Majumdar S, Weinstein R S, Prasad R R
Department of Radiology, University of California, San Francisco 94143.
Med Phys. 1993 Nov-Dec;20(6):1611-9. doi: 10.1118/1.596948.
It is well recognized that both trabecular bone density and structure affect the overall bone quality and strength. In this study the aim is to quantify variations in the structural network of trabeculae using the concepts of fractal geometry. Fractal objects are objects that appear statistically similar over a range of scales. Typically fractals do not have smooth surfaces, but instead have rather complex structures with highly convoluted surfaces. Associated with every fractal is a characteristic dimension, called the fractal dimension. In this study, techniques of fractal analysis were used to characterize the trabecular bone matrix on digital images acquired by quantitative computed tomography (QCT) of dried excised human vertebral bodies (density ranging from 76-220 mg/cc) and photomicrography of transiliac crest biopsies. An automatic boundary tracking algorithm was used to identify the trabecular-bone and bone marrow interface, and a box-counting algorithm was used to estimate the fractal dimension of the trabecular boundary. Using this technique for fractal objects, if the boundary being analyzed is covered with boxes of differing sizes, epsilon, then the number of boxes N required to cover the surface increases indefinitely according to the relation N = epsilon-D, where D is the fractal dimension. Using this relationship in a preliminary study on five specimens we have found that the trabecular-bone boundary is fractal in nature. Using photomicrographs of iliac crest biopsies, it is found that the fractal dimension changes with the fractional trabecular bone content.(ABSTRACT TRUNCATED AT 250 WORDS)
众所周知，小梁骨密度和结构都会影响整体骨质量和强度。本研究的目的是利用分形几何概念量化小梁结构网络的变化。分形对象是在一系列尺度上呈现统计相似性的对象。通常，分形没有光滑表面，而是具有表面高度复杂的相当复杂的结构。与每个分形相关联的是一个特征维度，称为分形维数。在本研究中，分形分析技术被用于通过对干燥切除的人体椎体（密度范围为76 - 220毫克/立方厘米）进行定量计算机断层扫描（QCT）以及对髂嵴活检组织进行显微摄影所获取的数字图像上的小梁骨基质进行表征。使用自动边界跟踪算法识别小梁骨与骨髓的界面，并使用盒计数算法估计小梁边界的分形维数。对于分形对象使用此技术，如果被分析的边界用不同大小的盒子（ε）覆盖，那么覆盖该表面所需的盒子数量N会根据关系N = ε-D无限增加，其中D是分形维数。在对五个标本的初步研究中使用这种关系，我们发现小梁骨边界本质上是分形的。通过髂嵴活检组织的显微照片发现，分形维数随小梁骨含量分数而变化。（摘要截短于250字）
