Assessment of 4D flow MRI's quality by verifying its Navier–Stokes compatibility

Jeremías Garay, Hernán Mella, Julio Sotelo, Cristian Cárcamo, Sergio Uribe, Cristóbal Bertoglio, Joaquín Mura

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

4D Flow Magnetic Resonance Imaging (MRI) is the state-of-the-art technique to comprehensively measure the complex spatio-temporal and multidirectional patterns of blood flow. However, it is subject to artifacts such as noise and aliasing, which due to the 3D and dynamic structure is difficult to detect in clinical practice. In this work, a new mathematical and computational model to determine the quality of 4D Flow MRI is presented. The model is derived by assuming the true velocity satisfies the incompressible Navier–Stokes equations and that can be decomposed by the measurements (Formula presented.) plus an extra field (Formula presented.). Therefore, a non-linear problem with (Formula presented.) as unknown arises, which serves as a measure of data quality. A stabilized finite element formulation tailored to this problem is proposed and analyzed. Then, extensive numerical examples—using synthetic 4D Flow MRI data as well as real measurements on experimental phantom and subjects—illustrate the ability to use (Formula presented.) for assessing the quality of 4D Flow MRI measurements over space and time.

Original languageEnglish
Article numbere3603
Number of pages18
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Volume38
Issue number6
DOIs
Publication statusPublished - Jun 2022
Externally publishedYes

Keywords

  • 4D flow MRI
  • blood flows
  • Navier–Stokes equations
  • stabilized finite elements

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