An approach to quantifying bone overloading and hypertrophy with applications to multiple experimental studies

Many studies have investigated mechanically induced bone formation in mice and rats by applying loads to the long bones, and measuring changes in periosteal cortical bone apposition rates. However, the results are difficult to compare among each other because the loading schemes are generally different. The purpose of the present study was to develop a theoretical framework for evaluating the mechanical stimulus based on the bone daily strain stimulus, which is a function of loading cycles and bone strains. The daily strain stimulus would act as a single unifying parameter for directly comparing data from existing in vivo experiments, and is applied here to twenty previous rat and mouse studies. To calculate the daily strain stimulus, we determined the periosteal daily strain stimulus necessary for bone maintenance (xi(peri,0)) and the strain-cycle weighting exponent (m). In the first approach, we applied data from Rubin and Lanyon's bone maintenance studies. We calculated xi(peri,0) to be 2793 microstrain/day, and m to be 4.5. In the second approach, we used Fritton et al. 's strain gage recordings to calculate xi(peri,0) to be 1496 microstrain/day, and used an m value of 11.88, equal to human bone compressive fatigue properties. Fatigue data provided physiological relevance, and was useful for applying an established remodeling theory to in vivo studies. For both approaches, xi(peri,0) was below the fracture level. We then analyzed the applied strains, cycles, and periosteal bone apposition rates from the previous studies. The range of daily strain stimuli calculated using the first approach was much larger than the range using the second approach (2793-17312 microstrain/day compared to 1496-7681 microstrain/day). None of the studies applied a daily strain stimulus above the complete fatigue failure level, but some studies applied loading that could result in major fatigue microdamage. Bone apposition rates generally increased with increasing daily strain stimulus, which was consistent with previous theoretical models. The results suggest that the daily strain stimulus may be a reasonable first approximation for predicting bone apposition rates in a consistent manner. The use of the daily strain stimulus may be helpful for improving the design of future bone loading studies.