## Materials and Methods
### Systolic Blood Pressure Estimation Model  
The mathematical-physical model for SBP estimation proposed in Reference [29] is based on [PERSON]'s law as defined in Equation (1):  
\[\sigma=E\cdot e\cdot h/\left(1-\theta^{2}\right), \tag{1}\]  
where \(d\) is the diameter of the artery, \(d_{0}\) is the initial diameter of the artery, \(h\) is the thickness of the artery wall, \(\varepsilon=d/d_{0}\) is strain, \(\sigma\) is stress, \(E\) is the Young's modulus, and \(\theta\) is [PERSON]'s ratio.  
Although pressure (\(p\)), stress and Young's modulus are different physical quantities, they have the same dimensions \(dim(p)=dim(\sigma)=dim(E)-L^{-1}MT^{-2}\), where \(L\) is length, \(M\) is mass, and \(T\) is time; hence, an equals sign can be written between them: \(p\equiv E\equiv\sigma\). Hence, [PERSON]'s modulus in Equation (1) can be changed with pressure without losing physical meaning. Changing one physical quantity to another when their dimensions are equal is quite common practice, which can be seen by comparing the Bramwell-Hill and Moens-Korteweg equations describing pulse wave velocity. The Moens-Korteweg equation uses [PERSON]'s modulus, while Bramwell-Hill uses pressure.  
Let us change stress in Equation (1) to pressure as defined in Equation (2):  
\[p=E\cdot e\cdot h/\left(1-\theta^{2}\right). \tag{2}\]  
Figure 2: The block diagram of the proposed methodology. PPG: Photoplethysmogram.  
When blood pressure \(p(t)\) changes during the cardiac cycle, the diameter of artery \(d(t)\) changes as well; therefore, Equation (2) can be re-written as a time function as given by Equation (3):  
\[p(t)=E\cdot\frac{d(t)}{d_{0}}.\frac{h}{(1-\theta^{2})}, \tag{3}\]  
where \(p(t)\) is the blood pressure change function during the cardiac cycle (blood pressure pulse wave). Function \(p(t)\) is called the pressure pulse wave (PPW) in the remainder of this paper, while relative deformation variation \(d(t)/d_{0}\) is the deformation pulse wave (DPW), where \(d_{0}\) is the artery diameter at the beginning of the cardiac cycle. Let us denote DPW as \(D(t)=d(t)/d_{0}\), and the remainder of Equation (3) as a constant \(K=E\left(h/\left(1-\theta^{2}\right)\right)\), leading to the following Equation (4):  
\[p(t)=K\cdot D(t). \tag{4}\]  
If the stress-strain characteristic is linear, i.e., \(E=const.\), then, if \(K\) is known, \(p(t)\) values can be calculated for the whole cardiac cycle interval. Usually, we are interested in finding the maximum PPW value, systolic blood pressure value \(p_{i}=max(p(t))\), which is achieved during time period \(t_{s}\) at the \(i\)-th cardiac cycle.  
If \(K=const.\) in Equation (4), then the DPW steepness \(tan(\gamma)_{i}=DPW(t)/t\) during \(i\)-th cardiac cycle is \(tan(\gamma)_{i}=const.\), while the systolic blood pressure value \(p_{i}=max(p(t))\), when \(0\leq t\leq t_{s}\), can be obtained as following Equation (5):  
\[p_{i}=K\cdot\tan(\gamma)\cdot t_{s}, \tag{5}\]  
where \(p_{i}\) and \(tan(\gamma)_{i}\) change equally during each cardiac cycle.  
The DPW form depends on the stress-strain characteristic, which is not linear in the case of blood vessels. Because of this, pressure and deformation pulse waveforms are different, while \(K\
eq const.\) The authors of [30; 31; 32] show that in the part where PPW and DPW are changing most rapidly, their trajectories concur (see Figure 3).  
Hence, \(tan(\gamma)_{max\_i}\) correlates with the systolic blood pressure value of the \(i\)-th cardiac cycle, and this SBP value can be calculated using Equation (5) and taking the steepest part of the DPW rising edge: \(tan(\gamma)_{max\_i}=max(tan(\gamma_{j}))\), \(1\leq j\leq M-1\), where M is the number of sampled points of DPW rising edge, \(\gamma_{j}\) is the angle between the base line and the line drawn through the \(j\)-th and \((j+1)\)-th points of rising edge, and \(i\) is the pulse wave number.