# A Novel Radial Artery P-S Curve Model Based on Radial Vibration of Vascular Wall
## 3 Model Validation Experiments and Results  
### Simulation Experiment  
To verify the accuracy of the above model, we first apply the model to simulate the changes in stress, blood flow velocity and intravascular pressure during the compression  
Figure 3: Vascular collapse model.  
deformation of the vascular wall. The software environment is COMSOL (COMSOL Multiphysics(r) 6.0). The initial parameter settings for the model are shown in Table 1, where \(R\) represents the radius of the blood vessel, \(h\) represents the thickness of the vascular wall, \(\sigma\) represents [PERSON]'s coefficient, \(E\) represents [PERSON]'s modulus, \(\eta\) represents the viscosity coefficient, _rho_ represents the fluid density, \(P_{out}\) represents the outlet pressure, and \(v_{in}\) represents the inlet velocity, \(L_{1}\) and \(L_{3}\) are fixed boundaries and \(L_{2}\) is the force boundary.  
Assuming that the blood vessels are isotropic, uniform, long straight tubes, we substituted the simulation parameters of the hemodynamic model shown in Table 1, and obtained the simulation results of Figure 4.  
As shown in Figure 4, it can be observed through the color scale chart that when the extravascular pressure \(P_{e}\) gradually increases, the vascular wall stress decreases first and then increases, but the vascular wall stress is opposite along the direction of the radial component. While the blood flow velocity gradually increases, the intravascular pressure  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter (Unit)** & **Value** \\ \hline \(R\) (m) & \(2\times 10^{3}\) \\ \(h\) (m) & \(1.5\times 10^{-4}\) \\ \(\sigma\) & \(4.95\times 10^{-1}\) \\ \(E\) (Pa) & \(9.65\times 10^{5}\) \\ \(\eta\) (Pa-s) & \(5\times 10^{-3}\) \\ _rho_ (kg/m\({}^{3}\)) & \(1.06\times 10^{3}\) \\ \(P_{out}\) (Pa) & 0 \\ \(v_{in}\) (m/s) & \(2\times 10^{-1}\) \\ \(L_{1}\) (m) & \(1\times 10^{-2}\) \\ \(L_{2}\) (m) & \(1\times 10^{-2}\) \\ \(L_{3}\) (m) & \(1\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hemodynamic model simulation parameters [26; 27].  
Figure 4: Simulation results of vascular wall stress, blood flow rate, and intravascular pressure under different pressure conditions of blood vessel. (**a–c**) Simulation results of vascular wall stress changes in \(P>P_{e}\), \(P=P_{e}\), \(P<P_{e}\). (**d–f**) Simulation results of blood flow velocity changes in \(P>P_{e}\), \(P=P_{e}\), \(P<P_{e}\). (**g–i**) Simulation results of intravascular pressure changes in \(P>P_{e}\), \(P=P_{e}\), \(P<P_{e}\).  
gradually decreases, which indicates that the change law of pulse strength \(F\) first increases and then decreases, and \(F\) reaches the maximum when \(P=P_{e}\). Taking the vascular wall collapse center as the reference point, the wall stress, blood flow velocity and intravascular pressure parameters of each reference point in \(P>P_{e}\), \(P=P_{e}\), \(P<P_{e}\) were extracted, as shown in Table 2. Through the simulation model of stress and intravascular pressure, it is found that the variation law of each parameter is in line with the theoretical calculation model proposed by this paper.  
According to the above analysis, when \(P=P_{e}\), the stress of the vessel wall almost disappears, and the pulse strength is mainly determined by the intravascular pressure. According to Formula (21), the intravascular pressure at this time is mainly affected by the blood flow, vessel radius and blood viscosity coefficient. To verify the positive correlation between blood viscosity and pulse strength, this paper simulates the changes in intravascular pressure under different blood viscosity coefficients, and the results are shown in Figure 5.  
As shown in Figure 5 and Table 3, the simulation results showed that the intravascular pressure increases with the increase in the blood viscosity coefficient. The theory that the pulse strength increases with the increase in the blood viscosity coefficient is verified.