Correction of B0 susceptibility induced distortion in diffusion-weighted images using large-deformation diffeomorphic metric mapping

Abstract

Geometric distortion caused by B0 inhomogeneity is one of the most important problems for diffusion-weighted images (DWI) using single-shot, echo planar imaging (SS-EPI). In this study, large-deformation, diffeomorphic metric mapping (LDDMM) algorithm has been tested for the correction of geometric distortion in diffusion tensor images (DTI). Based on data from nine normal subjects, the amount of distortion caused by B0 susceptibility in the 3-T magnet was characterized. The distortion quality was validated by manually placing landmarks in the target and DTI images before and after distortion correction. The distortion was found to be up to 15 mm in the population-averaged map and could be more than 20 mm in individual images. Both qualitative demonstration and quantitative statistical results suggest that the highly elastic geometric distortion caused by spatial inhomogeneity of the B0 field in DTI using SS-EPI can be effectively corrected by LDDMM. This postprocessing method is especially useful for correcting existent DTI data without phase maps.

Fig. 1

LDDMM registration on digital phantom with control of elastic warping. (a) is the image after local anterior expansion and posterior shrinkage of template image (b). (c) is the difference image of (a) and (b). (d) and (g) are the corrected results of LDDMM with α = 0.01 and α = 0.002, respectively. (e) is the difference image of (b) and (d) and (h) is the difference image of (b) and (g). (f) and (i) show the deformation field from LDDMM transformation.

Fig. 2

The target T₂-weighted (a), uncorrected b0 (b), uncorrected color-coded (c), SPM-corrected b0 (d), LDDMM-corrected b0 (e), and LDDMM-corrected, color-coded (f) images. The color map shown in (g) is a distortion map and the color bar indicates the distortion values in millimeters. (h) and (i) are enlarged uncorrected b0 and LDDMM-corrected b0, respectively. Axial slices at the level of the genu of the corpus callosum are shown. Red and yellow curves were defined by the brain boundary (red) and the lateral ventricle (yellow) of the target image and were superimposed on other images at the exact same locations. Yellow and white arrows indicate severely distorted regions that could be fully corrected by LDDMM and the regions where LDDMM performs better than SPM, respectively.

Fig. 3

The target T₂-weighted (a), uncorrected b0 (b), uncorrected color-coded (c), SPM corrected b0 (d), LDDMM-corrected b0 (e), and LDDMM-corrected, color-coded (f) images. The color map shown in (g) is a distortion map. (h) and (i) are enlarged uncorrected b0 and LDDMM-corrected b0, respectively. The reconstructed para-sagittal slices from acquired axial images are shown to demonstrate the overall severe distortion at prefrontal lobe and pons. See legend of Fig. 2 for representation of red and yellow lines and that of yellow and white arrows.

Fig. 4

Population-averaged 3D distortion map calculated from the nine subjects. Axial slices at the level of the internal capsule (a), the anterior commissure (b), the pons (c), the para-sagittal slice (d), and a coronal slice (e) are shown.

Fig 5

Cumulative distribution of distances between paired landmarks averaged across nine subjects. Solid, dot and dashed lines represent the distances before and after SPM and LDDMM distortion correction.