A fractal analysis of the radial distribution of bronchial capillaries around large airways

Abstract

We analyzed published measurements of the bronchial circulation and airway wall (Anderson JC, Bernard SL, Luchtel DL, Babb AL, and Hlastala MP. Respir Physiol Neurobiol 132: 329–339, 2002) and determined that the radial distribution of bronchial capillary cross-sectional area was fractal. We limited our analysis to bronchial capillaries, diameter ≤10 μm, that resided between the epithelial basement membrane and adventitia-alveolar boundary, the airway wall tissue. Thirteen different radial distributions of capillary-to-tissue area were constructed simply by changing the number of annuli (i.e., the annular size) used to form each distribution. For the 13 distributions created, these annuli ranged in size from to of the size of the airway wall area. Radial distributions were excluded from the fractal analysis if the sectioning procedure resulted in an annulus with a radial thickness less than the diameter of a capillary. To determine the fractal dimension for a given airway, the coefficient of variation (CV) for each distribution was calculated, and ln(CV) was plotted against the logarithm of the relative piece area. For airways with diameter >2.4 mm, this relationship was linear, which indicated the radial distribution of bronchial capillary cross-sectional area was fractal with an average fractal dimension of 1.27. The radial distribution of bronchial capillary cross-sectional area was not fractal around airways with diameter <1.5 mm. We speculated on how the fractal nature of this circulation impacts the distribution of bronchial blood flow and the efficiency of mass transport during health and disease. A fractal analysis can be used as a tool to quantify and summarize investigations of the bronchial circulation.