Mathematical modeling of two-dimensional flow through patent ductus arteriosus in an adult

Abstract

Adults and children can survive, and indeed thrive, with a small opening remaining in the ductus arteriosus. This is a shunt joining the aorta and pulmonary artery that forms during the fetal development in order to allow blood to bypass the lungs, and which normally closes soon after birth. Some patent ductus arteriosus cases appear asymptomatic since the heart and lungs can compensate for slight reductions in oxygen reaching the brain; and the condition is only found after further complications in the circulation. Thus it is important to quantify the hemodynamics in such patients. Pressures and stresses on the vascular wall near the shunt are of particular interest as they can predict functional defects. In this work, a mathematical model is presented of the flow in the two major vessels leading from the heart in a patient with patent ductus arteriosus. Results are presented for a typical set of physical parameters. The findings imply that the pressures must be significantly different from those in healthy individuals in order to produce normal ventricular flows. In addition, an estimation of the mixing between oxygenated and deoxygenated blood due to a shunt implies that as much as 35% of the flow reaching the systemic vessels at any given time can be delivered by the right ventricle. Finally, the model enables the calculation of shear stresses on the arterial walls. Results for a typical position in the domain are considered and the maximum stress there is estimated to be 3.5 dyne cm-2. © 2010 International Federation for Medical and Biological Engineering.