## 3 Results
### External Validation and Generalization Performance  
Table 4 presents the external validation performance on the VascuNET and ExIC-FEp datasets. The results on VascuNET, while generally aligned with the internal cross-validation, show a moderate decline in predictive performance across most models. However, both PR and NN maintained strong predictive capabilities, achieving \(R^{2}\) values of 0.95 and 0.94, respectively, with relatively low MSE values. In contrast, LR, BR, and SVR experienced a more pronounced drop in performance, suggesting that these models may be more sensitive to data shifts even within a healthy population. For instance, although both EVasCu and VascuNET include apparently healthy individuals, slight differences in the average age or clinical profiles may introduce variations in the data distribution. Such shifts can challenge certain models' ability to generalize effectively, which may explain the decreased performance observed in these cases. Interestingly, when evaluated on the ExIC-FEp dataset, which includes older patients with cardiovascular disease and higher aPWV values, a further decline in performance was observed across all models. Despite this, PR remained the best-performing model, achieving an \(R^{2}\) of 0.90 and an MSE of 0.3332, followed closely by NN (\(R^{2}=0.90\), MSE = 0.3388). On the other hand, SVR exhibited a drastic drop in predictive performance, with an R\({}^{2}\) of \(-0.21\) and an MSE of 4.08, indicating that it struggled significantly with this pathological dataset. Figure 4 displays the fit and residual analysis of the different models evaluated on the VascuNET dataset. Overall, PR and NN exhibit the best performance, with predicted values closely aligned along the identity line and minimal residual dispersion. In contrast, LR, BR, and SVR show clear deviations, particularly in the upper range of aPWV values, where systematic underestimation becomes evident for aPWV values above 10 m/s. This suggests that these models struggle to accurately capture arterial stiffness in individuals with higher vascular aging. Furthermore, the residual plots confirm these trends, as LR, BR, and SVR present increasing residual magnitudes for higher aPWV values, suggesting that these models struggle to generalize well in this range. On the other hand, PR and NN maintain more homogeneously distributed residuals around zero, indicating a more stable fit across the entire range of values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**VascuNET**} & \multicolumn{3}{c}{**ExIC-FEp**} \\  & **MSE** & **RMSE** & \(\mathbf{R^{2}}\) & **MSE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline LR & 1.4833 & 1.2179 & 0.7933 & 1.4348 & 1.1978 & 0.5753 \\ PR & 0.3388 & 0.5820 & 0.9528 & 0.3332 & 0.5772 & 0.9014 \\ BR & 2.2190 & 1.4896 & 0.6909 & 2.1375 & 1.4620 & 0.3673 \\ SVR & 2.9136 & 1.7069 & 0.5941 & 4.0829 & 2.0206 & \(-0.2086\) \\ NN & 0.4061 & 0.6372 & 0.9434 & 0.3388 & 0.5821 & 0.8997 \\ \hline \hline \end{tabular} Abbreviations: MSE = Mean Squared Error; RMSE = Root Mean Squared Error; \(R^{2}\) = Coefficient of Determination; LR = Linear Regression; PR = Polynomial Regression; BR = Boosting Regressor; SVR = Support Vector Regression; NN = Neural Network. VascuNET and ExIC-FEp are external datasets composed of healthy individuals and patients with cardiovascular disease, respectively.  
\end{table} 
Table 4: Performance metrics of the models during external validation on the VascuNET and ExIC-FEp datasets. Finally, Figure 5 further confirms these findings, highlighting the impact of arterial stiffness on model performance. Since the ExIC-FEp dataset includes patients with cardiovascular disease and markedly elevated AS, most models exhibit a considerable decrease in predictive accuracy. Notably, LR, BR, and SVR show clear limitations, struggling to adapt to the high PWV values present in this population.