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

Abstract

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 moduli, 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-finite element analysis with homogeneous material properties, while effective strain was the best predictor for micro-finite element 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 µm/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 4 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.

Combined physical and pharmaceutical anabolic osteoporosis therapies synergistically increase bone response and local mechanoregulation

“…To investigate if the investigated osteoporosis treatments influence Frost's mechanostat parameters, we calculated mean remodeling velocity curves according to Marques et al (14) for each treatment group (Figure 7 A-D). These curves show the net remodeling velocity for a given surface effective strain, where a negative remodeling velocity means net resorption and a positive value means net formation.…”

“…Mean conditional probabilities were calculated for all animals within one group and fitted with exponential functions. To compare parameters extracted from these functions, a bootstrapping approach was used by creating 2500 subsamples from each group (14,49), fitting the conditional probability functions to the mean curve of each subsample. For formation and resorption, the minimum probability, indicating the amount of non-targeted formation or resorption, were compared between groups.…”

“…(Re)modeling velocities and their mechanostat parameters were calculated according to Marques et al for each animal (14). As treatments altered the curve characteristics (Figure 7), Minimum and maximum remodeling velocity, as well as remodeling thresholds were extracted from the resulting curve.…”

“…As treatments altered the curve characteristics (Figure 7), Minimum and maximum remodeling velocity, as well as remodeling thresholds were extracted from the resulting curve. To enable statistical comparison of parameters derived from the curve fits, we used a bootstrapping approach creating 2500 subsamples from each group and fitting the extended hyperbolic function to the mean remodeling velocity curve of each subsample (14,49). In order to compare treatment effects, we subtracted each remodeling velocity curve with the control remodeling velocity curve for the VEH group.…”

“…Additionally, in vivo studies have shown the potential to increase the sensitivity of the bone's mechanoregulation mechanisms, thereby ensuring induced bone gain is more targeted to the mechanical need of the bone (14,15). Therefore, mechanical loading might have the capacity to improve the efficacy of pharmaceutical treatments in fracture risk reduction.…”