# Numerical Simulation and Analysis of Heart-Aorta Fluid-Structure Interaction Based on S-ALE Method
## 3 Results and Discussion
### Effect of Changes in LV Systole on Aortic Hemodynamic Response  
The ejection function of the heart changes in different physiological states, and the fundamental reason for this phenomenon is the change in the systole displacement of the LV. The effect of changes in LV systole on the aortic hemodynamic response at a blood viscosity of 0.0035 Pa\(\cdot\)s is shown in Figure 11. From the figure, it can be observed that with the increase in LV systole displacement, the peak blood velocity, flow rate, and WSS of sections 1-4 showed an increasing trend. The quantitative analysis of the effect of systole displacement on aortic hemodynamic parameters is shown in Table 4. The analysis reveals that the correlation coefficients between systole displacement and hemodynamic parameters are close to 1, demonstrating significant linear correlations. The sensitivity analysis indicates that systole displacement exerts a substantial influence on hemodynamic parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Section**} & \multicolumn{2}{c}{**Peak Velocity**} & \multicolumn{2}{c}{**Peak Flow Rate**} & \multicolumn{2}{c}{**Peak WSS**} \\ \cline{2-7}  & **r** & \(\varepsilon\) & **r** & \(\varepsilon\) & **r** & \(\varepsilon\) \\ \hline
1 & 0.9996 & 0.1620 & 0.9996 & 0.1622 & 0.9998 & 0.2028 \\
2 & 0.9998 & 0.1786 & 0.9996 & 0.1869 & 0.9935 & 0.1090 \\
3 & 0.9968 & 0.1869 & 0.9971 & 0.1891 & 0.9957 & 0.1701 \\
4 & 0.9978 & 0.1767 & 0.9978 & 0.1770 & 0.9932 & 0.1695 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quantitative analysis of the effects of systole displacement on aortic hemodynamic parameters.  
Figure 11: Effect of changes in LV systole on aortic hemodynamic response. (**a**) Section-averaged peak velocity; (**b**) section-averaged peak flow rate; (**c**) section-averaged peak WSS.  
In our study, the resistance to blood flow at the aortic outlet did not change. The increased systole displacement of the LV resulted in an increase in the volume of blood ejected (Table 2), which was the reason for the increase in blood velocity. Aortic deformation tended to increase significantly with increasing LV systole displacement, as shown in Figure 12. The maximum deformation of the aorta was located in the region of the ascending aorta. The increase in aortic deformation indicated that the sectional area would also change. The maximum strain of the aorta occurred at the inner side of the root. The area of strain gradually expanded with the increasing systole displacement of the LV.  
For the analysis of heart-aorta FSI, the LS-DYNA v971 R12.0 software is able to realize large deformation motions in the structural domains. This is a key factor in reproducing the hemodynamics of the systole and diastole processes in the LV. Most of the existing studies on aortic FSI have imposed time-dependent blood velocities at the root inlet location. Although it is possible to quantitatively study hemodynamic parameters, there is still a big gap with real human blood flow. There are also some limitations in our study. In the analysis of changes in different physiological states, variations in blood viscosity and LV ejection volume were assumed to occur without changes in rheological behavior, where blood was still treated as a Newtonian fluid. During the diastole phase, the absence of blood replenishment in the LV limited the heart-aortic FSI simulation to a single cardiac cycle under physiological states.