Application of fractal geometry to pathological morphology.

分形几何处理的是没有在简单的欧几里德几何框架内处理的不规则和支离破碎的图案。“分形图案”通常用术语ti-自相似性“或”标度不变“来描述，并且用非整数分形维来表征，它是图案不规则性的量度。由于医学研究中最重要的领域是发展定量形态计量学并将其应用于形态诊断，因此分形概念在这一领域有望具有巨大的潜力。我们开发了用盒法和质量半径法测定分维的计算机程序。二维分布在大脑皮质表面的动脉构筑具有分形性，并具有两种不同的分维值(不同尺度上的1.78和1.31)。两个分形区的交点比较清晰，确定为0.14 mm。人类视网膜的血管模式也用两个分形维来表征。这些发现表明，在量化真实生物系统中分支结构的不规则性和/或碎裂时，应该指定对象的分维所在的标尺长度，以及分维。此外，还发现分维的大小在一定程度上取决于所用的方法。

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.