence of LSQR-determined susceptibility on the error tolerance. A: The weights for LSQR reconstruction (W_I). B, C and D: LSQR reconstruction using a tolerance of 0.05, 0.02 and 0.005, respectively. E: COSMOS-determined susceptibility. F: Linear regression of QSM by LSQR with a tolerance of 0.02 against that by COSMOS using total least squares (TLS). G: The influence of error tolerance on the slope of TLS linear regression.

Fig. 4

Dependence of streaking artifact removal on D₂ threshold. A–F: The susceptibility artifacts estimated using a D₂ threshold of 0.02, 0.1 and 0.18. G–I: The corresponding final susceptibility maps. J: The influence of D_2,thres on the slope of TLS linear regression. K: The influence of slice thickness on the slope of TLS linear regression, in which a fixed error tolerance of 0.01 for LSQR and a fixed D_2,thres of 0.1 for susceptibility artifact estimation was used.

Fig. 5

The comparison of different QSM methods for a group of 10 subjects with a spatial resolution of 1 × 1 × 1 mm³. A: Susceptibility using LSQR with an error tolerance of 0.02. B: Susceptibility using iLSQR. C: Susceptibility using fast QSM. D: The susceptibility difference between LSQR and iLSQR. E: The susceptibility difference between fast QSM and iLSQR. F and G: Plot of susceptibility values by LSQR (F) and fast QSM (G) against that by iLSQR in selected ROIs. The ROIs included globus pallidus, putamen, caudate nucleus, red nucleus, substantia nigra, dentate nucleus, splenium of corpus callosum and internal capsule.

Fig. 6

Comparison of different QSM methods for delineating MS lesions. A, D and G: Susceptibility map determined using LSQR. B, E and H: Susceptibility map determined using iLSQR. C, F and I: Susceptibility map determined using fast QSM. J: Comparison of susceptibility contrast between white matter lesions and surrounding normal appearing white matter by different QSM methods.

Fig. 7

Comparison of magnitude, phase, and susceptibility estimates using the fast QSM method, and susceptibility reconstructed using the iLSQR method. d: dentate nucleus; g: globose nucleus; f: fastigial nucleus; e: emboliform nucleus. Magnitude was the summation of the magnitude from all echoes. Hollow black arrow pointed regions with difference between iLSQR and fast QSM method, in which the fast-QSM-determined susceptibility contained more residual non-local effects.

Fig. 8

High resolution magnetic susceptibility imaging of deep brain gray matter nuclei using the iLSQR method. MB: mammillary bodies; STN: subthalamas nucleus; RN: red nucleus; LDNT: the lateral dorsal nuclei of thalamus; Hipo: hippocampus; the inner and outer globus pallidus (iGP and oGP); SN: substantia nigra; PU: putamen.