Human photoplethysmogram through the Morse graph: Searching for the saddle point in experimental data

Photoplethysmogram (PPG) is one of the noninvasive biological signals widely used for the estimation of physiological parameters, such as heart rates in human health monitoring. Methods of its processing, its applications, and dynamics have been extensively investigated over the last several decades. However, there is still lack of the knowledge related to the fundamental structure of the PPG dynamics such as saddle equilibrium points, which have crucial importance to achieve the full understanding of the PPG dynamics and might provide useful information for establishing a mathematical model of the PPG. In this study, Morse graph theory was applied to the experimental PPG data in an attempt to verify the existence of saddle equilibrium and estimate its location with respect to the time-delay-reconstructed PPG attractor. The results demonstrated evidence that a saddle equilibrium point can be found in a neighborhood of the reconstructed PPG trajectory; moreover, it was found to be in the same reconstructed attractor's region for healthy subjects from different age groups that points toward fundamental importance of the found saddle equilibrium for a general understanding of the PPG dynamics.