Mechanostat parameters estimated from time-lapsed in vivo micro-computed tomography data of mechanically driven bone adaptation are logarithmically dependent on loading frequency

Mechanical loading is a key factor governing bone adaptation. Both preclinical and clinical studies have demonstrated its effects on bone tissue, which were also notably predicted in the mechanostat theory. Indeed, existing methods to quantify bone mechanoregulation have successfully associated the frequency of (re)modeling events with local mechanical signals, combining time-lapsed in vivo micro-computed tomography (micro-CT) imaging and micro-finite element (micro-FE) analysis. However, a correlation between the local surface velocity of (re)modeling events and mechanical signals has not been shown. As many degenerative bone diseases have also been linked to impaired bone (re)modeling, this relationship could provide an advantage in detecting the effects of such conditions and advance our understanding of the underlying mechanisms. Therefore, in this study, we introduce a novel method to estimate (re)modeling velocity curves from time-lapsed in vivo mouse caudal vertebrae data under static and cyclic mechanical loading. These curves can be fitted with piecewise linear functions as proposed in the mechanostat theory. Accordingly, new (re)modeling parameters can be derived from such data, including formation saturation levels, resorption velocity modulus, and (re)modeling thresholds. Our results revealed that the norm of the gradient of strain energy density yielded the highest accuracy in quantifying mechanoregulation data using micro-FE analysis with homogeneous material properties, while effective strain was the best predictor for micro-FE analysis with heterogeneous material properties. Furthermore, (re)modeling velocity curves could be accurately described with piecewise linear and hyperbola functions (root mean square error below 0.2 {micro}m/day for weekly analysis), and several (re)modeling parameters determined from these curves followed a logarithmic relationship with loading frequency. Crucially, (re)modeling velocity curves and derived parameters could detect differences in mechanically driven bone adaptation, which complemented previous results showing a logarithmic relationship between loading frequency and net change in bone volume fraction over four weeks. Together, we expect this data to support the calibration of in silico models of bone adaptation and the characterization of the effects of mechanical loading and pharmaceutical treatment interventions in vivo.