# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 3 Results and Discussion
### Pulse Wave Reflection  
Another phenomenon shown in the model is the reflection of the pulse wave. When pressure propagated to the load interface, seepage load played a hindering effect. Accordingly, not all the fluid was able to flow out of the flow field smoothly; part of it would be held in the flow field. At this time the tube wall near the outlet would expand, and the pressure would increase accordingly. When the pressure downstream was larger than that upstream, it would also propagate back towards the inlet, producing a reflection wave. If the pulse wave is taken as a major pressure wave, this reflection wave is typically called a secondary pressure wave. By overlapping this reflection wave with the incoming major pressure wave, a pressure-time curve with double wave peaks can be produced. In previous studies, such a curve failed to be simulated. However, in the results of physiological measurement and of simulation by our model, such a curve shape with a double wave peak was visible. Figure 9 shows a pressure-time curve, plotted with the observations of two measuring points at 0.3 m and 0.7 m away from the inlet. We can clearly see the double peak structure from the figure. The pressure-time curve was formed through the overlapping of a major pressure wave and a reflection wave; the reflection wave was obviously smaller than the major pressure wave. Comparing the curves of the two measuring points, it can be seen that though the difference between major pressure waves was not large, there was a significant difference between reflection waves. Figure 8: Moments corresponding to the pressure peak and their fitting results: (**a**) peak-occurring moments in short tube example; (**b**) peak-occurring moments in a normal physiology example. Figure 7: Pressure nephograms (A. \(t=0\) s; B. \(t=0.1\) s; C. \(t=0.16\) s; D. \(t=0.2\) s). This paper studied the occurring moments of the major pressure wave peak and reflection wave peak, as shown in Figure 10. It can be seen that the occurring moments of major pressure peak were in linear relationship with distance. However, the reflection wave peak presented a non-linear feature, e.g., the peak-occurring time was earlier at the position of 0.3 m than at the position of 0.1 m, while it was earlier at the position of 0.7 m than at the position of 0.9 m. This exactly suggests that secondary pressure wave is also propagated in the form of a wave. As shown by marks of the figure, the major pressure wave was a non-reflected primary pressure wave, propagating towards the outlet. However, at the positions of 0.3 m and 0.1 m, the pressure waves were secondary pressure waves that have been reflected once by the load and hence propagated towards the inlet. Similarly, the pressure waves at 0.7 m and 0.9 m were the third pressure waves that experienced another reflection by the inlet, and propagated towards the outlet again. Conclusively, in Figure 9, the reflection wave at 0.3 m was the secondary pressure wave undergoing one reflection, and that at 0.7 m was the third pressure wave undergoing two reflections. That is why there was a large difference between the magnitudes of reflection waves at these two positions. Through comparing with physiological measurements [9], it can be seen that the secondary pressure wave simulated by the model of this paper accords with the physiological reality. Without the coupling of liquid-solid-porous media seepage, it is impossible to simulate this physiological blood pressure, which is produced by repeated reflections and overlapping of pressure waves. In addition, this complex wave shape produced a profound influence on the flow field by influencing the tube wall deformation. The wall shear stress and other flow field parameters would change accordingly. Therefore, the simulation of this paper accords with the physiological reality, and this complex wave structure is also an important guarantee for the correctness of the study later. Figure 10: Moments corresponding to major pressure peak and reflection wave peak.