## 4 Discussion
### Validation of Selected Material Laws
#### 4.1.1 Fung Law for Wild-Type, Sgcd\(-/-\), and Mdx Mice
The accuracy is close to the defined earlier threshold value of 20 \(\upmu\)m and thus is considered acceptable for Eln+/\(-\) 2 (RMSE = 24.4 \(\upmu\)m/nRMSE = 5%), Eln+/\(-\) 5 (RMSE = 29.3 \(\upmu\)m/nRMSE = 6%), Eln+/\(-\) 6 (RMSE = 23.4 \(\upmu\)m/nRMSE = 5%), Fbln5\(-\)/\(-\) 2 (RMSE = 24.4 \(\upmu\)m/nRMSE = 5%), Fbln5\(-\)/\(-\) 5 (RMSE = 22.3 \(\upmu\)m/nRMSE = 5%), and Fbln5\(-\)/\(-\) 7 (RMSE = 22.2 \(\upmu\)m/nRMSE = 5%). The FEM estimations are not precise for the Fbln5\(-\)/\(-\) mean set, Eln+/\(-\) mean set, and Eln+/\(-\) 3, because in these cases, the RMSE/nRMSE values are higher and range from 41.5 \(\upmu\)m/7% to 71.0 \(\upmu\)m/14%. On the other hand, the Eln+/+ and Fbln5+/+ Fung law parameters are not as good as the previous ones. The Eln+/+ constitutive relation constants are the least accurate. The shapes of FEM estimations for Eln+/+ mice do not resemble the experiment well. Especially the carotid artery diameter after stretching and the slopes in the low-pressure zone are poorly predicted. The lowest RMSE/nRMSE is calculated for the Eln+/\(+\) 5 case and equals 27.1 \(\upmu\)m/5%. The other ones are much higher. For example, the RMSE/nRMSE for Eln+/+ is 71.8 \(\upmu\)m/13%, whereas it equals 89.8 \(\upmu\)m/16% for the Eln+/+ mean set. Both the third and seventh constitutive relations parameters, in the case of Fbln5+/+, have similar, reasonable accuracy (RMSE/nRMSE being \(\sim\)19 \(\upmu\)m/4%) and a quite satisfying shape of the \(p_{int}\)-\(D_{out}\) function, although the slope in the high-pressure zone (from 140 mmHg) should be steeper. However, the remaining ones are less accurate, as the RMSE/nRMSE values are 32.7 \(\upmu\)m/6% for the Fbln5+/\(+\) 2, 35.5 \(\upmu\)m/7% for the Fbln5+/\(+\) 4, 60.2 \(\upmu\)m/1% for the Fbln5+/\(+\) 1, 67.7 \(\upmu\)m/13% for the Fbln5+/\(+\) 5 and 140.5 \(\upmu\)m/26% for the Fbln5+/\(+\) mean set of constants. The incorrect prediction of the external diameter of the artery during stretching was the main problem regarding the accuracy of FEM results obtained with the aid of the Fbln5+/+ Fung law constants sets. Another conclusion can also be formulated here. It is noticeable that all of the \(p_{int}\)-\(D_{out}\) curves, calculated with the aid of the mean sets of constitutive relations parameters and mean initial stretch values, have good shapes but are shifted too much from the reference result. This is mainly due to an inaccurate carotid artery response description during initial loading in the axial direction. Therefore, averaging of material constants for specimens with quite scattered initial stretch values, as conducted in [19], seems to be ineffective. The attempt to use the Holzapfel law from [14], which has been determined for the Eln+/+ mouse aorta to model the response of the carotid artery, is also not fully successful. The inflection of this pressure-diameter relation occurs at very low pressure, and the response in the high-pressure zone is too stiff. The RMSE for this case is quite high and equals 49.2 \(\upmu\)m.  
A set of constants of the Holzapfel constitutive relation is also presented in [22]. Unfortunately, the authors of this paper did not say which type of mouse was tested. For this reason, it is rather difficult to use them in other analyses. However, the concept of defining the carotid artery properties by creating two layers of the hyperelastic anisotropic Holzapfel material with different fiber family angles (representing media and adventitia) is interesting. It is an improvement of the standard approach [34] and describes the mechanics of the artery in more detail. No modifications in the Abaqus code need to be introduced in order to define properties of such an artery.