FRACTAL DIMENSION AS A MEASURE OF ALTERED TRABECULAR BONE IN EXPERIMENTAL INFLAMMATORY ARTHRITIS

Our previous studies in experimental inflammatory arthritis (EIA) and in human rheumatoid arthritis demonstrated rapid remodeling with a 5-f old increase in bone resorption and bone formation. Normal condylar tr abecular bone is typically anisotropic, dth its orientation along line s of stress; rapid remodeling in a pathological state could disturb th e usual order of trabeculae. This study assessed change in the structu re of trabecular bone of the distal femoral epiphysis after induction of EIA, using a measure of ''fractal dimension,'' which may be conside red a quantitative description of the degree of irregularity of comple x surfaces. Data was obtained from specimens in which EIA had been ind uced 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 worksta tion was used to define repeatable regions of interest (ROIs) in the i mages. The ROIs were subjected to fractal analysis by a power law meth od. The fractal dimension of the trabecular bone pattern within the RO I was estimated by fitting an equation of the formA(epsilon) = lambda epsilon((2-D)) to the data. In this equation, A(epsilon) is the area o f the ''surface'' formed by modeling the ROI data as a three-dimension al structure with the grey-level magnitude providing the third dimensi on, 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 s howed that the two distributions of fractal dimension were significant ly different (p < 0.005), There were only two overlaps between data po ints for arthritis (with these values higher) and normal groups (n = 1 1 for each group). Since Howship's lacunae were too small to be resolv ed in the system utilized, we consider the difference in fractal dimen sion to be primarily related to trabecular surface orientation, rather than to the increased number of asperities (resorptive foci) occurrin g 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.