Fractal dimension of the bone marrow in metastatic lesions

We previously reported that the distribution of the cells in normal bone marrow is fractal and self-similar. The purpose of this study was to determine whether the same is true in metastatic tumors. Thirty-two bone marrow biopsy sections (3 to 5 microm thick) of 28 patients were used to measure the fractal dimensions of the metastatic tumor cells' distribution. Microscopic images were obtained and were used for the fractal measurements. In the two-dimensional images, the fractal dimensions were 1.98 +/- 0.02 (95% +/- 5% cellularity), suggesting a compact nonfractal structure. The dimensions, however, were 1.72 +/- 0.1 (56% +/- 11% cellularity) for the normal components, with a P-value of <.0001 that is in agreement with our previous study. These results suggest that loss of the fractal structure in the metastatic lesions may be attributable to loss or suppression of the regulatory mechanisms maintaining the fractal morphogenesis of the bone marrow. This report provides a novel objective approach in the study of pathophysiology of the bone marrow disorders.