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Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI

Prathamesh Pradeep Khole, Mario M. Brenes, Zahra Kais Petiwala, Ehsan Mirafzali, Utkarsh Gupta, Jing-Rebecca Li, Andrada Ianus, Razvan Marinescu

TL;DR

Spinverse is presented, a permeability-aware reconstruction method that inverts dMRI measurements through a fully differentiable Bloch-Torrey simulator and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions while improving both boundary accuracy and structural validity.

Abstract

Diffusion MRI (dMRI) is sensitive to microstructural barriers, yet most existing methods either assume impermeable boundaries or estimate voxel-level parameters without recovering explicit interfaces. We present Spinverse, a permeability-aware reconstruction method that inverts dMRI measurements through a fully differentiable Bloch-Torrey simulator. Spinverse represents tissue on a fixed tetrahedral grid and treats each interior face permeability as a learnable parameter; low-permeability faces act as diffusion barriers, so microstructural boundaries whose topology is not fixed a priori (up to the resolution of the ambient mesh) emerge without changing mesh connectivity or vertex positions. Given a target signal, we optimize face permeabilities by backpropagating a signal-matching loss through the PDE forward model, and recover an interface by thresholding the learned permeability field. To mitigate the ill-posedness of permeability inversion, we use mesh-based geometric priors; to avoid local minima, we use a staged multi-sequence optimization curriculum. Across a collection of synthetic voxel meshes, Spinverse reconstructs diverse geometries and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions while improving both boundary accuracy and structural validity.

Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI

TL;DR

Spinverse is presented, a permeability-aware reconstruction method that inverts dMRI measurements through a fully differentiable Bloch-Torrey simulator and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions while improving both boundary accuracy and structural validity.

Abstract

Diffusion MRI (dMRI) is sensitive to microstructural barriers, yet most existing methods either assume impermeable boundaries or estimate voxel-level parameters without recovering explicit interfaces. We present Spinverse, a permeability-aware reconstruction method that inverts dMRI measurements through a fully differentiable Bloch-Torrey simulator. Spinverse represents tissue on a fixed tetrahedral grid and treats each interior face permeability as a learnable parameter; low-permeability faces act as diffusion barriers, so microstructural boundaries whose topology is not fixed a priori (up to the resolution of the ambient mesh) emerge without changing mesh connectivity or vertex positions. Given a target signal, we optimize face permeabilities by backpropagating a signal-matching loss through the PDE forward model, and recover an interface by thresholding the learned permeability field. To mitigate the ill-posedness of permeability inversion, we use mesh-based geometric priors; to avoid local minima, we use a staged multi-sequence optimization curriculum. Across a collection of synthetic voxel meshes, Spinverse reconstructs diverse geometries and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions while improving both boundary accuracy and structural validity.
Paper Structure (6 sections, 3 equations, 5 figures, 1 table)

This paper contains 6 sections, 3 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Experiments and Results
  5. Conclusion

Figures (5)

  • Figure 1: Spinverse pipeline.Top: Given reference dMRI signals $S_{\mathrm{ref}}$ under multiple PGSE encodings, we optimize face permeabilities $\{\kappa_f\}$ on a fixed tetrahedral mesh by minimizing MSE loss with regularization. Gradients are backpropagated through a differentiable Bloch--Torrey simulator and used by Adam to update $\kappa_f$, recovering boundaries via thresholding. Bottom (a--e): Simulator internals: compartments and face permeabilities (a); coupling operator $\mathbf{B}(\kappa)$ assembly (b); Bloch--Torrey FEM system (c); reduced-order eigensolve and matrix-exponential propagation (d); signal readout (e).
  • Figure 2: Sample data and reconstructions. (Left) Representative ground-truth meshes: single-axon (A) and two-axon (B) geometries embedded in the ambient tetrahedral grid. (Right) Four example Spinverse reconstructions (red) shown alongside ground truth meshes (blue). Each pair reports CD-L2 (CD) and BadEdge% (BE).
  • Figure 3: Acquisition scheduling ablation (torus). Joint 50/50 optimization over $\mathcal{A}_{\mathrm{long}}\cup\mathcal{A}_{\mathrm{short}}$ (Split) versus a staged schedule $\mathcal{A}_{\mathrm{long}}\!\rightarrow\!\mathcal{A}_{\mathrm{short}}$ (Staged). Top: signal MSE and Chamfer (CD-L2) over iterations. Bottom: extracted interfaces at iterations 50/250/final (optimized, red) and ground truth (blue); staging yields a coherent torus boundary while joint optimization fails to recover the opening.
  • Figure 4: The left-hand plot shows average CD-L2 loss over 10 meshes for (i) baseline method (no regularization), (ii) baseline with continuity regularization and (iii) the full method with continuity/manifold regularization. The table shows final chamfer distance and BadEdge% values for each test configuration.
  • Figure 5: Comparison with learned predictors on single-axon (A) and two-axon (B) meshes. Spinverse recovers compact boundaries; baselines produce many spurious faces.