Mathematical model of the photoplethysmogram for testing methods of biological signals analysis

The purpose of this study was to develop a mathematical model of the photoplethysmogram, which can be used to test methods that introduce the instantaneous phases of the modulating signals. The model must reproduce statistical and spectral characteristics of the real photoplethysmogram, and explicitly incorporate the instantaneous phases of the modulating signals, so they can be used as a reference during testing. Methods. Anacrotic and catacrotic phases of the photoplethysmogram pulse wave were modeled as a sum of two density distributions for the skew normal distribution. The modulating signals were introduced as harmonic functions taken from the experimental instantaneous phases of the VLF (0.015...0.04 Hz), LF (0.04...0.15 Hz) and HF (0.15...0.4 Hz) oscillations in the real photoplethysmogram. The spectral power in the VLF, LF, and HF frequency ranges was calculated to compare the model and experimental data. Results. The model qualitatively reproduces the shape of the experimental photoplethysmogram pulse wave and shows less than 1% error when simulating the spectral properties of the signal. Conclusion. The proposed mathematical model can be used to test the methods for introduction of the instantaneous phases of the modulating signals in photoplethysmogram time-series.