Correlation between bone density and fractal dimension: A pilot study

Fractal analysis is a mathematical method used to describe the internal architecture of complex structures, such as the bone tissue. The aim of this study was to determine whether fractal dimension (FD) is able to distinguish between different bone densities (BD), assessed histomorphometrically, and whether there is a linear dependence between the FD and BD in order to support the use of FD as a supplementary non-invasive method for BD measurement. Microscopic photographs of bone specimens stained with acid fuchsin and toluidine blue obtained during block biopsies from nine segments of bovine ribs were used. A total of 42 regions of interest (ROI) were cut off from the original photo, converted into a bitmap and binarized. The evaluation of FD was carried out using the box counting method. Comparison of FD values in the four different densities bone sites (D1-D4) was made by means of Kruskal–Wallis test followed by Dunn’s multiple comparison test. The linear dependence between the two variables (FD and BD) was investigated calculating the Pearson’s r test correlation coefficient, which was considered significant when P <.05. The more the bone was compact, the higher were FD values. A strong positive correlation between BD evaluated by histomorphometry and FD (R: 0.9651), p-value <.00001 was found. The increase in the values of the FD strongly correlated with the increase of the percentage of the bone trabeculae observed in the histological slides. This pilot study demonstrates that FD might be able to distinguish different densities in bone sites and that there is a linear correlation between BD and FD on histological samples. Future studies will be addressed at evaluating whether this data can be confirmed on a larger samples size and on radiographic images. This will be useful for the early and non-invasive detection of structural changes in the trabecular bone pattern during healing, inflammatory processes and pathologies associated to bone breakdown.