The fractal lung: universal and species-related scaling patterns.

The mammalian lung exhibits features of a fractal tree: heterogeneity, self-similarity and the absence of a characteristic scale. The finite nature of the lung ultimately limits the range over which self-similarity scaling characteristics are applicable. However, generalization based on the scaling features of fractals, provides unique insight into geometric organization of anatomic structures. Furthermore, the mathematical theory of renormalization groups provides a description of the harmonically-modulated inverse power-law scaling observed for bronchial tree dimensions observed in different species. Compared to several mammalian species (dog, rat, hamster), the human lung shows marked differences in the phase of the harmonic modulation for both length and diameter measurements. These inter-species scaling differences suggest that evolutionary factors modify certain universal features of morphogenesis.