Characterization of Bifurcating Structures of Blood Vessels Using Fractal Dimensions

T. Matsuo¹, R. Okeda¹, M. Takahashi² and M. Funata²

¹Medical Research Institute, Tokyo Medical and Denial University, Bunkyo-ku, Tokyo 113, Japan
²Department of Ophthalmology, Tokyo Medical and Dental University, Bunkyo-ku, Tokyo 113, Japan

(Received May 23, 1990, Accepted July 18, 1990)

Keywords: Fractal, Bifurcation Pattern, Pial Artery, Retinal Vessel

Abstract. The box-counting method for determination of fractal dimensions was applied to the bifurcating structures of blood vessels distributed over the cortical surface of the brain and those of retinal vessels. These vascular patterns were demonstrated to be fractals characterized by two distinct fractal dimensions on different scales. The intersection point of the two fractal regions was found to be rather clear-cut. These findings suggest that when attempting to quantify the irregularity and/or fragmentation of bifurcation patterns in nature using fractal concepts, it is necessary to specify the range of scale over which the fractality will hold, as well as the fractal dimensionality.