细胞图像的分形与非分形分析：比较及其在神经元树突分支中的应用

Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization.

作者信息

Ristanović D, Nedeljkov V, Stefanović B D, Milosević N T, Grgurević M, Stulić V

机构信息

Department of Biophysics School of Medicine, University of Belgrade, Visegradska 26, 11000 Belgrade, Yugoslavia.

出版信息

Biol Cybern. 2002 Oct;87(4):278-88. doi: 10.1007/s00422-002-0342-1.

DOI:10.1007/s00422-002-0342-1

PMID:12386743

Abstract

Neurons of the rat spinal cord were stained using the Golgi impregnation method. Successfully impregnated neurons from laminae II, III, and VI were subjected to fractal and nonfractal analyses. Fractal analysis was performed using length-related techniques. Since an application of fractal methods to the analysis of dendrite arbor structures requires caution, we adopted as appropriate a nonfractal method proposing a generalized power-law model with two main nonfractal parameters: (i) the anfractuosity, characterizing the degree of dendritic deviation from straight lines; and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish between two sets of drawings where the fractal methods failed. We also redefine some basic concepts of fractal geometry, present the ruler-counting method, and propose a new definition of fractal dimension.

摘要

采用高尔基浸染法对大鼠脊髓神经元进行染色。对成功浸染的Ⅱ、Ⅲ和Ⅵ层神经元进行分形和非分形分析。分形分析采用与长度相关的技术。由于将分形方法应用于树突分支结构分析时需要谨慎，我们适当地采用了一种非分形方法，该方法提出了一个具有两个主要非分形参数的广义幂律模型：（i）曲折度，表征树突偏离直线的程度；（ii）树突分支总长度的估计值。曲折度能够区分分形方法无法区分的两组图形。我们还重新定义了分形几何的一些基本概念，介绍了标尺计数法，并提出了分形维数的新定义。