A non-iterative mathematical description of three-dimensional bifurcation geometry for biofluid simulations

We propose a mathematical model to describe the three-dimensional bifurcation geometry for airway flow simulations. The numerical scheme is explicit, non-iterative, and therefore stable and efficient. In addition, our model successfully reproduces the characteristic cross-sectional shape transition (from circular, to flattened elliptical, and then to 8-like shapes) across a bifurcation as observed in anatomical examinations. Several examples with various bifurcation parameters are presented, and these examples demonstrate the capacity and usefulness of our work in airway flow and transport simulations. The model developed here may also be useful for blood flow simulations and experimental model design.