Duncan J. Webster

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.

A novel in vivo mouse model for mechanically stimulated bone adaptation – a combined experimental and computational validation study

To facilitate the investigation of bone formation, in vivo, in response to mechanical loading a caudal vertebra axial compression device (CVAD) has been developed to deliver precise mechanical loads to the fifth caudal vertebra (C5) of the C57BL/6 female mouse. A combined experimental and computational approach was used to quantify the micro-mechanical strain induced in trabecular and cortical components following static and dynamic loading using the CVAD. Cortical bone strains were recorded using micro-strain gages. Finite element (FE) models based on micro-computed tomography were constructed for all C5 vertebrae. Both theoretical and experimental cortical strains correlated extremely well (R 2>0.96) for a Youngs modulus of 14.8 GPa, thus validating the FE model. In this study, we have successfully applied mechanical loads to the C5 murine vertebrae, demonstrating the potential of this model to be used for in vivo loading studies aimed at stimulating both trabecular and cortical bone adaptation.

In silico biology of bone modelling and remodelling: adaptation

Modelling and remodelling are the processes by which bone adapts its shape and internal structure to external influences. However, the cellular mechanisms triggering osteoclastic resorption and osteoblastic formation are still unknown. In order to investigate current biological theories, in silico models can be applied. In the past, most of these models were based on the continuum assumption, but some questions related to bone adaptation can be addressed better by models incorporating the trabecular microstructure. In this paper, existing simulation models are reviewed and one of the microstructural models is extended to test the hypothesis that bone adaptation can be simulated without particular knowledge of the local strain distribution in the bone. Validation using an experimental murine loading model showed that this is possible. Furthermore, the experimental model revealed that bone formation cannot be attributed only to an increase in trabecular thickness but also to structural reorganization including the growth of new trabeculae. How these new trabeculae arise is still an unresolved issue and might be better addressed by incorporating other levels of hierarchy, especially the cellular level. The cellular level sheds light on the activity and interplay between the different cell types, leading to the effective change in the whole bone. For this reason, hierarchical multi-scale simulations might help in the future to better understand the biomathematical laws behind bone adaptation.

Multiscale modelling and nonlinear finite element analysis as clinical tools for the assessment of fracture risk

The risk of osteoporotic fractures is currently estimated based on an assessment of bone mass as measured by dual-energy X-ray absorptiometry. However, patient-specific finite element (FE) simulations that include information from multiple scales have the potential to allow more accurate prognosis. In the past, FE models of bone were limited either in resolution or to the linearization of the mechanical behaviour. Now, nonlinear, high-resolution simulations including the bone microstructure have been made possible by recent advances in simulation methods, computer infrastructure and imaging, allowing the implementation of multiscale modelling schemes. For example, the mechanical loads generated in the musculoskeletal system define the boundary conditions for organ-level, continuum-based FE models, whose nonlinear material properties are derived from microstructural information. Similarly microstructure models include tissue-level information such as the dynamic behaviour of collagen by modifying the models constitutive law. This multiscale approach to modelling the mechanics of bone allows a more accurate characterization of bone fracture behaviour. Furthermore, such models could also include the effects of ageing, osteoporosis and drug treatment. Here we present the current state of the art for multiscale modelling and assess its potential to better predict an individuals risk of fracture in a clinical setting.

In silico models of bone remodeling from macro to nano—from organ to cell

Computational modeling is a tool through which researchers can achieve a greater understanding of the mechanisms governing biological systems. In the field of bone biology, a plethora of models exist which attempt to replicate and investigate bones dynamic behavior at different scales. At organ level, models are continuum based and describe the variation of bones apparent density as a function of both biological and external mechanical stimuli. At tissue level, models include bone microarchitecture and more descriptive parameters such as trabecular thickness, osteoclast resorption depth, and activation frequency. Finally, at cell level, models employ partial differential equations to describe complex cellular interactions in the temporal domain. Although informative, these models exist in isolation. Consequently, their interpretation is limited. In this review, we present an overview of the organ‐, tissue‐, and cell‐level models and assess their ability to reflect bones metabolic processes reliably. Existing interscale synergies are then presented along with a computational framework which could be exploited to achieve a fully integrated, multiscale modeling approach. WIREs Syst Biol Med 2011 3 241–251 DOI: 10.1002/wsbm.115

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.

Studying osteocytes within their environment

It is widely hypothesized that osteocytes are the mechano-sensors residing in the bones mineralized matrix which control load induced bone adaptation. Owing to their inaccessibility it has proved challenging to generate quantitative in vivo experimental data which supports this hypothesis. Recent advances in in situ imaging, both in non-living and living specimens, have provided new insights into the role of osteocytes in the skeleton. Combined with the retrieval of biochemical information from mechanically stimulated osteocytes using in vivo models, quantitative experimental data is now becoming available which is leading to a more accurate understanding of osteocyte function. With this in mind, here we review i) state of the art ex vivo imaging modalities which are able to precisely capture osteocyte structure in 3D, ii) live cell imaging techniques which are able to track structural morphology and cellular differentiation in both space and time, and iii) in vivo models which when combined with the latest biochemical assays and microfluidic imaging techniques can provide further insight on the biological function of osteocytes.

Toward Mechanical Systems Biology in Bone

Cyclic mechanical loading is perhaps the most important physiological factor regulating bone mass and shape in a way which balances optimal strength with minimal weight. This bone adaptation process spans multiple length and time scales. Forces resulting from physiological exercise at the organ scale are sensed at the cellular scale by osteocytes, which reside inside the bone matrix. Via biochemical pathways, osteocytes orchestrate the local remodeling action of osteoblasts (bone formation) and osteoclasts (bone resorption). Together these local adaptive remodeling activities sum up to strengthen bone globally at the organ scale. To resolve the underlying mechanisms it is required to identify and quantify both cause and effect across the different scales. Progress has been made at the different scales experimentally. Computational models of bone adaptation have been developed to piece together various experimental observations at the different scales into coherent and plausible mechanisms. However additional quantitative experimental validation is still required to build upon the insights which have already been achieved. In this review we discuss emerging as well as state of the art experimental and computational techniques and how they might be used in a mechanical systems biology approach to further our understanding of the mechanisms governing load induced bone adaptation, i.e., ways are outlined in which experimental and computational approaches could be coupled, in a quantitative manner to create more reliable multiscale models of bone.

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.