Mathematical model of flow through the patent ductus arteriosus (Q2435061)

The authors develop a mathematical model for the haemodynamics in patent ductus arteriosus (PDA, an anomalous shunt in the cardiovascular system), with the aim of investigating the resulting cardiovascular effects. The model is based on the non-dimensional Navier-Stokes equations, obtained by some simplifications and the flow is studied in three different idealized geometries by assuming that the entry flow is irrotational and remains so in the core until at least the shunt position. The geometries taken into account are: two channels with a shunt between them, two cylinders with a point singularity between them, and two semi-cylinders joined by a plate. It is also considered that the separation or diffusion of vorticity into the core flow is delayed due to the high frequency associated with the pulsatile component of the flow profile. The authors use complex potential theory, Schwarz-Christoffel transformations, conformal mappings and Fourier series. Numerical simulations are provided and the results of the study can predict the quantitative and qualitative changes in the blood flow through the patent ductus arteriosus, and enhance some medical interpretations in cardiology.