# Simulation-Driven Machine Learning for Predicting Stent Expansion in Calcified Coronary Artery
## 3 Results  
A total of 120 pairs of pre- and post-stenting cross sections were extracted from the FE models for training and testing regression models. Four area features (Area_A, Area_F, Area_C, Area_L, and stenting expansion), along with the calculated post-stenting lumen area, are depicted in Figure 3a. The length features (ArcLength_C, ArcLength_F, and Thickness_C) and the calcification angle are shown in Figure 3b. It is clear that the major features of these cross sections are different due to the presence of heterogeneous calcifications. The calcification area is associated with its angle (r = 0.64). The ArcLength_C is positively related to the calcification angle (r = 0.93), and the ArcLength_F is negatively related to the calcification angle (r = -0.80). Figure 3: _Cont._  
The prediction errors of four machine learning models are shown in Figure 4 in both scatter and box plots. The errors ranged from \(-\)9.85 to \(-\)5.44% for the linear regression (LR), \(-\)2.46 to 4.45% for SVR with a linear kernel (SVR_L), \(-\)2.89 to 2.08% for SVR with a polynomial kernel (SVR_P), and \(-\)1.73 to 8.73% for SVR with an RBF kernel (SVR_RBF). The bias values, i.e., the average values of prediction errors, were \(-\)7.24, 0.8446, \(-\)0.87, and 3.79% for the linear regression and the SVR with linear kernel, polynomial kernel, and RBF kernel, respectively. The ANOVA test showed significantly different prediction errors among these four groups (F = 176.06, \(p\) < 0.01). The maximum differences between the ML prediction and the FE simulation, in terms of area, were 0.32, 0.25, 0.22, and 0.16 mm\({}^{2}\) for the linear regression, the SVR with linear kernel, polynomial kernel, and RBF kernel, respectively. They were much lower than the area difference between the target lumen (7.06 mm\({}^{2}\)) and under expanded one (<5.65 mm\({}^{2}\)). Figure 4: _Cont._  
Figure 3: Eight features at 120 cross sections as well as the corresponding post-stenting lumen area: (a) area features, and (b) length features and calcification angle. The influence of the feature selection on the prediction accuracy using SVR_P is depicted in Figure 5. Two subgroups, stretch features (Area_L, ArcLength_C, and ArcLength_F) and calcification features (Area_C, Angle_C, and Thickness_C), were compared with the group with all eight features. For the subgroup with calcification features, the prediction error ranged from 3.20 to 9.42%, with the bias as 6.05%. For the subgroup with stretch features, the error ranged from -1.56 to 6.18%, with the bias as 1.56%. For the group with all eight features, the error ranged from -2.89% to 2.08%, with the bias as -0.87%. The group with all eight features demonstrated a better prediction capability than both subgroups. It is interesting to see that the stretch features performed better than the calcification features. The difference among the biases of these three groups is statistically significant (F = 148.9, \(p\) <0.01). Further, a simple t-test also demonstrated a statistically significant difference between stretch features and calcification features (t = 66.97, \(p\) < 0.01). Figure 4: Comparison of linear regression (LR) models and SVR models with linear (SVR_L), polynomial (SVR_P), and radial basic function (SVR_RBF) kernels: (**a**) scatter plot, and (**b**) box plot with median line and mean X.  
Figure 5: \(Cont\). The influence of neighboring cross sections on the prediction accuracy using SVR_P was evaluated and compared with the aforementioned individual cross sections (Figure 6a). Each feature in the cross section was averaged with the values from eight neighboring cross sections. The prediction errors for both cases showed minimal differences in terms of range and average. Specifically, the prediction error ranged from \(-2.28\) to \(2.33\%\) by using averaged features. It ranged from \(-2.89\) to \(2.08\%\) by using features from individual cross sections. The bias was \(-0.77\%\) and \(-0.87\%\) for neighboring cross sections and single cross sections, respectively.