Navier-Stokes-Based Regularization for 4d Flow MRI Super-Resolution

4D flow MRI is a promising tool in cardiovascular imaging. However, its lack of resolution can degrade some biomarkers’ evaluation accuracy. The computational fluid dynamics (CFD) simulation is considered as the reference method to improve numerically the image resolution. However, CFD simulations are complex and time consuming, and matching their results with 4D Flow MRI data is very challenging. This paper aims to introduce a fast and efficient super-resolution (SR) approach thanks to the minimization of a L2-penalized criterion, which combines a weighted least-squares data fidelity term and Navier-Stokes equations. The algorithm has been validated on synthetic and phantom datasets and compared to state-of-the-art solutions. Moreover, a prospective study is conducted on the segmentation-free application of the proposed algorithm.

[1]  J. Hennig,et al.  Quantitative 2D and 3D phase contrast MRI: Optimized analysis of blood flow and vessel wall parameters , 2008, Magnetic resonance in medicine.

[2]  Philipp Berg,et al.  Super-resolution and denoising of 4D-Flow MRI using physics-Informed deep neural nets , 2020, Comput. Methods Programs Biomed..

[3]  Magne Nordaas,et al.  Variational data assimilation for transient blood flow simulations: Cerebral aneurysms as an illustrative example , 2016, International journal for numerical methods in biomedical engineering.

[4]  Sebastian Schmitter,et al.  4D Flow MRI , 2018 .

[5]  Oliver Speck,et al.  Transient flow prediction in an idealized aneurysm geometry using data assimilation , 2019, Comput. Biol. Medicine.

[6]  Anna Vilanova,et al.  4D MRI Flow Coupled to Physics‐Based Fluid Simulation for Blood‐Flow Visualization , 2014, Comput. Graph. Forum.

[7]  Alastair J. Martin,et al.  Phase‐contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: Comparison with computational fluid dynamics , 2009, Magnetic resonance in medicine.

[8]  G. Glover,et al.  Encoding strategies for three‐direction phase‐contrast MR imaging of flow , 1991, Journal of magnetic resonance imaging : JMRI.

[9]  Mojtaba F. Fathi,et al.  Towards multi‐modal data fusion for super‐resolution and denoising of 4D‐Flow MRI , 2020, International journal for numerical methods in biomedical engineering.

[10]  Alessandro Veneziani,et al.  A Variational Data Assimilation Procedure for the Incompressible Navier-Stokes Equations in Hemodynamics , 2011, Journal of Scientific Computing.

[11]  Krishna S. Nayak,et al.  Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI , 2015, Biomedical engineering online.

[12]  Stuart M Grieve,et al.  Spatial resolution and velocity field improvement of 4D‐flow MRI , 2017, Magnetic resonance in medicine.

[13]  A. Stuart,et al.  The Bayesian Approach to Inverse Problems , 2013, 1302.6989.

[14]  Jérôme Idier,et al.  Towards quantitative evaluation of wall shear stress from 4D flow imaging. , 2020, Magnetic resonance imaging.

[15]  P. Paul-Gilloteaux,et al.  An LDV based method to quantify the error of PC-MRI derived Wall Shear Stress measurement , 2021, Scientific Reports.