Table 4:
Averaged Pearson correlation coefficients for each QoI category for all models between (a) the 3D and 1D models (3D-1D) and the 3D and 0D models (3D-0D) of the same resolution level and between (b) the 3D models of different mesh resolutions levels. The former correlations are needed for the control variate portion and the latter are needed for the MLMC portion of our approach. The correlations are very high for the global (flow and pressure) QoIs, and slightly lower for the local (TAWSS) QoIs. However, even for the local QoIs, the correlations are large enough to produce good performance from the MLMF UQ methods. No 0D model fine resolution level was used in our study, so no correlation is reported. Abbreviations: aorto-femoral healthy (AFH), aorto-femoral diseased (AFD), coronary healthy (CH), and coronary diseased (CD).
| Outlet Flow | Outlet Pressure | Model Pressure | Model TAWSS | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Model and Mesh | 3D-1D | 3D-0D | 3D-1D | 3D-0D | 3D-1D | 3D-0D | 3D-1D | 3D-0D | |
| AFH | Coarse | 0.997 | 0.995 | 0.995 | 0.995 | 0.995 | 0.992 | 0.825 | 0.647 |
| Medium | 0.997 | 0.996 | 0.995 | 0.989 | 0.995 | 0.990 | 0.843 | 0.782 | |
| Fine | 0.997 | — | 0.994 | — | 0.995 | — | 0.792 | — | |
| AFD | Coarse | 0.998 | 0.995 | 0.996 | 0.996 | 0.996 | 0.992 | 0.834 | 0.612 |
| Medium | 0.993 | 0.992 | 0.995 | 0.989 | 0.994 | 0.990 | 0.880 | 0.812 | |
| Fine | 0.998 | — | 0.994 | — | 0.995 | — | 0.818 | — | |
| CH | Coarse | 0.999 | 0.999 | 0.998 | 0.999 | 0.998 | 0.999 | 0.854 | 0.775 |
| Medium | 0.999 | 0.999 | 0.998 | 0.995 | 0.998 | 0.995 | 0.851 | 0.850 | |
| Fine | 0.999 | — | 0.998 | — | 0.998 | — | 0.811 | — | |
| CD | Coarse | 0.999 | 0.999 | 0.997 | 0.999 | 0.997 | 0.999 | 0.847 | 0.744 |
| Medium | 0.999 | 0.999 | 0.997 | 0.993 | 0.997 | 0.994 | 0.853 | 0.798 | |
| Fine | 0.999 | — | 0.996 | — | 0.996 | — | 0.799 | — | |
| (a) HF-LF Model Correlations | |||||||||
| Outlet Flow | Outlet Pressure | Model Pressure | Model TAWSS | ||
|---|---|---|---|---|---|
| Model and Mesh | 3D-3D | 3D-3D | 3D-3D | 3D-3D | |
| AFH | Coarse-Medium | 0.999 | 0.999 | 0.999 | 0.999 |
| Medium-Fine | 0.999 | 0.999 | 0.999 | 0.998 | |
| AFD | Coarse-Medium | 0.996 | 0.999 | 0.999 | 0.939 |
| Medium-Fine | 0.995 | 0.998 | 0.998 | 0.924 | |
| CH | Coarse-Medium | 0.999 | 0.999 | 0.999 | 0.999 |
| Medium-Fine | 0.999 | 0.999 | 0.997 | 0.998 | |
| CD | Coarse-Medium | 0.999 | 0.999 | 0.999 | 0.999 |
| Medium-Fine | 0.999 | 0.999 | 0.998 | 0.998 | |
| (b) HF Mesh Resolution Level Correlations | |||||