Stepwise hard constraint-biased Physics-informed Neural Networks for accurate Magnetic Resonance Electrical Properties Tomography (MREPT)

Motivation: MREPT faces challenges with insufficient constraints and bias when integrated with Physics-informed Neural Networks (PINN), impacting its accuracy. Goal(s): We aim to use only physics-based constraint to bias well-used numerical MREPT methods to enhance the PINN. Approach: We sequentially applied a Stabilized-EPT (Stab-EPT)-based supervised-learning, a biased-Convention-Reaction-EPT (CR-EPT)-based PINN. This stepwise process grounds and balances the multiple-terms in the partial differentiation equation of CR-EPT during learning, thus helps avoid local minima. Results: The proposed PINN approach shows the possibility to outperform Stab-EPT with improved SSIM and NRMSE, though stop criterion needs to be investigated. Further tuning of the bias might improve MREPT accuracy. Impact: This stepwise constraint-biased PINN approach could enable accurate MREPT without any ground truth, thus represent a step forward for clinical application of MREPT.