Application of a mathematical model of systemic circulation for determination of blood flow parameters after modified blalock-taussig shunt operation in newborns

The problem of infant mortality in children with congenital heart disease is relevant both in Russia and throughout the world. One of the surgical methods for treating congenital heart diseases is bypass surgery using a modified Blalock-Taussig shunt. This operation is used in newborns and infants with congenital heart defects to increase pulmonary blood flow in order to increase the oxygen content in the blood, bring it back to normal and ensure uniform development of the right and left lungs. To improve the efficiency of decision making in surgical practice, the results of a personalized blood flow model can be used. This article presents a conceptual 0D scheme of systemic blood flow, where aorta and pulmonary artery are replaced by a 3D model. A mathematical 0D formulation of the problem of modelling systemic circulation has been developed, which contains 13 differential equations and several dozen algebraic relations. The model parameters in the first approximation are obtained based on real survey data and analysis of literature sources. A numerical implementation is carried out to solve the model relations using the Runge-Kutta methods of 4 orders of magnitude. The simulation results allow to determine the parameters of pressure and blood flow from time to time in any part of the design scheme, as well as the blood flow passing through the shunt, depending on its resistance. Possible ways of further development of the model are to develop an iterative algorithm for coupling 0D and 3D models, develop an algorithm for identifying model parameters based on individual measurements, describe oxygen exchange processes, and formulate criteria based on the obtained hemodynamic characteristics for making decisions in surgical practice.