# A Novel Radial Artery P-S Curve Model Based on Radial Vibration of Vascular Wall
## 1 Introduction  
The arterial pulse is a phenomenon of periodic oscillation of flow, blood pressure and blood vessel wall caused by the periodic ejection activity of the heart [1; 2; 3]. The arterial pulse can be noninvasively detected at the body's surface with the radial artery, which contains abundant physiological and pathological information [4; 5; 6; 7]. In clinical practice, the pulse information that corresponds to the strongest point of radial artery vibration is often obtained through finger pressure and finger feeling. The finger pressure that corresponds to the strongest point represents the static pressure applied to the pulse, and the finger feeling represents the strength of the pulse [8; 9]. The P-S curve of pulse wave can be used to quantify the change trend of finger pressure and finger feeling. However, the traditional human perception has subjective factors and it is difficult to continuously record the two-dimensional information of pulse pressure and strength, so machine perception came into being. At present, the analysis and modeling of pulse waves mainly focuses on the single-cycle waveform of the maximum strength pulse wave. [PERSON] [10] systematically explained the waveform characteristics of pulse waves from the perspective of time domains. [PERSON] [11] used the linearization method of characteristic analysis to establishthe pulse wave propagation model in the aorta of the whole body. [PERSON] [12] established a lumped hemodynamic model of the arterial system based on resistance and compliance. [PERSON] [13] used the pulse wave peak average value and applied pressure as parameters to describe the pulse change trend and analyze the pulse static pressure. [PERSON] [14] established a single-cycle pulse wave spring model and carried out data verification. [PERSON] et al. [15] established a fluid model of elastic tubes and proved the importance of transverse vibration of the arterial tube. [PERSON] [16] proposed the R-C circuit model of pulse waves and analyzed the relationship between pressure and flow in the process of pulse wave propagation. [PERSON] et al. [17] proposed a gradient pressure measurement method for the differences in biological individuals, obtained the pulse wave under the optimal pulse pressure, and improved the automation and accuracy of pulse wave acquisition. These researchers above focused on the modeling of the time-domain single cycle pulse wave and the analysis of the optimal pulse pressure through the pulse P-S curve, but there is no accurate research model for the formation mechanism of the P-S curve. To solve this problem, based on the theory of radial vibration of vascular walls, this paper systematically analyzes the change in pulse strength with extravascular pressure from the perspectives of hemodynamics, fluid-structure interaction and elastic mechanics of the vascular wall, and establishes a theoretical model of the relationship between pulse strength and pressure. To verify the accuracy and applicability of this model, this paper simulates the changes in blood flow velocity, intravascular pressure and vascular wall stress when the vascular wall is deformed by extravascular pressure. Through the pulse diagnostic apparatus [18; 19; 20] independently by our laboratory, the radial pulse signals of 69 healthy human volunteers were collected. Based on the gradient compression method, the pulse strength envelope under the continuous pressure sequence of the radial artery was extracted, and the radial artery P-S curve of the sample was obtained. Furthermore, the relationship between sample P-S curve variability and BMI was analyzed. The results show that the actual human body data acquisition and analysis results are in line with the radial artery P-S curve theory based on the radial vibration of the vascular wall proposed in this paper. At the same time, the reason for the difference in the P-S curve of the pulse of a healthy human body can be explained by the model. The model can explain the formation mechanism of pulse P-S curves in healthy human bodies.