Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations

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.

Section: Numerical Examplessupporting

confidence: 89%

Section: Discussionsupporting

confidence: 64%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: State Of the Art Of Estimation Methodsmentioning

confidence: 99%

See 3 more Smart Citations

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

Bertoglio

Núñez

Galarce

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

Nolte

Bertoglio

2019

Numerical blood flow simulations are typically set up from anatomical medical images and calibrated using velocity measurements. However, the accuracy of the computational geometry itself is limited by the resolution of the anatomical image. We first show that applying standard no‐slip boundary conditions on inaccurately extracted boundaries can cause large errors in the results, in particular the pressure gradient. In this work, we therefore propose to augment the flow model calibration by slip/transpiration boundary conditions, whose parameters are then estimated using velocity measurements. Numerical experiments show that this methodology can considerably improve the accuracy of the estimated pressure gradients and 3D velocity fields when the vessel geometry is uncertain.

On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods

Pacheco

2021

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single-point data. Alternatively, relative pressure fields can be reconstructed from imaging-based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher-order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second-order differentiation without requiring surface integrals. In-silico and in-vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection-related errors.