Submitted on July 27, 2004
Accepted on November 10, 2004
A Fractal Analysis of the Radial Distribution of Bronchial Capillaries Around Large Airways
Joseph C Anderson1, Albert L Babb1, and Michael P Hlastala2*
1 Department of Chemical Engineering, University of Washington, Seattle, WA, USA
2 Department of Medicine, University of Washington, Seattle, WA, USA; Department of Physiology and Biophysics, University of Washington, Seattle, WA, USA
* To whom correspondence should be addressed. E-mail: hlastala{at}u.washington.edu.
We analyzed published measurements of the bronchial circulation and airway wall 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 thirteen distributions created, these annuli ranged in size from 1/2 to 1/128 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 speculate 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.
