Validation of numerical simulation methods in aortic arch using 4D Flow MRI

Abstract

Computational fluid dynamics (CFD) are the gold standard in studying blood flow dynamics. However, CFD results are dependent on the boundary conditions and the computation model. The purpose of this study was to validate CFD methods using comparison with actual measurements of the blood flow vector obtained with four-dimensional (4D) flow magnetic resonance imaging (MRI). 4D Flow MRI was performed on a healthy adult and a child with double-aortic arch. The aortic lumen was segmented to visualize the blood flow. The CFD analyses were performed for the same geometries based on three turbulent models: laminar, large eddy simulation (LES), and the renormalization group k-ε model (RNG k-ε). The flow-velocity vector components, namely the wall shear stress (WSS) and flow energy loss (EL), of the MRI and CFD results were compared. The flow rate of the MRI results was underestimated in small vessels, including the neck vessels. Spiral flow in the ascending aorta caused by the left ventricular twist was observed by MRI. Secondary flow distal to the aortic arch was well realized in both CFD and MRI. The average correlation coefficients of the velocity vector components of MRI and CFD for the child were the highest for the RNG k-ε model (0.530 in ascending aorta, 0.768 in the aortic arch, 0.584 in the descending aorta). The WSS and EL values of MRI were less than half of those of CFD, but the WSS distribution patterns were quite similar. The WSS and EL estimates were higher in RNG k-ε and LES than in the laminar model because of eddy viscosity. The CFD computation realized accurate flow distal to the aortic arch, and the WSS distribution was well simulated compared to actual measurement using 4D Flow MRI. However, the helical flow was not simulated in the ascending aorta. The accuracy was enhanced by using the turbulence model, and the RNG k-ε model showed the highest correlation with 4D Flow MRI.

Keywords: Computational fluid dynamics; Flow energy loss; Phase-contrast MRI; Wall shear stress.

Fig. 1

The flow visualization process using 4D Flow MRI and CFD

Fig. 2

Flow in the healthy adult. Streamline and in-plane velocity distributions of the systolic peak are compared among 3D Cine PC MRI and three CFD computations

Fig. 3

Flow in the child with DAA. Streamline and in-plane velocity distributions of the systolic peak are compared among 4D Flow MRI and three CFD computations. In the ascending aorta, helical flow is observed in 4D Flow MRI, whereas straight flow is computed in CFD

Fig. 4

Correlation between 4D Flow MRI and CFD (RNG k–ε) in the healthy adult. Flow vector components of anterior–posterior (AP) direction, right–left (RL) direction, and superior–inferior (SI) direction are compared in the ascending aorta (AAo), aortic arch (Arch), and descending aorta (DAo). The components in each part are well correlated

Fig. 5

Correlation between 4D Flow MRI and CFD (RNG k–ε) in the child with DAA. In the child, the flow vector components of the primary flow direction (w in AAo, u and w in the arch, w in DAo) are well correlated, but the secondary flow directional components show comparatively low correlation in AAo

Fig. 6

Distribution of WSS in the healthy adult. The WSS of the systolic peak are compared among 4D Flow MRI and three CFD computations using three turbulence models. The color scale of the MRI results was adjusted to conform to the area-averaged WSS of the CFD results. The average WSS was three to five times larger in CFD than in MRI

Fig. 7

Distribution of WSS in the child with DAA. The WSS of the systolic peak are compared among 4D Flow MRI and three CFD computations using three turbulence models. The average WSS in the CFD and MRI was of the same order

Fig. 8

Energy loss. The EL of the whole aorta volume and that of the volume without a boundary layer are shown. In LES and RNG k–ε, which use eddy viscosity for turbulence computations, EL was calculated with the eddy viscosity and with the viscosity property of blood