ReMiDi: Reconstruction of Microstructure Using a Differentiable Diffusion MRI Simulator

TL;DR

ReMiDi introduces a differentiable simulation framework that reconstructs complex neuronal microstructures from diffusion MRI signals by optimizing a latent mesh representation, enabling detailed 3D microstructure inference.

Contribution

The paper presents a novel end-to-end differentiable pipeline combining a semi-analytical dMRI simulator with latent space optimization for microstructure reconstruction.

Findings

Successfully reconstructs arbitrary 3D microstructures from dMRI signals.

Demonstrates accurate modeling of brain white matter fiber geometries.

Provides an efficient, differentiable simulation approach for microstructure inference.

Abstract

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.