## 1 Introduction
In fact, thanks to the high diffusion and low absorption of light in tissues, back-reflection modality allows to collect signal with a depth sensitivity of few centimeters from the investigation surface. This procedure is, for example, commonly employed for measuring hemodynamic oscillations in the cortical layers directly from the scalp; these oscillations are known to be associated with neuronal activity [19]. Whereas multiwavelength PPG can estimate arterial oxygen saturation (i.e., pulse oximetry), single wavelength PPG can be indicative of vascular status. In fact, although PPG is a volumetric measurement, thanks to the strict relation between blood volume and pressure, it has been extensively demonstrated that it is possible to evaluate parameters indicative of arterial stiffness from single-wavelength PPG signal features. In particular, the pulse wave velocity (PWV), the velocity of propagation of pressure wave through the arterial tree, is known to be monotonically associated with arterial stiffening and it can be estimated from PPG measurements performed at two different body locations [20; 21]. Furthermore, by using amplitudes of distinctive peaks of PPG second derivative, it is possible to compute a metric defined as ageing index (AGI) [22; 23], which is highly sensitive to vascular ageing. Moreover, PPGallows to estimate the augmentation index (AI) in similarity with pressure measurements [24; 25]. However, PPG evaluates changes in local blood volume, and simple substitution of absolute pressures with PPG metrics is not always a feasible procedure. For example, ABI is computed from absolute pressures, and it clearly cannot be directly evaluated from PPG. However, more complex approaches, such as data-driven multivariate statistical procedures (i.e., machine learning [26]) could be suitable to derive a model of ABI from PPG signal features. The model can be obtained through supervised learning [27], i.e., it can be derived from available PPG and ABI data, without interpretation of the underlying complex physiology involved. The only assumption of the procedure is the existence of a physiological association between PPG and ABI, and this assumption can be tested a-posteriori through the generalization performance of the model. Among machine learning approaches, linear models such as the general linear model (GLM) [28; 29; 30] are preferable, thanks to their simple application and robustness. In this study, the feasibility of predicting ABI from multisite PPG features employing a linear machine learning procedure (i.e., GLM) was investigated. ABI was measured using a commercially available instrument (Enverdis Vascular Explorer, VE) [31; 32], which is able to measure the ankle and brachial pressures. GLM was then employed in a supervised learning approach [27] to link different features extracted from the PPG signals at the ankle and at the arm with ABI estimated using the Vascular Explorer (VE-ABI). This analysis was performed to obtain an ABI prediction from PPG (PPG-ABI). Finally, a receiver operating characteristic (ROC) [33] analysis was performed to test the capability of PPG-ABI to discriminate cardiovascular disease assuming VE-ABI as the gold-standard.