A robust comparison approach of velocity data between MRI and CFD based on divergence-free space projection

Abstract

Recent achievements in 4D flow MRI increased the interest of CFD-MRI studies, which require comparison of velocity fields from both approaches for validation purposes. A novel flow regularization approach is proposed to provide a ground truth and to perform robust, mathematically reasonable comparisons between CFD and MRI. Our suggested method projects the measured and denoised data into the same space as the computational domain and applies the Helmholtz-Hodge theorem to recover the divergence-free property of the flow field by decomposing the velocity field into its divergence-free, curl-free and harmonic components. Furthermore, an aortic phantom study has been set-up under fully controlled laminar flow conditions with helical flow patterns to validate the proposed method using phase-contrast MRI measurements, whereas a dynamic stenosed case was used under turbulent flow conditions to analyse the robustness of applied pre-processings including the denoising of MRI data and the decomposition of velocity vector field.

Evaluation of Energy Harvesting from Different Sections of the Aortic Artery with Several Energy Harvester Materials

“…Pulse blood flow has been evaluated using the finite element method using PHASTA code. The governing equations of continuity and momentum are given below: [28]…”

A Partial Domain Approach to Enable Aortic Flow Simulation Without Turbulent Modeling

“…3). In [9], the feasibility of the decomposition was validated for a steady state. This is extended to a dynamic case under pulsatile flow conditions to enable robust comparisons between CFD and MRI.…”

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

“…To the best of the author's knowledge, quality control of 4D Flow in clinics is based on calculation of peak/mean flows, mean velocities, flow patterns, and stroke volumes. 2 , 9 , 10 A more systematic approach is to compute the divergence field of the data: assuming the blood flow is incompressible, jumps in the divergence field may indicate the presence of artifacts. Indeed, the incompressibility assumption has been used for denoising 9 , 11 , 12 , 13 and as a regularization term during the reconstruction process.…”

“… 2 , 9 , 10 A more systematic approach is to compute the divergence field of the data: assuming the blood flow is incompressible, jumps in the divergence field may indicate the presence of artifacts. Indeed, the incompressibility assumption has been used for denoising 9 , 11 , 12 , 13 and as a regularization term during the reconstruction process. 14 , 15 However, an important limitation of the divergence is that any measured velocity will have “infinitely” large divergence compared to its reference value which would be zero.…”