A multi-scale model of gas transport in the lung to study heterogeneous lung ventilation during the multiple-breath washout test
Fig 1
Trumpet lobule geometry and lung model morphology.
(a) Schematic representation of the trumpet model used for the lobules with the cross-section of the terminal pipe St and the time-variable cross-section S(x,t) and volume Vlb(,t) of a trumpet lobule model. (b) Idealized lung model morphology based on bifurcation rule (Eq 2). For better visibility of the airway structure, all diameters were scaled with the factor 0.1. The length and diameter ratio of airways until the fourth generation are irregular and follow from empirical data by Weibel [26]. After the fourth generation, airways bifurcate in a minor and major daughter airway according to Eq 2. From this scheme an asymmetric network of airways with different total lengths results. With each generation, airways get smaller, both in terms of length and of cross-section. In the lung model, when the diameter of the airways falls below a limit diameter dlim, a so-called terminal pipe is reached, and different model (the trumpet lobule) is used to represent smaller airways.