Page 227 - Artificial Intelligence for Computational Modeling of the Heart

200 Chapter 6 Additional clinical applications

Table 6.2 Quantitative comparison of the pressure drop models: Norms of differences between
3D CFD and analytically estimated pressure drop.

L 1 L 2 L ∞ Pearson
Original Y-T model 6.95 142.09 66.66 0.891
Optimized model 2.53 17.1 16.38 0.981
Coupled model 1.28 3.66 5.67 0.984

Training was performed on a subset containing 80% of the
samples while the remaining 20% were used for testing. Splitting
was performed at case level, to ensure that all computations per-
formed for the same synthetic case, always lie either in the training
or in the test set. Training was performed using the Tensorflow li-
brary [451] and the Adam optimizer [452], using mean absolute
error as loss function.

6.2.3 Results
6.2.3.1 Evaluation of the pressure drop model
First we evaluate the performance of the optimized and the
original Young-Tsai model using the 3D CFD computations as
ground truth: Fig. 6.10 displays the results on the test set. Fur-
thermore, Table 6.2 displays the results of the quantitative com-
parison of the three models. The original model underestimates
the pressure drop since the synthetic CoA models have a higher
degree of complexity than the original geometries used for fit-
ting Eq. (6.8), and the range of considered Reynolds numbers is
also larger. The herein introduced DL-based pressure drop model
reduces the mean absolute error from 6.95 to 1.28 mmHg when
comparing results against 3D CFD. Parameters p 1 , p 2 and p 3 from
the optimized model are related to the viscous pressure loss: p 1
decreases significantly in the optimized model, but the reduction
is partially compensated by the increase of p 2 and p 3 . Parame-
ter p 4 , which is related to the turbulent pressure loss, is modified
only marginally, while parameters p 5 , p 6 and p 7 are all non-zero,
indicating that convection, eccentricity and bulging are relevant
features for the overall trans-coarctation pressure drop. The er-
rors are further reduced by the coupled model, therefore providing
the best prediction. This suggests that the pressure drop is signif-
icantly affected by highly non-linear effects which are only cap-
tured by the neural network model.