Fluid – Dynamic Optimality in the Human Lung Airways

Abstract

Human bronchial tree is an efficient mass exchanger optimized for breathing. In this study, new theories for the optimality and an accurate loss correlation have been suggested using fluid dynamical approaches. Firstly, it is shown that the nearly constant length-to-diameter ratio observed with conducting airways of human bronchial tree can be explained based on the fluid dynamic optimality principle. In addition, 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. Then, the characteristics of pressure loss (ΔP) in human lung airways were numerically investigated using a realistic model bifurcation. The ΔP coefficient K showed a power-law dependence on Reynolds number (Re) and length-to-diameter ratio with exponent different for Re ≥ 100 than for Re < 100. Finally, it was shown that human lung’s asymmetrical bifurcation helps to improve breathing efficiency and thus it is the result of optimization.