## 4 Discussion  
Because of the high incidence of acute cardiovascular insults, the identification of asymptomatic cardiovascular impairment and its associated risks is of great importance, and it should be extensively performed. Several markers of cardiovascular risk have been identified, such as ABI. ABI is considered highly indicative of arteriosclerosis and vascular disease of the lower limbs. ABI is estimated as the ratio between the brachial and the tibial systolic blood pressure, and this ratio is considered pathological when its value is particularly low (ABI \(<\) 0.9) or particularly high (ABI \(>\) 1.4). Direct ABI estimation requires measurements of systolic pressures employing pressure sensors and supra-systolic cuff occlusion. This procedure can be time consuming, operator-dependent and stressful for the patient. PPG can be employed to estimate cardiovascular status. However, defining an intuitive and direct formula linking PPG to ABI is poorly feasible, and other approaches have to be investigated. In this study, the possibility of employing a data-driven machine learning approach to predict ABI from PPG was explored. PPG features, extracted from brachial and tibial arteries and known to be associated to cardiovascular status and arterial pressure, were used as independent variables in a linear multivariate regression (i.e., GLM) that was trained through a supervised learning approach to infer ABI. A leave-one-subject-out cross-validation approach was used to estimate the accuracy of the predictive model on a novel dataset, providing an unbiased estimation of the algorithm performance (generalization). The correlation between predicted ABI (estimated from PPG features, PPG-ABI) and gold-standard ABI (estimated through a validated procedure, VE-ABI) of r = 0.79 (\(p\) = -0) suggested good performances of the model. Importantly, the multivariate machine learning approach performed better than all the univariate regressions, including the PPG feature that was best correlated with VE-ABI (z = 3.71, \(p\) = 2.08 \(\times\) 10\({}^{-4}\)). Notably, a significant contribution to the VE-ABI variance was obtained for PPG temporal (TDAnkle) and amplitude (MaxAnkle) features measured at the ankle. These results suggest that the ankle could be an ideal location for PPG measurements. PPG temporal features are associated to PWV, which can be accurately inferred from particularly distal measurement such as those performed at the ankle. For such a reason, temporal PPG features evaluated at the ankle might be expected to significantly contribute to ABI prediction. However, amplitude PPG features generally tends to be poorly reliable and are not useful for quantitative physiological parameters estimation. Nonetheless, significant ABI prediction capabilities were obtained for the MaxAnkle parameter, depicting the stability and reliability of measuring PPG at the ankle. The null results obtained for the MaxArm parameter instead suggest less reliable estimation of PPG amplitude at the arm. As suggested by Bland-Altman plot, the errors in estimation of PPG-ABI with respect to VE-ABI were distributed within the 95% confidence interval, showing a good correspondence of the two methods without clear outliers. Moreover, in order to test the capability of PPG-ABI to evaluate cardiovascular impairment and risk, a ROC analysis of PPG-ABI for the classification of pathological ABI, as defined by the gold standard procedure of VE, was performed (i.e., a ROC curve for evaluating the PPG-ABI ability to correctly identify VE-ABI \(<\) 0.9 or VE-ABI \(>\) 1.4). The AUC was 0.85, and at a defined threshold, an accuracy of 88% was obtained. This analysis showed a good ability of PPG-ABI to discriminate between the physiological and pathological population, with better performance than univariate analysis. Interestingly, small but significant differences in VE-ABI as a function of gender and smoking status were found.