Mechanoregulation analysis of bone formation in tissue engineered constructs requires a volumetric method using time-lapsed micro-computed tomography.

Bone can adapt its microstructure to mechanical loads through mechanoregulation of the (re)modeling process. This process has been investigated in vivo using time-lapsed micro-computed tomography (micro-CT) and micro-finite element (FE) analysis using surface-based methods, which are highly influenced by surface curvature. Consequently, when trying to investigate mechanoregulation in tissue engineered bone constructs, their concave surfaces make the detection of mechanoregulation impossible when using surface-based methods. In this study, we aimed at developing and applying a volumetric method to non-invasively quantify mechanoregulation of bone formation in tissue engineered bone constructs using micro-CT images and FE analysis. We first investigated hydroxyapatite scaffolds seeded with human mesenchymal stem cells that were incubated over 8 weeks with one mechanically loaded and one control group. Higher mechanoregulation of bone formation was measured in loaded samples with an area under the curve for the receiver operating curve (AUCformation) of 0.633-0.637 compared to non-loaded controls (AUCformation: 0.592-0.604) during culture in osteogenic medium (p < 0.05). Furthermore, we applied the method to an in vivo mouse study investigating the effect of loading frequencies on bone adaptation. The volumetric method detected differences in mechanoregulation of bone formation between loading conditions (p < 0.05). Mechanoregulation in bone formation was more pronounced (AUCformation: 0.609-0.642) compared to the surface-based method (AUCformation: 0.565-0.569, p < 0.05). Our results show that mechanoregulation of formation in bone tissue engineered constructs takes place and its extent can be quantified with a volumetric mechanoregulation method using time-lapsed micro-CT and FE analysis. STATEMENT OF SIGNIFICANCE: Many efforts have been directed towards optimizing bone scaffolds for tissue growth. However, the impact of the scaffolds mechanical environment on bone growth is still poorly understood, requiring accurate assessment of its mechanoregulation. Existing surface-based methods were unable to detect mechanoregulation in tissue engineered constructs, due to predominantly concave surfaces in scaffolds. We present a volumetric approach to enable the precise and non-invasive quantification and analysis of mechanoregulation in bone tissue engineered constructs by leveraging time-lapsed micro-CT imaging, image registration, and finite element analysis. The implications of this research extend to diverse experimental setups, encompassing culture conditions, and material optimization, and investigations into bone diseases, enabling a significant stride towards comprehensive advancements in bone tissue engineering and regenerative medicine.

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 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.

Trabecular bone remodeling in the aging mouse: A micro-multiphysics agent-based in silico model using single-cell mechanomics.

Bone remodeling is regulated by the interaction between different cells and tissues across many spatial and temporal scales. Notably, in silico models are regarded as powerful tools to further understand the signaling pathways that regulate this intricate spatial cellular interplay. To this end, we have established a 3D multiscale micro-multiphysics agent-based (micro-MPA) in silico model of trabecular bone remodeling using longitudinal in vivo data from the sixth caudal vertebra (CV6) of PolgA(D257A/D257A) mice, a mouse model of premature aging. Our in silico model includes a variety of cells as single agents and receptor-ligand kinetics, mechanomics, diffusion and decay of cytokines which regulate the cells' behavior. We highlighted its capabilities by simulating trabecular bone remodeling in the CV6 of five mice over 4 weeks and we evaluated the static and dynamic morphometry of the trabecular bone microarchitecture. Based on the progression of the average trabecular bone volume fraction (BV/TV), we identified a configuration of the model parameters to simulate homeostatic trabecular bone remodeling, here named basal. Crucially, we also produced anabolic, anti-anabolic, catabolic and anti-catabolic responses with an increase or decrease by one standard deviation in the levels of osteoprotegerin (OPG), receptor activator of nuclear factor kB ligand (RANKL), and sclerostin (Scl) produced by the osteocytes. Our results showed that changes in the levels of OPG and RANKL were positively and negatively correlated with the BV/TV values after 4 weeks in comparison to basal levels, respectively. Conversely, changes in Scl levels produced small fluctuations in BV/TV in comparison to the basal state. From these results, Scl was deemed to be the main driver of equilibrium while RANKL and OPG were shown to be involved in changes in bone volume fraction with potential relevance for age-related bone features. Ultimately, this micro-MPA model provides valuable insights into how cells respond to their local mechanical environment and can help to identify critical pathways affected by degenerative conditions and ageing.

An in silico micro-multiphysics agent-based approach for simulating bone regeneration in a mouse femur defect model.

Bone defects represent a challenging clinical problem as they can lead to non-union. In silico models are well suited to study bone regeneration under varying conditions by linking both cellular and systems scales. This paper presents an in silico micro-multiphysics agent-based (micro-MPA) model for bone regeneration following an osteotomy. The model includes vasculature, bone, and immune cells, as well as their interaction with the local environment. The model was calibrated by time-lapsed micro-computed tomography data of femoral osteotomies in C57Bl/6J mice, and the differences between predicted bone volume fractions and the longitudinal in vivo measurements were quantitatively evaluated using root mean square error (RMSE). The model performed well in simulating bone regeneration across the osteotomy gap, with no difference (5.5% RMSE, p = 0.68) between the in silico and in vivo groups for the 5-week healing period - from the inflammatory phase to the remodelling phase - in the volume spanning the osteotomy gap. Overall, the proposed micro-MPA model was able to simulate the influence of the local mechanical environment on bone regeneration, and both this environment and cytokine concentrations were found to be key factors in promoting bone regeneration. Further, the validated model matched clinical observations that larger gap sizes correlate with worse healing outcomes and ultimately simulated non-union. This model could help design and guide future experimental studies in bone repair, by identifying which are the most critical in vivo experiments to perform.

Virtual supersampling as post-processing step preserves the trabecular bone morphometry in human peripheral quantitative computed tomography scans.

In the clinical field of diagnosis and monitoring of bone diseases, high-resolution peripheral quantitative computed tomography (HR-pQCT) is an important imaging modality. It provides a resolution where quantitative bone morphometry can be extracted in vivo on patients. It is known that HR-pQCT provides slight differences in morphometric indices compared to the current standard approach micro-computed tomography (micro-CT). The most obvious reason for this is the restriction of the radiation dose and with this a lower image resolution. With advances in micro-CT evaluation techniques such as patient-specific remodeling simulations or dynamic bone morphometry, a higher image resolution would potentially also allow the application of such novel evaluation techniques to clinical HR-pQCT measurements. Virtual supersampling as post-processing step was considered to increase the image resolution of HR-pQCT scans. The hypothesis was that this technique preserves the structural bone morphometry. Supersampling from 82 µm to virtual 41 µm by trilinear interpolation of the grayscale values of 42 human cadaveric forearms resulted in strong correlations of structural parameters (R2: 0.96-1.00). BV/TV was slightly overestimated (4.3%, R2: 1.00) compared to the HR-pQCT resolution. Tb.N was overestimated (7.47%; R2: 0.99) and Tb.Th was slightly underestimated (-4.20%; R2: 0.98). The technique was reproducible with PE%CV between 1.96% (SMI) and 7.88% (Conn.D). In a clinical setting with 205 human forearms with or without fracture measured at 82 µm resolution HR-pQCT, the technique was sensitive to changes between groups in all parameters (p < 0.05) except trabecular thickness. In conclusion, we demonstrated that supersampling preserves the bone morphometry from HR-pQCT scans and is reproducible and sensitive to changes between groups. Supersampling can be used to investigate on the resolution dependency of HR-pQCT images and gain more insight into this imaging modality.

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm.

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous.

Strain energy density gradients in bone marrow predict osteoblast and osteoclast activity: a finite element study.

Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.

Bone adaptation to cyclic loading in murine caudal vertebrae is maintained with age and directly correlated to the local micromechanical environment.

The ability of the skeleton to adapt to mechanical stimuli (mechanosensitivity) has most often been investigated at the whole-bone level, but less is known about the local mechanoregulation of bone remodeling at the bone surface, especially in context of the aging skeleton. The aim of this study was to determine the local and global mechanosensitivity of the sixth caudal vertebra during cyclic loading (8 N, three times per week, for six weeks) in mice aged 15, 52, and 82 weeks at the start of loading. Bone adaptation was monitored with in vivo micro-computed tomography. Strain energy density (SED), assumed as the mechanical stimulus for bone adaptation, was determined with micro-finite element models. Mechanical loading had a beneficial effect on the bone microstructure and bone stiffness in all age groups. Mineralizing surface was on average 13% greater (p<0.05) in loaded than control groups in 15- and 82-week-old mice, but not for 52-week-old mice. SED at the start of loading correlated to the change in bone volume fraction in the following 6 weeks for loaded groups (r(2)=0.69-0.85) but not control groups. At the local level, SED was 14-20% greater (p<0.01) at sites of bone formation, and 15-20% lower (p<0.01) at sites of bone resorption compared to quiescent bone surfaces for all age groups, indicating SED was a stimulus for bone adaptation. Taken together, these results support that mechanosensitivity is maintained with age in caudal vertebrae of mice at a local and global level. Since age-related bone loss was not observed in caudal vertebrae, results from the current study might not be translatable to aged humans.

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.

Image interpolation allows accurate quantitative bone morphometry in registered micro-computed tomography scans.

Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.

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 (R(2) = 0.99) whereas the probability of bone formation follows an exponential growth function to a maximum value (R(2) = 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.

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.

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.

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.

Longitudinal assessment of in vivo bone dynamics in a mouse tail model of postmenopausal osteoporosis.

Recently, it has been shown that transient bone biology can be observed in vivo using time-lapse micro-computed tomography (µCT) in the mouse tail bone. Nevertheless, in order for the mouse tail bone to be a model for human disease, the hallmarks of any disease must be mimicked. The aim of this study was to investigate whether postmenopausal osteoporosis could be modeled in caudal vertebrae of C57Bl/6 mice, considering static and dynamic bone morphometry as well as mechanical properties, and to describe temporal changes in bone remodeling rates. Twenty C57Bl/6 mice were ovariectomized (OVX, n = 11) or sham-operated (SHM, n = 9) and monitored with in vivo µCT on the day of surgery and every 2 weeks after, up to 12 weeks. There was a significant decrease in bone volume fraction for OVX (-35%) compared to SHM (+16%) in trabecular bone (P < 0.001). For OVX, high-turnover bone loss was observed, with the bone resorption rate exceeding the bone formation rate (P < 0.001). Furthermore there was a significant decrease in whole-bone stiffness for OVX (-16%) compared to SHM (+11%, P < 0.001). From these results we conclude that the mouse tail vertebra mimics postmenopausal bone loss with respect to these parameters and therefore might be a suitable model for postmenopausal osteoporosis. When evaluating temporal changes in remodeling rates, we found that OVX caused an immediate increase in bone resorption rate (P < 0.001) and a delayed increase in bone formation rate (P < 0.001). Monitoring transient bone biology is a promising method for future research.

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.

In vivo validation of a computational bone adaptation model using open-loop control and time-lapsed micro-computed tomography.

Cyclic mechanical loading augments trabecular bone mass, mainly by increasing trabecular thickness. For this reason, we hypothesized that an in silico thickening algorithm using open-loop control would be sufficient to reliably predict the response of trabecular bone to cyclic mechanical loading. This would also mean that trabecular bone adaptation could be modeled as a system responding to an input signal at the onset of the process in a predefined manner, without feedback from the outputs. Here, time-lapsed in vivo micro-computed tomography scans of mice cyclically loaded at the sixth caudal vertebra were used to validate the in silico model. When comparing in silico and in vivo data sets after a period of four weeks, a maximum prediction error of 2.4% in bone volume fraction and 5.4% in other bone morphometric indices was calculated. Superimposition of sequentially acquired experimental images and simulated structures revealed that in silico simulations deposited thin and homogeneous layers of bone whilst the experiment was characterized by local areas of strong thickening, as well as considerable volumes of bone resorption. From the results, we concluded that the proposed computational algorithm predicted changes in bone volume fraction and global parameters of bone structure very well over a period of four weeks while it was unable to reproduce accurate spatial patterns of local bone formation and resorption. This study demonstrates the importance of validation of computational models through the use of experimental in vivo data, including the local comparison of simulated and experimental remodeling sites. It is assumed that the ability to accurately predict changes in bone micro-architecture will facilitate a deeper understanding of the cellular mechanisms underlying bone remodeling and adaptation due to mechanical loading.

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.