Mathematical model of photoplethysmographic signal recorded in transmitted light
Authors: Koptev D.S. 
Published: November 2021

The use of near-infrared laser radiation is currently one of the most promising trends in the development of medical diagnostic research methods. The basic principle of operation of most optical diagnostic devices and systems is the interaction of the incident radiation with the biological environment under study, as a result of which the parameters of the light flux change. When choosing the principles of constructing optical measuring transducers parameters of biological tissue, it is necessary to take into account a number of its specific features as an object of research. The radiation of the optical range falling on the biological tissue under study is capable of influencing it, which manifests itself in the form of heating, additional photochemical reactions. This circumstance is due to the absorption of light, which occurs selectively in most cases. Therefore, the development of optical diagnostic devices and systems should be accompanied not only by taking into account the maximum intensity of the incident radiation, but also by analyzing its spectral composition, since the use of different wavelengths for the study of biological tissue is accompanied by different effects on the biological object and significantly different measurement results. When the light flux passes through biological tissue, its intensity is weakened as a result of absorption (absorption), reflection, scattering. In a number of thematic sources, the process of interaction of laser radiation with biological tissue is considered in detail and it is shown that it is characterized by a number of coefficients: specular reflection, absorption, scattered (diffuse) reflection, scattered (diffuse) transmission, directional transmission, which are completely determined by the following light fluxes: incident to the interface of media, diffusion reflection, reflected, diffusion transmission, directional transmission. It should be noted that the absorption and scattering of the light flux occurs selectively. Therefore, the quantitative characteristic of absorption is determined using monochromatic optical radiation with a strictly fixed spectral composition. This article discusses a photoplethysmographic diagnostic method, the key advantage of which is the ability to assess the dynamics of oxygen transport and consumption in the blood microcirculation system (determining the level of peripheral blood saturation). The low accuracy of the available mathematical models, which do not adequately describe the processes of interaction of optical radiation with biological tissue, should be attributed to the very topical problems of the application of this method. It should be said that there are two approaches to creating such models: analytical and simulation. However, analytical models make it possible to obtain more accurate values of the determined parameters, in contrast to simulation ones, which allow one to obtain only the probabilistic characteristics of their determination. Therefore, this article will use the analytical approach to model development.