APPLICATION OF FRACTAL GEOMETRY TECHNIQUES TO THE STUDY OF TRABECULAR BONE

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. These results suggest that fractal analysis may be useful in distinguishing osteoporotic bone structure from normal. Analysis and technique-dependent factors that affect the estimated fractal dimension are also discussed.