Fractal dimension as a measure of altered trabecular bone in experimental inflammatory arthritis

Abstract

Our previous studies in experimental inflammatory arthritis (EIA) and in human rheumatoid arthritis demonstrated rapid remodeling with a 5-fold increase in bone resorption and bone formation. Normal condylar trabecular bone is typically anisotropic, with its orientation along lines of stress; rapid remodeling in a pathological state could disturb the usual order of trabeculae. This study assessed change in the structure of trabecular bone of the distal femoral epiphysis after induction of EIA, using a measure of "fractal dimension," which may be considered a quantitative description of the degree of irregularity of complex surfaces. Data was obtained from specimens in which EIA had been induced in the rabbit knee by 10 injections of carrageenan over 49 days. Photographic enlargements of embedded undecalcified cross-sections of the distal femur were digitized, and software written on a Sun workstation was used to define repeatable regions of interest (ROIs) in the images. The ROIs were subjected to fractal analysis by a power law method. The fractal dimension of the trabecular bone pattern within the ROI was estimated by fitting an equation of the form A (epsilon) = lambda epsilon (2-D) to the data. In this equation, A (epsilon) is the area of the "surface" formed by modeling the ROI data as a three-dimensional structure with the grey-level magnitude providing the third dimension, lambda is a scaling constant, epsilon is the size of the measuring "tool" used to measure the area, and D is the fractal dimension. A Mann-Whitney U-test applied to the average of the data from all ROIs showed that the two distributions of fractal dimension were significantly different (p < 0.005). There were only two overlaps between data points for arthritis (with these values higher) and normal groups (n = 11 for each group). Since Howship's lacunae were too small to be resolved in the system utilized, we consider the difference in fractal dimension to be primarily related to trabecular surface orientation, rather than to the increased number of asperities (resorptive foci) occurring due to increased turnover in bone affected by inflammatory arthritis. The results suggest that fractal dimension may be a useful tool for assessing the degree of structural damage to trabeculae in conditions similar to EIA.