Abstract
<jats:p>Background and Objective: Simulation of diffusion MRI signals from tissue microstructure is a fundamental problem in quantitative imaging, as it enables controlled study of how cellular architecture influences measured signals. However, physics-based simulations at clinically relevant scales are challenging due to a scale mismatch between imaging and histology: clinical diffusion MRI spans centimeter-scale fields of view with millimeter-scale voxels, whereas histology resolves structure at micrometer scales. Capturing voxel-wise signal formation therefore requires repeated simulations over heterogeneous microstructure, which becomes computationally and memory intensive in classical solvers. We propose a neural operator framework that amortizes this cost by learning local microstructure-signal mappings once and applying them across large tissue regions. Methods: We train a Fourier Neural Operator on finite-element simulations of histology-derived cell segmentations to predict magnetization fields from diffusivity and permeability maps. The model is embedded in a subdomain tiling strategy that enables scalable inference over whole-slide histology images. Unlike most conventional simulation pipelines, inference operates directly on regular grids derived from cell segmentations and does not require meshing. Results: The proposed framework enables simulation of apparent diffusion coefficient maps over 2D liver histology spanning 28.224 mm × 18.144 mm. It achieves over 2,600-fold acceleration compared with CPU-based finite-element simulation, reducing runtime from an estimated 217 days to under 2 hours. The network yields mean relative signal errors of 0.34%–0.43% at high diffusion weighting and 0.03% at low diffusion weighting, with maximum errors below 5%. On manually segmented datasets with greater morphological variability, mean errors increased slightly to 1.37%–1.79%. Conclusions: Neural operators enable computationally practical, mesh-free diffusion MRI simulation by amortizing expensive physics-based computation into a reusable operator applied across local subdomains. This makes large-scale histology-based diffusion MRI modeling feasible while preserving high accuracy.</jats:p>