Relative pressure estimation from velocity measurements in blood flows: State‐of‐the‐art and new approaches

Abstract

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.

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

“…Method 2 – From the reconstruction of and the virtual works principle: As an alternative to the joint reconstruction strategy, we can use a method introduced in Reference 40 called Integral Momentum Relative Pressure estimator. As a starting point, it requires to work with a reconstruction of the velocity which, in our work, will be given by the PBDW method applied only to the reconstruction of the velocity field without pressure.…”

Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations

“…Intravascular pressure fields can be derived from 4D flow-based velocity fields through numerical methods that yield the approximate solution of the Navier-Stokes equations. Among the main proposed numerical formulations (Bertoglio et al, 2018), the solution of the pressure Poisson equation (PPE) has shown robustness and ease of implementation (Krittian et al, 2012). Nonetheless, 4D flow measurements are affected by noise-like phase errors arising from tissue motion, and are limited by low spatial and temporal resolutions and partial volume effects, which hamper the quantification of parameters, including pressure drops, that require computing velocity space-or time-derivatives (Ha et al, 2016;Ong et al, 2015).…”

Reducing the impact of geometric errors in flow computations using velocity measurements

“…The classical method is to obtain a pressure Poisson equation (PPE) by taking the divergence of the Navier‐Stokes equations and inserting the velocity measurements in the right‐hand‐side . More recently, several additional methods have been introduced, see a comprehensive review in Bertoglio et al In particular, the STE method, using a Stokes equation by including an auxiliary, nonphysical velocity field, and the WERP method, based on an integral energy balance of the Navier‐Stokes equation, was presented. These methods are computationally less expensive than solving the Navier‐Stokes equation but require full 3D measurements, the acquisition of which is prohibitive in the clinical practice due to large scan times and the rare availability of 3D PC‐MRI sequences.…”

“…These methods are computationally less expensive than solving the Navier‐Stokes equation but require full 3D measurements, the acquisition of which is prohibitive in the clinical practice due to large scan times and the rare availability of 3D PC‐MRI sequences. It is also important to remark that the performance of such data‐driven methods is strongly dependent on the image resolution and is susceptible to noise and image artifacts PDE‐constrained optimization methods require additionally to 2D or 3D velocity data the anatomy of the vessel.…”