FRACTAL DIMENSION AND ARCHITECTURE OF TRABECULAR BONE

The fractal dimension of trabecular bones was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. Th e 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 f or the Quantimet 520 performed the fractal analysis. The fractal dimen sion was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 mu-m in length. The mean fractal dimension for the 25 subjects was 1.195 +/- 0.064 and shows that in Euclidean terms the sur face 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 surfa ce/total volume (BS/TV) (mm(2)mm(3))=1.90 +/- 0.51, trabecular thickne ss (Tb.Tb)(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. Pearson' correlation coefficients showed a statistically significant relations hip between the fractal dimension and all the histomorphometric parame ters, with BV/TV (r=0.85, P<0.0001), BS/TV (r=0.74, P<0.001), 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 wit hin the dimensions of a structural unit for trabecular bone. Therefore , the fractal dimension of trabecular bone provides a measure which do es not rely on Euclidean descriptors in order to describe a complex ge ometry.