Numerical modeling of oxygen distributions in cortical and cancellous bone: oxygen availability governs osteonal and trabecular dimensions

• Published in: American Journal of Physiology: Cell Physiology 2010-11, Vol.299 (5), p.C922-C929
• Main Authors: Zahm, Adam M, Bucaro, Michael A, Ayyaswamy, Portonovo S, Srinivas, Vickram, Shapiro, Irving M, Adams, Christopher S, Mukundakrishnan, Karthik
• Format: Article
• Language: English
• Subjects: Animals; Bone and Bones - metabolism; Bone and Bones - ultrastructure; Bones; Cells; Cellular biology; Growth, Differentiation, and Apoptosis; Haversian System - metabolism; Haversian System - ultrastructure; Humans; Models, Biological; Models, Theoretical; Oxygen; Oxygen - metabolism; Reaction kinetics
• ISSN: 0363-6143; 1522-1563
• DOI: 10.1152/ajpcell.00465.2009

Whereas recent work has demonstrated the role of oxygen tension in the regulation of skeletal cell function and viability, the microenvironmental oxemic status of bone cells remains unknown. In this study, we have employed the Krogh cylinder model of oxygen diffusion to predict the oxygen distribution profiles in cortical and cancellous bone. Under the assumption of saturation-type Michaelis-Menten kinetics, our numerical modeling has indicated that, under steady-state conditions, there would be oxygen gradients across mature osteons and trabeculae. In Haversian bone, the calculated oxygen tension decrement ranges from 15 to 60%. For trabecular bone, a much shallower gradient is predicted. We note that, in Haversian bone, the gradient is largely dependent on osteocyte oxygen utilization and tissue oxygen diffusivity; in trabecular bone, the gradient is dependent on oxygen utilization by cells lining the bone surface. The Krogh model also predicts dramatic differences in oxygen availability during bone development. Thus, during osteon formation, the modeling equations predict a steep oxygen gradient at the initial stage of development, with the gradient becoming lesser as osteonal layers are added. In contrast, during trabeculum formation, the oxygen gradient is steepest when the diameter of the trabeculum is maximal. Based on these results, it is concluded that significant oxygen gradients exist within cortical and cancellous bone and that the oxygen tension may regulate the physical dimensions of both osteons and bone trabeculae.