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PRISM: Differentiable Analysis-by-Synthesis for Fixel Recovery in Diffusion MRI

Mohamed Abouagour, Atharva Shah, Eleftherios Garyfallidis

Abstract

Diffusion MRI microstructure fitting is nonconvex and often performed voxelwise, which limits fiber peak recovery in narrow crossings. This work introduces PRISM, a differentiable analysis-by-synthesis framework that fits an explicit multi-compartment forward model end-to-end over spatial patches. The model combines cerebrospinal fluid (CSF), gray matter, up to K white-matter fiber compartments (stick-and-zeppelin), and a restricted compartment, with explicit fiber directions and soft model selection via repulsion and sparsity priors. PRISM supports a fast MSE objective and a Rician negative log-likelihood (NLL) that jointly learns sigma without oracle information. A lightweight nuisance calibration module (smooth bias field and per-measurement scale/offset) is included for robustness and regularized to identity in clean-data tests. On synthetic crossing-fiber data (SNR=30; five methods, 16 crossing angles), PRISM achieves 3.5 degrees best-match angular error with 95% recall, which is 1.9x lower than the best baseline (MSMT-CSD, 6.8 degrees, 83% recall); in NLL mode with learned sigma, error drops to 2.3 degrees with 99% recall, resolving crossings down to 20 degrees. On the DiSCo1 phantom (NLL mode), PRISM improves connectivity correlation over CSD baselines at all four tracking angles (best r=.934 at 25 degrees vs. .920 for MSMT-CSD). Whole-brain HCP fitting (~741k voxels, MSE mode) completes in ~12 min on a single GPU with near-identical results across random seeds.

PRISM: Differentiable Analysis-by-Synthesis for Fixel Recovery in Diffusion MRI

Abstract

Diffusion MRI microstructure fitting is nonconvex and often performed voxelwise, which limits fiber peak recovery in narrow crossings. This work introduces PRISM, a differentiable analysis-by-synthesis framework that fits an explicit multi-compartment forward model end-to-end over spatial patches. The model combines cerebrospinal fluid (CSF), gray matter, up to K white-matter fiber compartments (stick-and-zeppelin), and a restricted compartment, with explicit fiber directions and soft model selection via repulsion and sparsity priors. PRISM supports a fast MSE objective and a Rician negative log-likelihood (NLL) that jointly learns sigma without oracle information. A lightweight nuisance calibration module (smooth bias field and per-measurement scale/offset) is included for robustness and regularized to identity in clean-data tests. On synthetic crossing-fiber data (SNR=30; five methods, 16 crossing angles), PRISM achieves 3.5 degrees best-match angular error with 95% recall, which is 1.9x lower than the best baseline (MSMT-CSD, 6.8 degrees, 83% recall); in NLL mode with learned sigma, error drops to 2.3 degrees with 99% recall, resolving crossings down to 20 degrees. On the DiSCo1 phantom (NLL mode), PRISM improves connectivity correlation over CSD baselines at all four tracking angles (best r=.934 at 25 degrees vs. .920 for MSMT-CSD). Whole-brain HCP fitting (~741k voxels, MSE mode) completes in ~12 min on a single GPU with near-identical results across random seeds.

Paper Structure

This paper contains 15 sections, 9 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Analysis-by-Synthesis Framework
  4. Tissue Signal Model
  5. Nuisance Intensity and Noise Calibration
  6. Regularization
  7. Optimization
  8. Experiments
  9. Results
  10. Robustness to Intensity Nuisance Factors.
  11. Crossing-Fiber Benchmark.
  12. DiSCo1 Tractography.
  13. In-Vivo Whole-Brain Fitting.
  14. Ablation.
  15. Discussion and Conclusion

Figures (1)

  • Figure 1: PRISM analysis-by-synthesis pipeline. The multi-compartment tissue signal model $\mathcal{S}(\boldsymbol{\theta}_{\mathrm{micro}})$ (top, green) combines up to $K$ white-matter fiber populations with gray matter, CSF, and a restricted compartment. A nuisance calibration module $\mathcal{A}(\boldsymbol{\theta}_{\mathrm{cal}})$ (bottom, orange) applies a smooth bias field $B(\mathbf{x})$, per-measurement affine correction $(\alpha_n, \beta_n)$, and noise level $\sigma$. The differentiable forward model synthesizes the expected measurement $\hat{y}{=}\mathcal{A}(\mathcal{S})$, which is compared to observed multi-shell dMRI via an MSE or NLL loss plus regularization $\mathcal{R}(\boldsymbol{\theta})$. Rprop updates tissue and calibration parameters jointly through gradient-based optimization.