Source-linked AI summary
Separating mixtures of single-fiber orientation distributions for increased sensitivity to crossing white matter fibers
Adam M. Saunders, Gaurav Rudravaram, Michael E. Kim, Elyssa M. McMaster, Yifan Shuai, Warren Boschen, Sophie Lin, Suzana Herculano-Houzel, Daniel C. Colvin, Yurui Gao, Kurt G. Schilling, Adam W. Anderson, Bennett Landman
TL;DR
Crossing white matter fibers reduce the sensitivity of downstream microstructural modeling and tractography, while peak-based methods can be biased by nearby fibers. FISSILE models voxel orientation distributions as mixtures of single-fiber distributions. It reports that 85.8% of voxels, and 79.4% in the raccoon, have at least two fibers with FISSILE.
Problem
Crossing white matter fibers reduce the sensitivity of downstream microstructural modeling and tractography, and peak-based methods can be biased by nearby fibers.
Source: Key Points · p. 3, §1 · p. 4Method
FISSILE models voxel-level orientation distributions as mixtures of single-fiber distributions and iteratively solves the unmixing problem.
Source: §4 · p. 11Results
85.8% of voxels, and 79.4% in the raccoon, had at least two fibers identified with FISSILE.
Source: §5 · p. 18Takeaways & Limitations
Modeling crossing fibers as a mixture of orientation distributions increases sensitivity to individual fibers for more precise anatomical characterization.
Source: §4 · p. 11, §5 · p. 12Voxel-wise non-convex optimization is computationally expensive, and the authors validated the method on only three subjects.
Source: §4 · p. 12
Abstract
from arXiv · showhide
Intro: Diffusion MRI allows for in vivo probing of brain tissue architecture via micron-level diffusion aggregated at the millimeter scale, but crossing white matter fibers decrease the sensitivity of downstream tasks such as microstructural modeling and tractography. Current fixel-based methods for identifying the number, orientation, and spread of fibers rely on finding the peaks of fiber orientation distributions from constrained spherical deconvolution. However, this method is biased by the spreads of nearby fibers and fails at angular separations lower than approximately 40-50 degrees. Methods: In this work, we perform a constrained nonlinear optimization called fiber segmentation by signal splitting and iterative least squares estimation (FISSILE), modeling each voxel as a mixture of single-fiber distributions. We use FISSILE to fit axially symmetric fibers in simulations and on three in vivo human subjects from the Human Connectome Project, an ex vivo raccoon brain, as well as the same human subject scanned twice at two different signal-to-noise ratios (SNRs). Results: On simulated data, FISSILE successfully identifies fibers at an angular separation of 40{\deg} and a volume fraction of 0.1 at an SNR as low as 30, while MRtrix3's fod2fixel is limited to 60{\deg} separation and 0.1 volume fraction at the same SNR. On acquired data, FISSILE identified 85.8% of white matter voxels on average in human brains and 79.4% in the raccoon with at least one fiber crossing, whereas fod2fixel identified 30.1% and 44.5%. The number of white matter fiber crossings was mildly sensitive to different noise levels in the human subject with two acquisitions. Conclusion: A method that models the crossing fiber phenomenon as an unmixing problem increases sensitivity to individual fibers for more precise characterization of anatomy.
Code and Data Availability Statement
The introduction describes limitations in identifying individual fibers from diffusion MRI and presents FISSILE’s mixture-based approach to separating them. The supplied sections also cover the study’s reported results, key points, data availability, and ethics approvals.
Code and Data Availability Statement
- The study states that its code and simulation data will be made openly available on Zenodo upon publication.The listed materials include fissile_simulations.tar.gz and fissile_v1.1.3.sif.Source: Code and Data Availability Statement · p. 2
Ethics Approval and Patient Consent Statement
- The raccoon brain hemisphere was obtained under USDA NWRC Animal Review Board approval, and human imaging had informed consent and institutional review board approval.The raccoon approval is identified as QA-2492.Source: Ethics Approval and Patient Consent… · p. 2
Key Points
- The key points identify reduced sensitivity of microstructural models and biased or merged orientation-distribution peaks at low crossing angles as central problems.They present mixture modeling of orientation distributions as the approach for increased sensitivity.Source: Key Points · p. 3
1. Introduction
- White matter crossings and complex geometries complicate downstream microstructural modeling, and low SNR makes some geometries difficult to distinguish.The text also notes that spatial resolution affects microstructural metrics.Source: §1 · p. 4
- Nearby-fiber spread biases fiber ODF peaks, while truncated spherical harmonics prevent representing peaks separated by less than around 50°.The text says this bias can occur even at angles that appear separable.Source: §1 · p. 5
- FISSILE models voxel-level orientation distributions as mixtures of single-fixel distributions to unmix and estimate underlying fiber populations.The method is named fiber segmentation by signal splitting and iterative least squares estimation.Source: §1 · p. 5
- FISSILE can disentangle simulated fibers at lower angular separations with high correlation to a reference set.The introduction also reports testing beyond simulations in human subjects and an ex vivo raccoon brain hemisphere.Source: §1 · p. 5
Theory
FISSILE separates a multi-fixel ODF into rotated single-fixel ODFs through constrained nonlinear optimization. Its generalized fitting costs and iterative splitting support application to in vivo and ex vivo diffusion MRI.
Theory
- FISSILE models a multi-fixel ODF as a mixture of rotated single-fixel ODFs and initializes fiber orientations from spherical maxima.The generalized version adds fitting costs for use with in vivo and ex vivo diffusion MRI, as well as simulated tractography phantoms.Source: Theory · pp. 5–6
- A regularized least-squares fit encourages axially symmetric fibers by penalizing coefficients with m≠0.The method assumes fibers are largely symmetric around their axes, while avoiding a hard symmetry constraint.Source: Theory · p. 6
- The objective includes fit, shape, volume, and belt cost terms, with empirically chosen weights of 1, 1, 1, and 2, respectively, for fit, shape, volume, and belt.The fit cost is the sum of squared errors. The volume fraction cost penalizes negative volume fractions of the single-fixel ODF.Source: Theory · p. 6
- A belt cost penalizes large coefficients that create a bulge around the FOD’s middle, perpendicular to the fiber axis.The cost allows the largest coefficient up to c=3 without penalty.Source: Theory · p. 7
- When relative error exceeds 0.05, FISSILE splits the most asymmetric fixel and refits until the solution falls below the threshold.The threshold was selected using simulated data; lower thresholds fit too many fibers to lobes from Gibbs ringing.Source: Theory · p. 7
Simulations
The simulations use Fiberfox-generated crossing-fiber data as a reference for comparing estimated fiber ODFs. The design varies noise and evaluates agreement with the reference.
Simulations
- Fiberfox provided a reference dataset because true fiber orientations are difficult to obtain without phantoms or histology.The simulation included two bundles crossing at 90 degrees, with 10,000 fibers each.Source: Simulations · p. 7
- Rician noise was varied across 15 levels, providing SNRs from approximately 30 to infinity, with acquisition parameters matched to HCP data.The simulated data were fit with the same ODF method used elsewhere in the study before running FISSILE and fod2fixel.Source: Simulations · p. 7
- The angular correlation coefficient measured correlation between estimated fixel ODFs and the reference ODFs.The coefficient measures correlation between two spherical functions.Source: Simulations · p. 7
Data acquisition
The study analyzes three HCP human subjects, an ex vivo raccoon brain, and two acquisitions from one human subject to examine different noise levels. The acquisitions use distinct diffusion protocols and resolutions.
Data acquisition
- The human and raccoon datasets used different approaches to distortion correction and white-matter masking.HCP data used reverse phase encoding acquisitions for distortion correction; the raccoon multi-shot acquisition reduced the impact of eddy currents.Source: Data acquisition · p. 8
- The ex vivo dataset was a raccoon brain acquired at 9.4T with 0.375 mm isotropic diffusion resolution.The multi-shell acquisition used 150 directions at b-values 3000 and 6000 s/mm2; a structural T2*-weighted image had 0.25 mm isotropic resolution.Source: Ethics Approval and Patient Consent… · p. 2, Data acquisition · p. 8
- The two acquisitions from one human subject differed in SNR, resolution, and diffusion sampling.One used 2.3 × 2.3 × 2.5 mm resolution and 195 directions; the other used 2 mm isotropic resolution and 168 directions.Source: Data acquisition · p. 8
Fiber analysis
Fiber analysis compares FISSILE with fod2fixel on white-matter voxels and evaluates fitted single-fixel ODFs using apparent fiber density. Both algorithms operate independently on each voxel.
Fiber analysis
- Fod2fixel identifies fiber directions by finding peaks in a multi-fixel ODF and segmenting it into lobes.It samples 1,281 directions and removes lobes whose peak amplitude is below 0.1.Source: Fiber analysis · p. 9
- For the comparison, fod2fixel lobe segmentations can be transformed into spherical-harmonic representations and treated as single-fixel ODFs.Typical fixel-based analyses instead represent each fiber as a vector associated with a metric such as dispersion, amplitude, or apparent fiber density.Source: Fiber analysis · p. 9
- FISSILE and fod2fixel were run on white-matter voxels from three HCP subjects and the raccoon brain.Both algorithms operate independently per voxel and do not use learned information across voxels or subjects.Source: Fiber analysis · p. 9
- The analysis compares single-fixel ODFs from FISSILE and fod2fixel using apparent fiber density, defined as the integral of the unnormalized single-fixel ODF.The ODFs were rescaled by the integral of the total multi-fixel ODF; at high b-values, AFD provides a voxelwise comparison metric under the assumption that fiber volume is proportional to diffusion signal.Source: Fiber analysis · pp. 9–10
Simulation
In simulations, FISSILE identifies fibers at smaller angular separations than fod2fixel, while both methods struggle with low-volume-fraction fibers. The performance difference is attributed mainly to angular sensitivity, not volume fraction.
Simulation
- At 40° separation FISSILE identifies fibers, whereas fod2fixel fails below 60°; both methods fail below a 0.2 volume fraction across SNRs.fod2fixel requires separable peaks, which merge at about 55° separation.Source: Simulation · p. 10
- FISSILE’s simulation advantage is mainly greater angular sensitivity, with no major performance difference across volume fractions.Source: Simulation · p. 10
Acquired data
Across human and raccoon acquired data, FISSILE identified secondary fibers in more white matter voxels than fod2fixel. It also distributed fiber density across more fibers, with crossing estimates only mildly sensitive to SNR in the repeated human scans.
Acquired data
- FISSILE identified more secondary and tertiary fibers than fod2fixel, including crossings without an obvious secondary fod2fixel peak; the pattern was similar but weaker in raccoon data.Source: Acquired data · p. 10
- FISSILE identified more fibers across the brain, especially in deep white matter, while fod2fixel usually identified one or two; both predicted fewest fibers in the corpus callosum’s middle.Superficial white matter near gyri also contained areas with three or more fibers.Source: Acquired data · p. 10
- 85.8% of human and 79.4% of raccoon white matter voxels had a secondary fiber with FISSILE, versus 30.1% and 44.5% with fod2fixel.Source: Acquired data · p. 11
- For the first three fibers, AFD was more spread across fibers with FISSILE than fod2fixel, which concentrated it in the first fiber (p < 0.05, Mann-Whitney test).The authors suggest fod2fixel ODFs represent larger fiber populations across fewer bundles.Source: Acquired data · p. 11
- With FISSILE, crossing voxels were 80.6% at SNR 53.8 and 87.3% at SNR 29.8; fod2fixel estimates were 25.7% and 33.0%, respectively.Both methods were slightly sensitive to SNR.Source: Acquired data · p. 11
4. Discussion
The discussion presents FISSILE as a mixture-unmixing approach for detecting fibers and compares its estimates with prior crossing-fiber findings. It also identifies computational cost, validation scope, threshold choice, and difficulty distinguishing crossings from fanning as limitations.
4. Discussion
- FISSILE models crossing fibers as a mixture of fixel ODFs and iteratively solves an unmixing problem, increasing sensitivity to individual fibers.Source: §4 · p. 11
- Human estimates agree with the upper end of Jeurissen et al.’s 60–90% crossing-fiber range, and raccoon estimates were similar.Jeurissen et al. also reported that CSD peak finding cannot resolve fibers smaller than about 40°, as observed in the simulations.Source: §4 · p. 11
- FISSILE’s voxel-level multi-fiber analysis differs from mapping fixels shared by multiple bundles, and could support a similar analysis of multi-fixel, multi-bundle voxels.Source: §4 · p. 11
- CSD-based fiber models assume a single fiber response across tissue, while the paper notes that a multi-bundle microstructural model fitted directly to diffusion MRI would be useful.The single-response assumption can have downstream impacts on tractography.Source: §4 · pp. 11–12
- Alternative ODF bases such as spherical needlets may provide more separable representations, but require high-SNR, high-b-value acquisitions.Source: §4 · p. 12
- Voxel-wise non-convex optimization is computationally expensive, and validation was limited to three young, healthy subjects from one widely used dataset.Source: §4 · p. 12
- The error threshold was chosen empirically; a dynamic threshold adapted to prior knowledge or SNR may be useful.Source: §4 · p. 12
- FISSILE has difficulty distinguishing crossing from fanning fibers because it penalizes asymmetry within a fixel ODF; adjacent-voxel or bundle knowledge could help at low SNR.Source: §4 · p. 12
5. Conclusion
FISSILE treats crossing fibers as a mixture-unmixing problem, increasing sensitivity to individual fibers and the number of detected crossings. This supports more precise fiber-based analysis, although the voxel-wise optimization is computationally expensive.
5. Conclusion
- FISSILE models fibers as a mixture, addressing the lack of mixture representations in prior fixel-based analysis and supporting fiber-bundle-specific metrics.Fiber-level models turn limits on probing sub-voxel diffusion into an opportunity for bundle-specific measures.Source: §5 · p. 12
- About 50% greater angular sensitivity accompanies FISSILE’s increased detection of crossing fibers by shifting from peak detection to fiber unmixing.The conclusion describes this as enabling more precise fiber-based analyses of brain microstructural anatomy.Source: §5 · p. 12
- FISSILE’s increased angular sensitivity allows detection of fibers at smaller separation, including when individual fiber peaks are not resolved.The conclusion links this shift from peak detection to unmixing with more precise characterization of brain anatomy.Source: §5 · p. 12
- 85.8% of human white matter voxels and 79.4% of raccoon voxels had at least two fibers with FISSILE, versus 30.1% and 44.5% with fod2fixel.FISSILE identifies smaller fibers, spreading fiber density across fiber numbers.Source: §5 · pp. 18–19
- 80.6% of voxels in the higher-SNR acquisition and 87.3% in the lower-SNR acquisition had at least two FISSILE-estimated fibers, compared with 25.7% and 33.0% for fod2fixel.The estimated fiber ODFs were similar across acquisitions, while total fiber counts varied slightly with SNR.Source: §5 · p. 20