Fractal geometry as a means of studying trabecular bone structure

Cross-sectional quantitative computed tomography (QCT) images of dried excised vertebral bodies, (density ranging from 76-220 mg/cm/sup 3/), immersed in saline, in conjunction with fractal geometry methods were used to characterize the trabecular matrix. 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 /sup -D/, where D is the fractal dimension. Using this relationship, it was found that the trabecular bone boundary is a fractal of dimension ranging from 1.57 to 1.72. Analysis and technique-dependent factors that affect the estimated fractal dimensional are also discussed. The fractal dimension calculated depended on the range of epsilon values selected for the calculation of the dimension D, and for the same boundary the D varied from 1.58 to 1.81.<>