# A Novel Radial Artery P-S Curve Model Based on Radial Vibration of Vascular Wall
## 3 Model Validation Experiments and Results
### Human Validation Experiments
#### 3.2.3 P-S Curve Analysis  
By using the method mentioned above, the P-S curve of the radial artery was extracted from 69 healthy samples, and the mean and standard deviation of pulse strength of the sample population were calculated under the same number of pressurizations. The P-S curve trend chart of 69 healthy samples was drawn with the number of times of pressurization as the abscissa and the normalized pulse strength as the ordinate. The results are shown in Figure 7.  
Figure 6: Pulse P-S curve acquisition process: (**a**) raw pulse signal; (**b**) the original signal period division, the red dotted line is the initial boundary of the pulse cycle, and the blue solid line is the actual single cycle pulse waveform; (**c**) time domain averaging of single-period signals, the dotted lines with different colors are the single cycle pulse wave after dividing the cycle, and the solid red lines are the pulse wave after time domain average; (**d**) full pressure segment pulse strength envelope. Figure 7: Number of pressurizations–normalized strength curve. The experimental results in Figure 7 demonstrated that when the number of pressurizations increases from 1 to 9, the average pulse strength gradually increases, with an increment \(\Delta S=0.59\). When the number of pressurizations reaches 9, the average pulse strength reaches the maximum. When the number of pressurizations increases from 9 to 14, the pulse strength gradually decreases, with an increment \(\Delta S=-0.32\). Therefore, the pulse P-S curve of the healthy sample population generally shows a trend of increasing first and then decreasing. However, due to the small number of samples, and the fact that the maximum strength and position of the P-S curve vary from person to person, the standard deviation of the pulse strength of the group pulse P-S curve at the same number of pressurizations is large. According to the simulation results in Table 2, as \(P_{e}\) gradually increases to equal to \(P\), the stress increment of blood vessel wall is \(\Delta\tau=-32.10\) kPa, but the increment of intravascular pressure is small, so the pulse strength gradually increases. When the vessel wall stress is close to zero, the pulse strength reaches the maximum, and as \(P_{e}\) continues to increase, the flow rate also increases, which leads to the increment in intravascular pressure drop and \(\Delta P=-14\) Pa, so the pulse strength gradually decreases. According to Formulas (21)-(24), when \(P_{e}<P\), the pulse strength gradually increased with the increase in \(P_{e}\). When \(P_{e}=P\), the pulse strength reaches the maximum, and the maximum pulse strength is mainly affected by blood flow, vessel radius and the blood viscosity coefficient. When \(P_{e}\) continues to increase to \(P_{e}>P\), the internal pressure of blood vessel decreases, leading to the decrease in pulse strength. In conclusion, the experimental and simulation results are consistent with the theoretical model proposed in this paper. To verify the relationship between blood viscosity and pulse strength, this study divided 69 samples into 3 categories according to the BMI (body mass index) and explored the influence of the BMI on the pulse strength. Then, the theoretical model verified that the pulse strength is positively correlated with the blood viscosity coefficient. Specifically, according to the Chinese BMI classification standard, the 69 samples are divided into the following 3 categories:  
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2. 1. It can be observed from Figure 8 that by drawing the statistical box graph of the pulse strength of the three groups of people, the change trend of the pulse strength of the three groups of people with BMI is fitted. And, the mean value and variance in the pulse strength of the three groups of people are calculated, as shown in Table 5. The above data statistics results all demonstrate that the pulse strength is positively correlated with BMI.