Fractal Geometric Analysis of the Renal Arterial Tree in Infants and Fetuses

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Abstract
Fractal geometry is a useful method of quantitating the space-filling properties of complex objects and has a particular advantage in pediatric pathology because it is independent of organ size. The fractal dimensions of angiographic images of 44 renal arterial trees from 23 consent pediatric autopsies were measured by the box-counting method. The mean fractal dimension was 1.64 and all values were greater than the topological dimension (one), indicating that the renal arterial tree in fetuses and infants has a fractal element to its structure. There was no significant association with size of the kidneys, confirming the size-independent nature of the fractal dimension. There was no significant association with age of the subject, and the mean value was not significantly different from values obtained in studies of adult kidneys, suggesting that the degree of branching, at a labor and lobular level, does not increase after about the 21st week of gestation. The results are compatible with a diffusion-limited aggregation model of development.