Characterising respiratory airway gas mixing using a lumped parameter model of the pulmonary acinus

A lumped parameter model of a human pulmonary acinus is derived using results from gas mixing simulations in an anatomically-based asymmetric multi-branching model of the acinus coupled to a symmetric conducting airway model. The model respiratory airways change length in proportion to the cube root of their volume change, and the diameters are updated accordingly assuming constant duct cross-sectional area. The lumped parameter model applies a flux boundary condition at the end of a transitional bronchiole during inspiration to enable realistic concentration changes at this position; during expiration inspiratory parameters are used to predict concentrations at the end of the associated transitional bronchiole. The predicted concentrations are used as time-varying fixed boundary conditions at the end of the transitional bronchiole in conducting airway models during expiration. The current lumped parameter model is most accurate for tidal volumes between 500 and 1500 ml, and equal inspiration and expiration durations of 2 sec. The model's accuracy decreases for changes in breath duration.