Computational model of the fluid dynamics in systemic-to-pulmonary shunts

Abstract 

A systemic-to-pulmonary shunt is a connection created between the systemic and pulmonary arterial circulations in order to improve pulmonary perfusion in children with congenital heart diseases. Knowledge of the relationship between pressure and flow in this new, surgically created, cardiovascular district may be helpful in the clinical management of these patients, whose survival is critically dependent on the blood flow distribution between the pulmonary and systemic circulations. In this study a group of three-dimensional computational models of the shunt have been investigated under steady-state and pulsatile conditions by means of a finite element analysis. The model is used to quantify the effects of shunt diameter (D), curvature, angle, and pulsatility on the pressure–flow (ΔP–Q) relationship of the shunt. Size of the shunt is the main regulator of pressure–flow relationship. Innominate arterial diameter and angles of insertion have less influence. Curvature of the shunt results in lower pressure drops. Inertial effects can be neglected. The following simplified formulae are derived: ΔP=(0.097Q+0.521Q²)/D⁴ and ΔP=(0.096Q+0.393Q²)/D⁴ for the different shunt geometries investigated (straight and curved shunts, respectively).

Keywords:  Congenital heart disease, Finite element method, Pressure–flow relationship, Mathematical model