*2.3. FSI Simulations of Blood Flow in the Aorta–Pulmonary Artery–Shunt System* 2.3.1. Problem Formulation

A concomitant pathology of congenital heart disease in children is impaired pulmonary circulation. This leads to abnormal lung growth and insufficient oxygenation. The use of a modified Blalock–Taussig shunt (MBTS) in such cases is one of the most common methods for eliminating pathology. Biomechanical modeling methods are used to objectify the choice of shunt parameters. An individualized three-dimensional model of the aorta–pulmonary artery–shunt system based on CT images (computed tomography) with contrast was built to analyze the local hemodynamics.

The study's protocol was approved by the Ethics Committee of the Perm Federal Center of Cardiovascular Surgery (Protocol No. 12 on 25 October 2021). Informed consent was obtained from parents of patients involved in the study.

Three-dimensional (3D) anatomical data were obtained via a 64-channel, dual-source multidetector-row CT scanner (Siemens Somatom Definition AS, Forchheim, Germany) with a 0.6-mm slice thickness and 0.6-mm slice interval, a 0.5 s rotation time, and a pitch of 0.25 (Gantry opening is 70 cm; the number of reconstructed slices is 67). The tube current was adjusted according to the body weight. Before CT examination, all patients were sedated. Intravenous propofol was given by anesthesiologist at a dose of 1–2 mg/kg body weight for induction. In some cases, the dose was increased to maintain sedation. Anatomical coverage extended from above the thoracic inlet to below the level of the L2 vertebra, including the origin of the celiac trunk. For vascular opacification, a non-ionic low-osmolar contrast agent containing 350 mg/mL was injected through the peripheral vein (the right ulnar vein if it was accessible). Contrast was administered with a mechanical injector at a dose of 2 mL/kg body weight. A flow rate of 1–2 mL/s was used, depending on the size and location of the venous access, as well as the size of the cannula used. Postprocessing was carried out on a dedicated workstation Singo via (Siemens Healthcare GmbH, Erlangen, Germany). Image reconstruction was performed in 3D volume rendering (VRT) maximum intensity projection (MIP) of multiplanar reconstruction (MPR) in coronary, sagittal oblique views.

Three variants of a modified Blalock–Taussig shunt were considered: the central, connecting the aorta with the pulmonary artery trunk; the right, connecting the left subclavian artery and the right pulmonary artery; and the left, connecting the brachiocephalic trunk and the left pulmonary artery.

The results obtained for two modifications of the model were compared: the first model the so-called "simplified" model accounting for the aortic wall's isotropy and the shunt

elastic properties; the second model accounting the aortic wall's anisotropy and the shunt hyperelasticity. The calculations were performed in Ansys Workbench software (Ansys Workbench 18, Ansys Inc., Canonsburg, PA, USA). The two-way fluid–solid interaction problem of blood flow in the aorta–pulmonary artery system in children was solved.
