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

The signal dynamics in MRI are influenced by the geometry of the dephasing domain, as well as by diffusion and susceptibility effects. Analytical solutions exist only for simple models, and there is a clear need for improved simulation methods. The purpose of this work is to develop and validate a physics-informed neural network (PINN) framework for predicting MR signal dynamics from arbitrary local Larmor field distributions. We implemented a PINN-based simulation framework to solve the Bloch-Torrey equation including diffusion and susceptibility terms, with the complex Bloch-Torrey operator formulated with reflecting boundary conditions and an initially isotropic magnetization. The spatiotemporal magnetization distribution was represented as the output of a neural network, with spatial coordinates and time as inputs. We demonstrated that predicting local and total magnetization is feasible using the PINN-based framework for parameter regimes with intermediate oscillation frequencies, though adapted neural networks incorporating dual encoders or Fourier features were necessary, as conventional multilayer perceptrons failed to learn higher-frequency solutions. Most PINN algorithms performed similarly, except for the gradient-enhanced PINN algorithm, which failed to converge to a correct solution. Evidence of significant spectral bias was found and was partially alleviated by the use of Fourier features. We show that simulating the signal dynamics of MRI is possible using a PINN framework, demonstrating high accuracy and greater flexibility than conventional methods.