An index of the fractal characteristic of an airway tree is associated with airflow limitations and future body mass index reduction in COPD patients.

Disorders of the fractality of an airway tree and a vessel tree have been studied in pulmonary diseases. Here we successfully applied Mishima's D to the bronchial minimal inner cross-sectional area (iCSA) measured in multidetector computed tomography (MDCT) images of chronic obstructive pulmonary disease (COPD) and non-COPD smokers (n = 162), by defining D in the following formula: logN(≥X) = -D × logX + c, where X is a certain iCSA value, N(≥X) is the number of airway branches having iCSA greater than or equal to X, and c is a constant. Mathematically, this D of iCSA was associated with the expected reduction ratio of iCSA at bifurcations, which can be estimated by 2-1/D. This D of iCSA also correlated weakly with the box-counting fractal dimension and Weibel's reduction ratio over airway generations, which indicated that the airway tree was not a perfect fractal object and that the branch bifurcation was asymmetric. The D of iCSA showed positive correlations with lung function measurements of airflow limitation in study participants. In addition, D of iCSA representing the periphery showed an association with future body mass index reduction, most likely as an indicator of energy efficacy for breathing as predicted by Hess-Murray's law. D of iCSA may be helpful to understanding the pathogenesis of obstructive lung diseases.NEW & NOTEWORTHY An airway tree is a fractal object. We showed that the distribution of minimal inner cross-sectional area (iCSA) of airway branches can be expressed by a fractal index, D, of minimal iCSA. This D was correlated with airflow limitation and future body mass index reduction in chronic obstructive pulmonary disease patients, as predicted by Hess-Murray's law.