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

TL;DR

Spinverse introduces a differentiable physics-based method for reconstructing microstructural tissue interfaces from diffusion MRI data by learning face permeabilities on a fixed mesh, enabling explicit boundary recovery.

Contribution

It presents a novel permeability-aware reconstruction approach that optimizes interface boundaries via differentiable PDE simulation, without changing mesh topology.

Findings

Successfully reconstructs diverse microstructural geometries in synthetic data.

Sequence scheduling and regularization improve boundary accuracy and structural validity.

Demonstrates the importance of priors and staged optimization in permeability inversion.

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.