Mathematical Modeling of Photoplethysmography: Model Assessment and Validation

Photoplethysmography (PPG) is a well-known technique employed to assess optically perfused bio-tissue volume changes. A PPG apparatus consists of a light emitter and a receptor. The analysis of the received light is used to infer properties of the illuminated tissues. This paper aims at presenting a novel distributed mathematical model for PPG signals, which combines a poroelastic model of tissue perfusion with a diffusion model for light absorption and scattering.

We assume that the tissues undergo small deformations, allowing for a linear poroelastic description of perfusion. Since many PPG devices are applied to the fingertips (due to the rich vascularization in that area) we model the system specifically on the finger, with arterial blood pulse pressure serving as the primary perfusion driver. The numerical discretization of the governing equations is carried out using the finite element method. After calibration of the model, 216,000 simulations are performed with varying parameters (quasi-Monte Carlo approach). The aggregated results for two key biomarkers, AC/DC PPG amplitude ratio and pulse pressure, are compared against experimental PPG and pulse pressure measurements obtained from 20 volunteers.

Within the prescribed parameter ranges, numerical simulations successfully reproduce the AC/DC PPG amplitude biomarker in both the red and infrared wavelengths, with a few outliers observed for the green. Furthermore, in the vicinity of the combined red and infrared measured biomarkers, there are simulated biomarkers whose corresponding pulse pressures closely match the mapped-to-finger measured pulse pressure, with a difference of less than $1\mathrm{mmHg}$ .

This work demonstrates the relevance of the proposed mathematical model for simulating PPG signals and highlights its potential for estimating tissue perfusion parameters, such as arterial pulse pressure.