# Blood Pressure Estimation by Photoplethysmogram Decomposition into Hyperbolic Secant Waves
###### Abstract  
Photoplethysmographic (PPG) pulses contain information about cardiovascular parameters. In particular, blood pressure can be estimated using PPG pulse decomposition analysis, which assumes that a PPG pulse is composed of the original heart ejection blood wave and its reflections in arterial branchings. Among pulse decomposition wave functions that have been studied in the literature, Gaussian waves are the most successful ones. However, a more adequate pulse decomposition function could be found to improve blood pressure estimates. In this paper, we propose pulse decomposition analysis using hyperbolic secant (sech) waves and compare results with corresponding Gaussian wave decomposition. We analyze how the parameters of each of the two types of decomposition waves correlate with blood pressure. For this analysis, continuous blood pressure data and PPG data were acquired from ten healthy volunteers. The blood pressure of volunteers was varied by asking them to hold their breath for up to 60 s. The results suggested sech wave decomposition had higher accuracy in estimating blood pressure than the Gaussian function. Thus, sech wave decomposition should be considered as a more robust alternative to Gaussian wave pulse decomposition for blood pressure estimation models. blood pressure; hyperbolic secant function; photoplethysmography; pulse decomposition analysis +
Footnote †: journal:wrapping a cuff around the arm. This is called the oscillometric method and measures blood pressure by detecting pressure pulses that occur when the cuff pressure is between systolic blood pressure and diastolic blood pressure [4; 5]. However, the oscillometric method cannot measure blood pressure continuously because the tightening of the cuff may cause discomfort to the patient. Thus, it is desirable to develop alternative non-invasive cuffless methods for continuous blood pressure measurement. Pulse Decomposition Analysis (PDA) [6; 7] is a non-invasive method of measuring blood pressure without a cuff. The pulse in PDA is a wave resulting from blood pressure and volume changes in the peripheral vasculature, and associated with one heartbeat. With each heartbeat, blood flows from the heart's left ventricle to the aorta, and the resulting blood pressure fluctuations propagate to the peripheral arteries, generating a pulse wave. The pulse wave is usually measured non-invasively using a device called a photoplethysmograph (PPG). A PPG is an optical device that measures light transmission, typically on a finger or earlobe. As the volume of the arteries changes with each heart pulsation, the amount of light reflected or transmitted by the skin changes, allowing the non-invasive measurement of pulse waves. The PDA considers that the shape of the peripheral pulse consists of a primary wave coming directly from the heartbeat and its reflected wave, which is shown in Figure 1. Reflection occurs when the pulse wave propagates to the lower extremities and is reflected in the aorta bifurcations at the iliac artery and at the renal artery. The most successful PDAs use Gaussian pulse decomposition [6; 7]. For example, in [7], the authors use Gaussian PDA and define the primary systolic pulse as P\({}_{1}\), the renal reflection pulse as P\({}_{2}\), and the iliac reflection pulse as P\({}_{3}\). The amplitude ratios P\({}_{2}\) to P\({}_{1}\), the T\({}_{13}\) interval, and the time delay between systolic (P\({}_{1}\)) and iliac peak (P\({}_{3}\)) are used as parameters to estimate the blood pressure. Their results show statistically significant correlations between P\({}_{2}\), P\({}_{1}\), T\({}_{13}\), and blood pressure as measured by central line catheters (systole: R\({}^{2}\): 0.92, \(p\) < 0.0001, diastole: R\({}^{2}\): 0.78, \(p\) < 0.0001). Several PDA parameters, such as systolic upstroke time, diastolic time, 2/3, and 1/2 pulse amplitude, are possible candidates for estimating blood pressure from pulse waves using PPG [8; 9; 10; 11].