A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison

Application Challenge AC7-04 © copyright ERCOFTAC 2021

Evaluation - Comparison of Test Data and CFD

The comparisons between the post-processed MRI images and downsampled CFD were done on the MRI grid on which both velocity fields are expressed.

Qualitative comparison

First a qualitative comparison between the corrected MRI velocity data and the downsampled CFD is shown in several planes of interest. In Fig. 9 the velocity field along its three components as well as the magnitude of the velocity are presented in the coronal plane. The velocity field along the X-direction ( $u$ -component, see Fig. 5 for the definition of the axis) is also shown in a plane along the middle of the collateral (Fig. 10) and in the cross-section in the middle of the bend (Fig. 11). These maps are given for four time instants: peak systole, peak diastole and the time instants in between. Similar velocity patterns are seen even in complex flow regions. Both CFD and MRI succeed in capturing main flow features, such as the small separation region in the main branch at peak systole and the recirculation in the aneurysm and the back flow in the bifurcation at peak diastole. Through-plane velocity comparison ( $v$ -component) shows larger visual discrepancies, which was expected given the low signal amplitudes collected in the MRI scanner due to the low velocities in this direction.

Figure 9: Qualitative comparison in the coronal plane

Figure 10: Qualitative comparison across the collateral - Velocity along the X-direction

Figure 11: Qualitative comparison in the cross-section of the bend - Velocity along the X-direction

Pearson's correlation

The Pearson's product moment correlation was computed over the cardiac cycle to assess the linearity between MRI and downsampled CFD (LR-CFD) results. Indeed this indicator is widely used for statistics within the medical community. It is defined as:

$r_{\vert \vert {\textbf {u}}\vert \vert }^{2}={\frac {(\sum _{i=1}^{N}(\vert \vert {\textbf {u}}_{i,LR-CFD}\vert \vert -\vert \vert {\overline {{\textbf {u}}_{LR-CFD}}}\vert \vert )(\vert \vert {\textbf {u}}_{i,MRI}\vert \vert -\vert \vert {\overline {{\textbf {u}}_{MRI}}}\vert \vert ))^{2}}{\sum _{i=1}^{N}(\vert \vert {\textbf {u}}_{i,LR-CFD}\vert \vert -\vert \vert {\overline {{\textbf {u}}_{LR-CFD}}}\vert \vert )^{2}\sum _{i=1}^{N}((\vert \vert {\textbf {u}}_{i,MRI}\vert \vert -\vert \vert {\overline {{\textbf {u}}_{MRI}}}\vert \vert )^{2}}}$

where $\vert \vert {\textbf {u}}_{i}\vert \vert$ is the magnitude of the velocity at the $i^{th}$ node and $\vert \vert {\overline {\textbf {u}}}\vert \vert$ is the averaged magnitude velocity. The correlation over the cardiac cycle is shown on Fig. 12. At peak systole, a $r_{\vert \vert {\textbf {u}}\vert \vert }^{2}$ value of 0.84 is found when the MRI image is denoised and unwrapped (phase offset correction) and 0.97 when the additional no-slip boundary condition is applied at walls. This is in agreement with the results reported in Puiseux et al. [2] (cf. table 3).

Figure 12: Pearson's correlation $r_{\vert \vert {\textbf {u}}\vert \vert }^{2}$ between post-processed MRI and downsampled CFD

Flowrates

The flowrates were compared at four planes displayed in Fig. 13, including the inlet, outlet, collateral and bend. They were computed from the post-processed MRI images and downsampled CFD (LR-CFD) velocity field, both expressed on the MRI grid. The results are shown in Fig. 14, where the flowrates obtained from the CFD are also given as reference and prove that the downsampling process do not affect the flowrate computation. Very good agreement is found at the inlet (Fig. 1a) and in the collateral (Fig. 14c). However MRI overestimates the flowrates at the outlet (Fig. 14b) and in the middle of the bend (Fig. 14d). The recirculation after the collateral and just upstream of the outlet could explained this overestimation, due to velocity displacement artefacts (Steinman et al., 1997 [18]).