RESUMEN
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.
