The effect of gradient nonlinearities on fiber orientation estimates from spherical deconvolution of diffusion magnetic resonance imaging data

Abstract

Gradient nonlinearities in magnetic resonance imaging (MRI) cause spatially varying mismatches between the imposed and the effective gradients and can cause significant biases in rotationally invariant diffusion MRI measures derived from, for example, diffusion tensor imaging. The estimation of the orientational organization of fibrous tissue, which is nowadays frequently performed with spherical deconvolution techniques ideally using higher diffusion weightings, can likewise be biased by gradient nonlinearities. We explore the sensitivity of two established spherical deconvolution approaches to gradient nonlinearities, namely constrained spherical deconvolution (CSD) and damped Richardson-Lucy (dRL). Additionally, we propose an extension of dRL to take into account gradient imperfections, without the need of data interpolation. Simulations show that using the effective b-matrix can improve dRL fiber orientation estimation and reduces angular deviations, while CSD can be more robust to gradient nonlinearity depending on the implementation. Angular errors depend on a complex interplay of many factors, including the direction and magnitude of gradient deviations, underlying microstructure, SNR, anisotropy of the effective response function, and diffusion weighting. Notably, angular deviations can also be observed at lower b-values in contrast to the perhaps common assumption that only high b-value data are affected. In in vivo Human Connectome Project data and acquisitions from an ultrastrong gradient (300 mT/m) scanner, angular differences are observed between applying and not applying the effective gradients in dRL estimation. As even small angular differences can lead to error propagation during tractography and as such impact connectivity analyses, incorporating gradient deviations into the estimation of fiber orientations should make such analyses more reliable.

Link between structural connectivity of the medial forebrain bundle, functional connectivity of the ventral tegmental area, and anhedonia in unipolar depression

“…Thus, additional studies are needed to explore the role of the imMFB ( MacNiven et al, 2020 ). Ideally, future studies should apply advanced tractography methods to improve the reconstruction of this small pathway ( Guo et al, 2021 ).…”

What’s new and what’s next in diffusion MRI preprocessing

“…In addition, B-matrix deviations can increase the variability between scanners ( Hansen et al, 2021 ; Tax et al, 2019a). In contrast to the perhaps common assumption that deviations in the B-matrix mostly affect measurements with a high diffusion weighting, also lower-to-moderate diffusion-weighted signals are affected as the absolute signal change as a function of b -value is larger in this regime ( Guo et al, 2020 ).…”

“…each voxel has a unique B-matrix (or set of b -values and gradient directions). Not accounting for this can lead to significant biases, as was shown in the case of gradient nonlinearities for the estimated diffusion coefficient (up to 30% even on 1.5T 40 mT/m ( Bammer et al, 2003 )), diffusion tensor directions and diffusion/kurtosis tensor scalar measures (up to 10% and 3% respectively ( Mesri et al, 2020 )), fibre orientation distribution functions and derived fibre directions (several degrees, ( Guo et al, 2020 ; Morez et al, 2021 )), tissue signal fractions (up to 34% for WM ( Morez et al, 2021 )), tractography and connectivity analysis ( Guo et al, 2019 ; Mesri et al, 2020 ; Morez et al, 2021 ), group statistics (changes in significance and effect sizes ( Mesri et al, 2020 )), and measures derived from sequences beyond Stejskal-Tanner encoding ( Paquette et al, 2020 ). In addition, B-matrix deviations can increase the variability between scanners ( Hansen et al, 2021 ; Tax et al, 2019a).…”

“…b) B-matrix deviations due to gradient nonlinearities in an HCP dataset. From left to right: the logarithm of the determinant of the coil tensor L , which provides information about the voxel-wise scaling of the b -values (with positive values indicating an increase in the effective b -values and the negative values a decrease relative to the prescribed value), the total rotation (as sum of the absolute values of Euler angles) in degrees induced by the rotation component of L , the corresponding T1W anatomical image showcasing the location of the slice, and an example of the imposed and effective sampling in a voxel with coil tensor Δ L = diag([−0.13, −0.14, −0.05]) (Figure adapted from Guo et al (2020) ). c) Direction-encoded color map (first DT eigenvector modulated by FA with maximum brightness indicating FA = 0.05) of an isotropic phantom.…”

Measuring compartmental T2-orientational dependence in human brain white matter using a tiltable RF coil and diffusion-T2 correlation MRI

“…Both the mono-exponential and compartmental models were fitted using a nonlinear least-squares trust-region-reflective algorithm in Matlab (The Mathworks), with an implementation of the compartmental model as described by Lampinen et al. (2020) but with the possibility of inputting spatially varying -matrices obtained from the gradient nonlinearity correction ( Bammer, Markl, Barnett, Acar, Alley, Pelc, Glover, Moseley, 2003 , Guo et al., 2020 , Rudrapatna et al., 2021 ). The fit in each voxel was initialised three times within boundaries (which also served as constraints) and for and respectively.…”