FORMULA FOR CALCULATION OF ANGLES OF A MICROVASCULAR NODE
Objective. Analysis of the Murray’s equations, obtaining an analytical and graphic relationship between the angles of deviations of the vessels in a microvascular node. Methods. The system of the Murray's equations is solved, which describes a microvascular node of the human’s or animal’s circulatory system. Using the apparatus of linear algebra, the linear dependence of the system of the Murray’s equations is proved. Therefore, one equation of the system of equations was replaced by the equation of continuity of blood flow. The solution of the new system of equations is the equation for the angles of the microvascular node, which has not previously been found in the literature. The equation is solved using the mathematical packages MATCAD and the algorithmic language Python. Results. An equation for the angles of deviations from each other of the vessels in a node of the microvascular circulatory system of a person or an animal is obtained. The equation was solved on a computer using the mathematical package MATCAD, as well as the algorithmic language Python. As a result, the graphical relationship between the angles of deviations of the vessels in a microvascular node of the circulatory system is given, a graph of the dependence of one angle on another is plotted. The three-dimensional graphs of functions describing the dependence of the angles of deviations of the vessels from each other in a node of the circulatory system are presented. Conclusion. The derived equation for the angles of deviations from each other of the vessels in a node of the circulatory system has the practical application in construction of artificial capillary networks, as well as pipeline networks for optimal, in terms of energy consumption, pumping oil, gas and any liquid. The resulting equation can be used for experimental testing of the Murray’s equations.