Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development

The cerebellar Purkinje cell has highly branched dendrites extending in a transverse plane to the cerebellar folium. Branching patterns of the dendrites were subjected to fractal analysis to obtain a quantitative measure of their intricacy. Using a square-covering method, we found that dendrites have a statistical self-similarity so that their fractal dimension can be evaluated. In postnatal mouse, dimensions of Golgi-stained Purkinje cells increased as dendrites developed. The time course of the dimension increase was correlated with development of the width and area of the dendritic fields. After the dimension reached the maximum value at postnatal day 20, the width and area further continued to grow until day 100. In human cerebellum, dimensions of Purkinje cell dendrites increased greatly during pregnancy and reached 97% of the adult value at birth. On the other hand, 41% of the adult dendritic field width and 11% of the adult area had been attained at birth. The physical size of dendrites increased in a more lagged phase than the dimensions, and growth proceeded mainly after birth. These observations indicate that after the maximum complexity and fundamental tree pattern have been attained, the overall tree size further increases. It is observed that phylogenetic development of dendritic trees of Purkinje cells in several species of vertebrates showed a correlation with the increase in dimensions. These studies demonstrated the potency of the fractal analysis in evaluating development of dendritic trees of neurons.