# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 3 Results and Discussion
### Physiological Pressure Level  
Calculation results showed that the influence of load on the flow field was tremendous. Thus, between calculation examples with load and without load, the properties of flow field exhibited major differences. In Figure 5, there is a comparison between the pressure results of calculation examples with normal physiology and no seepage load. Therein, A is the systolic pressure of various positions in the tube, B is the diastolic pressure, and C is the amplitude of the pressure in the tube. In the example of normal physiology, the systolic pressure of all positions in the tube was maintained at around 120 mmHg; the diastolic pressure was kept at 80 mmHg, and the amplitude of pressure at 30-40 mmHg. These observations accord with the physiological reality. In the example without seepage load, the systolic pressure near the inlet was 29 mmHg, while that near the outlet was 6 mmHg. The diastolic pressure near the inlet was \(-\)32 mmHg, while that near the outlet was \(-\)6 mmHg. With the approach to the outlet, the amplitude decreased continuously. It can be seen that the use of pressure alone as the outlet condition led to a larger negative pressure, and the pressure amplitude in the tube was changing. These results do not accord with the physiological conditions. The seepage load played a role in impeding flow in the model, which had a great effect on whether the fluid would be stored  
Figure 4: Boundary condition of the flow field.  
in the deformation of the tube wall. Thus the pressure in the tube was redistributed and reached the physiological pressure level.  
Through studying the process of the flow field developing in the tube, the internal mechanism of how the normal physiology example maintained the physiological pressure level can be revealed. When the load had a very strong hindering effect, the fluid entering the flow field was not able to flow out completely. Part of the fluid was stored in the deformation of tube wall and participated in the next cardiac cycle. Thus, the initial pressure of the second cycle would be increased. After several cardiac cycles, when the initial pressure of the flow field increased to a certain level, the newly input fluid was able to pass through the load and flow out of the flow field in one cycle. Accordingly, the fluid in the tube resumed a stable state, and the initial pressure of flow field also reached a dynamic balance.  
Figure 6 is the curve of pressure change with time in the flow field of the normal physiology example, which shows the whole process of flow field developing from completely static to stable. The five lines in the figure represent the five positions from inlet to outlet in the tube. The time ranged from 0 s to 16 s, with 20 cycles in total. It can be seen from the figure that the pressure in flow field increased rapidly from 0 s to 7 s, and gradually became stable after 7 s. The final pressure at all measuring points in the tube was kept in the range of physiological pressure of 80-120 mmHg. This indicates that the load influenced the total fluid quantity stored through the elastic deformation of tube wall, which further influenced the systolic pressure, diastolic pressure, and pressure amplitude in the tube.  
Figure 5: Comparisons of pressure in the examples with seepage load and pressure-free outlet: (**a**) maximum vascular pressure; (**b**) minimum vascular pressure; (**c**) pressure amplitude.