Issues of threshold selection when determining the fractal dimension in HRCT slices of lumbar vertebrae

The box counting dimension is a frequently applied tool for the classification of trabecular bone structure. The algorithm requires a binarization of the gray value data, for example that acquired by high resolution CT (HRCT). We recently proposed a method to eliminate bone mineral density (BMD) by applying a linear normalization scheme. Further consideration has shown that full BMD independence has not been achieved, and the structural parameter proposed was therefore difficult to interpret. In this study we present an alternative approach to obtain a structural parameter that is independent of BMD. HRCT volume data was acquired on 21 lumbar vertebrae from five cadavers. In the segmented spongiosa, thresholding was based on different quantiles of the gray value histogram, yielding invariance over linear and non-linear transformations. Thresholding at high gray value levels (80% quantile) shows the highest level of significance when discriminating between osteoporotic and non-osteoporotic cases. As an addition to the measurement of BMD alone, the determination of structural properties allows an improvement of the assessment of the individual fracture risk.