## 1 Introduction  
The appropriate response analysis of biomedical materials, modeling of medical phenomena, description of flow in the arteries, or optimization of treatment techniques, together with imaging of biological tissues, internal organs, or blood vessels, are some examples of the current research topics under consideration [1; 2; 3; 4; 5; 6]. Problems of a similar kind are often identified or determined by medics and doctors and investigated with the aid of medical testing devices or laboratory apparatus. However, the processes ruling the medical phenomena may be described with equations of, e.g., mechanics, dynamics, fluid flow, etc. In the majority of cases, the numerical methods are the most efficient ways allowing one to obtain the solutions of the equations in the course of a computational analysis. Such an analysis enables a deep insight into the mechanics of the medical problem, which is driven by many parameters that often may not be straightforwardly identified in standard medical diagnostic tests. That is why the importance of numerical methods and computational analyses in the field of biomedical engineering has increased strongly in recent years. In effect, testing with the aid of numerical analyses seems to be the future of advanced health assessment and clinical diagnosis. Bioengineering analyses are becoming more and more popular, because they open up huge opportunities to diagnose and describe bioprocesses occurring in live organisms. Computational methods allow for a reduction in the number of experiments conducted in laboratories. Moreover, numerical calculations enable almost unlimited insight into the physics and essence of the cases studied, even extending the quality of data collected during standard medical examinations. Nevertheless, this is only possible if the computer models are reliable. When computations are conducted, it is very important to validate the modeling approach, and that is why some experiments, but to a limited extent, are necessary. These problems are strongly underlined in this article. The amount of results in these fields is vast, since whenever a computational analysis is started, a lot of data need to be collected to appropriately define the equations of the problem. One of the issues that is currently the attention of the researchers is the appropriate definition of biomaterial stiffness, through a specific and carefully chosen constitutive relation. Some papers in which the material law is an important contribution to the discussion are, for example, [7; 8; 9; 10; 11; 12; 13; 14]. From many materials available for testing, mice are chosen as the research object because their parts are easily obtainable, and the analysis of their behavior enables the formulation of new approaches and the development of modern procedures for the purpose of the bioengineering field. Here, attention is focused on the response of mice carotid arteries and the process of the appropriate choice and definition of material laws describing the relation between stress and strain in the artery. These problems are important when the mechanical behavior of a body is studied. In this context, some selected recent papers describing or related to mouse arteries' mechanics are mentioned. The important actual achievements in this field can be found in the following: [PERSON] et al. [14]; [PERSON] et al. [15]; [PERSON] et al. [16]; [PERSON] et al. [17]; [PERSON] et al. [18]; [PERSON] et al. [19]; [PERSON] et al. [20]; [PERSON] et al. [21]; [PERSON] et al. [22]; [PERSON] et al. [23]; [PERSON] et al. [24]; and [PERSON] and [PERSON]. [25]. The common feature of the above-mentioned articles is the experimental identification of the mechanical properties of mouse arteries, which has been carried out by inflating the artery attached to cannulas by knots, according to multiple pressure protocols. The preconditioning of the artery is performed before the main test is started. The material law constants are then fitted to the biaxial experimental data gathered during the experiments.