Preprint 2021-01
Cristóbal Bertoglio, Cristian Cárcamo, Jeremías Garay, Hernán Mella, Joaquín Mura, Julio Sotelo, Sergio Uribe:
A new mathematical model for verifying the Navier-Stokes compatibility of 4D flow MRI data
Abstract:
A new model to determine the quality of three-dimensional, time-resolved MRI velocity measurements is presented. By assuming that the true flow velocity satisfies the incompressible Navier-Stokes equations, it is decomposed by measurements $\uu_{meas}$ plus a corrective field $\ww$. Therefore, a non-linear problem for the corrective field. We first introduce the continuous formulation, developing and analyzing a stabilized finite element formulation tailored to this problem. Then, extensive numerical examples – using synthetic and experimental data – illustrate the potential to use $\ww$ for assessing the quality of the measurements under the main sources of error encountered in practice: noise and aliasing.
