# Blood Pressure Estimation Algorithm Based on Photoplethysmography Pulse Analyses
## 2 Materials and Methods  
Systolic blood pressure (SBP) and diastolic blood pressure (DBP) information can be obtained as per existing studies using PTT from PPG data measured noninvasively at the fingers [16]. The BP and PTT are inversely correlated. Specifically, small PTT values correspond to short blood transfer times and highly rigid blood vessels, demonstrating that blood flow rates in blood vessels are high [17]. Therefore, we propose that the individual's vascular conditions could affect the PPG. A graph representing the measured finger PPG is shown in Figure 1, and was obtained by filtering two single wavelengths using an infrared light-emitting diode of 940 nm. In this study, PPGs were collected and analyzed (Figure 1). The peak starting point of the PPGs can be identified using ECGs. Recognizing the initial ECG R peak of the PPG as R1 allows for continuous BP estimation with two PPGs without any additional ECG measurements [18; 19]. Therefore, PTT can be defined as the time taken by the pulse wave generated by the heart at R1 to reach P1 of the 1 st PPG. The pulse interval time (PT) of P1 and P2 can then be quantified on the basis of the differences between the two PPGs. According to the Bramwell-Hill model, the PWV can be defined [20] as  
\[\text{PWV}=\frac{L}{PT}=\sqrt{\frac{V_{dia}\Delta P}{\rho\Delta V}} \tag{1}\]  
where the distance between the sensors is denoted by \(L\), and the time difference between the two PPGs is denoted by \(PT\). In the above equation, \(V\) is the cross-sectional area of a blood vessel, and \(\rho\) is its specific gravity. Moreover, \(\Delta P\) is the difference between the pulse pressure and DBP, and \(\Delta\)V = V\({}_{dia}\) - V\({}_{sys}\)[18]. Furthermore, \(\rho\) varies in different individuals and is difficult to estimate using a PPG. If the specific values of individual V and \(\rho\) are set as constant values, and the distance is fixed, the following Equation (2) can be obtained:  
\[\mathrm{P-DBP}=\frac{\Delta V\cdot\rho L^{2}}{V_{dia}\cdot PT^{2}}=\frac{ \alpha}{PT^{2}} \tag{2}\]  
Furthermore, BP can be estimated using the mean arterial pressure (MAP). In turn, MAP can be estimated as the sum of the central venous pressure to the product of the cardiac output (CO) and system vascular resistance (SVR) [21]. The central venous pressure is very small and can be ignored. Additionally, the cardiac output is defined as the product of the heart rate (HR) and stroke volume (SV). Thus, MAP can be defined as follows [22]:  
\[\mathrm{MAP}=\mathrm{HR\cdot SV\cdot SVR} \tag{3}\]  
It can be alternatively defined as MAP = (SBP + 2 DBP)/3 [23] and can be expressed as:  
\[\mathrm{SBP}+2\mathrm{DBP}=3(\mathrm{HR\cdot SV\cdot SVR}) \tag{4}\]  
SV and SVR are individual values and cannot be obtained from the PPG measurement; therefore, they are summarized as the constant. The heart rate (HR) is the same as the peak number of the pulse rate (PR) in the PPG measurement [24]. Therefore, DBP and SBP can be obtained by calculating the parameters shown in Equation (5) using two PPG sensors on the basis of the Bramwell-Hill model,  
\[\mathrm{DBP}=\left(PR\cdot\alpha-\frac{1}{3}\right)\left(\frac{b}{PT^{2}} \right)\mathrm{SBP}=\left(PR\cdot\alpha+\frac{2}{3}\right)\left(\frac{b}{PT^{2 }}\right) \tag{5}\]  
where PT is the interval between P1 and P2. Figure 1: Analyzed results based on recordings from two photoplethysmographies (PPGs). PTT: pulse transit time, PT: the time difference between the two PPGs P1 and P2. In order to calculate the BP value accurately using the PPG, a and b, treated as constants, can be calculated as in Equation (6) [18]. Equation (6) can be obtained from Equations (4) and (5). \[\alpha=\text{MAP}/(\text{PP}\cdot\text{PR}),\;\text{b}=\text{PP}\cdot\text{PT}^{2} \tag{6}\]  
To estimate the BP values, the input SBP and DBP from existing BP values can be obtained, whereas the remaining values can be obtained via algorithms. Because PR and PT can be obtained using PPGs, specific values of a and b for different individuals can be obtained using individual PPGs.