Handling Phase Offset Errors in Processing 3-point Encoded 4D-Flow MRI Using Machine Learning

4D-Flow MRI is a non-invasive in vivo time resolved three dimensional blood flow velocity measuring technique. It requires 1 reference and 3 velocity encoded scans to estimate blood velocities. It is time consuming, has low spatio-temporal resolution, is impacted by acquisition noise, and artefacts resulting from velocity aliasing and phase offset errors. We present a novel physics informed deep learning framework called Input-Parameterized Physics Informed Neural Nets (IP-PINN) to address these limitations. IP-PINN parametrizes the output of a PINN with respect to a region of interest of fixed size within a 4D-Flow MRI image. It facilitates pre-training to increase the speed and accuracy of PINNs. Velocities, pressure, transverse magnetization, and phase offset errors are modeled as deep neural nets. The continuous outputs are processed to mimic the 4D-Flow MRI acquisition process. The data fidelity term in the loss function is formulated in the complex Cartesian image space to naturally handle velocity aliasing and phase offset artefacts. Fluid flow physics are imposed using regularization. The method only uses data from the velocity encoded scans. Tests with synthetic 4D-Flow MRI derived from computational fluid dynamics simulations of aneurysmal flows demonstrate accurate high-resolution velocity estimation while attenuating noise and eliminating artefacts. The method also enables precise estimation of lumen boundaries through the transverse magnetization neural net.