Validating PINNs against In-Vitro 4D Flow MRI in Aortic Phantoms Using Measurements Away from the Wall

Physics-informed Neural Networks (PINNs) have the potential to improve the accuracy and scan times of 4D Flow MRI; however, validation against in-vitro data is still lacking. The goal of this study was to validate the accuracy of PINNs in reconstructing 3D velocity field using 4D Flow MRI training data measured away from the wall. 4D Flow MRI data was obtained from an open-source repository. A 3D printed aortic phantom (Radius=1.8cm) was connected to a flow-loop circuit with pulsatile inflow (Q_avg=66 mL/s, HR=60bpm). 4D Flow MRI scans were acquired using conventional Cartesian k-space sampling (V_enc=120 cm/s, dt=20ms, dx=2.5 mm isotropic). PINNs training was performed in Nvidia PhysicsNeMo library. Loss functions included those from sparse 4D Flow MRI training data, no-slip boundary conditions, and integral boundary losses at inlets and outlets. Training data was decreased incrementally by masking velocities near the wall (1.4mm to 0.4 mm, N=6 cases). PINNs architecture included adaptive loss balancing, swish activation function, 4 layers with 256 neurons, and exponential learning decay from 0.1 to 0.001 over 50,000 iterations. PINNs reconstruction with the densest training data was used as ground-truth and point-wise velocity RMSE were computed for all of the remaining cases. As training data was decreased, the velocity errors increased from 25% to 55% at peak systole. Future work will investigate the accuracy of wall biomarkers, such as wall shear stresses and oscillatory shear index.