Neural fields for adaptive white matter microstructural modeling

1. INTRODUCTION

• Diffusion MRI provides a non-invasive way to probe white-matter tissue because water diffusion is constrained by fiber architecture.Changes in cerebral white-matter fibers can serve as biomarkers for aging, neurodegeneration, and disease status [1].Source: §1 · p. 1
• Fiber directions and microstructural properties are interdependent: properties cannot be estimated without directions, while accurate directions require knowledge of fiber properties.This coupling complicates the usual two-stage tractography process of estimating voxelwise geometry and then generating streamlines.Source: §1 · p. 1
• Crossings occur in 60-90% of voxels, and single-tensor modeling cannot represent multiple orientations, making fractional anisotropy artificially lower and nonspecific in crossings.Multi-tensor models help mitigate these limitations.Source: §1 · p. 1
• FOD-based models have angular-resolution limits, while voxelwise multi-compartment models typically assume fiber properties remain constant across tissue types or voxels.The Standard Model can overestimate intra-axonal diffusivity in simulated crossings.Source: §1 · p. 2, Figure 1 · p. 2
• COMMIT [3] fits properties using candidate tractogram directions, while FORCE [18] matches signals to simulated dictionaries; neither exploits local spatial context.These methods jointly address orientation and microstructural modeling but rely on predefined tractograms or discrete parameter dictionaries.Source: §1 · p. 2
• FiberField represents diffusion signals across space, incorporates local spatial context, models fiber-specific properties, and selects candidate models based on voxel fiber count.The introduction presents this as an alternative to independent voxelwise fitting.Source: §1 · p. 2

2. METHOD

• The multi-stick model represents fibers and their properties while setting extra-axonal and free-water volume fractions to zero.The authors chose it as the simplest model describing both fiber directions and properties, while noting that other microstructural models could be used.Source: Theory · p. 3
• The objective marginalizes probability across one-, two-, and three-fiber models and uses a fiber-count prior to favor simpler models.The prior uses α = 0.002, selected for accurate simulated crossing detection at 20° and 30° separations.Source: Theory · pp. 3–4
• FiberField uses an implicit neural field to estimate model-specific microstructural parameters across image coordinates, incorporating spatial context rather than fitting each voxel independently.Separate output heads estimate diffusivities, volume fractions, fiber directions, and baseline signal for candidate models.Source: Theory · p. 4
• Simulations used Fiberfox crossings separated by 5°–90°, with 10 noisy simulations per separation; acquired data came from a 2 mm isotropic, three-shell HARDI scan.The simulated signals used 270 directions across shells at b = 1000, 2000, and 3000 s/mm^2; the acquired scan used 168 directions across shells at b = 800, 1600, and 2400 s/mm^2.Source: Simulations · p. 5
• Simulation comparisons matched estimated fibers to ground truth and measured angular error, intra-axonal diffusivity RMSE, and fiber sensitivity; in vivo comparisons measured angular and diffusivity differences against baselines.The baselines were MRtrix3 fod2fixel and the Standard Model; fod2fixel-derived fiber directions were used to map Standard Model voxel parameters onto fibers.Source: Baselines and validation metrics · pp. 5–6
• The evaluation also applied FiberField with the full Standard Model, including intra-axonal, extra-axonal, and free-water compartments, fixing free-water diffusivity at 0.003 mm^2/s.Table 1 gives the microstructural parameters used for simulated crossing fibers.Source: Table 1 · p. 5, Baselines and validation metrics · p. 6

3. RESULTS

• 52% lower intra-axonal diffusivity RMSE within crossings and 25% higher angular sensitivity than fod2fixel were reported for FiberField.Its angular error and intra-axonal diffusivity RMSE were also lower than the other methods; angular-error differences were significant above 10° separation.Source: §3 · p. 7
• In simulation, FiberField estimated fibers up to about 30° separation, versus about 40° for fod2fixel and Standard Model with fod2fixel.It was significantly more accurate than the Standard Model and fod2fixel in angular error and intra-axonal diffusivity RMSE.Source: Figure 5 · p. 7
• On acquired HARDI data, FiberField directions were similar to fod2fixel’s, but it estimated more corpus-callosum fibers; its matched directions differed by 10.5 ± 7.1° on average.FiberField estimated two to three fibers in most corpus-callosum voxels where the other methods estimated one; its diffusivity estimates were lower than the Standard Model’s.Source: §3 · p. 8, Figure 6 · p. 8, Fitting the full Standard Model · p. 9
• FiberField training and inference took 29 minutes 44 seconds, versus 17 seconds for fod2fixel and 5 minutes 37 seconds for Standard Model fitting.The FiberField timing was for an in vivo acquisition on an NVIDIA RTX 6000 GPU.Source: §3 · p. 8
• In full Standard Model simulations, FiberField was more accurate in crossings, but identified nonexistent fibers outside them.The Standard Model overestimated diffusivities and underestimated free-water fraction in crossings; the false fibers had small volume fractions and diffusivities.Source: Fitting the full Standard Model · p. 8

• Unlike COMMIT [3], FiberField does not require tractography beforehand, and its model backbone can be tailored to available data or scanning-time constraints.The backbone can be a multi-stick model or the Standard Model.Source: §4 · p. 9
• Potential applications include mapping fiber metrics across subjects, tractometry along bundles, and using multi-stick estimates as fiber-specific response functions for CSD [34].Source: §4 · p. 9
• In simulation, FiberField outperformed fod2fixel in angular error and the Standard Model in diffusivity estimation within fiber crossings.Source: §4 · p. 9
• FiberField was more accurate than typical Standard Model fitting for diffusivities and free-water fractions within crossings, but identified non-existent fibers outside them.The spurious fibers had high diffusivities and low volume fractions.Source: Figure 7 · p. 9
• With α=0.002, FiberField estimated two to three fibers in the corpus callosum, where a single fiber was expected; the prior may be too liberal for in-vivo data.The authors call for further prior justification and in-vivo validation, including checking parameter consistency along tracts.Source: §4 · p. 10

• FiberField uses implicit neural fields and a model-selection loss to jointly estimate fiber directions and properties while selecting candidate models by voxel fiber count.The approach is inspired by Bayesian model averaging.Source: §5 · p. 10