**5. Conclusions**

There is no obviously ideal type and location for shunt insertion. Many studies have attempted to find a universal way to guide such a choice, in particular, using mathematical models. Our study offers a new step in the modeling of MBTS operations. In contrast to the well-known and more commonly used CFD method, we have proposed the FSI method, which takes into account not only the elasticity of the vessel wall but also its anisotropy. Changes in a number of the main hemodynamic parameters of local blood flow have been established depending on the accounting of elasticity properties. We consider this important for further research in modeling MBTS operations.

Modeling is an activity aimed at understanding and quantifying an event, object, or function. In state-of-the-art science, numerical modeling is often used to study a particular process. In our study, we also used already known tools (FSI) to simulate a specific event (MBTS). The use of the FSI method for MBTS operations has not been used before, so we called it a "new step".

We have carried out complicated FSI modeling for MBTS operations, taking into account the anisotropic properties of vessel materials. No one has done this before. We have established the importance of taking anisotropy into account when modeling central bypass surgery. Therefore, we consider this a "new step" of modeling in MBTS operations.

A comparison between the effect of isotropic and anisotropic aorta material properties was performed. It was shown that the anisotropic model of the aortic material showed higher stress values at the peak moment of systole, which may be a key factor in determining the strength characteristics of the aorta and pulmonary artery. Additionally, this mechanical parameter is important when installing a central shunt, since it is in the area of the central anastomosis that an increase in stresses on the aortic wall is observed. According to computations, the anisotropic model shows smaller values of the displacements of both the aorta and the shunt, which in turn may affect the success of preoperative prediction. Thus, it can be concluded that the anisotropic properties of the aorta play an important role in preoperative modeling.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/ma15082719/s1. Table S1. Parameters of computational mesh., Table S2. Mechanical parameters for aorta and shunt used in the study., Figure S1. Meshes and boundary conditions of the "straight vessel": upper–boundary conditions and fluid mesh, lower–solid mesh., Figure S2. Stress distribution at time t = 0.09 s: (a) isotropic properties of the vessel, (b) anisotropic properties of the vessel., Figure S3. Displacements distribution at time t = 0.09 s: (a) isotropic properties of the vessel, (b) anisotropic properties of the vessel., Figure S4. Comparison of parameters: (a) maximum values of displacements, (b) maximum Von Mises stress values, (c) maximum wall shear stress values.

**Author Contributions:** Conceptualization, A.G.K. and M.S.; methodology, A.G.K.; validation, A.K. and A.G.K.; investigation, A.G.K., A.K. and A.M.; resources, A.G.K.; data curation, A.G.K., A.M. and A.P.; writing—original draft preparation, A.G.K., A.K., A.P. and M.S.; writing—review and editing, A.G.K.; visualization, A.K. and A.M.; supervision, A.G.K.; funding acquisition, A.G.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** A.G.K. acknowledges the financial support of the Ministry of Science and Higher Education of the Russian Federation in the framework of the program of activities of the Perm Scientific and Educational Center "Rational Subsoil Use". Artem Porodikov acknowledges financial support of RFBR and Perm Territory, project number 20-41-596005. Marina Shmurak acknowledges financial support of Perm National Research Polytechnic University in the framework of the Federal Academic Leadership Program «Priority-2030».

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Ethics Committee of S.G. Sukhanov Cardiovascular Center, Perm, Russia (protocol No. 12 on 25 October 2021).

**Informed Consent Statement:** Informed consent was obtained from parents of patients involved in the study.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
