Towards resolving hemodynamic velocities from time-resolved contrast-enhanced magnetic resonance angiography using physics-informed machine learning

Time-resolved contrast-enhanced magnetic resonance angiography (TR-CEMRA), a non-invasive imaging technique to track contrast techniques in-vivo, is typically used to visualize unusual vascular flow patterns such as retrograde filling near an occlusion. In this research, we investigate the possibility of estimating the time-resolved three-dimensional blood velocities from TR-CEMRA data. We use the newly developed physics-informed neural networks (PINN). Variables of interest such as velocities, pressure, and contrast concentration are modeled as deep neural nets. The hidden variables (velocity and pressure) are inferred from assimilating time-resolved TR-CEMRA data during the training process. The training process also imposes the physics, namely, Navier-Stokes equation and mass conservation for blood flow, and advection-diffusion equation for contrast. The method requires time stamping every 2D Cartesian scan in the 3D region of interest.  Gaussian quadrature is used to volume average neural net outputs to match the TR-CEMRA acquisition process for data fidelity. We demonstrate examples in 2D and 3D aneurysm models wherein the reference flow and contrast dynamics were obtained with computational fluid dynamics simulations.