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Interpretable Brain Age Prediction Using White Matter Fiber Orientation Distributions with Rotation-Equivariant Deep Learning

Chenyang Fan, Robert D. Sanders, Elie Matar, Yixuan Yuan, Xiang Li, Sharon L. Naismith, Fernando Calamante, Jinglei Lv

arXiv:2610.34825v1cs.CVcs.LG

TL;DR

Many dMRI brain-age models rely on DTI scalars that omit orientation, and conventional CNNs do not explicitly respect orientation-dependent geometry. This study combines WM-FODs with an SE(3)-equivariant CNN; the combined approach achieved the best performance among evaluated configurations, with age-dependent tract sensitivity.

  • Problem

    Many dMRI brain-age models use DTI-derived scalar metrics that omit diffusion orientation, while conventional CNNs do not explicitly account for orientation-dependent feature transformations.

    Source: §I · p. 1

  • Method

    The framework processes WM-FOD spherical harmonic coefficients directly with an SE(3)-equivariant CNN and uses tract-level occlusion to assess regional model sensitivity.

    Source: D. Model Architectures · p. 3, §V · p. 7

  • Results

    WM-FODs combined with SE(3)-equivariant processing achieved the best prediction performance; accuracy peaked at Lmax = 2, and the model was more stable under input rotations than conventional CNNs.

    Source: §I · p. 2, §V · p. 7

  • Takeaways & Limitations

    The findings support matching network processing to WM-FOD geometry, whose SH coefficients transform under rotation, for brain-age prediction.

    Source: B. SE(3)-Equivariant Processing of… · p. 7, §V · p. 7

    Evaluation used one healthy-aging cohort, and tract occlusion also masks crossing-fiber signals, so sensitivity reflects tract-defined regions rather than isolated bundles.

    Source: D. Limitations and Future Work · p. 8

Abstract

from arXiv · show

Diffusion MRI (dMRI) provides information about white matter microstructure that can support brain age prediction. However, many existing prediction models use diffusion tensor imaging (DTI) scalar metrics that omit orientation information. Deep learning is increasingly used for brain age prediction, but conventional CNNs do not explicitly respect the geometric structure of orientation-dependent features. We present an interpretable brain age prediction framework that combines white matter fiber orientation distributions (WM-FODs) with an SE(3) (Special Euclidean group in 3 dimensions) equivariant CNN. The network operates directly on spherical harmonic (SH) coefficients of the FOD, preserving their transformation properties under rotation. Evaluation in 692 participants aged 36-90 years from the Human Connectome Project Aging dataset showed that the combined framework outperformed the evaluated DTI-based models and conventional CNNs. Averaging predictions from five cross-validation models yielded a mean absolute error of 3.54 years and Pearson's correlation of 0.958. Our results indicated that the performance advantage depended on combining WM-FODs with equivariant processing. Prediction accuracy was highest at a maximum SH order of Lmax = 2 and declined at higher orders. Tract-level occlusion, where each segmented tract was masked in turn, revealed age-dependent patterns of model sensitivity, with importance peaks in frontal projection pathways at 36-44 years, the fornix at 45-54 years, the callosal isthmus at 55-64 years, the middle cerebellar peduncle at 65-74 years, and the callosal genu at 75-90 years. These findings support rotation-equivariant processing of WM-FODs for accurate brain age prediction with anatomically interpretable model sensitivity.

I. INTRODUCTION

Diffusion MRI offers information about white matter microstructure, but many dMRI brain-age models use DTI scalars that omit orientation, while conventional CNNs do not explicitly account for orientation-dependent geometry. This study combines WM-FODs with equivariant processing and uses tract-level occlusion to examine anatomical model sensitivity.

I. INTRODUCTION

  • WM-FODs combined with equivariant processing outperformed the evaluated DTI-based models, with prediction accuracy peaking at Lmax = 2.The study compares WM-FODs with DTI-derived features and evaluates the effect of maximum SH order.Source: §I · p. 2
  • The SE(3)-equivariant CNN operates directly on WM-FOD SH coefficients, and its accuracy, rotation stability, and computational cost are evaluated against conventional CNNs.SH components transform together under rotation; the network treats each order as a geometric field and combines fields using steerable kernels.Source: §I · pp. 1–2, Figure 1 · p. 2
  • Tract-level occlusion measures model sensitivity to anatomically defined white matter regions and characterizes how pathway importance varies across adult age groups.Anatomically informed occlusion identifies regions relevant to prediction but does not establish causal roles in aging.Source: §I · p. 2

II. RELATED WORK

Prior dMRI brain-age studies used varied methods and diffusion features, often relying on scalar or handcrafted representations. This section situates WM-FOD inputs, equivariant processing, and tract-level occlusion within that work.

II. RELATED WORK

  • Prior dMRI brain-age studies used methods ranging from regression to deep learning and inputs including DTI scalars, advanced diffusion metrics, and tract-wise summaries; age-range differences complicate comparisons.Studies reported MAEs of approximately 3.5–7.6 years; reporting both MAE and correlation alongside cohort age range supports more informative comparisons.Source: §II · p. 2

B. From Scalar Metrics to WM-FODs

  • DTI uses a Gaussian tensor model and is susceptible to partial-volume effects, whereas MSMT-CSD estimates WM-FODs that represent complex fiber configurations while separating tissue signals.Although FOD-derived measures are widely used in fixel-based analyses, their use as direct deep-learning inputs for brain-age prediction remains relatively unexplored.Source: B. From Scalar Metrics to WM-FODs · p. 2

C. Geometric Deep Learning for Diffusion MRI

  • Prior diffusion-signal methods use joint spatial–angular equivariant convolutions, whereas this framework processes precomputed WM-FOD SH coefficient fields with a volumetric SE(3)-equivariant CNN.Because the coefficient fields already encode angular information, the framework does not require the additional angular convolution used by the cited methods.Source: C. Geometric Deep Learning for… · p. 2

D. Tract-Level Occlusion in Diffusion MRI Brain-Age Models

  • Earlier occlusion studies localized sensitivity mainly in gray matter or atlas-defined regions, while prior dMRI tract features did not test a trained whole-brain model’s sensitivity to tract-defined regions.The study applies tract-level occlusion as an anatomically informed post-hoc analysis.Source: D. Tract-Level Occlusion in Diffusion… · pp. 2–3

III. METHODS

The methods pipeline preprocesses diffusion-weighted images, estimates WM-FODs, predicts brain age, and assesses anatomical sensitivity through tract-defined occlusion. The study uses HCP-A data from healthy adults aged 36–90 years.

III. METHODS

  • The pipeline estimates WM-FODs at different maximum SH orders, processes them with SE(3)-ResNet34 for age prediction, and masks 72 tract-defined regions to derive |ΔMAE| importance scores.Figure 2 summarizes the processing, prediction, and interpretation pipelines.Source: Figure 2 · p. 3, §III · p. 3

A. Dataset and Acquisition

  • The final sample comprised 692 healthy HCP-A participants aged 36–90 years after excluding participants older than 100 and cases with considerable residual imaging artifacts.The data came from a 3T multi-shell acquisition with 1.5-mm isotropic resolution.Source: A. Dataset and Acquisition · p. 3

B. Preprocessing

  • Preprocessing included denoising, Gibbs ringing removal, susceptibility-distortion and motion correction, bias-field correction, and upsampling to 0.8-mm isotropic resolution.The pipeline followed MRtrix3 and used FSL topup and eddy and ANTs N4 for correction steps.Source: B. Preprocessing · p. 3

C. Diffusion Feature Extraction

The methods compare DTI-derived features with WM-FOD inputs at several SH orders, then assess model architectures, training, and prediction stability under input rotations.

C. Diffusion Feature Extraction

  • DTI inputs comprised FA, MD, AD, RD, and six tensor elements, evaluated through early or late fusion of scalar maps or as a six-channel input.Late fusion averaged age predictions from separate models trained on each scalar metric.Source: C. Diffusion Feature Extraction · p. 3
  • WM-FODs were computed at Lmax values of 0, 2, 4, 6, and 8, yielding 1, 6, 15, 28, and 45 coefficient channels, respectively.MSMT-CSD used averaged tissue-specific response functions estimated for each participant.Source: C. Diffusion Feature Extraction · p. 3

D. Model Architectures

  • SE(3)-ResNet34 maps even SH orders to geometric fields, uses hidden fields of orders ℓ = 0–3, and pools final scalar fields for age prediction; ResNet50, ResNet152, and SFCN served as baselines.The maximum hidden order ℓ ≤ 3 was selected because preliminary experiments found higher accuracy than ℓ ≤ 1 or ℓ ≤ 5.Source: D. Model Architectures · p. 3

E. Training Procedure

  • Participants were split into training and held-out test sets, with five-fold cross-validation within training; models minimized MAE using Adam and early stopping.Training used mixed precision on four Tesla V100 GPUs, with per-GPU batch sizes of 4 for standard CNNs and 1 for SE(3)-ResNet34.Source: E. Training Procedure · p. 3

F. Evaluation of Prediction Stability Under Rotation

  • Rotation stability was assessed by rotating WM-FOD volumes and reorienting SH coefficients with Wigner D-matrices, then measuring predicted-age variability across rotations.The evaluation compared SE(3)-ResNet34, ResNet50, and a rotation-augmented ResNet50; all 104 test participants were evaluated at discrete rotations about each anatomical axis.Source: F. Evaluation of Prediction Stability… · p. 4

G. Regional Occlusion Analysis

The regional occlusion analysis measures how masking each tract changes prediction error, then adjusts importance for tract size and compares sensitivity across age bins.

G. Regional Occlusion Analysis

  • Each tract mask was zeroed, predictions were recomputed across all 692 participants, and importance was defined as the absolute change in MAE after age-bias correction.Cross-validation participants were evaluated with out-of-fold models, while held-out test predictions were averaged across the five models.Source: G. Regional Occlusion Analysis · p. 4
  • Dividing absolute MAE change by tract volume produced a per-voxel importance measure reported in 10^-4 years per voxel.The analysis also compared mean absolute importance within five age bins: 36–44, 45–54, 55–64, 65–74, and 75–90 years.Source: G. Regional Occlusion Analysis · p. 4

H. Statistical Analysis

  • Performance was assessed with held-out-test MAE and Pearson’s r, and paired comparisons used false-discovery-rate-adjusted tests at q < 0.05.Rotation stability comparisons used participant-wise standard deviations of predicted age across rotations.Source: H. Statistical Analysis · p. 4

1) DTI-Derived Baseline Features

The study benchmarks DTI-derived inputs, tests WM-FOD spherical harmonic orders, and compares network architectures. SE(3)-ResNet34 performed best at Lmax = 2, while registration did not substitute for equivariant processing.

1) DTI-Derived Baseline Features

2) Effect of Maximum SH Order

  • All tested architectures had their lowest prediction error at Lmax = 2; for SE(3)-ResNet34, this order significantly outperformed Lmax = 0, 6, and 8, but not 4.The figure reports test-set MAE across maximum SH orders and shows 4.04 ± 0.40 years for SE(3)-ResNet34 at Lmax = 2.Source: 2) Effect of Maximum SH Order · p. 4, Figure 3 · p. 4

3) Effect of Network Architecture

  • At Lmax = 2, SE(3)-ResNet34 achieved MAE 4.04 ± 0.40 years and r = 0.942, outperforming ResNet50, ResNet152, and SFCN.It had the highest accuracy at every evaluated maximum SH order; registered ResNet50 remained inferior at every order.Source: 3) Effect of Network Architecture · p. 5, Table 2 · p. 5

4) Combining WM-FODs with Equivariant Processing

The evaluated single-component changes did not significantly improve on the DTI benchmark, but WM-FODs paired with SE(3)-ResNet34 did. The ensemble was more accurate and rotation-stable, with fewer parameters but higher epoch cost than the ResNet baselines.

4) Combining WM-FODs with Equivariant Processing

  • Accuracy improved significantly only when WM-FODs were combined with SE(3)-ResNet34; changing the input or architecture alone did not significantly improve the DTI benchmark.The best WM-FOD model improved on the early-fusion DTI benchmark by 0.93 years.Source: 4) Combining WM-FODs with Equivariant… · p. 5

5) Ensemble Prediction Performance

  • Five-model averaging reduced SE(3)-ResNet34 MAE from 4.04 to 3.54 years and yielded r = 0.958; its ensemble significantly outperformed all baseline ensembles.Fig. 4 compares ensemble-predicted with chronological age for the held-out test set (n = 104); each prediction averages five cross-validation models.Source: 5) Ensemble Prediction Performance · p. 5, Figure 4 · p. 5

1) Prediction Stability Under Rotation

  • Across all test participants, rotation-induced prediction SD was 0.90 ± 0.40 years for SE(3)-ResNet34, versus 2.99 ± 0.89 for ResNet50 and 2.04 ± 0.45 for rotation-augmented ResNet50.For the illustrative participant, ResNet50 errors exceeded 8 years at −15° coronal rotation, while both models had unrotated error of 0.5 years.Source: 1) Prediction Stability Under Rotation · p. 5, Figure 5 · p. 6

2) Computational Cost

  • SE(3)-ResNet34 required 406 seconds per epoch versus 258 seconds for ResNet50, but had 2.95 million parameters versus 46.27 million and 117.47 million for ResNet50 and ResNet152.It was comparable in parameter count to SFCN (2.95 million), while achieving the best prediction performance.Source: 2) Computational Cost · p. 5

C. Tract-Level Importance

Tract occlusion identifies white matter pathways associated with model sensitivity, with rankings depending on whether importance is measured by total error change or per voxel. The highest-importance tracts also vary across age bins.

C. Tract-Level Importance

  • Occlusion produced the largest absolute MAE changes for callosal genu CC_2 (3.99 years), callosal isthmus CC_6 (3.92 years), and the middle cerebellar peduncle (3.81 years).Projection pathways including T_PREF, FPT, and ATR also ranked highly; Fig. 6A shows participant-level changes across 692 participants.Source: C. Tract-Level Importance · p. 6, Figure 6 · p. 6
  • After normalization by tract volume, the bilateral fornix ranked highest, at 6.70 × 10^-4 years/voxel on the right and 5.60 × 10^-4 on the left.The anterior commissure followed at 1.08 × 10^-4 years/voxel; Fig. 6B displays the 10 highest-ranked tracts for each measure.Source: C. Tract-Level Importance · p. 6, Figure 6 · p. 6

D. Age-Stratified Tract Importance

  • Peak tract importance shifted across age bins: frontal projection pathways at 36–44, fornix at 45–54, callosal isthmus at 55–64, MCP at 65–74, and callosal genu at 75–90 years.These age-group differences describe model sensitivity, not longitudinal changes within individuals.Source: D. Age-Stratified Tract Importance · pp. 6–7, Figure 7 · p. 6

V. DISCUSSION

The strongest prediction performance required combining WM-FODs with SE(3)-equivariant processing; accuracy peaked at Lmax = 2. The ensemble compared favorably with published unimodal dMRI studies, though cross-study differences limit direct ranking.

V. DISCUSSION

  • The best performance required combining WM-FODs with SE(3)-equivariant processing; changing either component alone did not significantly improve accuracy in one-component-at-a-time comparisons.Replacing DTI fusion with WM-FODs in ResNet50 or applying SE(3)-ResNet34 to DTI fusion likewise produced no significant gain.Source: §V · p. 7, A. WM-FOD Representations for Brain… · p. 7

A. WM-FOD Representations for Brain Age Prediction

  • WM-FOD SH coefficients retain orientation information absent from DTI scalar maps, while MSMT-CSD separates white matter, gray matter, and CSF signal components.These are proposed properties that may contribute to the observed result.Source: A. WM-FOD Representations for Brain… · p. 7
  • Accuracy peaked at Lmax = 2 and declined at higher orders, as input dimensionality rose from 6 to 45 channels between Lmax = 2 and 8.The authors suggest low-order coefficients may capture age-related fiber-density and anisotropy changes without resolving crossing-fiber populations as distinct peaks.Source: A. WM-FOD Representations for Brain… · p. 7
  • 3.54 years MAE and r = 0.958 were achieved by the SE(3)-ResNet34 ensemble, which compared favorably with published unimodal dMRI studies.These comparisons provide general context rather than a controlled ranking because cohorts and evaluation procedures differ.Source: A. WM-FOD Representations for Brain… · p. 7, Figure 8 · p. 7

B. SE(3)-Equivariant Processing of WM-FODs

SE(3)-equivariant processing aligns the network with WM-FOD geometry and outperformed conventional CNN alternatives, with a training-time trade-off. Tract-level occlusion identified age-varying model sensitivities, which describe model behavior rather than tissue degeneration.

B. SE(3)-Equivariant Processing of WM-FODs

  • SE(3)-equivariant processing improved prediction from WM-FODs relative to conventional CNNs, and the network processes SH coefficients without an additional SO(3) angular convolution.The SH representation maps to irreducible representations used by SE(3)-steerable kernels; the authors identify this as the first volumetric SE(3)-equivariant CNN application to whole-brain WM-FOD SH images for brain-age prediction.Source: B. SE(3)-Equivariant Processing of… · p. 7
  • SE(3)-ResNet34 without registration outperformed registered ResNet50 at every evaluated SH order.Rotation augmentation narrowed but did not close the stability gap with ResNet50 and did not significantly improve accuracy.Source: B. SE(3)-Equivariant Processing of… · p. 7
  • SE(3)-ResNet34 required approximately 1.6 times ResNet50's training time per epoch but used approximately 1/16 of its parameters; parameter-matched SFCN performed significantly worse.The comparison indicates that the performance gain cannot be attributed to model size alone.Source: B. SE(3)-Equivariant Processing of… · pp. 7–8

C. Age-Dependent Model Sensitivity to White Matter Regions

  • At 36–44 years, the largest importance peaks were in the prefrontal thalamic radiation, fronto-pontine tract, and anterior thalamic radiation; the bilateral fornix peaked at 45–54 years.The fornix also had the highest per-voxel importance, though its small size and proximity to ventricles leave susceptibility to age-increasing CSF partial-volume effects.Source: C. Age-Dependent Model Sensitivity to… · p. 8
  • The callosal isthmus reached highest importance at 55–64 years, the middle cerebellar peduncle at 65–74 years, and the callosal genu at 75–90 years.Evidence specific to age-related differences in the middle cerebellar peduncle is limited.Source: C. Age-Dependent Model Sensitivity to… · p. 8
  • Across age groups, prominent model sensitivities involved projection, limbic, commissural, and cerebellar bundles, but these patterns do not establish causal mechanisms of aging or directly measure cognitive function.Peak predictive importance does not directly indicate the timing or rate of tissue degeneration.Source: C. Age-Dependent Model Sensitivity to… · p. 8

D. Limitations and Future Work

Evaluation was limited to one healthy aging cohort, and tract-level occlusion has confounds that constrain interpretation of regional importance. The conclusion presents the combined WM-FOD and SE(3)-equivariant approach as promising for accurate, interpretable prediction.

D. Limitations and Future Work

  • Evaluation was restricted to one healthy aging cohort, so generalization across scanners, acquisition protocols, and clinical populations remains to be established.External validation is identified as an important future direction.Source: D. Limitations and Future Work · p. 8
  • Voxel-wise tract occlusion can remove signals from crossing fiber populations, with greater confounding for larger tract volumes; volume normalization does not account for tract topology or overlap.The authors identify fiber-specific perturbation methods as an important future direction.Source: D. Limitations and Future Work · p. 8

VI. CONCLUSION

  • The combined WM-FOD and SE(3)-equivariant framework achieved the best performance among evaluated configurations, with ensemble MAE of 3.54 years and r = 0.958.The conclusion also reports greater rotation stability and approximately 1/16 of ResNet50's parameters; one-component-at-a-time comparisons found significant gain only for the combined approach.Source: §VI · p. 8
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