Optimality in the variation of average branching angle with generation in the human bronchial tree

In the human bronchial tree the branching angle becomes larger with generation or for the smaller branches. Previous theories based on single parameter optimization have not been successful at all in predicting the consistent increasing trend of branching angle with continued bifurcation. In this study a new theory for the optimality of the branching angle is proposed, which is based on the optimization between dual competing performances, the maximum space-filling capability at the expense of minimum energy loss. A large-angle branching gives an effect of delivering air into a new direction away from the preceding airways. It then has an effect of utilizing the lung volume with better uniformity, but at the same time inevitably requires a high pressure loss. It is shown in this paper that the ever increasing branching angle with generation can be well explained as the optimum branching structure where the dual opposing performance of space filling and pressure loss is optimized. In estimating the pressure loss, branching loss is considered in addition to the Poiseuille loss. Change of predicted optimum branching angle with generation shows an excellent agreement with the observed data found in the human conducting airways.