Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.