Fractal properties of subchondral cancellous bone in severe osteoarthritis of the hip

Primary osteoarthritis of the hip results in changes to the architecture of subchondral cancellous bone. These changes in architecture occur through the action of osteoclasts and osteoblasts in selectively removing and adding bone. The quantitative description of the bone architecture helps in understanding the etiology of primary osteoarthritis. Fractal analysis is a method for describing complex shapes, which is expressed numerically as the fractal dimension. A box counting method was used, where the perimeter of binary profiles of cancellous bone samples was measured for different box sizes. The fractal dimension was the absolute value of the slope of the straight line segments from the plot of the log number of boxes versus the log box size. Cancellous bone samples from two subchondral regions, superior and inferomedial, to the fovea were analyzed from primary severe osteoarthritic specimens taken following total hip replacement surgery (n = 19, aged 51-80 years) and autopsy controls (n = 25, aged 18-90 years). There were three straight line segments identified on the log-log plot, for each subject, indicating a fractal dimension over three different ranges of scale. The results show that in the superior region there is a highly significant difference between the groups (p < 0.0001) for fractal 1 and pivot point 2. The histomorphometry shows significant differences for bone volume/total volume, bone surface/total volume, trabecular separation, and osteoid surface/total volume between groups. In the inferomedial region fractal 1 and fractal 2 are significantly different. For the histomorphometry, trabecular thickness and eroded surface/total volume are significantly different between the groups. The pivot points, i.e., the box size at which the fractal dimension changes, were of similar magnitude to the trabecular thickness and trabecular separation. These data suggest that the fractal geometry analysis of cancellous bone identifies architectural features not easily recognized by conventional bone histomorphometry. The fractal dimension is a descriptor of bone structure which simplifies the description of a complex structure and enables changes in cancellous bone architecture, due to disease, to be identified.