Gallbladder disease is one of the most spread pathologies in the world. Despite the number of operations dealing with biliary surgery increases, the number of postoperative complications is also high. The aim of this study is to show the influence of the biliary system pathology on bile flow character and to numerically assess the effect of surgical operation (cholecystectomy) on the fluid dynamics in the extrahepatic biliary tree, and also to reveal the difference between 1-way and 2-way FSI algorithms on the results. Moreover, the bile viscosity and biliary tree geometry influence on the choledynamics were evaluated. Bile velocity, pressure, wall shear stress (WSS), displacements and von Mises stress distributions in the extrahepatic biliary tree are presented, and comparison is made between a healthy and a lithogenic bile. The patient-specific biliary tree model is created using magnetic resonance imaging (MRI) and imported in a commercial finite element analysis software. It is found that in the case of lithogenic bile, velocities have lower magnitude while pressures are higher. Furthermore, stress analysis of the bile ducts shows that the WSS distribution is found mostly prevailing in the common hepatic duct and common bile duct areas. It is shown that when it is necessary to evaluate the bile flow dynamics in urgent medical situations, 1-way analysis is acceptable. Nevertheless, 2-way FSI provides more accurate data, if necessary to evaluate the stress–strain state of bile ducts. The proposed model can be applied to medical practice to reduce the number of post-operative complications.

Cardiovascular surgery requires the use of state-of-the-art artificial materials. For example, microporous polytetrafluoroethylene grafts manufactured by Gore-Tex^® are used for the treatment of cyanotic heart defects (i.e., modified Blalock–Taussig shunt). Significant mortality during this palliative operation has led surgeons to adopt mathematical models to eliminate complications by performing fluid–solid interaction (FSI) simulations. To proceed with FSI modeling, it is necessary to know either the mechanical properties of the aorta and graft or the rheological properties of blood. The properties of the aorta and blood can be found in the literature, but there are no data about the mechanical properties of Gore-Tex^® grafts. Experimental studies were carried out on the mechanical properties vascular grafts adopted for modified pediatric Blalock–Taussig shunts. Parameters of two models (the five-parameter Mooney–Rivlin model and the three-parameter Yeoh model) were determined by uniaxial experimental curve fitting. The obtained data were used for patient-specific FSI modeling of local blood flow in the “aorta-modified Blalock–Taussig shunt–pulmonary artery” system in three different shunt locations: central, right, and left. The anisotropic model of the aortic material showed higher stress values at the peak moment of systole, which may be a key factor 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 stress on the aortic wall is observed. According to computations, the anisotropic model shows smaller values for the displacements of both the aorta and the shunt, which in turn may affect the success of preoperative predictions. Thus, it can be concluded that the anisotropic properties of the aorta play an important role in preoperative modeling.

Surgical treatment of congenital heart defects with the obstruction of the outflow tract of the right ventricle can be performed in several stages. The first stage of surgical correction is the creation of a systemic-pulmonary shunt, followed by radical correction. The main complications of systemic-pulmonary shunts are associated with the development of shunt thrombosis and hypervolemia of the pulmonary circulation. Currently, considering the importance of individual selection of a shunt for effective functioning, the main scientific search is aimed at creating optimal methods that consider all the hemodynamic features of a particular patient. Recently, the direction of mathematical modelling and biomechanical analysis in medicine has been actively developing, facilitating the objective evaluation of the accumulated clinical experience and is one of the main tools in evidence-based medicine. The use of computational fluid dynamics methods for modified Blalock–Taussig shunt analysis allows us evaluate the hemodynamic parameters for various configurations of shunts and anastomosis angles and improve the understanding of pathophysiological processes in the cardiovascular system before or after an application of the modified Blalock–Taussig shunt. Here, we provide an overview of the work related to the use of modelling for the calculation of the currents in the aorta–shunt–pulmonary artery system. It is noteworthy that most studies consider the personalised characteristics of the patients and are therefore highly likely to be used in clinical practice. The main hemodynamic parameters that are analysed with the computer calculations are described. Part of the work is devoted to the stages of computer modelling and the limitations in the implementation of these stages. We believe that this manuscript will be of interest to specialists in cardiovascular surgery and to the several scholars working in areas related to the use of digital technologies in medicine, mathematical modelling in medicine and biomechanics. Received 30 January 2020. Revised 25 May 2020. Accepted 9 June 2020. Conflict of interest: Authors declare no conflict of interest. Funding: The work is supported by the program for the development of the Scientific and Educational Mathematical Center of the Volga Federal District (No. 075-02-2020-1478) and a grant for the development of the scientific school of the Perm Region “Computer biomechanics and digital technologies in biomedicine”. Author contributionsConception and design: Yu.S. Sinelnikov, V.B. Arutunyan, A.A. Porodikov, A.N. Biyanov, V.S. Tuktamyshev, M.I. Shmurak, A.R. KhairulinDrafting the article: A.A. Porodikov, A.N. Biyanov, A.G. KuchumovCritical revision of the article: A.N. Biyanov, A.G. KuchumovFinal approval of the version to be published: Yu.S. Sinelnikov, V.B. Arutunyan, A.A. Porodikov, A.N. Biyanov, V.S. Tuktamyshev, M.I. Shmurak, A.R. Khairulin, A.G. Kuchumov

Coarctation of the aorta is a localized narrowing of the aortic lumen. This pathology leads to hypertension in upper extremity vessels, left ventricular hypertrophy and to impaired perfusion of the abdominal cavity and lower extremities. Along with traditional diagnostic methods, mathematical modeling is used for risk assessment and the prediction of disease outcomes. However, when applying numerical models to describe hemodynamic parameters, the choice of turbulence model to describe swirling flow occurring in the aorta in this pathology must be justified. Thus, three turbulence models, namely k-ε, k-ω, and SST were analyzed for the description of swirling flows in the study of coarctation’s effect on hemodynamic parameters and analysis of the mechanisms leading to various cardiovascular diseases caused by altered hemodynamics. The results revealed significant differences in swirling flow patterns between the k-ε and k-ω models, while the k-ω and SST models showed consistent results over the cardiac cycle. In the peak systolic phase, average velocity rises to 1.07–1.98 m·s⁻¹ for the k-ε model, 0.82–2.12 m·s⁻¹ for the k-ω model, 1.22–2.12 m·s⁻¹ for the SST model and 0.8–2.12 m·s⁻¹ for laminar flow. WSS values increase rapidly to 11–22 Pa in k-ε, 25–50 Pa in k-ω and SST models of turbulence, and 30–55 Pa for laminar flow. Significant differences were also evident in the prediction of wall shear stress, with the k-ε model giving values more than twice as high as the k-ω and SST models. The data obtained confirm the necessity of careful model selection for accurate hemodynamic parameter estimation, especially in coarctation. The findings of this study can be used for further physics-informed neural network analysis of evaluation of treatment evaluations for congenital heart disease patients.