Zahra Kais Petiwala

Prathamesh Pradeep Khole, Zahra Kais Petiwala, Shri Prathaa Magesh et al.

We propose ReMiDi, a novel method for inferring neuronal microstructure as arbitrary 3D meshes using a differentiable diffusion Magnetic Resonance Imaging (dMRI) simulator. We first implemented in PyTorch a differentiable dMRI simulator that simulates the forward diffusion process using a finite-element method on an input 3D microstructure mesh. To achieve significantly faster simulations, we solve the differential equation semi-analytically using a matrix formalism approach. Given a reference dMRI signal $S_{ref}$, we use the differentiable simulator to iteratively update the input mesh such that it matches $S_{ref}$ using gradient-based learning. Since directly optimizing the 3D coordinates of the vertices is challenging, particularly due to ill-posedness of the inverse problem, we instead optimize a lower-dimensional latent space representation of the mesh. The mesh is first encoded into spectral coefficients, which are further encoded into a latent $\textbf{z}$ using an auto-encoder, and are then decoded back into the true mesh. We present an end-to-end differentiable pipeline that simulates signals that can be tuned to match a reference signal by iteratively updating the latent representation $\textbf{z}$. We demonstrate the ability to reconstruct microstructures of arbitrary shapes represented by finite-element meshes, with a focus on axonal geometries found in the brain white matter, including bending, fanning and beading fibers. Our source code is available online.

Prathamesh Pradeep Khole, Mario M. Brenes, Zahra Kais Petiwala et al.

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.