Numerical Simulation of the Human Lung: A Two--scale Approach

Abstract

In this paper we introduce a two-scale model for the numerical simulation of the human lung. The airflow in the upper, resolvable part of the human lungs is modelled by the Navier-Stokes equations, which couple to a dyadic bronchiole tree model through boundary conditions. This model depends mainly on the generation, where the inlet is located, and the radius of the bronchiole at this generation. In the bronchioles a linear flow is assumed, hence the Hagen-Poiseuille formula can be applied. The pressure at the alveoles and the starting resistance for the dyadic tree are used as input parameters. To illustrate the approach, we simulate a patient-specific human lung geometry with a Lattice-Boltzmann method and show qualitative convergence results for the pressure drop as well as a comparison with Neumann boundary conditions that are commonly used in one-scale models. Results for an overall flux of Q=150 ml/s, which corresponds to a Reynolds number of R=1650 are presented.