The relative pressure difference across stenotic blood vessels serves as an important clinical index for the diagnosis of many cardiovascular diseases. While the clinical gold standard for relative pressure difference measurements is invasive catheterization, Phase-Contrast Magnetic Resonance Imaging has emerged as a promising tool for enabling a noninvasive quantification, by linking highly spatially resolved velocity measurements with relative pressures via the incompressible Navier-Stokes equations. In this work, we provide a review and analysis of current methods for relative pressure estimation and propose 3 additional techniques. Methods are compared using synthetic data from numerical examples, and sensitivity to subsampling and noise was explored. Through our analysis, we verify that the newly proposed approaches are more robust with respect to spatial subsampling and less sensitive to noise and therefore provide improved means for estimating relative pressure differences noninvasively.
The present contribution deals with the estimation of haemodynamics Quantities of Interest by exploiting Ultrasound Doppler measurements. A fast method is proposed, based on the Parameterized Background Data‐Weak (PBDW) method. Several methodological contributions are described: a sub‐manifold partitioning is introduced to improve the reduced‐order approximation, two different ways to estimate the pressure drop are compared, and an error estimation is derived. A fully synthetic test‐case on a realistic common carotid geometry is presented, showing that the proposed approach is promising in view of realistic applications.
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