Fractal analysis of surfactant deposition in rabbit lungs

The effect of exogenous surfactant in the treatment of acute lung injury may depend on homogeneity of distribution of the material delivered. Analyses of distribution rely on sectioning the lung, determining surfactant concentration for each piece, and describing the variation in that value. Results of such analyses are influenced by how finely the lung is sectioned. We have reanalyzed data from prior experiments to determine whether the distribution of administered surfactant is fractal, that is, is independent of the scale of measurement. Lungs from animals receiving surfactant radiolabeled with [3H]dipalmitoylphosphatidylcholine were cut into 108 pieces, and the normalized radioactivity in each piece was determined. Sectioning of the lungs into different numbers of pieces (n = 2, 6, 12, 18, 36, 54, or 108) was simulated, and corresponding radioactivity contents were calculated. The coefficient of variation (CV) of these normalized values was then calculated for each scale of measurement (expressed as relative piece volume), and ln(CV) was plotted as a function of the logarithm of relative piece volume. These relationships were linear (average correlation coefficient = 0.96) for all animals, consistent with CV being a fractal property. We conclude that the intrapulmonary distribution of surfactant may be fractal and is therefore a property of the lung. This study demonstrates the utility of fractal analysis in describing the pulmonary distribution of substances introduced via the airway.