# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 3 Results and Discussion
### Pulse Wave Propagation  
This model showed very complex phenomena in time and in space, which included the propagation of pulse wave. When fluid entered the tube, fluid would be stored in the increased flow field from tube wall deformation, which would not cause influence for downstream flow field temporarily. Due to such property, the moments when the pressure wave peak occurred at various positions of the tube were different. Figure 7 is the pressure nephogram of the tube cross-section, wherein A, B, C, and D represent four moments (0 s, 0.1 s, 0.16 s, and 0.2 s, respectively). From the nephogram, we can clearly observe the propagation of the pressure wave peak, that is, the propagation of the pulse wave. At the initial moment, the pressure in the tube was maintained at a stable value. At 0.1 s, inlet velocity just reached the wave peak, and the inlet pressure reached the maximum. At 0.16 s, the pressure wave peak started to move forward, and the pressure decreased on both sides of the wave peak. Until0.2 s, the pressure wave peak was near the outlet. Comparing the flow field of these moments, the whole process of the pressure wave peak moving from inlet to outlet can be seen distinctly. This is the same as the result of [PERSON]'s research [18]. According to the academic monograph of [PERSON] [13], propagation of the pulse wave exists widely. Therefore, it is necessary to take the effect of the pulse wave into account in hemodynamic simulations.  
Results of the short tube example show that the difference in peak occurring moment was small. As shown in Figure 8a, the pressure peak values in tube all occurred at 0.18 s. The tube with a length of only 200 mm failed to show the phenomenon of pressure wave propagation. Comparatively, in the model of this paper, the tube length was the same as the actual aorta length. This provided the flow field with enough developing space. It follows that tube length is one of the essential conditions for simulation results to accord with the physiological reality.  
Through data treatment, the moments when pressure peaks occurred at five measuring points were obtained and subjected to linear fitting, as seen in Figure 8b. It can be seen that the measuring point P1 at 0.1 m away from the inlet reached the pressure maximum first. Other measuring points showed the pressure peak value successively; the closer to the inlet, the earlier the peak occurred. The two measuring points at 0.1 m and 0.9 m away from the inlet had a time difference of 0.12 s in the occurrence of pressure peak. Through the linear fitting for peak-occurring moments, we can obtain the relationship between peak-occurring moment and the distance from inlet. According to the fitting result, the velocity of the pulse wave in the tube was 6.25 m/s, which is close to the actual pulse wave velocity [19]. Also, it is the same as the one-dimensional pressure wave velocity [20]. This confirms that this model was able to correctly simulate the pulse wave propagation in human aortas.  
Figure 6: Changing process of pressure in the tube from static flow field (P1–P5 are five measuring points distributing axially along the tube).