Relating osteon diameter to strain.

Osteon diameter is generally smaller in bone regions that experience larger strains. A mechanism relating osteon diameter to strain is as yet unknown. We propose that strain-induced osteocyte signals inhibit osteoclastic bone resorption. This mechanism was previously shown to produce load-aligned osteons in computer simulations. Now we find that it also predicts smaller osteon diameter for higher loads. Additionally, we find that our model predicts osteon development with two cutting cones, one moving up and one moving down the loading axis. Such 'double-ended osteons' were reported in literature as a common type of osteon development. Further, we find that a steep gradient in strain magnitude can result in an osteonal tunnel with continuous resorption along the less strained side, which corresponds to 'drifting osteons' reported in literature.

A unified theory for osteonal and hemi-osteonal remodeling.

The process of bone remodeling is carried out by 'basic multicellular units' of osteoclasts and osteoblasts. Osteoclasts excavate a resorption space that is subsequently filled with new bone by osteoblasts. In cortical bone osteoclasts dig tunnels through solid bone, in cancellous bone they dig trenches across the trabecular surface. Osteoblasts fill these tunnels and trenches, creating osteons and hemi-osteons, respectively. Both the osteons of cortical bone and the trabeculae of cancellous bone are aligned to the dominant loading direction, indicating that BMU's are mechanically regulated. How mechanical forces guide these cells is still uncertain. We hypothesize that strain-induced osteocyte signals inhibit osteoclast activity and stimulate osteoblast activity. This hypothesis was implemented in a finite element-based bone adaptation model, that was extended with a cell simulation model. This allowed us to examine tunneling and trenching by osteoclasts. We found that our simulations capture key features of BMU-based remodeling: (1) cortical BMU's create load-aligned osteons; (2) cancellous BMU's move across the surface of trabeculae instead of piercing them; (3) resorption-formation coupling occurs in response to strains around resorption sites; and (4) resorbing osteoclasts target nearby regions of osteocyte death, thus providing a mechanism for bone repair.

A 3-dimensional computer model to simulate trabecular bone metabolism.

Mechanical loading of trabecular bone affects the bone architecture. Bone mass is correlated to the magnitude of the external load and trabeculae are aligned to the loading direction. Physical exercise increases bone mass while disuse or microgravity decreases it. In previous work we have presented a mathematical model of bone metabolism that could explain the emergence, maintenance and adaptation of trabecular bone under influence of the load imposed, using a 2-dimensional computer model (Huiskes et al., Nature 404 (2000), 704-706). This model was based on hypothetical mathematical descriptions of bone formation by osteoblastic cells, and resorption by osteoclastic cells, both as governed by mechanical stimuli. In order to quantitatively compare the behavior of the proposed regulation mechanism to real trabecular bone metabolism we present a 3-dimensional computer simulation model. The first 3-dimensional simulation results show that the regulatory rules proposed earlier mimic trabecular bone metabolism in a robust way.