Quantitative Susceptibility Mapping Using the Multiple Dipole-inversion Combination with k-space Segmentation Method

Abstract

Quantitative susceptibility mapping (QSM) is a new magnetic resonance imaging (MRI) technique for noninvasively estimating the magnetic susceptibility of biological tissue. Several methods for QSM have been proposed. One of these methods can estimate susceptibility with high accuracy in tissues whose contrast is consistent between magnitude images and susceptibility maps, such as deep gray-matter nuclei. However, the susceptibility of small veins is underestimated and not well depicted by using the above approach, because the contrast of small veins is inconsistent between a magnitude image and a susceptibility map. In order to improve the estimation accuracy and visibility of small veins without streaking artifacts, a method with multiple dipole-inversion combination with k-space segmentation (MUDICK) has been proposed. In the proposed method, k-space was divided into three domains (low-frequency, magic-angle, and high-frequency). The k-space data in low-frequency and magic-angle domains were obtained by L1-norm regularization using structural information of a pre-estimated susceptibility map. The k-space data in high-frequency domain were obtained from the pre-estimated susceptibility map in order to preserve small-vein contrasts. Using numerical simulation and human brain study at 3 Tesla, streaking artifacts and small-vein susceptibility were compared between MUDICK and conventional methods (MEDI and TKD). The numerical simulation and human brain study showed that MUDICK and MEDI had no severe streaking artifacts and MUDICK showed higher contrast and accuracy of susceptibility in small-veins compared to MEDI. These results suggest that MUDICK can improve the accuracy and visibility of susceptibility in small-veins without severe streaking artifacts.

Keywords: k-space; quantitative susceptibility mapping; regularization; vein.

Fig 1.

Illustrations of the proposed method. (a) Schematic view of k-space (in the plane of k_y = 0) with the proposed method. (b) Processing flow of susceptibility calculation by the proposed method. FT, fourier transformation; IFT, inverse fourier transformation.

Fig 2.

Simulation models. (a, d) Model susceptibility distribution, including four deep-gray-matter nuclei with different susceptibilities and 36 small veins with different susceptibilities, diameters and angles. (b, e) Model magnitude image. (c, f) Model phase image. Figures in the top row show slices, including deep-gray-matter nuclei, and figures in the bottom row show slices including small veins.

Fig 3.

Dependences of small-vein visibility and susceptibility on reconstruction parameters (n_s and k_th). (a) Dependence of coefficient of variation (CV) in small veins with minimum diameter and susceptibility (d_v = 0.25, x_v = 0.1) on ns. (b) Dependence of CV in small veins with minimum diameter and susceptibility on k_th. (c) Dependence of mean susceptibility in small veins with maximum diameter (d_v = 0.7) on k_th.

Fig 4.

Comparison of artifacts around deep gray matter nucleus between the conventional and proposed methods in numerical simulation. (a–c) Susceptibility maps calculated by (a) thresholdbased k-space division (TKD), (b) morphology enabled dipole inversion (MEDI), and (c) multiple dipole-inversion combination with k-space segmentation (MUDICK) in slices of deep gray matter nucleus. Solid arrows in (a) indicate artifacts visible only in TKD, and outlined arrows in (a–c) indicate artifacts visible in all methods. (d) Quantitative comparison of artifacts. Mean susceptibilities in ppm are calculated in the two regions of interest (ROI) set as 5 × 5 pixels in the positions indicated by thin arrows in (b). The positions of ROI (A) and ROI (B) are selected visually to indicate the position of the above two types of artifacts.

Fig 5.

Comparison of small vein contrasts between the conventional and proposed methods in numerical simulation. (a–c) Susceptibility maps calculated by (a) thresholdbased k-space division (TKD), (b) morphology enabled dipole inversion (MEDI), and (c) multiple dipole-inversion combination with k-space segmentation (MUDICK) in slices of small veins. Solid arrows indicate veins visible in all methods. (d–f) Enlarged images of susceptibility maps in the regions marked as white dashed-line squares in (a–c). Outlined arrows indicate the positions of veins barely visible in any methods, and circle-ended arrows in (e) indicate positions of veins invisible in MEDI but visible in MUDICK.

Fig 6.

Comparison of estimation accuracy in small veins between the conventional and proposed methods. (a–c) Plots of mean susceptibilities in regions of interest (ROIs) of reference and calculated susceptibility maps. ROIs are set in small veins with diameters of (a) 0.25 mm, (b) 0.5 mm, and (c) 0.7 mm. Mean susceptibilities in brain ROI are also plotted in (a–c). Dashed lines in (a–c) indicate the lines of y = x. Note that the values of reference susceptibilities are untrue values that include partial volume effects. (d) Comparison of calculation errors in small veins. χ_ref denotes mean susceptibilities in ROIs of reference map. ΔχTKD, ΔχMEDI, and ΔχMUDICK denote calculation errors of TKD, MEDI, and MUDICK, respectively. Calculation errors are defined as the absolute difference between mean susceptibilities of reference and calculated susceptibility maps. MEDI, morphology enabled dipole inversion; MUDICK, multiple dipole-inversion combination with k-space segmentation; TKD, thresholdbased k-space division.

Fig 7.

Comparison of susceptibilities calculated by conventional and proposed methods in human brain study. (a–c) Coronal images of susceptibility maps of (a) thresholdbased k-space division (TKD), (b) morphology enabled dipole inversion (MEDI), and (c) multiple dipole-inversion combination with k-space segmentation (MUDICK). (d–f) Sagittal images of susceptibility maps of (d) TKD, (e) MEDI, and (f) MUDICK. Solid arrows in (a) and (d) indicate streaking artifacts. (g–i) Enlarged axial images of susceptibility maps around small veins calculated by (g) TKD, (h) MEDI and (i) MUDICK. Outlined arrows indicate veins. (j) Line profile of susceptibility of veins. Position of line is indicated in right image (which is the same as (i). Black circles indicate positions of veins.