Mathematical modeling of bone in-growth into undegradable porous periodic scaffolds under mechanical stimulus

Undegradable scaffolds, as a key element in bone tissue engineering, prevail in the present clinical applications, and the bone in-growth into such scaffolds under mechanical stimulus is an important issue to evaluate the bone-repair effect. This work aims to develop a mathematical framework to investigate the effect of mechanical stimulus on the bone in-growth into undegradable scaffolds. First, the osteoclast and osteoblast activities were coupled by their autocrine and paracrine effects. Second, the mechanical stimulus was empirically incorporated into the coupling cell activities on the basis of experimental observations. Third, the effect of mechanical stimulus including intensity and duration on the bone in-growth process was numerically studied; moreover, the homeostasis of scaffold–bone system under the mechanical stimulus was also treated. The results showed that the numbers of osteoblasts and osteoclasts in the scaffold–bone system tended to constants representing the system homeostasis. Both the mechanical intensity and duration optimized the final bone formation. The numerical results of the bone formation were comparable to the experimental results in rats. The findings from this modeling study could be used to explain many physiological phenomena and clinical observations. The developed model integrates both cell and tissue scales, which can be used as a platform to investigate bone remodeling under mechanical stimulus.