APPLICATION OF FRACTAL GEOMETRY TECHNIQUES TO THE STUDY OF TRABECULARBONE

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 app ear statistically similar over a range of scales. Typically fractals d o not have smooth surfaces, but instead have rather complex structures with highly convoluted surfaces. Associated with every fractal is a c haracteristic dimension, called the fractal dimension. In this study, techniques of fractal analysis were used to characterize the trabecula r bone matrix on digital images acquired by quantitative computed tomo graphy (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 trab ecular-bone and bone marrow interface, and a box-counting algorithm wa s used to estimate the fractal dimension of the trabecular boundary. U sing this technique for fractal objects, if the boundary being analyze d is covered with boxes of differing sizes, epsilon, then the number o f boxes N required to cover the surface increases indefinitely accordi ng to the relation N = epsilon(-D) where D is the fractal dimension. U sing this relationship in a preliminary study on five specimens we hav e 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-depend ent factors that affect the estimated fractal dimension are also discu ssed.