Моделирование течения воздуха в упруго-деформируемой пористой среде, аппроксимирующей легкие человека: алгоритм реализации и анализ результатов применения модели

The work is devoted to the implementation of the mathematical model of the human respiratory system developed by the authors to predict the occurrence of respiratory pathologies caused by the negative effects of atmospheric air pollution. The proposed model describes human lungs as an elastically deformable saturated two-phase porous medium with large displacement gradients. Since the analytical solution of the formulated essentially nonlinear problem seems unfeasible, it is suggested that the solution can be obtained by applying numerical methods with step-by-step procedures. An algorithm is proposed for solving the related problem of air filtration in an elastic deformable porous medium. The nonlinear sub-problem of deformation of a two-phase lung medium is solved numerically by finite element method, and the filtration subproblem — by finite volume method. A set of programs was developed (in the C++ programming language) using parallel computing technologies to implement the algorithm. Based on the tomographic images of the lungs obtained with the ITK-SNAP software package, the three-dimensional shape of the lungs was reconstructed. Using the engineering software ANSYS ICEM CFD, a volumetric finite element mesh was constructed. Numerical modeling of air flow in the human lungs was performed for personalized three-dimensional geometry. The pressure fields of the gas phase in the human lungs at various moments of the respiratory cycle are presented. The developed model is planned to be used in the future to determine the areas of risk of respiratory pathologies caused by the negative impact of aerogenic environmental factors.