## 2 Methods  
### Tidal Wave Terminology  
Efficiently evaluating the tidal wave feature for LVET estimation capabilities requires a parametric approach. The starting point for this approach is represented by the first derivative of the signal, as it provides a more detailed view of the blood flow gradient evolution. Based on the visualization and interpretation of various waveform morphologies  
Figure 1: Correlation of ABP or PPG features with LVET. (**a**) First initial definition by [PERSON]: ending of the ejection phase is marked by the dicrotic notch; (**b**) Updated correction following recent cardiovascular findings: ending of the ejection time is marked by the tidal wave, an earlier event compared to the notch.  
from our previous studies [33; 34], we have defined the following TDW terminology, as depicted in Figure 2.  
Following the systolic phase, central arterial pressure seeks to return to its initial value, depending on the mechanical resistance encountered in the blood flow. Therefore, when examining the first derivative (FD) domain, the following behavior is observed: after reaching the minimum gradient per cardiac cycle, the trace will eventually converge to a zero value. External or internal stimuli can induce disturbances in blood flow, altering the trajectory of this convergence path. In the context presented here, the onset of aortic valve closure serves as the initial stimulus, leading to the appearance of an inflection point in the gradient trace, labeled as tidal peak (TDW_PK). After the complete closure of the valves, no further disturbances occur, and the convergence trajectory returns to its initial path. This phase creates an additional inflexion point, which is marked as the tidal last valley (TDW_LV). The moment when arterial pressure decay reaches the minimum gradient value just before TDW is labeled as the first valley (TDW_FV).  
An essential physiological phenomenon to consider in this context is [PERSON]'s effect [35; 36]. Due to compliant nature of the arterial tree, rapid spikes or changes in flow disturbance are attenuated and prolonged. The elasticity of the blood vessel wall is responsible for this effect, influenced by smooth muscle behavior. When the time constant of compliance capability is shorter than the time duration of a given event, the resulting flow can closely track the change. This is typically observed in predominantly rigid systems. Conversely, when the time constant is longer compared to the disturbance duration, the resulting flow poorly tracks the change. In the human body, this effect, stemming from arterial elasticity, serves to protect vessels' walls from abrupt spikes in blood flow or pressure. Consequently, rapid events are masked both in terms of their amplitude and their time duration. To address this, we introduced a linear compensation fiducial point, TDW_COMP, aimed at reducing [PERSON]'s effect. For the ABP component, this marker is computed as the midpoint between TDW_PK and TDW_LV. In PPG recordings, the wave propagation time from a central to a peripheral location must be considered. Therefore, the compensation point becomes the midpoint between TDW_FV and TDW_PK.  
Regarding the characterization of the dicrotic wave, only one parameter, NOTCH, was considered. This point occurs after the tidal wave's last valley within the FD domain. Thus, measuring notch time duration serves as a spot check to verify the obsolete association with LVET.  
Figure 2: Morphological detail of tidal wave region from first derivative analysis of ABP or PPG waveform. Black line represents zero value. Green dotted line represents gradient convergency to zero value in absence of tidal wave phase. TDW components are highlighted by pointing triangles.