Fazzalari N L, Parkinson I H
Division of Tissue Pathology, Institute of Medical and Veterinary Science, Adelaide, Australia.
J Pathol. 1996 Jan;178(1):100-5. doi: 10.1002/(SICI)1096-9896(199601)178:1<100::AID-PATH429>3.0.CO;2-K.
The fractal dimension of trabecular bone was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. The average age was 67.7 years. A binary profile of the trabecular bone in the biopsy was obtained from a digitized image. A program written for the Quantimet 520 performed the fractal analysis. The fractal dimension was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 microns in length. The mean fractal dimension for the 25 subjects was 1.195 +/- 0.064 and shows that in Euclidean terms the surface extent of trabecular bone is indeterminate. The Quantimet 520 was also used to perform bone histomorphometric measurements. These were bone volume/total volume (BV/TV) (per cent) = 11.05 +/- 4.38, bone surface/total volume (BS/TV) (mm2/mm3) = 1.90 +/- 0.51, trabecular thickness (Tb.Th) (mm) = 0.12 +/- 0.03, trabecular spacing (Tb.Sp) (mm) = 1.03 +/- 0.36, and trabecular number (Tb.N) (number/mm) = 0.95 +/- 0.25. Pearsons' correlation coefficients showed a statistically significant relationship between the fractal dimension and all the histomorphometric parameters, with BV/TV (r = 0.85, P < 0.0001), BS/TV (r = 0.74, P < 0.0001), Tb.Th (r = 0.50, P < 0.02), Tb.Sp (r = -0.81, P < 0.0001), and Tb.N (r = 0.76, P < 0.0001). This method for calculating fractal dimension shows that trabecular bone exhibits fractal properties over a defined box size, which is within the dimensions of a structural unit for trabecular bone. Therefore, the fractal dimension of trabecular bone provides a measure which does not rely on Euclidean descriptors in order to describe a complex geometry.
对25名接受髋关节置换术患者股骨近端活检组织的小梁骨分形维数进行了测定。平均年龄为67.7岁。活检组织中小梁骨的二元轮廓由数字化图像获得。为Quantimet 520编写的程序进行了分形分析。使用边长从65至1000微米的盒子计算每个标本的分形维数。25名受试者的平均分形维数为1.195±0.064，这表明从欧几里得几何学角度来看，小梁骨的表面范围是不确定的。Quantimet 520还用于进行骨组织形态计量学测量。这些测量结果为：骨体积/总体积（BV/TV）（百分比）=11.05±4.38，骨表面积/总体积（BS/TV）（mm2/mm3）=1.90±0.51，小梁厚度（Tb.Th）（mm）=0.12±0.03，小梁间距（Tb.Sp）（mm）=1.03±0.36，以及小梁数量（Tb.N）（个/mm）=0.95±0.25。皮尔逊相关系数表明，分形维数与所有组织形态计量学参数之间存在统计学显著关系，BV/TV（r = 0.85，P < 0.0001），BS/TV（r = 0.74，P < 0.0001），Tb.Th（r = 0.50，P < 0.02），Tb.Sp（r = -0.81，P < 0.0001），以及Tb.N（r = 0.76，P < 0.0001）。这种计算分形维数的方法表明，小梁骨在定义的盒子大小范围内呈现分形特性，该范围在小梁骨结构单元的尺寸之内。因此，小梁骨的分形维数提供了一种不依赖欧几里得描述符来描述复杂几何形状的测量方法。
