Morphogenesis of the bone marrow: fractal structures and diffusion- limited
growth
F Naeim, F Moatamed and M Sahimi
Hematopathology Laboratories, Department of Pathology, UCLA Medical Center,
Los Angeles, CA 90024, USA.
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.
Volume 87,
Issue 12,
pp. 5027-5031,
06/15/1996
Copyright © 1996 by The American Society of Hematology
