Fractal pattern formation in human retinal vessels

Abstract

The mechanism for the formation of retinal vessel patterns in the developing human eye is an unresolved question of considerable importance. The current hypothesis is based on the existence of a variable oxygen gradient across the developing photoreceptors which stimulates the release of angiogenic factors which diffuse in the plane of the retina and result in the growth of retinal vessels. This implies that the limiting step in the formation of retinal blood vessels is a diffusion process. To test this hypothesis we have performed a fractal analysis of the human retinal vessels using two different methods. Within the limited range of length scales available in the red-free fundus photographs, we find that the human retinal blood vessels have a self-similar structure with a fractal dimension D ≈ 1.7. Since this value of D is the same as the value found for a diffusion limited growth process, our result supports the hypothesis that diffusion is the fundamental process in the formation of human retinal vessel patterns.