Pulsatile Pressure Measurements Via Harmonics-Based Orthogonal Projection of Noisy Pressure Gradients

摘要

In the past, several methods based on iterative solution of pressure-Poisson equation have been developed for measurement of pressure from phase-contrast magnetic resonance (PC-MR) data. We have developed a novel non-iterative harmonics-based orthogonal projection method which can keep the pressures measured based on the Navier-Stokes equation independent of the path of integration. The gradient of pressure calculated with Navier-Stokes equation is expanded with a series of orthogonal basis functions, and is subsequently projected onto an integrable subspace. Before the projection step however, a scheme is devised to eliminate the discontinuity at the vessel boundaries. The approach was applied to noise-added velocities obtained for both steady and pulsatile stenotic flows from computational fluid dynamics (CFD) simulations and compared with pressures independently obtained by CFD. Additionally, MR velocity data for steady flows measured in in-vitro phantom models with different degree of stenoses and different flow rates were used to test the algorithm and results were compared with CFD simulations.