## 2 Materials and Methods
### Geometrical Properties of the Artery  
Generally speaking, it is reported that a mouse carotid artery is a vessel of almost cylindrical shape with no branches [23], despite the fact that geometrical properties of the artery are a little more complicated, as documented, for example, in [24; 36]. So, the aforementioned complexity is omitted in most of the papers that deal with the mechanical response of carotid arteries. In effect, specific and simplified models that treat the artery as a 2D thick-walled cylinder are used in many papers, to establish constants of some hyperelastic stress-strain constitutive relations (see, for example, [17; 19; 21; 22; 23]). The results presented in the previously mentioned articles do not indicate that the accuracy of the analysis is significantly affected, in the case when the artery is treated as a perfect cylindrical vessel. In this paper, we validate the constants of hyperelastic material laws, that have been determined under this assumption. Therefore, in view of the above, we also treat the carotid artery as a perfect cylindrical vessel. Geometrical dimensions of the arteries in an unloaded state without applied axial stretch are well described in the analyzed papers and are taken from there. Typically, the external diameter of the carotid artery ranges from \(340\)\(\upmu\)m to \(450\)\(\upmu\)m, while the ratio between the inner and outer diameter of the artery is close to \(0.7\). Averaged values of the artery diameter and wall thickness are given for each mouse model under consideration [14; 22; 23] or individual values are presented for all arteries analyzed, as in [19]. The mean values of the geometrical parameters of the arteries reported in the aforementioned articles are shown in Table 1.  
The length of the carotid artery also needs to be specified when creating a 3D numerical model. The inflation of carotid arteries is the most common way to establish their mechanical properties. Therefore, the length of the artery in such a test is used in the analysis here. Some interesting recommendations on the lengths of the carotid arteries, with regard to inflation tests, can be found, for example, in [19; 20]. As mentioned in [20], the lengths of extracted carotid arteries specimens vary from 3 mm for a 3-day-old mouse newborn to 6 mm for a mouse whose age is more than 30 days. However, when an artery is mounted on the cannulas in the myograph, the testing length (see Figure 1), namely, the distance between the knots, is smaller, for example, 1.65 mm for a 3-day-old mouse (see [20]), which is 55% of the total length of the extracted specimen. It is reported in [19] that testing lengths of carotid arteries in the buckling analyses were typically equal to 3.05 mm for 2-to-3-month-old mice. The total length of the extracted artery has not been specified in [19]. Nevertheless, if it is assumed to be 6 mm (as described in [20] for mice which are more than 30 days old), then the ratio between the testing length and total artery length is 51%, so almost the same as in [20]. It is worth mentioning that in most of the published works that aim to identify the constants of some hyperelastic material laws, the length of the carotid artery is not given. That is because the response of an inflated mouse carotid artery can be described using the model of an axisymmetric cylinder subjected to internal pressure, which is quite often chosen. This analytical model does not require definition of the exact length of the artery, but it rather needs information on the amount of the applied longitudinal stretch (see, for example, [14; 21; 23]). However, the length parameter cannot be omitted in the analyses conducted here, because a more detailed 3D FEM model is employed that also accounts for buckling. Some preliminary tests were ordered and performed by the Medical University of Gdarsk to take a look at the arteries' response during inflation and buckling problems.