Morphogenesis of the bone marrow: fractal structures and diffusion- limited growth

Bone marrow (BM) provides a particular spatial organization that allows interaction between its various components. Characterization of the spatial patterns in the BM and understanding the mechanisms that give rise to them may play a role in better understanding of the BM pathologic processes. Morphometric analyses were performed in BM biopsy samples from 30 patients (16 men and 14 women) with an average age of 46 years, ranging from 17 to 77 years. The biopsies were obtained during the course of patient care to rule out BM involvement in a variety of hematologic disorders before or after therapy. Three different, but structurally interrelated, parameters were measured: (A) cellular area, (B) nuclear area, and (C) cell numbers. All three methods, in all cases, showed that the spatial structure of the BM is fractal. The average values of the fractal dimensions (Df) were 1.7 +/- 0.08, 1.64 +/- 0.1, and 1.69 +/- 0.04 for categories A, B, and C, respectively. The overall value of Df for the cellularity in the range of 40% to 60% was about 1.67 +/- 0.09. Fractal dimensions of 1.6 to 1.7 represent configurations that correspond to two-dimensional diffusion limited aggregation structures, suggesting that the structural configuration of hematopoietic cells is dependent on the diffusion of regulatory cytokines in the BM.