## 2 Materials and Methods
### MRI Acquisition and Post-Processing  
MRI acquisition included a multi VENC 4D Phase-Contrast flow acquisition on 3T Siemens magnet (Trio TIM, Siemens Medical Solutions, Erlangen, Germany) with the following settings: TE: 2.83-3.65 ms, TR: 12.85-26.36 ms, encoding velocities: 260-310 cm/s, pixel spacing: 0.78-0.94 mm, slice thickness: 2.5-3 mm. 2D Phase-Contrast was also performed at the inlet and outlet of the BMHV.  
Pre-processing includes: (1) aliasing correction and eddy current correction of the 4D Phase-Contrast flow acquisition using the dedicated 4D flow demonstrator Siemens software with background corrections and phase aliasing modification, (2) VTK format transformation using Matlab script (Mathworks, Natik, MA, USA), and (3) AST computation using python and Paraview software (Kitware, Clifton Park, NY, USA and Los Alamos National Laboratory, New Mexico, USA). Segmentation of the volume of interest was performed using the maximum intensity projection.  
Assessment of the MRI signal alteration induced by the mechanical structure of the valve was performed at the center of the valve (symmetry plane) and at the distal location between the two volumes created by the blurring effect.  
Comparison with numerical results was performed for analysis of the influence of BMHV design: OnX29 versus SJM25 (similar internal diameters: 23.4 versus 23 mm and opening angle 90\({}^{\circ}\) and 85\({}^{\circ}\)), of the influence of inner diameter: SJM25 and SJM23 (internal diameters 23 versus 21.4 mm) and of the influence of a blocked leaflet on SJM25.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**Name** & & & & & & & & & & & & \\ \hline BMHV\_Leaflet85-21-30 & 85 & 21 & 3.0 & 70 & 90 & 0.5 & 1.62 & 0.20 & 0.99 & 1.75 & 8 (16) & 1.66 \\ BMHV\_Leaflet85-22-35 & 85 & 22 & 3.5 & 70 & 90 & 0.5 & 1.65 & 0.21 & 0.99 & 1.77 & 3 (6) & 1.69 \\ BMHV\_Leaflet85-23-35 & 85 & 23 & 3.5 & 70 & 90 & 0.5 & 1.34 & 0.38 & 0.76 & 1.74 & 3 (6) & 1.72 \\ BMHV\_Leaflet85-24-40 & 85 & 24 & 4.0 & 70 & 90 & 0.5 & 1.76 & 0.06 & 1.58 & 1.83 & 2 (4) & 1.77 \\ BMHV\_Leaflet90-20-30 & 90 & 20 & 4.0 & 70 & 90 & 0.5 & 1.49 & 0.23 & 0.91 & 1.64 & 4 (8) & 1.60 \\ BMHV\_Leaflet90-21-30 & 90 & 21 & 4.0 & 70 & 90 & 0.5 & 1.62 & 0.17 & 1.07 & 1.73 & 3 (6) & 1.68 \\ BMHV\_leaflet90-22-35 & 90 & 22 & 3.5 & 70 & 90 & 0.5 & 1.47 & 0.24 & 0.83 & 1.66 & 3 (6) & 1.66 \\ BMHV\_Leaflet90-23-35 & 90 & 23 & 3.5 & 70 & 90 & 0.5 & 1.60 & 0.18 & 1.01 & 1.71 & 4 (8) & 1.61 \\ BMHV\_leaflet90-24-40 & 90 & 24 & 4.0 & 70 & 90 & 0.5 & 1.54 & 0.20 & 0.89 & 1.67 & 5 (10) & 1.59 \\ BMHV\_Leaflet90-22-35 & HR60 & 90 & 22 & 3.5 & 60 & 90 & 0.5 & 1.45 & 0.23 & 0.83 & 1.69 & 5 (10) & 1.57 \\ BMHV\_Leaflet90-22-35 & HR120 & 90 & 22 & 3.5 & 120 & 90 & 0.5 & 1.45 & 0.25 & 0.84 & 1.70 & 5 (10) & 1.58 \\ BMHV\_leaflet90-22-35 & M03 & 90 & 22 & 3.5 & 70 & 90 & 0.3 & 1.69 & 0.21 & 0.99 & 1.80 & 2 (4) & 1.74 \\ BMHV\_leaflet90-22-35 & M07 & 90 & 22 & 3.5 & 70 & 90 & 0.7 & 1.49 & 0.19 & 0.87 & 1.67 & 3 (6) & 1.56 \\ BMHV\_leaflet90-22-35 & M09 & 90 & 22 & 3.5 & 70 & 90 & 0.9 & 0.89 & 0.11 & 0.75 & 1.08 & 5 (10) & 0.94 \\ BMHV\_Leaflet90-22-35 & SV70 & 90 & 22 & 3.5 & 70 & 70 & 0.5 & 1.44 & 0.23 & 0.83 & 1.61 & 6 (12) & 1.57 \\ BMHV\_Leaflet90-22-35 & SV120 & 90 & 22 & 3.5 & 70 & 120 & 0.5 & 1.60 & 0.18 & 1.01 & 1.71 & 3 (6) & 1.66 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Numerical simulation setting (geometrical parameters of the BMHV) and results: EOA\({}_{\text{AST}}\) computation (mean, max, and mean) and location of the recording plane.