Тенсорная диффузия МРТ и NODDI в классификации множественных склерозов.

Introduction

Diffusion MRI probes tissue microstructure in vivo, and fractional anisotropy (FA), derived from diffusion tensor imaging (DTI), has been its most widely used scalar metric for nearly three decades ( Basser et al., 1994 ). Applied across neurological and psychiatric conditions ( Alexander et al., 2019 ; Müller and Kassubek, 2024 ), FA is sensitive to a broad range of tissue alterations but cannot distinguish among their underlying sources: myelination, axonal organization and density, fibre orientation complexity, extracellular water, and cerebrospinal-fluid partial volume can all influence FA in overlapping ways ( Novikov et al., 2019 ). This limited biological specificity has motivated multi-compartment approaches such as Neurite Orientation Dispersion and Density Imaging (NODDI) ( Zhang et al., 2012 ) and free-water elimination methods intended to reduce isotropic contamination of tensor-derived measures ( Pasternak et al., 2009 ). NODDI is conventionally estimated from multi-shell data, whereas free-water elimination can also be applied to constrained single-shell data; both add modelling assumptions, and additional diffusion weightings may increase acquisition time ( Jelescu et al., 2020 ; Lampinen et al., 2017 ).

Multiple sclerosis (MS) provides a particularly relevant setting in which to test these approaches. MS combines focal inflammatory demyelinating lesions with abnormalities beyond visible plaques, including diffuse white-matter injury and cortical and deep-grey-matter involvement ( Filippi et al., 2018 ; Lassmann, 2018 ; Kutzelnigg et al., 2005 ; Moll et al., 2011 ; Calabrese et al., 2015 ). Demyelination, axonal injury, inflammation, oedema, gliosis, and tissue loss can all alter diffusion measurements, but none maps uniquely onto FA, MD, AD, RD, or a single NODDI parameter. In coherently organized white matter, demyelination is often associated with increased RD and reduced FA, whereas axonal injury can alter AD, but these relationships depend on lesion stage, fibre architecture, extracellular water, and partial-volume effects ( Song et al., 2002 ; Wheeler-Kingshott et al., n.d. ). NODDI-derived NDI, ODI, and the isotropic volume fraction, termed free-water fraction (FWF) here, may provide complementary tissue-sensitive information, but they remain model-derived parameters estimated under compartment and diffusivity assumptions rather than direct histological measurements ( Zhang et al., 2012 ; Jelescu et al., 2020 ). The metrics examined here are therefore expected to be sensitive to MS-related abnormalities but specific to none of their individual pathological mechanisms.

The central empirical question is whether multi-compartment modelling provides additional classification information beyond fuller use of the diffusion tensor. We address this question at three levels: the metric level, the acquisition level, and the correction level.

At the metric level, clinical applications of DTI have most often emphasized FA and mean diffusivity (MD), although the tensor eigenvalues support a broader family of scalar summaries. These include axial and radial diffusivity (AD and RD) ( Song et al., 2002 ), linear, planar, and spherical anisotropy (CL, CP, and CS) ( Westin et al., 2002 ), and rotational invariants (I1-I4) ( Ennis and Kindlmann, 2006 ). These measures are mathematically related and strongly correlated, but they weight different aspects of tensor magnitude and geometry and may therefore contain complementary discriminative information. NODDI provides a different representation through NDI, ODI, and FWF. Previous MS studies suggest that NODDI can reveal abnormalities not fully reflected by conventional DTI ( Collorone et al., 2020 ; Caranova et al., 2023 ; Seyedmirzaei et al., 2023 ), although other work indicates complementary rather than consistently superior discrimination ( Granberg et al., 2017 ; Grussu et al., 2017 ; Preziosa et al., 2023 ).Importantly, NODDI is only one multi-compartment approach and is not a proxy for multi-shell diffusion MRI in general; diffusional kurtosis imaging ( Jensen et al., 2005 ), the spherical mean technique ( Kaden et al., 2016 ), Standard Model Imaging ( Coelho et al., 2022 ), and other multi-shell approaches were not evaluated here.

At the acquisition level, multi-shell schemes support compartment-based modelling but require additional diffusion weightings, and it remains unclear whether multiple shells improve group discrimination when analysis is restricted to tensor-derived measures. Retrospectively derived shell-specific datasets allow this question to be tested under matched participant and scanner conditions, although they are not equivalent to prospectively shortened clinical protocols. At the correction level, free-water elimination may reduce isotropic contamination of tensor estimates ( Pasternak et al., 2009 ), but single-shell free-water estimation can require additional constraints and may introduce systematic bias ( Correia et al., 2024 ). Its effect across a broader range of tensor-derived measures also remains incompletely characterized.

Interpretation is further complicated by focal pathology and partial-volume effects. ROI averages may combine lesion and non-lesion tissue, while ventricular and CSF-labelled regions are particularly sensitive to partial volume ( Vos et al., 2011 ; Martínez-Heras et al., 2020 ). Because lesion burden is strongly associated with disease status and represents part of the MS phenotype rather than a conventional pre-exposure confounder, we assess its influence through lesion masking rather than treating lesion volume as a primary adjustment covariate. Potential effects of age and intracranial volume are evaluated separately, and ventricular, CSF-labelled, and tissue-specific analyses are used to test anatomical robustness.

In a single-centre cohort of 220 participants (84 healthy controls and 136 patients with relapsing-remitting MS with predominantly low disability), we extracted 13 tensor-derived metrics (FA, MD, AD, RD, λ2, λ3, CL, CP, CS, and I1-I4) and three NODDI-derived metrics (NDI, ODI, and FWF) from 98 SynthSeg-parcellated regions ( Billot et al., 2023 ). The overall aim was to compare broader tensor-derived representations with the evaluated NODDI metrics for HC-versus-RRMS discrimination within a common classification framework. Specifically, we aimed to: (1) determine which tensor-derived metrics and combinations carry discriminative information and compare them with NODDI at matched feature dimensionality; (2) test multi-shell against independently processed shell-specific tensor datasets, including reduced angular sampling; (3) quantify the effect of NODDI-informed free-water correction; (4) assess robustness to age, intracranial volume, lesion, ventricular/CSF, and tissue-specific effects; and (5) identify the regions contributing most strongly to classification and characterize the direction and stability of their contributions.

Materials and methods

Participants

This prospective, single-centre study was approved by the Bioethics Committee at the Regional Medical Chamber (No. 282/KBL/OIL/2020; 18 December 2020), and written informed consent was obtained from all participants. Between January 2021 and January 2022, consecutive patients with relapsing-remitting multiple sclerosis (RRMS) were recruited at the University Hospital. Inclusion criteria were age 18 to 55 years, a diagnosis of RRMS according to the 2017 revision of the McDonald criteria ( Thompson et al., 2018 ), and ongoing disease-modifying therapy. Exclusion criteria comprised standard contraindications to MRI and pregnancy. All patients underwent neurological assessment and brain MRI as part of the study protocol. Healthy controls were volunteers aged 18 to 50 years with no history or clinical signs of multiple sclerosis or other central nervous system disease. The flow of recruitment and exclusion is shown in Supplementary Fig. S2.

The final analytic sample comprised 220 participants: 84 healthy controls (59 female; mean age 34.0 ± 8.1 years) and 136 patients with RRMS (89 female; mean age 36.2 ± 7.1 years). Patients had a median Expanded Disability Status Scale (EDSS) score of 1.0 (interquartile range 1.0 to 2.0; full range 0.0 to 5.5). The groups did not differ in sex distribution or total intracranial volume, and the nominal age difference of 2.2 years did not survive correction for the three demographic comparisons ( Table 1 ). Table 1 Demographic and clinical characteristics of the study sample. Values are mean ± standard deviation unless otherwise indicated. Group comparisons by independent-samples t -test (age, ICV) or χ 2 test (sex). EDSS = Expanded Disability Status Scale; ICV = total intracranial volume. HC ( n = 84) MS ( n = 136) p (fdr) Age, years (mean ± SD) 34.0 ± 8.1 36.2 ± 7.1 0.129 Sex, F / M (% female) 59 / 25 (70%) 89 / 47 (65%) 0.834 ICV, mm 3 (mean ± SD) 1,409,248 ± 113,575 1,410,528 ± 127,376 0.938 EDSS, median (IQR) – 1.0 (1.0–2.0) – EDSS, range – 0.0–5.5 – SDMT, median (IQR) 55.5 (50.0–59.0) 56.0 (49.0–62.2) 0.306 Lesion volume, mm 3 287 5593 <0.001 Disease duration from diagnosis, years – 6.2 (4.1–9.2) – Disease duration from onset, years – 8.2 (5.2–12.5) –

MRI acquisition

All examinations were performed on a 3 T MAGNETOM Vida Fit scanner (Siemens Healthineers, Erlangen, Germany) at the University Hospital using a 20-channel head/neck coil and the same standardized acquisition protocol. Participants were positioned consistently at the magnet isocenter using the scanner laser system, and scout images were used for standardized volume prescription. The same vendor-provided 20-direction diffusion gradient scheme, defined in the scanner coordinate system and kept unchanged across examinations, was used for all participants. Diffusion-weighted imaging was acquired with a multi-shell spin-echo echo-planar imaging (SE-EPI) sequence with the following parameters: 20 diffusion gradient directions per shell (4 averages per direction); b = 0, 1000, and 2000 s/mm 2 ; repetition time (TR) = 3900 ms; echo time (TE) = 88 ms; acquisition time (AT) = 680 s; field of view (FOV) = 191 × 191 mm 2 ; voxel size = 2.5 × 2.5 × 2.5 mm 3 .

This multi-shell design enabled the evaluation of five DTI protocol variants: (i) single-shell at b = 1000 s/mm 2 (ss-b1000), combining the shared b = 0 volumes with the lower b-value directions; (ii) single-shell at b = 2000 s/mm 2 (ss-b2000), combining the shared b = 0 volumes with the higher b-value directions; (iii) multi-shell combining both b-values (ms-b1000/2000); and (iv, v) reduced-direction variants ss-b1000-6dir and ss-b2000-6dir, retaining six of the twenty directions in each shell. The six directions were selected by minimising electrostatic repulsion energy under antipodal symmetry, before any classification result was examined. Each variant was constructed at the level of the raw diffusion volumes and processed independently through the complete pipeline, including separate eddy-current and motion correction with b-vector rotation. No preprocessing output was shared between variants, so that a reduced variant was corrected using only the volumes it contained. A sixth variant, ss-b1000 + ss-b2000, was constructed by concatenating the feature vectors obtained independently from the two single-shell protocols. This pooled approach doubles the feature dimensionality (196 features for a single metric) without requiring joint tensor estimation, and tests whether complementary information from two separate single-shell fits can substitute for a single multi-shell fit.

Image processing

Preprocessing followed the same steps for all scans. Data were first denoised with a local PCA method and had Gibbs ringing suppressed using routines from the DIPY library ( Garyfallidis et al., 2014 ). Head-motion and eddy-current-related distortions were then corrected with FSL eddy, called through the dwifslpreproc interface of MRtrix3 ( Tournier et al., 2019 ), using a linear second-level movement model and a quadratic first-level eddy-current model; the b-vectors rotated by eddy were used for all subsequent tensor and NODDI fitting. Residual intensity inhomogeneity was then removed with the dwibiascorrect tool from MRtrix3. Brain masks and regional parcellation were generated with SynthSeg ( Billot et al., 2023 ), run on the b0 images, resulting in 98 regions of interest (ROIs) comprising cortical parcels from the Desikan-Killiany atlas ( Desikan et al., 2006 ), subcortical structures, ventricular compartments, and white matter regions. White-matter lesions were segmented on FLAIR using FLAMeS ( Dereskewicz et al., 2025 ), an nnU-Net model trained for multiple sclerosis. Lesion masks were transferred to diffusion space by label-driven registration (Supplementary Table S4).

Diffusion tensors were estimated by χ 2 minimization using in-house software and diagonalized to obtain the three eigenvalues (λ 1 ≥ λ 2 ≥ λ 3 ). From these eigenvalues, 13 scalar DTI metrics were computed for each ROI, comprising diffusivity measures (MD, AD, RD, λ 2 , λ 3 ) anisotropy (FA), tensor shape descriptors (CL, CP, CS), and rotational invariants (I1-I4).

NODDI and free-water correction. Neurite orientation dispersion and density imaging (NODDI) parameters were estimated from the multi-shell data ( b = 0, 1000, 2000 s/mm 2 ) using the Accelerated Microstructure Imaging via Convex Optimization (AMICO) framework ( Daducci et al., 2015 ), which provides a computationally efficient linear reformulation of the original NODDI model ( Zhang et al., 2012 ). Three NODDI metrics were extracted for each ROI: the neurite density index (NDI), the orientation dispersion index (ODI); and the free water fraction (FWF).

The voxel-wise FWF maps obtained from NODDI were subsequently used to perform free-water correction (FWC) of the diffusion tensors. For each protocol variant, the diffusion signal at every voxel was decomposed into a tissue compartment and a free-water compartment whose volume fraction was fixed to the NODDI-derived FWF estimate. The diffusion tensor was then re-estimated from the tissue-only signal, resulting in corrected eigenvalues from which all 13 DTI metrics were recomputed. Because the FWF maps are derived from the complete multi-shell acquisition, the single-shell FWC variants are not attainable from a single-shell acquisition alone. This procedure was applied independently to each of the three protocol variants, producing three FWC datasets (ss-b1000-fwc, ss-b2000-fwc, ms-b1000/2000-fwc) (Supplementary Table S2).

Classification framework

Binary classification of HC versus MS was performed using L2-regularized logistic regression (regularization parameter C = 0.1 (Supplementary Table S5)), as implemented in scikit-learn ( Pedregosa et al., 2011 ), within a 5 × 5 repeated stratified cross-validation (CV) scheme, producing 25 folds in total. Within each fold, features were standardized to zero mean and unit variance using parameters estimated exclusively from the training set. Thresholds were determined using the Youden criterion within each training fold. Each participant appeared in the test set once per repetition, and the threshold applied to that participant was the mean of the thresholds from the folds in which that participant was held out, ensuring that threshold determination used only models that had not seen that participant.

The primary evaluation metric was the area under the receiver operating characteristic curve (AUC). Secondary metrics included balanced accuracy (BAcc), Matthews correlation coefficient (MCC), sensitivity, specificity, positive and negative predictive value, and calibration slope, intercept and Brier score. All measures were computed from out-of-fold predictions averaged across repetitions, giving one value per participant.

Feature importance was assessed by averaging the logistic regression coefficients across all 25 CV folds, after standardization. Absolute values were used to rank regions; the direction of effects was established from group mean differences, expressed as Cohen's d, because coefficients of a penalised model with correlated features index conditional contribution rather than effect magnitude.

Analyses

Eight analyses were performed. (1) Single metric discrimination : each of the 13 DTI metrics was evaluated independently across all applicable tensor-estimation protocol variants, whereas each of the three NODDI metrics was evaluated independently using the complete multi-shell acquisition. For each metric, the 98 ROI-level mean values were used as features. (2) Metric combinations: four nested DTI combinations of increasing complexity were tested: FA alone (98 features), FA + MD (196 features), FA + MD + CS + CL (392 features), and all 13 DTI metrics (1274 features). The combined NODDI model (NDI + ODI + FWF; 294 features) and the joint DTI + NODDI model (1568 features) were also evaluated. (3) Single-shell versus multi-shell: the ss-b1000, ss-b2000, ss-b1000-6dir, ss-b2000-6dir, and pooled ss-b1000 + ss-b2000 protocols were compared against ms-b1000/2000 for each metric and combination. (4) NODDI added value: the contribution of NODDI was assessed by comparing All DTI + NODDI against All DTI alone, by comparing each individual NODDI metric against FA, and by comparing the three NODDI metrics against three tensor metrics at matched feature dimensionality, both across the whole brain and within tissue classes. (5) Free-water correction: the effect of FWC (based on NODDI-derived FWF maps) was quantified by comparing each standard metric against its FWC counterpart for every protocol. (6) Lesion masking: white-matter lesions were segmented on FLAIR, transferred to diffusion space, and removed from the parcellation before regional averaging. Classification was repeated on the lesion-masked features, for the whole brain and separately for cortical, subcortical, white-matter and ventricular region sets. (7) Tissue specificity: models were refitted within cortical parcels, subcortical structures, cerebral white matter, and ventricular regions separately, and with ventricular and CSF-labelled regions excluded from the full model. (8) Confounder robustness: the sensitivity of classification performance to potential confounders (age, sex, ICV) was assessed by linearly regressing out these variables from all ROI features within each cross-validation fold. For each fold, regression coefficients were estimated on the training partition only and applied to both the training and test partitions. The change in AUC (ΔAUC = AUC residualized - AUC raw ) was then computed. This procedure was applied for each variable alone and jointly, for two representative feature sets (FA + MD; FA + MD + CS + CL) on the ms-b1000/2000 and ss-b2000 protocols. Because a classifier drawing on more than a thousand correlated features can compensate for the removal of one dimension, an unchanged AUC does not establish independence from the covariate; covariate distributions and effect sizes are therefore reported alongside ΔAUC.

Statistical testing

Uncertainty in AUC was quantified by a participant-level bootstrap (2000 resamples, stratified by group) of the out-of-fold predictions. Pairwise comparisons of classification performance between models or protocol variants used a paired bootstrap over the same resampled participants, so that the interval reflects the difference rather than the sum of two independent uncertainties. Reported differences are the observed ones; the bootstrap supplies the interval and the p value.

Twenty-five contrasts were specified in advance: for each of the four confirmatory models, the four acquisition variants against multi-shell and the two reduced-direction variants against their full-direction counterparts, together with the addition of NODDI to the full tensor set. The Benjamini-Hochberg false-discovery-rate procedure ( Benjamini and Hochberg, 1995 ) was applied to this family at α = 0.05, and separately within each other family of tests. Comparisons added after the analysis plan was fixed, including the pooled single-shell variant, are reported with intervals and uncorrected p values and identified as such.

Differences between protocols are reported as estimates with confidence intervals rather than as formal equivalence tests. An equivalence margin in AUC has no established clinical anchor, so declaring one would determine the conclusion as much as the data would; the interval allows a reader to apply whatever margin they consider relevant. Group comparisons of continuous variables used the Mann-Whitney test, with the independent-samples t -test for demographic characteristics, and the chi-squared test for categorical variables; these were likewise FDR-corrected within each family of tests.

Results

Single metric discrimination

Fractional anisotropy achieved the highest classification performance on every acquisition protocol ( Fig. 1 A), with AUC ranging from 0.917 on ss-b2000 to 0.929 on the pooled single-shell variant. On the multi-shell protocol the full DTI metric ranking was: FA (0.922), CS (0.915), λ3 (0.911), CL (0.907), CP (0.901), λ2 (0.898), RD (0.885), AD (0.880), I1 and MD (0.874 each), I4 (0.869), I2 (0.867), and I3 (0.863). The ranking was largely preserved across protocols ( Fig. 1 A), with modest and interpretable shifts: b = 2000 favoured diffusivity-related measures, raising λ2 from 0.872 to 0.909 and RD from 0.864 to 0.895, whereas b = 1000 favoured tensor-shape descriptors, raising CS from 0.891 to 0.926 and CP from 0.882 to 0.909. These differences were small (median |ΔAUC| = 0.011 for ss-b2000 against multi-shell) and none reached statistical significance after correction. Fig. 1 Single metric classification performance. (A) AUC for all 13 DTI metrics across four acquisition protocols, ordered by maximum AUC. Points show the AUC from participant-level out-of-fold predictions; error bars are 95% bootstrap confidence intervals (2000 resamples, stratified by group). FA achieves the highest AUC on every protocol, peaking at 0.929 on the pooled single-shell variant. (B) The five best DTI metrics (blue and green; multi-shell) against the three NODDI metrics (orange). NDI (0.912) ranks below FA but above most tensor metrics; ODI (0.891) and FWF (0.804) fall below all leading DTI metrics. (C) ROC curves for selected DTI (solid) and NODDI (dashed) metrics on the multi-shell protocol, built from the same predictions as panels A and B; bands are 95% bootstrap intervals. Fig. 1

A direct comparison of the leading DTI metrics against the three NODDI metrics is shown in Fig. 1 B, with the corresponding ROC curves in Fig. 1 C. Among the NODDI metrics, NDI reached 0.912, ranking below FA but above most tensor-derived measures, while ODI (0.891) and FWF (0.804) fell below the leading DTI metrics. No NODDI metric surpassed FA on any protocol. Paired bootstrap comparisons confirmed that FA outperformed the NODDI metrics numerically on the multi-shell protocol (ΔAUC = +0.010 versus NDI, +0.031 versus ODI, and + 0.118 versus FWF), although the margin over the strongest tensor alternatives was narrow: on ss-b1000 the difference between FA (0.926) and CS (0.926) was below 0.001.

Metric combinations

Combining tensor-derived metrics improved classification performance ( Fig. 2 ). The prespecified combination of FA + MD + CS + CL (4 metrics, 392 features) achieved an AUC of 0.967 on the multi-shell protocol, a gain of +0.045 over FA alone on the same protocol. This four-metric combination performed comparably to the full 13-metric DTI model (0.966), and the reduction from 13 metrics to 4 entailed no measurable loss. The effective dimensionality of the full feature set was 7.85 for 1274 nominal features, which explains why performance is insensitive to the number of metrics included beyond a small core. Fig. 2 Metric combinations across acquisition variants. AUC with 95% bootstrap confidence intervals, grouped by metric combination. Colour identifies the protocol, marker shape the angular sampling: circles for 20 directions, diamonds for 6. The dashed line marks the prespecified four-metric model on multi-shell (0.967). Fig. 2

A conditional analysis identified which shape descriptor carries the improvement ( Table 2 ). Adding CS to FA + MD left performance unchanged (ΔAUC = −0.001, 95% CI -0.008 to +0.008, p = 0.872), whereas adding CL raised it by 0.010 (95% CI −0.001 to +0.023, p = 0.082). Tested directly against one another, CL added to FA + MD + CS gave +0.010 ( p = 0.056), while CS added to FA + MD + CL gave −0.001 ( p = 0.728). A three-metric alternative (FA + MD + CL; 294 features) reached 0.968, marginally above the prespecified four-metric model (ΔAUC = +0.001, p = 0.728). The point-estimate gain over FA + MD was concentrated in the linear anisotropy descriptor, whereas the spherical descriptor did not increase performance; with a difference of 0.010, an interval spanning zero and p between 0.056 and 0.082, this distinguishes the two descriptors more clearly than it establishes the magnitude of the gain from either. Table 2 Conditional contribution of individual shape descriptors, multi-shell protocol. Model Features AUC ΔAUC vs FA + MD 95% CI p FA + MD 196 0.958 reference FA + MD + CS 294 0.957 −0.001 −0.008 to +0.008 0.872 FA + MD + CL 294 0.968 +0.010 −0.001 to +0.023 0.082 FA + MD + CP 294 0.966 +0.009 −0.005 to +0.023 0.208 FA + MD + CS + CL 392 0.967 +0.009 −0.001 to +0.021 0.084 All 13 metrics 1274 0.966 +0.008 −0.003 to +0.023 0.178

Adding all three NODDI metrics to the full DTI feature set did not improve classification (0.964 versus 0.966; ΔAUC = −0.002, 95% CI −0.008 to +0.004, p = 0.431). Because the combined NODDI model comprises 294 features against 392 for the four-metric tensor model, the two were additionally compared at matched dimensionality, using three metrics from each family ( Table 3 ). NODDI did not outperform tensor-derived metrics in any tissue class, including cerebral white matter where its modelling assumptions are best satisfied (0.830 versus 0.835, p = 0.685), and performed significantly worse in subcortical grey matter (0.866 versus 0.914; ΔAUC = −0.048, p = 0.001). Table 3 NODDI against tensor-derived metrics at matched feature dimensionality. ROI set ROIs NODDI (3) DTI (3) ΔAUC 95% CI All regions 98 0.945 0.957 −0.012 −0.032 to +0.007 Cortical parcels 68 0.894 0.897 −0.002 −0.031 to +0.026 Subcortical structures 14 0.866 0.914 −0.048 −0.083 to −0.016 Extended white matter 7 0.835 0.854 −0.019 −0.055 to +0.017 Cerebral white matter 2 0.830 0.835 −0.006 −0.034 to +0.023

The evaluated DTI combinations were defined a priori rather than selected through exhaustive subset search. FA and MD were chosen as the conventional benchmark pair, while CS and CL were added as less commonly used but geometrically complementary tensor-shape descriptors. An all-subsets approach was intentionally avoided because, in a dataset of this size, it would increase the risk of overfitting and selection bias and would blur the distinction between confirmatory benchmarking and exploratory model search.

Single-shell versus multi-shell acquisition

Of the 25 contrasts specified in advance, three reached significance after FDR correction, all involving reduction of angular sampling to six directions at b = 2000 s/mm 2 : FA alone against multi-shell (ΔAUC = −0.062, pFDR = 0.006), FA alone against its full-direction counterpart (−0.057, pFDR = 0.006), and FA + MD against its full-direction counterpart (−0.025, pFDR = 0.008). No comparison between the full-direction single-shell protocols and the multi-shell protocol reached significance for any model.

For the prespecified four-metric model, ss-b2000 gave 0.964 against 0.967 on multi-shell (ΔAUC = −0.003, 95% CI -0.009 to +0.004, p = 0.379) and ss-b1000 gave 0.960 (ΔAUC = −0.007, 95% CI -0.019 to +0.004, p = 0.210). Reducing to six directions preserved performance at b = 1000 for every model, but not at b = 2000, where the difference reached −0.022 for the four-metric model ( p = 0.010, pFDR = 0.050) and − 0.062 for FA alone.

Concatenating the feature sets obtained independently from the two single-shell protocols doubled the dimensionality without benefit (0.966 versus 0.967 for the four-metric model; ΔAUC = −0.001, 95% CI -0.007 to +0.004, p = 0.675). The contribution of the second shell therefore operates through joint tensor estimation rather than through an increase in the number of measurements available to the classifier.

These results indicate that a single-shell acquisition at either b-value, with full angular sampling, results in similar point estimates, with no significant difference detected.

Effect of free-water correction

Free-water correction reduced discriminative performance for most metrics and combinations, but the pattern was not a simple division between anisotropy and diffusivity ( Fig. 3 ). On the multi-shell protocol the largest decreases were observed for λ3 (ΔAUC = −0.025), λ2 (−0.024) and FA (−0.023), while axial diffusivity increased (+0.034), as did the higher-order invariants I3 (+0.018) and I4 (+0.013). Mean diffusivity was essentially unchanged (−0.002). The median change was −0.009 across anisotropy and shape descriptors and − 0.002 across diffusivity measures. Fig. 3 Effect of free-water correction on single metrics. ΔAUC (corrected minus standard) across three protocols, coloured by the direction of change (blue increase, orange decrease) and ordered by the change on multi-shell. Fig. 3

For metric combinations the effect was consistently negative but small ( Fig. 4 ). The four-metric model fell from 0.967 to 0.955 on the multi-shell protocol (ΔAUC = −0.013, 95% CI -0.026 to −0.001, p = 0.031), and comparable reductions were observed on both single-shell protocols. None of the 15 combination comparisons reached significance after FDR correction, and the median change was −0.011. Fig. 4 Free-water correction and metric combinations. Standard (solid bars) versus corrected (hatched) AUC on three protocols. Correction reduced performance for every combination, median change −0.011; the largest reduction was for the four-metric model on multi-shell (0.967 to 0.955). None of the 15 comparisons reached significance after FDR correction. Fig. 4

These findings should be interpreted cautiously for the single-shell FWC variants, because the correction was informed by NODDI-derived FWF maps estimated from the full multi-shell dataset rather than from the single-shell data alone. The single-shell corrected variants are therefore not attainable from a single-shell acquisition.

Most discriminative brain regions

Feature importance based on mean absolute logistic regression coefficients identified subcortical, periventricular and association cortical structures as the most discriminative regions ( Fig. 5 A). The right hippocampus ranked first (summed |coefficient| across six key metrics = 0.580), followed by the left supramarginal gyrus (0.503), left medial orbitofrontal cortex (0.477), fourth ventricle (0.476), right fusiform gyrus (0.471) and left cerebral white matter (0.448). The ranking was stable across cross-validation partitions: the right hippocampus appeared in the top twenty in every fold, and twelve of the top twenty regions did so in at least 80% of folds. Fig. 5 Regional contributions, multi-shell model ( n = 220). (A) Group difference for the 20 most discriminative regions, as Cohen's d for each of six metrics. Blue indicates higher values in patients, red lower; values not surviving FDR correction are printed in a lighter shade. (B) The same regions ranked by summed absolute logistic regression coefficient across the six metrics, averaged over 25 folds. Region names between the panels apply to both. (C) Axial overlay of per-metric importance on one participant's SynthSeg parcellation; colour intensity reflects the absolute coefficient. Fig. 5

Because the absolute coefficient discards the sign, and because coefficients of a penalised model with correlated features index conditional contribution rather than effect magnitude, the direction of the group difference was established separately from the regional means ( Fig. 5 B). Of 588 regional features, 330 differed significantly between groups after FDR correction. The direction was unanimous for the diffusivity measures: mean diffusivity was higher in patients in all 93 significant features (median d = +0.80) and radial diffusivity in all 91 (median d = +0.81). Anisotropy and shape descriptors were regionally mixed: FA was lower in patients in 25 of 39 significant features (median d = −0.35), CL lower in 21 of 41 (−0.29), CP lower in 18 of 32 (−0.38), and CS higher in 24 of 34 (+0.36). The sign of the fitted coefficient agreed with the raw group difference in 80% of significant features.

This dissociation provides a plausible explanation for why metric combinations may outperform individual metrics. The widespread increases in MD and RD are compatible with increased extracellular water and other MS-related tissue alterations, whereas anisotropy and shape changes were more region dependent. The axial anatomical overlays ( Fig. 5 C) show the corresponding spatial distributions: FA-related model importance is broadly distributed across cortical and subcortical structures, MD and RD show stronger contributions in deep grey matter and periventricular white matter, and CL-related importance is most prominent in supramarginal and posterior cingulate cortices.

Lesion masking and tissue specificity

To determine whether classification reflected focal lesions or diffuse microstructural change, white-matter lesions were segmented on FLAIR, transferred to diffusion space, and removed from the parcellation before regional averaging. Because tensors were fitted voxel-wise and the mask entered only at the averaging stage, the difference between the two variants isolates the removal of lesion voxels.

Removing lesion voxels had a negligible effect on whole-brain classification (0.967 to 0.965; ΔAUC = −0.002, pFDR = 0.491) and no effect within cortical parcels (0.937 to 0.937) or subcortical structures (0.909 to 0.909), where the mean lesion fraction in patients was 0.001 and 0.005 respectively ( Table 4 ). The effect was confined to white matter: extended white matter fell from 0.867 to 0.858 (ΔAUC = −0.009, pFDR = 0.004) and cerebral white matter from 0.837 to 0.812 (ΔAUC = −0.026, pFDR = 0.004), where the lesion fraction reached 0.010 and 0.030. Table 4 Classification performance before and after removal of lesion voxels, prespecified four-metric model. ROI set ROIs Lesion fraction Full Lesions removed ΔAUC All regions 98 – 0.967 0.965 −0.002 Cortical parcels 68 0.001 0.937 0.937 −0.000 Subcortical structures 14 0.005 0.909 0.909 +0.000 Extended white matter 7 0.010 0.867 0.858 −0.009 Cerebral white matter 2 0.030 0.837 0.812 −0.026 Ventricles and CSF 7 0.043 0.823 0.828 +0.005

Classification remained well above chance in white matter after lesion removal (0.812), which indicates that the discriminative signal in this tissue is not confined to focal lesions. Ventricular regions carried a high nominal lesion fraction (0.043), almost entirely attributable to the inferior lateral ventricles, which are thin structures adjacent to periventricular white matter; this reflects partial volume rather than lesion tissue, and masking there changed nothing (0.823 to 0.828, pFDR = 0.971).

Models restricted to individual tissue classes showed that no single compartment accounts for the result. Cortical parcels alone reached 0.937, subcortical structures 0.909, extended white matter 0.867 and ventricular regions 0.821. Excluding all ventricular and CSF-labelled regions from the full model changed performance by −0.003 for the prespecified model ( p = 0.220); the only model materially affected was the 13-metric one (−0.008, p = 0.011, pFDR = 0.055), consistent with a larger feature set drawing on fluid compartments that a parsimonious one does not require.

The classifier score within the patient group was moderately associated with lesion volume (Spearman ρ = 0.538, pFDR <0.001), as expected given that lesions contribute to the regional diffusion metrics, and inversely associated with information-processing speed measured by the SDMT (ρ = −0.255, pFDR = 0.008), an association that persisted after partialling out education (ρ = −0.204, p = 0.018) and age (ρ = −0.284, p = 0.001). No association was found with EDSS, relapse count or disease duration, although disability in this cohort was low and narrowly distributed, which limits what such an analysis can detect.

Confounder robustness

To assess whether classification performance was driven by demographic confounders rather than by microstructural differences, ICV, age, sex, or all three were linearly regressed out from all ROI features within each cross-validation fold, with coefficients fitted on the training partition only. The largest absolute change across all 16 confounder-by-feature-set-by-protocol combinations was 0.005, and every bootstrap 95% confidence interval included zero ( Table 5 ). Table 5 Effect of confounder residualization on classification performance. For each confounder (ICV, age, sex, or all three), all 98 ROI features were residualized by fold-wise linear regression, with coefficients fitted on the training partition only and applied to both partitions, within the 5 × 5 cross-validation pipeline. ΔAUC = AUC(residualized) - AUC(raw). Confidence intervals are 95% percentile intervals from a participant-level bootstrap with 2000 resamples, stratified by group. All intervals include zero. Results are shown for two representative feature sets on the multi-shell protocol. Confounder Feature set AUC (raw) AUC (residualized) ΔAUC 95% CI ICV FA + MD 0.958 0.957 −0.001 −0.005 to +0.004 FA + MD + CS + CL 0.967 0.967 +0.001 −0.003 to +0.004 Age FA + MD 0.958 0.954 −0.003 −0.012 to +0.005 FA + MD + CS + CL 0.967 0.965 −0.002 −0.011 to +0.007 Sex FA + MD 0.958 0.962 +0.004 −0.004 to +0.012 FA + MD + CS + CL 0.967 0.970 +0.003 −0.004 to +0.010

Discussion

Diffusion MRI studies in neurological disease have increasingly turned to multi-compartment models and multi-shell acquisitions to improve upon the limitations of conventional DTI metrics. The present results suggest a complementary, lower-cost strategy: expanding the set of metrics derived from the standard diffusion tensor. A combination of four tensor-derived measures (FA, MD, CS and CL) achieved an AUC of 0.967 for HC-versus-MS classification and showed no measurable disadvantage relative to the more complex NODDI-based feature sets evaluated here, while relying only on standard tensor-derived features. FA remained the strongest individual metric (AUC up to 0.929), but adding a tensor-shape descriptor improved classification further.

A conditional analysis showed that this improvement is attributable to the linear anisotropy descriptor rather than to the spherical one. Adding CS to FA + MD left performance unchanged, whereas adding CL raised it by 0.010, and a three-metric model (FA + MD + CL) matched the prespecified four-metric model with a quarter fewer features. The prespecified combination is retained here for the confirmatory comparisons, but the practical recommendation that follows from these data concerns CL specifically. This is a narrower claim than the one we set out to test, and it should be treated as such until replicated: with a difference of 0.010 and an interval spanning zero, the evidence distinguishes the two descriptors more clearly than it establishes the magnitude of the gain from either.

Why does a metric combination outperform any individual metric? The directional analysis offers a more specific answer than regional heterogeneity alone. Mean and radial diffusivity were higher in patients in every region where they differed significantly, with median effect sizes near 0.8, which is consistent with a spatially uniform expansion of the extracellular space. Anisotropy and shape descriptors behaved differently: FA was lower in patients in most but not all significant regions, and CL and CP varied in direction between regions. Diffusivity therefore contributes a global signal and the shape descriptors a regionally specific one whose sign depends on local fibre architecture, so the two are complementary rather than redundant. This interpretation is consistent with the geometric meaning of the descriptors ( Westin et al., 2002 ; Ennis and Kindlmann, 2006 ), with CL emphasising the linear component of tensor shape. Together, these metrics appear to capture much of the practically useful discriminative information available in the diffusion tensor for this task, since expanding to all 13 metrics did not improve performance and the effective dimensionality of the full feature set was below eight.

NODDI metrics did not improve classification beyond the DTI feature set in this cohort (DTI + NODDI AUC = 0.964 versus DTI alone 0.966). Because the combined NODDI model comprises fewer features than the four-metric tensor model, the two were also compared at matched dimensionality, using three metrics from each family. NODDI did not outperform the tensor metrics in any tissue class, including cerebral white matter where its modelling assumptions are best satisfied, and performed significantly worse in subcortical grey matter. One possible interpretation is that this reflects a distinction between diagnostic sensitivity and biological specificity. FA may perform well in classification in part because it is non-specific: it aggregates demyelination, axonal loss, oedema and free-water contamination into a single number, which tends to maximise the group-level signal. NODDI, by contrast, decomposes the signal into narrower components, each capturing a subset of what FA conflates. It is plausible that, for applications in which biological characterisation is a primary objective, such as longitudinal monitoring or mechanistically oriented analyses, NODDI may provide complementary information that a cross-sectional classification framework is not designed to capture ( Zhang et al., 2012 ; Caranova et al., 2023 ; Seyedmirzaei et al., 2023 ). These results should therefore not be taken as evidence against the utility of NODDI in general, but as indicating that its added value may lie outside the scope of group-level discrimination.

A central question is whether classification reflects focal lesions or diffuse microstructural change. Removing lesion voxels from the parcellation before regional averaging left whole-brain performance essentially unchanged and had no effect within cortical parcels or subcortical structures. The effect was confined to white matter, where performance fell from 0.837 to 0.812, and it scaled with the lesion burden of the tissue class. Classification nonetheless remained well above chance in white matter after masking, and the tissue classes carrying almost no lesions retained substantial discriminative power.

In this dataset, single-shell acquisition at either b-value showed closely comparable performance to the multi-shell protocol across the metrics and combinations tested, with differences below 0.008 for the prespecified model and none reaching significance. Reducing angular sampling was tolerated at b = 1000 but not at b = 2000, where six directions cost 0.062 AUC for FA alone. Concatenating features from the two single-shell fits, which doubles the dimensionality without joint tensor estimation, gave no benefit, indicating that whatever the second shell contributes operates through the fit rather than through the additional measurements. If confirmed in other cohorts, these observations would have practical implications for study design, including broader applicability to existing single-shell datasets. However, multi-shell acquisitions serve purposes beyond tensor estimation, including multi-compartment modelling and potentially more robust voxel-wise analyses, and the present comparison is limited to ROI-based classification.

Free-water correction produced a heterogeneous pattern that does not divide cleanly between anisotropy and diffusivity. The transverse eigenvalues and the measures derived from them lost discriminative power (λ3–0.025, λ2–0.024, FA -0.023, CL -0.016, RD -0.012), whereas axial diffusivity and the higher-order invariants gained (AD +0.034, I3 + 0.018, I4 + 0.013), and mean diffusivity was essentially unchanged. One possible explanation is that removing the isotropic compartment principally affects the transverse eigenvalues, which the free-water signal inflates most, so that measures dominated by transverse diffusion lose the contribution that aided separation while the axial direction is comparatively unaffected. The present analysis was not designed to test this mechanism directly. It does, however, raise the possibility that part of the classification signal in uncorrected FA reflects free-water contamination, which, although biologically non-specific, may itself track pathology.

Residualizing for age, sex and intracranial volume changed AUC by at most 0.005, with all confidence intervals including zero. This is consistent with limited sensitivity to these demographic factors, although it does not by itself establish independence: a classifier drawing on hundreds of correlated features can compensate for the removal of one dimension. The covariate distributions provide the more direct evidence, showing no group difference in sex or intracranial volume and an age difference of 2.2 years that did not survive correction.

Study limitations include the single-centre design, ROI-based rather than voxel-wise analysis, the restriction to a priori metric combinations, and the absence of an independent validation cohort: all estimates derive from repeated cross-validation within a single sample and therefore reflect internal, rather than external, validation. The observed AUCs do not establish transferability to other scanners, acquisition protocols, preprocessing pipelines, or centres. Susceptibility-induced distortion was not corrected because no reversed phase-encoding acquisition or field map was available. The phase-encoding direction and readout parameters were identical across participants and groups, so there was no group-specific acquisition difference in susceptibility weighting. The design is also cross-sectional, and the cohort was young with low and narrowly distributed disability, which limits inference about progression and about associations with clinical status; the isotropic voxel size of 2.5 mm further limits sensitivity in thin structures, where partial-volume contributions are correspondingly larger. A further methodological consideration is that the diffusion-encoding b-matrix varies spatially across the imaging volume due to gradient non-linearities, and accounting for this spatial variability improves the physical accuracy of tensor-derived metrics ( Krzyżak et al., 2024 ; Krzyzak et al., 2025 ). The present study did not apply such corrections, as the aim was to compare protocols within a standard clinical processing framework. While this increases relevance to typical diffusion MRI pipelines, spatially varying b-matrix effects may still introduce region-dependent bias. Future work should examine how b-matrix correction and other advanced preprocessing steps affect diffusion biomarkers and classification performance across acquisition protocols.

From a practical standpoint, the present findings suggest that in machine learning studies using diffusion MRI, it may be worthwhile to expand the tensor-derived feature set beyond FA and MD before turning to more complex models or longer acquisitions. Computing the shape descriptors from existing eigenvalues requires minimal additional effort, yet they are rarely included. Our results indicate that this convention may leave discriminative information unused, specifically in the linear anisotropy descriptor. While the generalizability of this observation requires confirmation in other populations and analytical frameworks, the principle of extracting richer information from available data before increasing acquisition complexity appears to be a reasonable starting point for diffusion-based classification pipelines.

CRediT authorship contribution statement

Julia Lasek: Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Weronika Mazur-Rosmus: Writing – original draft, Supervision, Methodology, Investigation, Conceptualization. Marcin Wnuk: Writing – review & editing, Resources, Data curation. Monika Marona: Writing – review & editing, Resources, Data curation. Klaudia Kaczówka: Writing – review & editing, Resources, Data curation. Agnieszka Słowik: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Data curation. Artur Krzyżak: Writing – original draft, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Ethics approval

The studies involving humans were approved by Bioethics Committee at the Regional Medical Chamber, No. 282/KBL/OIL/2020. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Agnieszka Slowik reports financial support was provided by Medical Research Agency. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Supplementary data

Supplementary material

Data availability

The code and data supporting the findings of this study are available in Zenodo at Doi: https://doi.org/10.5281/zenodo.20512670

Acknowledgments

The author(s) declare that financial support was received for the research. The clinical trial entitled “Assessment of the clinical effectiveness of the BSD-MS (B-matrix Spatial Distribution for Multiple Sclerosis) technology and algorithms based on artificial intelligence for the analysis of MRI images in the course of multiple sclerosis” was financed by Medical Research Agency contract no: 2020/ABM/01/00006–00 .

Supplementary data to this article can be found online at https://doi.org/10.1016/j.nicl.2026.104057 .