Mapping the impact of nonlinear gradient fields with noise on diffusion MRI

Abstract

In diffusion MRI, gradient nonlinearities cause spatial variations in the magnitude and direction of diffusion gradients. Studies have shown artifacts from these distortions can results in biased diffusion tensor information and tractography. Here, we investigate the impact of gradient nonlinearity correction in the presence of noise. We introduced empirically derived gradient nonlinear fields at different signal-to-noise ratio (SNR) levels in two experiments: tensor field simulation and simulation of the brain. For each experiment, this work compares two techniques empirically: voxel-wise gradient table correction and approximate correction by scaling the signal directly. The impact was assessed through diffusion metrics including mean diffusivity (MD), fractional anisotropy (FA), axial diffusivity (AD), radial diffusivity (RD), and principal eigen vector (V1). The study shows (1) the correction of gradient nonlinearities will not lead to substantively incorrect estimation of diffusion metrics in a linear system, (2) gradient nonlinearity correction does not interact adversely with noise, (3) nonlinearity correction suppresses the impact of nonlinearities in typical SNR data, (4) for SNR below 30, the performance of both the gradient nonlinearity correction techniques were similar, and (5) larger impacts are seen in regions where the gradient nonlinearities are distinct. Thus, this study suggests that there were greater beneficial effects than adverse effects due to the correction of nonlinearities. Additionally, correction of nonlinearities is recommended when region of interests are in areas with pronounced nonlinearities.

Keywords: Diffusion preprocessing; Diffusion tensor imaging; Gradient nonlinearity; Magnetic resonance distortion; Signal-to-noise; Tensor simulation.

Fig. 1.

Diffusion weighted images (a) experience nonlinear magnetic fields (b). In theory, these nonlinearities are well controlled but in practice we may achieve b-value and gradients (shown in red in (c) and (d)) instead of the desired b-value and gradients (shown in green in (c) and (d)) that were provided as scan parameters.

Fig. 2.

From tensor simulation or synthetic DW-MRI signal, we obtained ground truth tensor (gray). This simulated signal from the ground truth tensor was corrupted with noise (brown) as well as noise and nonlinear fields L(r) (purple) to simulate the corrupt DW-MRI signals. These corrupt DW-MRI signals were corrected for gradient nonlinearities using the approximate correction (green) and empirical correction (yellow). Tensors were fit to the corrected signal and corrected gradients and b-value from approximate correction and empirical correction respectively. Derived indices were recomputed to compare the impact of nonlinear fields and correction techniques.

Fig. 3.

The interaction of L(r) corruption and L(r) correction with noise in tensor simulation at FA = 0.25 averaged across orientation. a) A noisy linear system with L (r) correction (green) shows a 0.88%, 0.11% increase in median APE for FA, MD, and 0.09° increase in median AE for V1. b) The change in the derived metrics with noise and L(r) correction (green) shows decreases in median APE by 7.89% in FA, 3.2% in MD, and decrease in median AE by 1.48° in V1 from that of noise and L(r) corruption (blue). c) The effect of L(r) correction with ground truth noise subtracted (green) has median APE of 0.38% in FA, 0.07% in MD, and median AE of 0.28° in V1.

Fig. 4.

The interaction of L(r) corruption and L(r) correction with noise in synthetic imaging data. a) A noisy linear system L(r) correction (green) shows a 0.43%, 0.1%, increase in median APE for FA, MD, and 0.28° increase in median AE for V1. b) The change in the derived metrics with noise and L(r) correction (green) shows decrease in median APE by 0.55% in FA, 0.41% in MD, and decrease in median AE by 0.23° in V1 from that of noise and L(r) corruption (blue). c) The effect of L(r) correction with ground truth noise subtracted (green) has median APE of 0.13% in FA, 0.01% in MD, and median AE of 0.11° in V1.

Fig. 5.

Regional impacts of gradient nonlinearity for synthetic data. (a) GM parcellation of L(r) corruption and (b) WM parcellation of L(r) corruption. We show the APE and AE by region according to the BrainCOLOR and JHU DTI-based white matter atlas. Sagittal and axial views are shown for FA, MD, AD, RD, and V1. Large variation was observable in the superior regions of WM and GM.