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

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 u ! meas plus an extra field w ! . Therefore, a non-linear problem with w ! 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 w ! for assessing the quality of 4D Flow MRI measurements over space and time. K E Y W O R D S 4D flow MRI, blood flows, Navier-Stokes equations, stabilized finite elements Crist obal Bertoglio and Joaquín Mura are Joint last authors, in alphabetical order.

The Functioning of the Frog’s Single Ventricle

“…• Amphibians such as the Xenopus Laevis have a single ventricle, both in terms of morphology and function, whereas children with functionally single ventricle typically have two ventricles albeit in a setting of one ventricle being severely hypoplastic • Our observations with flows measurements performed using echocardiography constitute another initial step towards a complete analysis of the function of the frog's single ventricle [62] • because of logistic reasons the echocardiographic measurements were performed at a room temperature of 22 • C, higher than the 17 • C, normal environmental temperature for frogs • Studies of the systemic and pulmonary flows distribution with the more modern methodologies of ECG-gated MRI, validated in small vessels in experimental as well as clinical studies could provide high quality of innovation and creativity for our translational research [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77] • We always have to be aware of the species-to-species differences…”