Modelling Pressure Losses at Arterial Junctions With Application to Junctions of the Fetal Ductus Arteriosus

In one-dimensional (1D) models of arterial networks, branch junctions are represented by flow and mechanical energy (or total pressure, i.e. p + 1/2ρu²) coupling conditions. The flow condition simply ensures conservation of mass, but the pressure condition is less trivial because pressure losses are known to occur in the vicinity of junctions, caused by regions of complex flow that depend on the vascular geometry and prevailing flow patterns. These losses are commonly ignored in 1D models under the assumption that area ratios and branching angles of arterial junctions are optimally designed. However, one setting where pressure losses are likely to be important is the junction of the ductus arteriosus (DA) with the aorta in the fetus, considering the high kinetic energy of blood in the DA [1], the acute angle between the aortic isthmus (Aols) and DA, and the redirection of DA blood flow towards the descending aorta (DAo, Figure 1). Previously, pressure losses have been approximated in 1D models by enforcing continuity of static (rather than total) pressure [2] or by using empirical loss coefficients obtained from experiments in 90 degree T-tubes [3]. In the current study, we implemented a loss formulation described by Bassett et al [4] for 1D gas dynamics simulations, which unlike previous methods, can be used to model junctions with any number of branches and any orientation of branch angles, and explicitly accounts for the influence of area and flow ratios on pressure losses. Results of the model are validated against high fidelity measurements in fetal lambs.