A Model of Skeletal Remodeling Should (but Does Not Currently) Include Mechanical Feedback

Authors


To the Editor:

Dr. Reeve correctly emphasizes the importance of mechanical forces for bone adaptation and maintenance. We do not deny this in our article, and we certainly do not think that a mechanical strain-related feedback loop should be discarded as an important mechanism in bone biology.

There is far too much evidence that shows that mechanical loading does affect the skeleton. For example, the stiffness of cancellous bone is higher in the main load-bearing direction than in transversal directions; bedrest and space travel result in bone loss, and extra loading of bone in animal experiments results in bone apposition. Therefore, we agree that to really mimic bone remodeling in computer models, mechanical feedback should be included. This is, however, not straightforward. It would require a lot of computing time, and because the exact mechanisms of the strain-sensitivity in bone tissue are not known, we have not yet investigated the effect of mechanical feedback in our model. We decided to investigate the effect of random remodeling first.

The most important differences between Dr. Reeve's model and ours(1) are (a) our model is three-dimensional (3D), representing the trabecular architecture, whereas Dr. Reeve's is two-dimensional with a certain trabecular thickness distribution and (b) in Dr. Reeve's model, fenestrated trabeculae were completely removed, whereas in our model the remainders of fenestrated trabeculae were still connected to the main structure and were not removed. In a way, our model is much simpler than Dr. Reeve's. Because we start with a realistic 3D architecture from computed tomography (CT) scans, we can just make resorption cavities and refill these later to simulate remodeling. The resorption cavities are not refilled completely to simulate the formation deficit. No further assumptions are needed in our model. Thin trabeculae were only removed relatively fast when they were fenestrated twice. This resulted in a loose fragment, which was removed. Of course, this happened more in thin than in thick trabeculae.

Because the remainders of fenestrated trabeculae were not removed from our model, they would still be taken into account in a determination of the trabecular thickness. Therefore, a slow decrease in thickness, as seen by Wakamatsu and Sissons,(2) and shown in 3D by Ding et al,(3) will occur in our model. We did not quantify this, because we did not have the software for determining 3D trabecular thickness at the time of the study.

In Dr. Reeve's model, he found that the fenestration of thin trabeculae resulted in an unrealistic increase of the trabecular thickness. To correct for this, he assumed that thin trabeculae were relatively highly loaded; for this reason, he increased the bone apposition on thin trabeculae. However, the strain in trabeculae depends on their location in the 3D architecture and not on their thickness. Actually, we found that the strain in the thin transversal trabeculae is rather low under loads applied in the main load bearing direction.(4) Therefore, based on our calculations, we would not expect a higher osteoblastic activity on these trabeculae. However, it could be that the increased strain at the bottom of resorption cavities stops the osteoclastic resorption and thereby prevents complete fenestration of the trabeculae.

The results of our simulation model show that changes in architecture with aging could result from random remodeling. We started our simulations with 3D models of human vertebral trabecular bone specimens. The architectures of these specimens were anisotropic; the structures were already adapted to the normal daily loading and had a higher stiffness in the main load-bearing (superior-inferior, [SI]) direction. During the simulated random remodeling process, the anisotropy increased, because the thinner horizontal trabeculae had a higher chance of fenestration. This led to a larger decrease of the stiffness in the transversal than in the SI direction and thus to an increase in mechanical anisotropy, besides the slow decrease in bone mass also seen in vivo. These results show that strain-regulated remodeling is not necessary to induce changes in anisotropy and connectivity during remodeling.

Complete removal of the remaining struts in a 3D model is hardly possible; it is not well-defined where a trabecula ends and where the node that connects trabeculae begins. The reason why fenestrated trabeculae are assumed to be removed relatively fast in vivo is that the remainders of the trabecula are not loaded anymore.(5) The only proper way to remove these remainders in a 3D computer model would be to implement a mechanical feedback loop where resorption of unloaded tissue is assumed. The remainders, which do not carry loads anymore, will then be removed rapidly from the model.

Mechanical feedback could be implemented in a lot of ways; for example, bone apposition could be driven by a local stimulus, resorption could be regulated by a local stimulus, or both resorption and apposition could be regulated by local stimuli. The local stimulus could be strain, stress, strain-energy density, or fluid flow. To incorporate mechanical feedback in our model, we need information about the stimulus itself, whether it is stress, strain, or something else, showing which cells react to the stimulus and how these cells react. This information is not yet available.

On the other hand, simulation models can help to elucidate these issues(6); hypothesized mechanisms can be simulated and when the results do not resemble in vivo results of remodeling (e.g., changes in architecture with aging), the simulated mechanism can be rejected, as Dr. Reeve did in his study.

In conclusion, although our simulation model without mechanical feedback yielded results similar to the effects of bone remodeling in vivo, we do think that mechanical feedback does influence the bone remodeling process. The increased strain at the bottom of resorption cavities might protect trabeculae against fenestration. While there is still a lot to be investigated in the reaction of bone cells to mechanical stimuli, simulation models like Dr. Reeve's and ours could distinguish between feasible and unfeasible mechanisms. In the meantime, we will consider implementing strain-sensitive regulation of bone turnover in our simulation model.

Ancillary