It is well-established that cyclic, but not static, mechanical loading has anabolic effects on bone. However, the function describing the relationship between the loading frequency and the amount of bone adaptation remains unclear. Using a combined experimental and computational approach, this study aimed to investigate whether trabecular bone mechano-regulation is controlled by mechanical signals in the local in vivo environment and dependent on loading frequency. Specifically, by combining in vivo micro-computed tomography (micro-CT) imaging with micro-finite element (micro-FE) analysis, we monitored the changes in microstructural as well as the mechanical in vivo environment [strain energy density (SED) and SED gradient] of mouse caudal vertebrae over 4 weeks of either cyclic loading at varying frequencies of 2, 5, or 10 Hz, respectively, or static loading. Higher values of SED and SED gradient on the local tissue level led to an increased probability of trabecular bone formation and a decreased probability of trabecular bone resorption. In all loading groups, the SED gradient was superior in the determination of local bone formation and resorption events as compared to SED. Cyclic loading induced positive net (re)modeling rates when compared to sham and static loading, mainly due to an increase in mineralizing surface and a decrease in eroded surface. Consequently, bone volume fraction increased over time in 2, 5, and 10 Hz (+15%, +21% and +24%, p ≤ 0.0001), while static loading led to a decrease in bone volume fraction (−9%, p ≤ 0.001). Furthermore, regression analysis revealed a logarithmic relationship between loading frequency and the net change in bone volume fraction over the 4 week observation period ( R 2 = 0.74). In conclusion, these results suggest that trabecular bone adaptation is regulated by mechanical signals in the local in vivo environment and furthermore, that mechano-regulation is logarithmically dependent on loading frequency with frequencies below a certain threshold having catabolic effects, and those above anabolic effects. This study thereby provides valuable insights toward a better understanding of the mechanical signals influencing trabecular bone formation and resorption in the local in vivo environment.

Bone healing and remodeling are mechanically driven processes. While the generalized response to mechanical stimulation in bone is well-understood, much less is known about the mechanobiology-regulating tissue-scale bone formation and resorption during the reparative and remodeling phases of fracture healing. In this study, we combined computational approaches in the form of finite element analysis and experimental approaches by using a loaded femoral defect model in mice to investigate the role of mechanical stimulation in the microenvironment of bone. Specifically, we used longitudinal micro-computed tomography to observe temporal changes in bone at different densities and micro-finite element analysis to map the mechanics of the microenvironment to tissue-scale formation, quiescence (no change in bone presence between time points), and resorption dynamics in the late reparative and remodeling phases (post bridging). Increasing levels of effective strain led to increasing conditional probability of bone formation, while decreasing levels of effective strain led to increasing probability of bone resorption. In addition, the analysis of mineralization dynamics showed both a temporal and effective strain level-dependent behavior. A logarithmic-like response was displayed, where the conditional probability of bone formation or resorption increased rapidly and plateaued or fell rapidly and plateaued as mechanical strain increased.

15It is well established that cyclic, but not static, mechanical loading has anabolic effects on bone. 16 However, the function describing the relationship between the loading frequency and the 17 amount of bone adaptation remains unclear. Using a combined experimental and computational 18 approach, this study aimed to investigate whether bone mechano-regulation is controlled by 19 mechanical signals in the local in vivo environment and dependent on loading frequency. 20Specifically, by combining in vivo micro-computed tomography (micro-CT) imaging with 21 micro-finite element (micro-FE) analysis, we monitored the changes in microstructural as well 22 of the mechanical signals influencing bone formation and resorption in the local in vivo 39 environment. 40 Keywords: 41Bone adaptation, mechanical loading, in vivo micro-CT imaging, frequency dependency 42