Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI
Authors: Prathamesh Pradeep Khole, Mario M. Brenes, Zahra Kais Petiwala, Ehsan Mirafzali, Utkarsh Gupta, Jing-Rebecca Li, Andrada Ianus, Razvan Marinescu
Organizations: University of California Santa Cruz, Santa Cruz, CA, USA · University of California San Diego, San Diego, CA, USA · Inria-Saclay, France · Kings College London, London, UK
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.
Figures & tables
Figure 1: Spinverse pipeline. Top: Given reference dMRI signals Sref under multiple PGSE encodings, we optimize face permeabilities {κf} 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 κf , recovering boundaries via thresholding. Bottom (a–e): Simulator internals: compartments and face permeabilities (a); coupling operator B(κ) 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 Along∪Ashort ( Split ) versus a staged schedule Along→Ashort ( 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.
Geometry
Metric
MLP
GraphSAGE
GATv2+JK
Spinverse
1 Axon
CD-L2 ↓
10.81±5.95
10.75±6.26
8.91±4.25
4.19±1.57
BE% ↓
67.12±6.47
68.18±8.56
71.07±8.91
23.40±9.10
2 Axon
CD-L2 ↓
8.28±2.42
9.03±2.63
8.42±2.52
9.79±3.64
BE% ↓
73.81±4.25
75.76±3.65
72.77±5.82
35.62±5.64
Table 1: CD-L2 and BE% (mean ± std) across 100 test reconstructions each.