Diffusion Tensor Imaging (DTI) is an MRI technique that utilizes the phenomenon of water diffusion (1, 2) as a natural source of contrast. Since its introduction nearly three decades ago (3), DTI has become an important modality in neuroradiology, with increasing utility in the imaging of the musculoskeletal system, abdomen, and heart (4–8). A distinctive advantage of DTI lies in its ability to yield quantitative metrics derived from the eigenvalues and eigenvectors of the diffusion tensor, which are closely related to the underlying tissue microstructure (9–11).

Nevertheless, the comparability of DTI metrics across scanners, protocols, and sites remains limited. This is largely due to the dependence of the measured diffusion tensor on MRI hardware and sequence-specific parameters (12–15), resulting in an apparent rather than absolute tensor representation. Moreover, DTI is sensitive to random noise, affecting the signal-to-noise ratio (16, 17), as well as systematic spatial errors induced by gradient field inhomogeneities (18–23). While the former can be mitigated by increasing voxel size or signal averaging, the latter requires the precise characterization of the spatial error distribution specific to the scanner and protocol in use.

In this study, we aim to determine whether a multi-shell diffusion tensor imaging (DTI) protocol and its subsets can reliably distinguish healthy individuals from patients with multiple sclerosis (MS) with low Expanded Disability Status Scale (EDSS) scores, and to identify which variant offers the best diagnostic performance in individuals with mild neurological and magnetic resonance imaging (MRI) findings. To ensure accuracy, spatial systematic errors in diffusion measurements were corrected using the B-matrix Spatial Distribution method (BSD-DTI).

In contrast to previous work (31), which analyzed the discriminative power of DTI metrics in a different context, we evaluate the effectiveness of fractional anisotropy (FA) and mean diffusivity (MD) across three large brain regions, whole brain (WB), white matter (WM), and gray matter (GM) using both the full protocol and its subsets. Additionally, we propose a more detailed classification approach based on the segmentation of the brain into 95 regions of interest (ROIs) and the analysis of four DTI-derived metrics: FA, MD, axial diffusivity (AD), and radial diffusivity (RD), applying a stringent statistical criterion.

The influence of protocol design on group differentiation is assessed through a comparison of several protocol variants acquired on an MRI system optimized for high signal-to-noise ratio (SNR) and corrected for spatial systematic errors related to gradient nonuniformities, offering insights into optimal acquisition strategies for clinical application.

The phenomenon of spatial heterogeneity in magnetic field gradients, observed in Diffusion Weighted Imaging (DWI) and DTI, was first addressed by researchers in 2003 (18). They attributed this effect to the nonlinearity of magnetic field gradients generated by gradient coils. This spatial heterogeneity is undesirable in DWI/DTI as it introduces systematic errors, negatively affecting the accuracy of diffusion measurements. To mitigate this issue, Bammer introduced a correction based on characteristics in the form of spherical harmonic functions that describe the magnetic field produced by the gradient coils. This correction led to significant improvements in the accuracy of DTI metric calculations (18).

An alternative approach to addressing this issue was proposed in 2008, utilizing diffusion tensor norms in the form of anisotropic and isotropic phantoms with well-defined structures and known distributions of diffusion tensors (24). Diffusion tensor norms here refer to the known, spatially resolved diffusion tensor field of the phantom for each voxel, serving as a reference diffusion tensor D(r). By applying the Stejskal-Tanner (Equation 1), a system of equations is solved to accurately determine the spatial distribution of the b(r) matrix. This matrix represents the effective diffusion weighting at each voxel, reflecting local distortions caused by magnetic field gradient heterogeneity. The definition of b(r) is given explicitly in Equation 3. This approach does not require explicitly identifying the sources of heterogeneity in magnetic field gradients. Instead, the known diffusion tensor norms for each voxel within the studied region inside the RF coil are necessary. Methods for determining these reference diffusion tensor fields for isotropic and anisotropic phantoms have been described in detail in previous publications. This method, referred to as B-matrix Spatial Distribution in DTI (BSD-DTI), was thoroughly described both theoretically and experimentally, with successful implementation on a 9.4 T MRI system (22).

A complementary method involves mapping the spatial distribution of magnetic field gradients by directly measuring the magnetic field (21, 25). From this mapping, the spatial distribution of the b(r) matrix can be derived. This technique demonstrates the inherent heterogeneity in magnetic field gradients. However, it raises a critical concern regarding the accuracy of determining the true distribution of the b(r) matrix when utilizing MR sequences different from the one intended for the specific experimental setup.

It should be noted that the above experimental observations are contrary to the current theoretical approach, namely that the Stejskal-Tanner (S-T) equation assumes the constancy of the diffusion gradient vector in space. An attempt was made to find a solution (20). The derived Equation 2, the Generalized Stejskal-Tanner (GS-T) equation for non-uniform magnetic field gradients, allows for the analysis of any gradient distribution. In addition, the classical S-T equation is a unique solution of GS-T, assuming the constancy of gradient vector G in space.

In the classical approach, the value of matrix b is calculated for time t = 2τ, i.e., at the spin echo center of the dependence, (1) ln ( A ( 2 τ ) A ( 0 ) ) = − b : D where:

A(2τ), A(0) are the signal intensities with and without diffusion gradients,

With the gradient vector G(t) = [Gx(t), Gy(t), Gz(t)]^T, the following relation applies where k ( t , ′ ) = γ ∫ 0 t ′ G ( t ′ ′ ) dt ″ − 2 H ( t ′ − τ ) k ( τ ) , and k ( τ ) = γ ∫ 0 τ G ( t ′ ′ ) dt ′ ′

In fact, the diffusion gradient vector G has a non-uniform distribution in space dependent on the MR scanner, the sequence and its parameters. The solution of the Bloch-Torrey equation proposed in (20), with this assumption of the nonlinearity of the magnetic field, led to the known empirical form of the S-T equation, where matrix b has a spatial relationship b(r), (2) ln ( A ( 2 τ ) A ( 0 ) ) = − b ( r ) : D

The above equation is true, assuming a spin echo signal and symmetry of magnetic field gradients. Then the spatial distribution b(r) has the form, (3) b ( r ) def ¯ ¯ L ( r ) ∫ 0 2 τ k ( t ) k T ( t ) dt L T ( r ) ︸ = b ( t )

The L(r) tensor, which Bammer called the coil tensor, is now called the field correction tensor. It can also be interpreted as the Jacobian matrix for coordinates changing from Cartesian ones to those given by a curvilinear coordinate system, in which the diffusion gradient vector G is constant in space.

Over the last twenty years, researchers have continued to develop the three approaches mentioned above (18, 21, 23, 24, 26). However, no approach has so far provided a definitive solution to the problem. Recently, a large clinical study performed on a modern 3 T MR scanner confirmed the existence of systematic errors related to the spatial heterogeneity of magnetic field gradients.

The DTI metrics included in Table 2 show the impact of the MR protocol and its subsets on the accuracy of the measurement of a single diffusion tensor, here water in an isotropic phantom. The diversity of subsets and the use of the BSD method also allowed for a clear distinction between the influence of Gaussian noise and the physical phenomenon related to the inhomogeneity of magnetic field gradients, generating systematic errors with a specific spatial distribution. After operating the BSD calibration, the most beneficial improvement effects are observed for the 1000(20) subset. The MD standard deviation decreased more than 5 times, from 1.9 to 0.37%, and the FA value decreased approximately 3.7 times from 0.0353 to 0.0096. The improvement recorded for the primary protocol— 1000/2000(40) is significant, although less spectacular. We note an approximately 3.4-fold reduction in the standard deviation of MD from 2.71 to 0.8% and a 1.4-fold decrease in FA from 0.0402 to 0.0283. Therefore, the removable component of systematic errors in the total noise for the MD measurement is as much as 80 and 70%, respectively. This effect will similarly apply to any apparent diffusion tensor in a voxel for any examined object. This is well illustrated by a strong SSD, typically p < 0.001, and an associated huge effect size, an effect size > 0.8 between the STD and BSD approaches.

The subsequent results in Table 3, Supplementary Table S1, and Supplementary Figures S1–S3 help us understand the impact of non-uniform magnetic field gradients in combination with the type of MR protocol’s subset on DTI metrics.

The effectiveness of distinguishing 50-person HC and MS groups with MD and FA parameters in the Whole Brain ROI is similar regardless of the STD or BSD protocol’s subset and approach adopted. In Table 3, we observe strong SSD (p < 0.001) combined with a large effect size (~ 0.4–0.6) between the mean values of the DTI metrics. Considering the group size (Supplementary Table S1), SSD with p < 0.001 is achieved already for 30 persons regardless of the protocol subset. Surprisingly, as demonstrated in Table 4, applying metrics for 95 ROIs and the combined criteria, an SSD with p < 0.005 and an effect size greater than medium (0.3) or large (0.5), the most influential criterion is FA and subset 1000(6), i.e., with the minimum number of directions of the diffusion gradient vector, regardless of the size of the measurement group.

In turn, the numerical values of MD and FA are highly variable depending on the protocol’s subset and insignificant due to the group size. The extreme MD variability reaches ~ 40% and occurs between subsets 2000(20) and 1,000(20). In the case of FA, this variability is even greater and reaches a value of ~50% when comparing the results for main protocol 1000/2000(40) and subset 1,000(6), ~ 0.021 and ~ 0.031. At the same time, the BSD correction did not introduce any significant changes numerically. Note, however, that these values (and distributions) between approaches are characterized by a strong SSD with p < 0.001, combined with a huge effect size (effect size > 0.8). The small variability in metrics between the STD and BSD approaches is easier to understand by looking simultaneously at the extensive distributions of FA and MD (Figures S1-S3), which suggest the dominant influence of anatomical variation on mean FA and MD. Moreover, large ROIs can average the impact of systematic errors, which introduce much greater variation locally.

The above observations lead to several important conclusions. First, the primary correction of the MD and FA distributions is achieved by accounting for the actual spatial distribution of magnetic field gradients present during acquisition. As a result, increasing the number of signal averages (accumulations) has only a marginal effect in experiments with sufficiently high SNR. Crucially, this correction procedure is entirely independent of the imaged object; it depends solely on the MRI system, the sequence type, and specific acquisition parameters (20, 32).

Furthermore, comparing DTI-derived metrics across different acquisition protocols has limited interpretive value. These metrics should be evaluated within the context of a specific protocol, and only after verifying and correcting for the impact of spatially dependent systematic errors in each region of interest (ROI).

In addition, a recent study (30) demonstrated the effect of BSD correction on DTI metrics and tractography, while incorporating standard preprocessing steps commonly used in diffusion MRI studies. These steps included denoising (Local PCA), Gibbs oscillations correction, eddy current correction, motion correction, B1 inhomogeneity correction, and rigid body registration for geometric distortion correction. The findings confirmed that BSD maintains its effectiveness across these conditions, with denoising showing the most significant additional benefit. This reinforces the practical utility of BSD in clinical and research protocols aiming for higher anatomical precision.