Cb. Caldwell et al., FRACTAL DIMENSION AS A MEASURE OF ALTERED TRABECULAR BONE IN EXPERIMENTAL INFLAMMATORY ARTHRITIS, Journal of bone and mineral research, 13(6), 1998, pp. 978-985
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.