The Mechanism of Movement and Calculation of Blood Balance in the Flow Channel From the Left Atrium to the End of the Aorta

Abstract

Today, there are a lot of works studying the mechanisms of formation and evolution of self-organizing tornado-like jets of viscous fluid. In these works, the exact solution of the Navier-Stokes equation for such a class of flows are obtained, the geometry of the generating surface for that flows is established and the necessary and sufficient conditions for the formation and evolution of such swirling jets are formulated. However, important aspects of the mechanics of such flows remain unclear — the structure of the boundary layer, the shape of streamlines in general form, the structure of such flows under a pulsating flow regime, and others. After obtaining the exact solution, attempts were made to obtain relations for streamlines in the corresponding projections. However, due to computational complexity, streamlines were constructed only for regions far from the axis of the swirling flow evolution. In this work, an alternative method of calculating streamlines was used, which made it possible to obtain general relations for these lines at each point in space. Expressions for streamlines contain easily computed functions, which simplifies their practical use Based on the expressions for streamlines, expressions were formulated declaring the conservation of the mass of the swirling blood flow from the left atrium to the aorta and the balance of the medium was calculated. The results of this work are of great theoretical and practical importance. On the one hand, the established expressions for streamlines allow a better study of the mechanisms of formation and evolution of swirling flows in the axial region. On the other hand, obtaining quantitative ratios for the balance of blood in the heart and aorta allows a more accurate study of the mechanics of blood circulation.