Abstract
The cancellous bone adjacent to major load-bearing joints such as the hip and knee has complex architecture. The loading patterns across these joints influence the architecture of the cancellous bone, which varies according to the magnitude and direction of these forces. Articular lesions are associated with alterations in the loading patterns and hence change to the cancellous architecture. The fractal dimension, as a numerical descriptor of complex shapes, enables these changes to be quantitated.
The fractal analysis was performed by a box counting method. The perimeter of binary profiles of cancellous bone samples was measured for different box sizes. The fractal dimension is 1-D (where D is the slope of the straight-line segments from the plot of log of perimeter versus of log box size). Samples of cancellous bone were taken at autopsy from three subchondral regions, superior to the fovea in the femoral head (n=56) and the tibial (n=25) and femoral (n=25) condyles of the knee. 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. Fractal 1 describes the complexity of bone surface detail influenced by osteoclast and osteoblast activity, fractal 2 describes the shape or form of individual trabeculae and fractal 3 describes the overall spatial complexity of the cancellous structure.
The results show that for fractal 1, all three regions are the same. For fractal 2, the femoral head is greater than the condyles (1.40±0.07 versus 1.36±0.05 and 1.36±0.05) and for fractal 3, the femoral head is significantly greater than the condyles (1.76±0.06 versus 1.73±0.04 and 1.70±0.05).
These data show that cancellous bone architecture differs between skeletal sites. In particular, the fine surface detail influenced by bone cell activity and described by fractal 1 is the same in each region, while the shape of individual trabeculae as described by fractal 2 is more complex in the femoral head. The overall spatial complexity of the cancellous structure as described by fractal 3 is the same in each condyle of the knee while in the femoral head it is significantly greater. The fractal dimension, as a descriptor of complexity, enables the effect of differences in the mechanical micro-environment on cancellous bone architecture to be quantified so that pathology affecting these regions can be studied.
The abstracts were prepared by Professor Jegan Krishnan. Correspondence should be addressed to him at the Flinders Medical Centre, Bedford Park 5047, Australia.
