The emergence of the fractal bronchial tree.

The fractal design of the bronchial tree, as described by the Hess-Murray law, facilitates energy-efficient lung ventilation, yet its developmental origins remain unclear. Here, we quantify the rearrangement of the embryonic bronchial tree into its fractal architecture using SkelePlex, a new neural network-based image processing pipeline, and elucidate the biophysical principles governing its formation. We find that the branch shapes are such that pressure drop, shear, axial, and hoop stresses are equal across all branches. The seemingly random diameters of sister branches reflect the different number of tips they connect to in the asymmetric lung tree. By analyzing lungs after pneumonectomy and those affected by chronic obstructive pulmonary disease (COPD), we show that the same principles persist in adulthood and disease, potentially providing quantitative biomarkers for disease progression and therapeutic guidance.