## 4 Discussion
### Validation of Selected Material Laws
#### 4.1.1 Fung Law for Wild-Type, Sgcd\(-/-\), and Mdx Mice
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Stretch**} & \multirow{3}{*}{
\begin{tabular}{c} **Experiment** \\ **from**[19] \\ \end{tabular} } & \multicolumn{6}{c}{**FEM Predictions**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Analysis of the**} & \multicolumn{2}{c}{**The Pressure at \(u_{A}\) = \(D_{out}\)/2**} \\ \cline{3-8}  & & **Post-Buckling Response** & & & & & \\ \cline{3-8}  & & **Fung Constants from [19]** & **Holzapfel, Set “B”** & **Fung Constants from [19]** & **Holzapfel, Set “B”** \\ \hline \multirow{2}{*}{\(\lambda_{z}\)} & \(p_{exp}\) & \(p_{break,FEM}\) & \(p_{break,FEM}\) & \(p_{break,FEM}\) & \(p_{uA,FEM}\) & **Relative** & \(p_{uA,FEM}\) & **Relative** \\  & [mmHg] & **[mmHg]** & **[mmHg]** & **[mmHg]** & **Error [\%]** & **[mmHg]** & **Error [\%]** \\ \hline
1.0 & 58 & 52 & 81 & 83 & 43.1 & 82 & 41.4 \\
1.2 & 115 & 135 & 135 & 105 & 8.7 & 136 & 18.3 \\
1.4 & 227 * & \textgreater{}400 & 205 & \textgreater{}400 & \textgreater{}100 & 330 & 45.4 \\ \hline \hline \end{tabular}  
* \({}^{*}p_{exp}\) was determined in [19] by linear extrapolation of results for lower stretch ratios.  
\end{table} 
Table 3: Comparison of the buckling pressures for the Fbln5\(-/-\) mice determined experimentally by [19] and in FEM calculations. accuracy of the Fung laws denoted as 112204 and 012205 in [23] is very good, with the RMSE/nRMSE values being 11.9 \(\upmu\)m/3% and 12 \(\upmu\)m/3%, respectively. It is still accurate for the averaged mdx Fung constants (RMSE = 18.9 \(\upmu\)m/nRMSE = 4%) and the 121504 mice (RMSE = 20.1 \(\upmu\)m/nRMSE = 4%), whereas the prediction becomes slightly less precise for the specimen 020105 (RMSE = 30.6 \(\upmu\)m/nRMSE = 7%). The Fung law denoted with the number 121404 is rather inaccurate, because of the quite low RMSE/nRMSE value, which is almost 58 \(\upmu\)m/12%. It is also worth mentioning that not only the response during carotid artery pressurization is correctly recreated for the successfully validated laws from [23]. The effect of the diameter change during the initial stretching is also accurately captured in FEM computations, which means that the law provides a good correlation with the experimental data for different loading conditions. However, one must keep in mind that the experiments from [24] have been carried out to the pressure level of 140 mmHg and this is the validity range of the laws. It is noticeable in Figure 3 that in most cases, the slope of the \(p_{int}\)-\(D_{out}\) relation near the 140 mmHg pressure level should be steeper, and thus the computational prediction for higher values of \(p_{int}\) would be inaccurate. 1.2 Fung Law for Eln+/\(-\), Eln+/+, Fbln5\(-\)/\(-\), and Fbln5+/\(+\) Mice and Holzapfel Law for Eln+/+ Mice  
At first, it has to be emphasized that some of the Fung constants sets from [19] did not allow for a solution to be obtained. The calculations were terminated for Eln+/\(-\) 4 and Fbln5\(-\)/\(-\) 3 at an internal pressure close to 65 mmHg, due to convergence errors and some unphysical behavior. It was not possible to launch calculations for the laws Fbln5+/\(+\) 6 and Fbln5+/\(+\) 8. That is because the stiffness matrices defined for the Fung orthotropic hyperelastic model, based exactly on the data from [19], are not positive definite and, therefore, are numerically instable [39; 40]. Nevertheless, the remaining calculations were successful. These can be divided into two groups to some extent. It is observed for the Eln+/\(-\) and Fbln5\(-\)/\(-\) FEM results that almost all of the \(p_{int}\)-\(D_{out}\) curves have reasonable shapes, close to the experimental one. The predicted pressure-diameter relations from the quantitative point of view are also quite precise. Very low RMSE/nRMSE values are achieved for the following: Eln+/\(-\) 1 (14.8 \(\upmu\)m/3%), Fbln5\(-\)/\(-\) 1 (3.1 \(\upmu\)m/1%), Fbln5\(-\)/\(-\) 4 (11.1 \(\upmu\)m/2%), and Fbln5\(-\)/\(-\) 6 (14.1 \(\upmu\)m/3%).