**1. Introduction**

The mortality rate of cardiovascular diseases in children is 5–16% globally [1]. Obstructive lesions of different segments of the right ventricular outflow tract (RVOT) are congenital heart defects, the treatment of which is possible only by surgical intervention. A modified Blalock–Taussig shunt (MBTS) is adopted as the first step in surgical treatment of RVOT. A shunt made of polytetrafluoroethylene (PTFE, Gore-Tex) is used to provide blood flow from the systemic circulation to the pulmonary circulation. In particular, the following pathologies are considered in the present study: pulmonary artery stenosis, pulmonary atresia, and Tetralogy of Fallot. However, MBTS operations cause a number of

**Citation:** Kuchumov, A.G.; Khairulin, A.; Shmurak, M.; Porodikov, A.; Merzlyakov, A. The Effects of the Mechanical Properties of Vascular Grafts and an Anisotropic Hyperelastic Aortic Model on Local Hemodynamics during Modified Blalock–Taussig Shunt Operation, Assessed Using FSI Simulation. *Materials* **2022**, *15*, 2719. https:// doi.org/10.3390/ma15082719

Academic Editors: Antonio Lamura and Maria Cinefra

Received: 19 November 2021 Accepted: 30 March 2022 Published: 7 April 2022

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complications, such as excessive volumetric load, acute thrombosis, and low diastolic blood pressure leading to coronary insufficiency. Modern modeling techniques can be applied to predict and evaluate complications in the postsurgical period.

Computational modeling is used to study the local hemodynamics of MBTS surgery. The first such studies using numerical simulation were conducted in [2,3] using the computational fluid dynamics (CFD) method. The shunt size, its location, and its angles of proximal anastomoses for an idealized geometry were considered in these works. A similar study was [4]. CFD is a method determining the parameters of flow in a channel with solid walls. It allows for a detailed description of the local flow in a complex geometry. The hemodynamic effects of nonclosure of patent ductus arteriosus [5] on pulmonary blood flow were analyzed using the CFD method. The degree of shunt occlusion after MBTS surgery using CFD was determined by Arthurs et al. [6]. MBTS and right ventricle–pulmonary artery shunts were compared in [7,8]. Liu et al. conducted a series of studies [9–12] of MBTS shunts using real geometry to analyze the hemodynamic parameters of local blood flow, including the degree of shunt occlusion. In [10,13], the effect of MBTS location on blood flow distribution was investigated. Using the CFD method, the hemodynamics of the central shunt and modified Blalock–Taussig shunt were compared [14].

Vascular walls are flexible, which can affect the hemodynamics. The fluid–solid interaction (FSI) method is another method of computer modeling. This method, as opposed to the CFD method, takes into account the wall elasticity of the computational flow area. This numerical method is used to study the parameters of blood flow for different problems. Luo et al. [15] studied fluid flow in aortic and iliac arteries bifurcations with the use of FSI simulation. Stergiou et al. [16] investigated the occurrence and development of abdominal aortic aneurysm using the FSI method. Sousa et al. [17] analyzed the hemodynamics of the stenosis carotid bifurcation by FSI simulation. The deformability/elasticity of the vessel wall is an important factor in the study of blood flow. FSI simulation has not yet been used to study MBTS surgery. Therefore, this method was used in our study.

In this study, the shunt walls were modeled as an isotropic hyperelastic material, while the aortic walls were modeled as both anisotropic and isotropic elastic material. An experimental study of Gore-Tex shunts was performed to determine the parameters of the hyperelastic material of the shunt. FSI modeling of MBTS bypass surgery is an actual research method and has not been used before. The local distribution of velocities, pressures, wall shear stresses, and displacements of the aortic wall and shunt were analyzed in this study. The aim of the study was to show the effect of anisotropy on the main characteristics of local hemodynamics for the MBTS surgery. Results for the three methods for different shunt locations (central, right, and left) were obtained in this study.
