On the fractal nature of trabecular structure

Fractal analysis has recently been suggested [Med. Phys. 20, 1611-1619 (1993)] as a means to characterize the structure of cancellous bone by measuring the fractal dimension using a box counting algorithm. This work re-examines the possible fractal nature of such structures on nuclear magnetic resonance (NMR) images of cancellous bone by estimating the trabecular boundary length as a function of box size under various experimental conditions. On high-resolution images (pixel sizes on the order of 50 microns) and signal-to-noise ratios of 30, the trabecular boundary turns out to be a smooth surface relative to the achievable resolution and is thus nonfractal. The fractal dimension of the trabecular structure is undefined and can vary significantly as a function of image signal-to-noise ratio. The present work further indicates the "apparent" fractal dimension obtained by box counting to be a reflection of marrow pore size. In conclusion, the results indicate that, at the currently achievable resolution, the box counting algorithm is not suitable for fractal analysis on images of cancellous bone and that the fractal appearance of the trabecular network reported previously is artifactual.