On a new liquid filtration model

This paper studies the model of blood circulation in human lower extremities by Penkovsky and Korsakova. To more precisely study the dynamics, the common case of a mathematical model was considered without neglecting vessel elasticity, and taking into account different vascular conductivity. The model was adapted to new conditions by taking into account additional factors and adding new variables. The analogy between the mathematical model and the mathematical elastic-filtration hydraulic seam fracture model is emphasized. The mathematical apparatus for hydraulic flow design is also applicable to the description of blood flow. The important role of positive solutions was taken into account in the model. Such characteristics as vascular wall resistance, blood speed and pressure, speed and pressure profiles, and muscle pump performance speed do not involve negative solutions. It is critical to understand the physical sense of the values of variables in terms of the model, using physiologically correct data and to obtain realistic and applicable results for further forecasting and optimization and for the use of positive solutions providing more stable and efficient computations. A solution for such a model modification can be used for debugging and testing numerical methods, without a direct physiological analogy.