Simulation of spin dephasing in arbitrary Larmor fields using physics-informed neural networks

Motivation: Signal dynamics in MRI are influenced by multiple factors at different scales, complicating analyses. Existing analytical solutions and simulation methods are inadequate for complex geometries or susceptibility distributions. Goal(s): We aim to demonstrate and validate a physics-informed neural network (PINN) capable of handling arbitrary susceptibility-induced Larmor fields and diffusion terms. Approach: We implemented a flexible PINN-based simulation framework for solving the underlying the Bloch-Torrey equation which is able to predict the signal dynamics over time. Results: The framework produced accurate results for local and total magnetization across various Larmor field configurations at low to moderate oscillation frequencies, closely matching finite difference method results. Impact: By accommodating complex susceptibility distributions and geometries, our PINN-based framework enhances the simulation of MRI signal dynamics in tissues with varying properties —such as hemorrhages, amyloid deposits, iron accumulation, and vascular malformations —offering significant clinical relevance.