Application of fractal geometry to pathological morphology.

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Fractal geometry deals with irregular and fragmented patterns which have not been treated in the framework of the straightforward Euclidean geometry. The "fractal patterns" are usually described using the terms ti self-similarity" or "scale-invariance" and are characterized by a non-integer fractal dimensionality, which is a measure of irregularity of patterns. Since the most important fields of medical research is to develop quantitative morphometery and to apply it for morphological diagnosis, fractal concepts are expected to have enormous potential in this area.In this study, we analyzed bifurcation patterns of vessels in the brain and the human retina on the basis of fractal geometry. We developed computer programs for ttie determination of fractal dimensions using the box-counting method and the mass-radius method. The arterial architecture distributed two-dimensionally over the cortical surface of the brain was revealed to be fractal and, characterized by two different fractal dimensions(1.78 and 1.31 on different scales. The intersection point of the two fractal zones was found to be rather clear-cut, and determined to be 0.14 mm. The vascular pattern of the human retina was also characterized by two fractal dimensions. In addition, It was possible to quantify the difference in retinal vessel patterns due to disease using fractal dimensionality.These findings suggest that in quantifying the irregularity and/or fragmentation of bifurcating structures ill real biological systems, the scale-lengths in which the fractal dimensions of the object hold should be specified, as well as the fractal dimensionality. In addition, the values of fractal dimension were found to be to some extent dependent on the method used.