<title>Fractal patterns in the human retina and their physiological correlates</title>

Abstract

The biological mechanism for the formation of retinal vessel patterns in the developing human eye is unknown even though it is a question of 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 rate-limiting step in the formation of the vessel pattern is a diffusion process. In order to analyze this hypothesis the fractal dimension of the retinal blood vessel patterns was determined. Several methods were used to calculate the fractal dimension. Red-free fundus images of normal humans were traced and two methods of analysis were used: the massradius relation and the scaling relation of the two-point densitydensity correlation. In addition the vessel patterns were digitized using a digital image processing system and the number of pixels corresponding to the retinal vessels were determined within circles of various diameters. The slope of the log of the size of the circle versus the log of the number of voxels yielded the fractal dimension. All three methods applied to retinal patterns derived from 15 different normal humans (age 14-65) showed that the human retinal blood vessels have a self-similar structure with a fractal dimension of about 1 . 7. This is the same fractal dimension found for