Pressure difference is an accepted clinical biomarker for cardiovascular disease conditions such as aortic coarctation. Currently, measurements of pressure differences in the clinic rely on invasive techniques (catheterization), prompting development of non-invasive estimates based on blood flow. In this work, we propose a non-invasive estimation procedure deriving pressure difference from the work-energy equation for a Newtonian fluid. Spatial and temporal convergence is demonstrated on in silico Phase Contrast Magnetic Resonance Image (PC-MRI) phantoms with steady and transient flow fields. The method is also tested on an image dataset generated in silico from a 3D patient-specific Computational Fluid Dynamics (CFD) simulation and finally evaluated on a cohort of 9 subjects. The performance is compared to existing approaches based on steady and unsteady Bernoulli formulations as well as the pressure Poisson equation. The new technique shows good accuracy, robustness to noise, and robustness to the image segmentation process, illustrating the potential of this approach for non-invasive pressure difference estimation. 
Non-invasive pressure difference estimation from PC-MRI using the work-energy equation