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Mathematical Modeling and Simulation of Photoplethysmography

Modeling of the measurement of the heart rate is an important parameter because this model presents one of the simpler methods to detect any abnormalities in the human heart. The heart rate can be controlled by maintaining the stroke volume which is the amount of blood pumped by the ventricle with each heartbeat and thus maintaining the cardiac output. One of the efficient ways to measure this stroke volume is obtained with the help of the lumped parameter model. This paper proposes a mathematical model of photoplethysmograph during the flow of bloodstream from the left ventricle of the heart towards the fingertip. The light passes through the biological tissue of the fingertip which is detected by the photodiode. The amount of light absorbed by the blood vessels, veins, bones, and arteries present inside the finger directly depends on the physical properties of the finger along with the placement of the finger, skin temperature which is detected by the photodetector. The proposed mathematical model is based on the lumped parameter method of the electrical equivalent circuit of the derived photoplethysmograph signal during the pumping action of the left ventricle. LabVIEW software is utilized for the validation of the simulated result. The PPG signal after stimulation in the LabVIEW is approximately the same as that of standard PPG signal. This output tells about the pulse rate of the heart.