Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo 164-8525, Japan.
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
Chaos. 2019 Apr;29(4):043121. doi: 10.1063/1.5088989.
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.
光体积描记图（PPG）是一种广泛用于估计生理参数的非侵入性生物信号，例如人体健康监测中的心率。过去几十年中，已经对其处理方法、应用和动态进行了广泛的研究。然而，对于 PPG 动态的基本结构，例如鞍点平衡点，仍然缺乏相关知识，这些知识对于全面理解 PPG 动态至关重要，并且可能为建立 PPG 的数学模型提供有用信息。在这项研究中，应用 Morse 图论对实验 PPG 数据进行分析，以验证鞍点平衡点的存在，并估计其相对于时滞重构 PPG 吸引子的位置。结果表明，在重构的 PPG 轨迹附近可以找到一个鞍点平衡点；此外，对于来自不同年龄组的健康受试者，在相同的重构吸引子区域中也发现了鞍点平衡点，这表明找到的鞍点平衡点对于全面理解 PPG 动态具有重要意义。
