Estimation of respiratory volumes from the photoplethysmographic signal. Part 2: a model study

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Abstract
A Windkessel model has been constructed with the aim of investigating the respiratory-volume dependence of the photoplethysmographic (PPG) signal. Experimental studies show a correlation between respiratory volume and the peak-to-peak value of the respiratory-induced intensity variations (RIIV) in the PPG signal. The model compartments are organised in two closed chambers, representing the thorax and the abdomen, and in a peripheral part not directly influenced by respiration. Cardiac pulse and respiration are created by continuous adjustment of the pressures in the affected compartments. Together with the criteria for heart and venous valves, the model is based on a set of 17 differential equations. These equations are solved for varying thoracic and abdominal pressures corresponding to different respiratory volumes. Furthermore, a sensitivity analysis is performed to evaluate the properties of the model. The PPG signals are created as a combination of peripheral blood flow and pressure. From these signals, the respiratory synchronous parts are extracted and analysed. To study some important limitations of the model, respiratory type and rate are varied. From the simulations, it is possible to verify our earlier experimental results concerning the relationship between respiratory volume and the peak-to-peak value of the RIIV signal. An expected decrease in the amplitude of the respiratory signal with increased respiratory rate is also found, which is due to the lowpass characteristics of the vessel system. Variations in the relationship between thoracic and abdominal respiration also affect the RIIV signal. The simulations explain and verify what has been found previously in experimental studies.