Floor M. Lambers

In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging

Bone is a living tissue able to adapt its structure to external influences such as altered mechanical loading. This adaptation process is governed by two distinct cell types: bone-forming cells called osteoblasts and bone-resorbing cells called osteoclasts. It is therefore of particular interest to have quantitative access to the outcomes of bone formation and resorption separately. This article presents a non-invasive three-dimensional technique to directly extract bone formation and resorption parameters from time-lapsed in vivo micro-computed tomography scans. This includes parameters such as Mineralizing Surface (MS), Mineral Apposition Rate (MAR), and Bone Formation Rate (BFR), which were defined in accordance to the current nomenclature of dynamic histomorphometry. Due to the time-lapsed and non-destructive nature of in vivo micro-computed tomography, not only formation but also resorption can now be assessed quantitatively and time-dependent parameters Eroded Surface (ES) as well as newly defined indices Mineral Resorption Rate (MRR) and Bone Resorption Rate (BRR) are introduced. For validation purposes, dynamic formation parameters were compared to the traditional quantitative measures of dynamic histomorphometry, where MAR correlated with R = 0.68 and MS with R = 0.78 (p < 0.05). Reproducibility was assessed in 8 samples that were scanned 5 times and errors ranged from 0.9% (MRR) to 6.6% (BRR). Furthermore, the new parameters were applied to a murine in vivo loading model. A comparison of directly extracted parameters between formation and resorption within each animal revealed that in the control group, i.e., during normal remodeling, MAR was significantly lower than MRR (p < 0.01), whereas MS compared to ES was significantly higher (p < 0.0001). This implies that normal remodeling seems to take place by many small formation packets and few but large resorption volumes. After 4 weeks of mechanical loading, newly extracted trabecular BFR and MS were significantly higher (p < 0.01) in the loading compared to the control group. At the same time, ES was significantly decreased (p < 0.01). This indicates that modeling induced by mechanical loading takes place primarily by increased area, not width of formation packets. With these results, we conclude that the non-invasive direct technique is well suited to extract dynamic bone morphometry parameters and eventually gain more insight into the processes of bone adaptation not only for formation but also resorption.

Local Mechanical Stimuli Regulate Bone Formation and Resorption in Mice at the Tissue Level

Bone is able to react to changing mechanical demands by adapting its internal microstructure through bone forming and resorbing cells. This process is called bone modeling and remodeling. It is evident that changes in mechanical demands at the organ level must be interpreted at the tissue level where bone (re)modeling takes place. Although assumed for a long time, the relationship between the locations of bone formation and resorption and the local mechanical environment is still under debate. The lack of suitable imaging modalities for measuring bone formation and resorption in vivo has made it difficult to assess the mechanoregulation of bone three-dimensionally by experiment. Using in vivo micro-computed tomography and high resolution finite element analysis in living mice, we show that bone formation most likely occurs at sites of high local mechanical strain (p<0.0001) and resorption at sites of low local mechanical strain (p<0.0001). Furthermore, the probability of bone resorption decreases exponentially with increasing mechanical stimulus (R2 = 0.99) whereas the probability of bone formation follows an exponential growth function to a maximum value (R2 = 0.99). Moreover, resorption is more strictly controlled than formation in loaded animals, and ovariectomy increases the amount of non-targeted resorption. Our experimental assessment of mechanoregulation at the tissue level does not show any evidence of a lazy zone and suggests that around 80% of all (re)modeling can be linked to the mechanical micro-environment. These findings disclose how mechanical stimuli at the tissue level contribute to the regulation of bone adaptation at the organ level.

Mouse tail vertebrae adapt to cyclic mechanical loading by increasing bone formation rate and decreasing bone resorption rate as shown by time-lapsed in vivo imaging of dynamic bone morphometry

It is known that mechanical loading leads to an increase in bone mass through a positive shift in the balance between bone formation and bone resorption. How the remodeling sites change over time as an effect of loading remains, however, to be clarified. The purpose of this paper was to investigate how bone formation and resorption sites are modulated by mechanical loading over time by using a new imaging technique that extracts three dimensional formation and resorption parameters from time-lapsed in vivo micro-computed tomography images. To induce load adaptation, the sixth caudal vertebra of C57BL/6 mice was cyclically loaded through pins in the adjacent vertebrae at either 8 N or 0 N (control) three times a week for 5 min (3000 cycles) over a total of 4 weeks. The results showed that mechanical loading significantly increased trabecular bone volume fraction by 20% (p<0.001) and cortical area fraction by 6% (p<0.001). The bone formation rate was on average 23% greater (p<0.001) and the bone resorption rate was on average 25% smaller (p<0.001) for the 8 N group than for the 0 N group. The increase in bone formation rate for the 8 N group was mostly an effect of a significantly increased surface of bone formation sites (on average 16%, p<0.001), while the thickness of bone formation packages was less affected (on average 5% greater, p<0.05). At the same time the surface of bone resorption sites was significantly reduced (on average 15%, p<0.001), while the depth of resorption pits remained the same. For the 8 N group, the strength of the whole bone increased significantly by 24% (p<0.001) over the loading period, while the strain energy density in the trabecular bone decreased significantly by 24% (p<0.001). In conclusion, mouse tail vertebrae adapt to mechanical loading by increasing the surface of formation sites and decreasing the surface of resorption sites, leading to an overall increase in bone strength. This new imaging technique will provide opportunities to investigate in vivo bone remodeling in the context of disease and treatment options, with the added value that both bone formation and bone resorption parameters can be nondestructively calculated over time.

Bone morphology allows estimation of loading history in a murine model of bone adaptation.

Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.

Comparison of bone loss induced by ovariectomy and neurectomy in rats analyzed by in vivo micro-CT

We hypothesized that osteoporosis due to estrogen deficiency progresses faster than due to disuse and that at the same amount of bone loss, disuse leads to less favorable bone structure and mechanical properties than estrogen deficiency. Adult rats were either ovariectomized (OVX) (n = 9) or neurectomized (NX) (n = 8). At week 0, 1, 2, 3, and 4, in vivo micro‐CT scans were made of the proximal tibia. Segmented CT‐scans at weeks 0 and 4 were used to build a 3D voxel‐based micro finite element model (FEM). Displacement in the longitudinal direction was prescribed at the proximal end leading to a compression step of 1%. The severe reduction in metaphyseal bone volume fraction was not significantly different between OVX and NX. Epiphyseal bone loss was less severe in both groups, and BV/TV was significantly lower after NX. Trabecular separation and degree of anisotropy in the metaphysis and connectivity and trabecular number in the epiphysis were significantly more deteriorated after NX. FEM‐derived stiffness decreased in both groups, but more after NX. Osteoporosis due to estrogen‐deficiency progressed overall at a rate similar to osteoporosis due to disuse. At the same amount of induced bone loss, disuse led to more deteriorated bone structure and mechanical properties than estrogen deficiency.

Strain-adaptive in silico modeling of bone adaptation — A computer simulation validated by in vivo micro-computed tomography data

Computational models are an invaluable tool to test different mechanobiological theories and, if validated properly, for predicting changes in individuals over time. Concise validation of in silico models, however, has been a bottleneck in the past due to a lack of appropriate reference data. Here, we present a strain-adaptive in silico algorithm which is validated by means of experimental in vivo loading data as well as by an in vivo ovariectomy experiment in the mouse. The maximum prediction error following four weeks of loading resulted in 2.4% in bone volume fraction (BV/TV) and 8.4% in other bone structural parameters. Bone formation and resorption rate did not differ significantly between experiment and simulation. The spatial distribution of formation and resorption sites matched in 55.4% of the surface voxels. Bone loss was simulated with a maximum prediction error of 12.1% in BV/TV and other bone morphometric indices, including a saturation level after a few weeks. Dynamic rates were more difficult to be accurately predicted, showing evidence for significant differences between simulation and experiment (p<0.05). The spatial agreement still amounted to 47.6%. In conclusion, we propose a computational model which was validated by means of experimental in vivo data. The predictive value of an in silico model may become of major importance if the computational model should be applied in clinical settings to predict bone changes due to disease and test the efficacy of potential pharmacological interventions.

In vivo loading increases mechanical properties of scaffold by affecting bone formation and bone resorption rates

A successful bone tissue engineering strategy entails producing bone-scaffold constructs with adequate mechanical properties. Apart from the mechanical properties of the scaffold itself, the forming bone inside the scaffold also adds to the strength of the construct. In this study, we investigated the role of in vivo cyclic loading on mechanical properties of a bone scaffold. We implanted PLA/β-TCP scaffolds in the distal femur of six rats, applied external cyclic loading on the right leg, and kept the left leg as a control. We monitored bone formation at 7 time points over 35 weeks using time-lapsed micro-computed tomography (CT) imaging. The images were then used to construct micro-finite element models of bone-scaffold constructs, with which we estimated the stiffness for each sample at all time points. We found that loading increased the stiffness by 60% at 35 weeks. The increase of stiffness was correlated to an increase in bone volume fraction of 18% in the loaded scaffold compared to control scaffold. These changes in volume fraction and related stiffness in the bone scaffold are regulated by two independent processes, bone formation and bone resorption. Using time-lapsed micro-CT imaging and a newly-developed longitudinal image registration technique, we observed that mechanical stimulation increases the bone formation rate during 4-10 weeks, and decreases the bone resorption rate during 9-18 weeks post-operatively. For the first time, we report that in vivo cyclic loading increases mechanical properties of the scaffold by increasing the bone formation rate and decreasing the bone resorption rate.

Trabecular bone adapts to long-term cyclic loading by increasing stiffness and normalization of dynamic morphometric rates.

Bone has the ability to adapt to external loading conditions. Especially the beneficial effect of short-term cyclic loading has been investigated in a number of in vivo animal studies. The aim of this study was to assess the long-term effect (>10 weeks) of cyclic mechanical loading on the bone microstructure, bone stiffness, and bone remodeling rates. Mice were subjected to cyclic mechanical loading at the sixth caudal vertebra with 8N or 0N (control) three times per week for a total period of 14 weeks. Structural bone parameters were determined from in vivo micro-computed tomography (micro-CT) scans performed at week 0, 4, 6, 8, 10, 12, and 14. Mechanical parameters were derived from micro-finite element analysis. Dynamic bone morphometry was calculated using registration of serial micro-CT scans. Bone volume fraction and trabecular thickness increased significantly more for the loaded group than for the control group (p = 0.006 and p = 0.002 respectively). The trabecular bone microstructure adapted to the load of 8N in approximately ten weeks, indicated by the trabecular bone volume fraction, which increased from 16.7% at 0 weeks to 21.6% at week 10 and only showed little change afterwards (bone volume fraction of 21.5% at 14 weeks). Similarly bone stiffness - (at the start of the experiment 649N/mm) - reached 846N/mm at 10 weeks in the loaded group and was maintained to the end of the experiment (850N/mm). At 4 weeks the bone formation rate was 32% greater and the bone resorption rate 22% less for 8N compared to 0N. This difference was significantly reduced as the bone adapted to 8N, with 8N remodeling rates returning to the values of the 0N group at approximately 10 weeks. Together these data suggest that once bone has adapted to a new loading state, the remodeling rates reduce gradually while maintaining bone volume fraction and stiffness.

Mineralization kinetics in murine trabecular bone quantified by time-lapsed in vivo micro-computed tomography

Trabecular bone is a highly dynamic tissue due to bone remodeling, mineralization and demineralization. The mineral content and its spatial heterogeneity are main contributors to bone quality. Using time-lapsed in vivo micro-computed tomography (micro-CT), it is now possible to resolve in three dimensions where bone gets resorbed and deposited over several weeks. In addition, the gray values in the micro-CT images contain quantitative information about the local tissue mineral density (TMD). The aim of this study was to measure how TMD increases with time after new bone formation and how this mineralization kinetics is influenced by mechanical stimulation. Our analysis of changes in TMD was based on an already reported experiment on 15-week-old female mice (C57BL/6), where in one group the sixth caudal vertebra was mechanically loaded with 8N, while in the control group no loading was applied. Comparison of two consecutive images allows the categorization of bone into newly formed, resorbed, and quiescent bone for different time points. Gray values of bone in these categories were compared layer-wise to minimize the effects of beam hardening artifacts. Quiescent bone in the control group was found to mineralize with a rate of 8 ± 1 mgHA/cm(3) per week, which is about half as fast as observed for newly formed bone. Mechanical loading increased the rate of mineral incorporation by 63% in quiescent bone. The week before bone resorption, demineralization could be observed with a drop of TMD by 36 ± 4 mgHA/cm(3) in the control and 34 ± 3 mgHA/cm(3) in the loaded group. In conclusion, this study shows how time-lapsed in vivo micro-CT can be used to assess changes in TMD of bone with high spatial and temporal resolution. This will allow a quantification of how bone diseases and pharmaceutical interventions influence not only microarchitecture of trabecular bone, but also its material quality.

The Clinical Biomechanics Award 2012 — Presented by the European Society of Biomechanics: Large scale simulations of trabecular bone adaptation to loading and treatment

BACKGROUND Microstructural simulations of bone remodeling are particularly relevant in the clinical management of osteoporosis. Before a model can be applied in the clinics, a validation against controlled in vivo data is crucial. Here we present a strain-adaptive feedback algorithm for the simulation of trabecular bone remodeling in response to loading and pharmaceutical treatment and report on the results of the large-scale validation against in vivo data. METHODS The algorithm follows the mechanostat principle and incorporates mechanical feedback, based on the local strain-energy density. For the validation, simulations of bone remodeling and adaptation in 180 osteopenic mice were performed. Permutations of the conditions for early (20th week) and late (26th week) loading of 8N or 0N, and treatments with bisphosphonates, or parathyroid hormone were simulated. Static and dynamic morphometry and local remodeling sites from in vivo and in silico studies were compared. FINDINGS For each study an individual set of model parameters was selected. Trabecular bone volume fraction was chosen as an indicator of the accuracy of the simulations. Overall errors for this parameter were 0.1-4.5%. Other morphometric indices were simulated with errors of less than 19%. Dynamic morphometry was more difficult to predict, which resulted in significant differences from the experimental data. INTERPRETATION We validated a new algorithm for the simulation of bone remodeling in trabecular bone. The results indicate that the simulations accurately reflect the effects of treatment and loading seen in respective experimental data, and, following adaptation to human data, could be transferred into clinics.