## 5 Conclusions  
More than 70 nonlinear, static analyses have been conducted, on reliable FEM models, to verify whether the constants of the Fung or Holzapfel laws, available in the literature, are capable of describing the change in the carotid artery outer diameter, while it is subjected to increasing internal pressure during static inflation.  
It turned out in the course of the calculations that a set of constants enabling the reasonable description of the carotid artery response is available for almost every mouse model under consideration (wild-type, mdx, sgcd\(-\)/ \(-\), Eln+/+, Eln\(-\)/ \(-\), Fbln5+/+, and Fbln5\(-\)/ \(-\)). However, many of the constitutive relation parameter sets did not allow us to estimate the behavior of the artery with a good accuracy.  
A total number of 53 different material law constants sets were analyzed. The RMSE/nRMSE values between the FEM estimations and the experimental response were kept within reasonable limits for only 13 of them.  
In effect, some recommendations on the constants that seem to be accurate are provided. We suggest the use of the following sets of the Fung constants from [23]: 102704 for wild-type, mean for sgcd\(-\)/ \(-\), and 112204 for mdx. Similarly, the following Fung law constants sets from [19] are positively validated: Eln+/ \(-\) 1, Fbln5\(-\)/ \(-\) 1, and Fbln5+/ 3; while the Eln+/+ seems to be imprecise.  
It has been proven that valid Holzapfel law parameters can be efficiently determined with the aid of parametric FEM analysis. New constant sets for Eln+/+ and Fbln5\(-\)/ \(-\) mice have been proposed.  
The modeling of a mouse carotid artery, as a domain made of two layers of Holzapfel material, is efficient, has physical reasoning, and improves the accuracy of the artery response description.  
The buckling of carotid arteries still requires investigation. This phenomenon can be effectively recreated and studied with the aid of nonlinear static FEM analysis. The results presented here indicate that the Holzapfel law seems to be better suited for the description of loss of stability.  
The constant sets that have been successfully validated or proposed can be now used in further studies. It is possible to apply them not only in static analyses but also in others, like, for instance, in Fluid-Structure Interaction (FSI) calculations.  
The main advantage of the approach presented in this paper is its versatility. Computational 3D analysis is a modern way of diagnostics and health monitoring. It allows for a reduction in the number of experiments conducted in laboratories. The obtained FEM results enable detailed insight into the physics and essence of the studied problems.  
Conceptualization, B.S., J.C. and K.W.; methodology, B.S., J.C. and K.W.; validation, B.S. and J.C.; formal analysis, B.S. and J.C.; investigation, B.S.; resources, K.W.; data curation, B.S.; writing--original draft preparation, B.S.; writing--review and editing, B.S.; visualization, B.S.; supervision, J.C. and K.W.; project administration, B.S.; funding acquisition, B.S. All authors have read and agreed to the published version of the manuscript.  
These studies have received financial support from Gdansk University of Technology by the DEC-4/2020/IDUB/1.3.3 grant under the Argentum Triggering Research Grants--Excellence Initiative--Research University' program.  
Animal study protocols were ordered and conducted at the Medical University of Gdansk.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Computations were carried out using the computers of the Centre of Informatics Trinity Academic Supercomputer & Network.  
The authors declare no conflicts of interest.