# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 3 Results and Discussion
### Influence of Cardiac Cycle  
In order to verify the reliability of the model in terms of physiological parameter change, this paper used the cardiac cycle as the study subject. In human physiological phenomena, a change in the cardiac cycle has a great influence on the pressure in a blood vessel. The blood flux output after every cardiac pulse is fixed. However, with a change in the cardiac cycle, the time of fluid flowing out of the flow field will change, and the pressure required by a fluid to pass through the load will increase, finally influencing the pressure in the tube. Therefore, the pressure change caused by heart rate is not only related to flux but also has a close connection with vascular wall deformation and load. It can be seen that the influence of the cardiac cycle on vascular pressure is produced by a coupling of multiple factors, and all factors in the system are required to accord with the physiological reality. In a numerical simulation, a short straight tube could not meet the needs of storing fluid, and normal pressure outlet conditions could not change with the tube's flow field. Hence, both could not simulate the pressure change caused by cardiac cycle change. Comparatively, the model in this paper provides fluid with enough developing space and storing ability, as well as the load condition changing with the flow field. Therefore it can complete the task the numerical simulation cannot. This paper selected two cardiac cycles (0.6 s and 1 s), and compared them with the normal physiology example. First, this paper analyzed the systolic pressure and diastolic pressure of various positions under the circumstances of different cardiac cycles. As shown in Figure 11, three lines represent the results of the three calculation examples with cardiac cycles of 0.6 s, 0.8 s, and 1 s, respectively. It can be seen that the shortening of the cardiac cycle brought simultaneous increases in diastolic pressure and systolic pressure. When the cardiac cycle was 0.6 s, the systolic pressure was 140-150 mmHg and diastolic pressure was 110-115 mmHg. When the cardiac cycle was 1 s, systolic pressure was 90-100 mmHg and diastolic pressure was about 60 mmHg. The above described pressure change was the same as the actual changing principle of human blood pressure under rest and motion states. Thus the change of vascular pressure in our model accords with the physiological reality. Secondly, this paper analyzed the changes of tube displacement under different cardiac cycles. In Figure 12, three lines represent the tube displacement circumstances in the three examples, with cardiac cycles of 0.6 s, 0.8 s, and 1 s. Figure 12a shows the initial displacement circumstance of tube at 0 s. Figure 12b shows the circumstance of tube displacement at 0.1 s, when the peak occurred at the inlet. Figure 12c shows the circumstance of tube displacement at 0.16 s, when the peak had not reached the outlet. Figure 12d shows the displacement circumstance at 0.2 s, when the peak reached the outlet. It can be seen that when the cardiac cycle decreased, tube wall deformation increased markedly, and _vice versa_. The inlet pressure reached its peak value at 0.1 s. The pressure peak moved forward at 0.16 s  
Figure 11: Comparison of pressure in tube under different cardiac cycle (**a**) systolic pressure; (**b**) diastolic pressure. and arrived at the outlet at 0.2 s. However, like the pressure distribution, the curve shape changed little under different frequencies. This illustrates that the cardiac cycle has limited influence on the change of flow in the tube, and the pressure change is mainly caused by a change in the fluid amount stored through tube wall deformation. With the coupling effect of three major systems, the proposed model successfully simulated the pressure changes in the tube only by adjusting cardiac cycle length. The simulated pressure changes have been proved to accord with the actual physiological features.