Resonance in the mouse tibia as a predictor of frequencies and locations of loading-induced bone formation

To enhance new bone formation for the treating of patients with osteopenia and osteoporosis, various mechanical loading regimens have been developed. Although a wide spectrum of loading frequencies is proposed in those regimens, a potential linkage between loading frequencies and locations of loading-induced bone formation is not well understood. In this study, we addressed a question: Does mechanical resonance play a role in frequency-dependent bone formation? If so, can the locations of enhanced bone formation be predicted through the modes of vibration? Our hypothesis is that mechanical loads applied at a frequency near the resonant frequencies enhance bone formation, specifically in areas that experience high principal strains. To test the hypothesis, we conducted axial tibia loading using low, medium, or high frequency to the mouse tibia, as well as finite element analysis. The experimental data demonstrated dependence of the maximum bone formation on location and frequency of loading. Samples loaded with the low-frequency waveform exhibited peak enhancement of bone formation in the proximal tibia, while the high-frequency waveform offered the greatest enhancement in the midshaft and distal sections. Furthermore, the observed dependence on loading frequencies was correlated to the principal strains in the first five resonance modes at 8.0-42.9 Hz. Collectively, the results suggest that resonance is a contributor to the frequencies and locations of maximum bone formation. Further investigation of the observed effects of resonance may lead to the prescribing of personalized mechanical loading treatments.