Mechano-Regulation of Trabecular Bone Adaptation Is Controlled by the Local in vivo Environment and Logarithmically Dependent on Loading Frequency

Abstract

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.

Keywords: bone adaptation; frequency dependency; in vivo micro-CT imaging; mechanical loading; micro-finite element analysis.

FIGURE 1

Relative changes of structural bone morphometric parameters in the trabecular compartment over the 4-week loading period as assessed by in vivo micro-CT. (A) Bone volume fraction (BV/TV), (B) trabecular thickness (Tb.Th), (C) trabecular number (Tb.N), and (D) trabecular spacing (Tb.Sp). (Data represent mean ± standard deviation (SD) for n = 5–8/group, p-values for interaction effect between group and time are shown as determined by linear mixed effects model). (E) The relative change from week 4 relative to baseline (BV/TV_week4/week0) (F) was fitted with a logarithmic regression line. (Data represent mean ± SD for n = 5–8/group, p-value for main effect of group determined by one-way ANOVA, ****p ≤ 0.0001 denotes significant difference between groups determined by post hoc Tukey’s multiple comparisons test).

FIGURE 2

Dynamic bone morphometric parameters in the trabecular compartment in the different loading groups as assessed by in vivo micro-CT. (A) Changes in the net (re)modeling rate shown as the difference between bone formation rate (BFR) and bone resorption rate (BRR) over the 4-week loading period. Overall difference between groups of (B) BFR and (C) BRR. (D) Mineralized surface (MS) and eroded surface (ES) over the 4-week loading period. Overall difference between groups of (E) MS and (F) ES. (G) Mineral apposition rate (MAR) and mineral resorption rate (MRR) over the 4-week loading period. Overall difference between groups of (H) MAR and (I) MRR. [Data represent mean ± SD for n = 5–8/group, p-values for interaction effect between group and time are shown as determined by linear mixed effects model (A,D,G), boxplots showing the differences between groups as determined by Tukey’s post hoc multiple comparisons test *p < 0.05, **p ≤ 0.01, ***p ≤ 0.001, ****p ≤ 0.0001 (B,C,E,F,H,I)].

FIGURE 3

Qualitative visualization linking bone (re)modeling sites (formation, quiescence, resorption) with the mechanical environments in vivo. (A) Overlay of time-lapsed micro-CT images showing sites of bone formation (orange), quiescence (gray) and resorption (purple). Corresponding map of the (B) strain energy density (SED) and (C) gradient thereof (▽SED) showing sites of higher (red) and lower (blue) SED/▽SED values obtained by micro-finite element (micro-FE) analysis.

FIGURE 4

Conditional probabilities connecting SED (left side) and SED gradient (▽SED, right side) with (re)modeling events. The plots show the exponential fitting functions for (A,B) bone formation (top row), (C,D) quiescence (middle row), and (E,F) resorption (bottom row) in all the loading groups averaged over all time points.

FIGURE 5

Area under the curve (AUC) values for the comparison of the modeling performance of SED and SED gradient. (A) Formation (orange), (B) quiescence (gray), and (C) resorption (purple) sites for the different loading groups comparing modeling performance of SED (solid bars) and SED gradient (▽SED, striped bars). (Boxplots for n = 5–8/group, ^∗p < 0.05, ^****p ≤ 0.0001 differences between groups determined by Tukey’s multiple comparisons test).