The local and global geometry of trabecular bone

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. Statement of significance: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface curvatures and Minkowski functionals, which are the most fundamental local and global shape quantifiers. Our results show that these shape metrics are sensitive to differences between bone types and unify traditional metrics within a single mathematical framework. This geometrical framework could also be useful to design bone-mimicking scaffolds and understand geometry-driven tissue growth.ISSN:1742-7061ISSN:1878-756

Perspectives on in Silico Bone Mechanobiology: Computational Modelling of Multicellular Systems

Bone mechanobiology is the study of the physical, biological and mechanical processes that continuously affect the multiscale multicellular system of the bone from the organ to the molecular scale. Current knowledge derives from experimental studies, which are often limited to gathering qualitative data in a cross-sectional manner, up to a restricted number of time points. Moreover, the simultaneous collection of information about 3D bone microarchitecture, cell activity as well as protein distribution and level is still a challenge. In silico models can expand qualitative information with hypothetical quantitative systems, which allow quantification, testing and comparison to existing quantifiable experimental data. An overview of multiscale, multiphysics, agent-based and hybrid techniques and their applications to bone mechanobiology is provided in the present review. The study analysed how mechanical signals, cells and proteins can be modelled in silico to represent bone remodelling and adaptation. Hybrid modelling of bone mechanobiology could combine the methods used in multiscale, multiphysics and agent-based models into a single model, leading to a unified and comprehensive understanding of bone mechanobiology. Numerical simulations of in vivo multicellular systems aided in hypothesis testing of such in silico models. Recently, in silico trials have been used to illustrate the mechanobiology of cells and signalling pathways in clinical biopsies and animal bones, including the effects of drugs on single cells and signalling pathways up to the organ level. This improved understanding may lead to the identification of novel therapies for degenerative diseases such as osteoporosis.ISSN:1473-226

Individualized cyclic mechanical loading improves callus properties during the remodelling phase of fracture healing in mice as assessed from time-lapsed in vivo imaging

Fracture healing is regulated by mechanical loading. Understanding the underlying mechanisms during the different healing phases is required for targeted mechanical intervention therapies. Here, the influence of individualized cyclic mechanical loading on the remodelling phase of fracture healing was assessed in a non-critical-sized mouse femur defect model. After bridging of the defect, a loading group (n = 10) received individualized cyclic mechanical loading (8–16 N, 10 Hz, 5 min, 3 × /week) based on computed strain distribution in the mineralized callus using animal-specific real-time micro-finite element analysis with 2D/3D visualizations and strain histograms. Controls (n = 10) received 0 N treatment at the same post-operative time-points. By registration of consecutive scans, structural and dynamic callus morphometric parameters were followed in three callus sub-volumes and the adjacent cortex showing that the remodelling phase of fracture healing is highly responsive to cyclic mechanical loading with changes in dynamic parameters leading to significantly larger formation of mineralized callus and higher degree of mineralization. Loading-mediated maintenance of callus remodelling was associated with distinct effects on Wnt-signalling-associated molecular targets Sclerostin and RANKL in callus sub-regions and the adjacent cortex (n = 1/group). Given these distinct local protein expression patterns induced by cyclic mechanical loading during callus remodelling, the femur defect loading model with individualized load application seems suitable to further understand the local spatio-temporal mechano-molecular regulation of the different fracture healing phases.ISSN:2045-232

The local and global geometry of trabecular bone

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. Statement of significance: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface curvatures and Minkowski functionals, which are the most fundamental local and global shape quantifiers. Our results show that these shape metrics are sensitive to differences between bone types and unify traditional metrics within a single mathematical framework. This geometrical framework could also be useful to design bone-mimicking scaffolds and understand geometry-driven tissue growth.Biomaterials & Tissue Biomechanic

Evaluation of longitudinal time-lapsed in vivo micro-CT for monitoring fracture healing in mouse femur defect models

Longitudinal in vivo micro-computed tomography (micro-CT) is of interest to non-invasively capture the healing process of individual animals in preclinical fracture healing studies. However, it is not known whether longitudinal imaging itself has an impact on callus formation and remodeling. In this study, a scan group received weekly micro-CT measurements (week 0–6), whereas controls were only scanned post-operatively and at week 5 and 6. Registration of consecutive scans using a branching scheme (bridged vs. unbridged defect) combined with a two-threshold approach enabled assessment of localized bone turnover and mineralization kinetics relevant for monitoring callus remodeling. Weekly micro-CT application did not significantly change any of the assessed callus parameters in the defect and periosteal volumes. This was supported by histomorphometry showing only small amounts of cartilage residuals in both groups, indicating progression towards the end of the healing period. Also, immunohistochemical staining of Sclerostin, previously associated with mediating adverse radiation effects on bone, did not reveal differences between groups. The established longitudinal in vivo micro-CT-based approach allows monitoring of healing phases in mouse femur defect models without significant effects of anesthesia, handling and radiation on callus properties. Therefore, this study supports application of longitudinal in vivo micro-CT for healing-phase-specific monitoring of fracture repair in mice.ISSN:2045-232

The association between mineralised tissue formation and the mechanical local in vivo environment: Time-lapsed quantification of a mouse defect healing model

An improved understanding of how local mechanical stimuli guide the fracture healing process has the potential to enhance clinical treatment of bone injury. Recent preclinical studies of bone defect in animal models have used cross-sectional data to examine this phenomenon indirectly. In this study, a direct time-lapsed imaging approach was used to investigate the local mechanical strains that precede the formation of mineralised tissue at the tissue scale. The goal was to test two hypotheses: 1) the local mechanical signal that precedes the onset of tissue mineralisation is higher in areas which mineralise, and 2) this local mechanical signal is independent of the magnitude of global mechanical loading of the tissue in the defect. Two groups of mice with femoral defects of length 0.85 mm (n = 10) and 1.45 mm (n = 9) were studied, allowing for distinct distributions of tissue scale strains in the defects. The regeneration and (re)modelling of mineralised tissue was observed weekly using in vivo micro-computed tomography (micro-CT), which served as a ground truth for resolving areas of mineralised tissue formation. The mechanical environment was determined using micro-finite element analysis (micro-FE) on baseline images. The formation of mineralised tissue showed strong association with areas of higher mechanical strain (area-under-the-curve: 0.91 ± 0.04, true positive rate: 0.85 ± 0.05) while surface based strains could correctly classify 43% of remodelling events. These findings support our hypotheses by showing a direct association between the local mechanical strains and the formation of mineralised tissue.ISSN:2045-232

Spatio-temporal characterization of fracture healing patterns and assessment of biomaterials by time-lapsed in vivo micro-computed tomography

Thorough preclinical evaluation of functionalized biomaterials for treatment of large bone defects is essential prior to clinical application. Using in vivo micro-computed tomography (micro-CT) and mouse femoral defect models with different defect sizes, we were able to detect spatio-temporal healing patterns indicative of physiological and impaired healing in three defect sub-volumes and the adjacent cortex. The time-lapsed in vivo micro-CT-based approach was then applied to evaluate the bone regeneration potential of functionalized biomaterials using collagen and bone morphogenetic protein (BMP-2). Both collagen and BMP-2 treatment led to distinct changes in bone turnover in the different healing phases. Despite increased periosteal bone formation, 87.5% of the defects treated with collagen scaffolds resulted in non-unions. Additional BMP-2 application significantly accelerated the healing process and increased the union rate to 100%. This study further shows potential of time-lapsed in vivo micro-CT for capturing spatio-temporal deviations preceding non-union formation and how this can be prevented by application of functionalized biomaterials. This study therefore supports the application of longitudinal in vivo micro-CT for discrimination of normal and disturbed healing patterns and for the spatio-temporal characterization of the bone regeneration capacity of functionalized biomaterials.ISSN:2045-232

The association between mineralised tissue formation and the mechanical local in vivo environment:time-lapsed quantification of a mouse defect healing model

\u3cp\u3eAn improved understanding of how local mechanical stimuli guide the fracture healing process has the potential to enhance clinical treatment of bone injury. Recent preclinical studies of bone defect in animal models have used cross-sectional data to examine this phenomenon indirectly. In this study, a direct time-lapsed imaging approach was used to investigate the local mechanical strains that precede the formation of mineralised tissue at the tissue scale. The goal was to test two hypotheses: 1) the local mechanical signal that precedes the onset of tissue mineralisation is higher in areas which mineralise, and 2) this local mechanical signal is independent of the magnitude of global mechanical loading of the tissue in the defect. Two groups of mice with femoral defects of length 0.85 mm (n = 10) and 1.45 mm (n = 9) were studied, allowing for distinct distributions of tissue scale strains in the defects. The regeneration and (re)modelling of mineralised tissue was observed weekly using in vivo micro-computed tomography (micro-CT), which served as a ground truth for resolving areas of mineralised tissue formation. The mechanical environment was determined using micro-finite element analysis (micro-FE) on baseline images. The formation of mineralised tissue showed strong association with areas of higher mechanical strain (area-under-the-curve: 0.91 ± 0.04, true positive rate: 0.85 ± 0.05) while surface based strains could correctly classify 43% of remodelling events. These findings support our hypotheses by showing a direct association between the local mechanical strains and the formation of mineralised tissue.\u3c/p\u3

Spatio-temporal characterization of fracture healing patterns and assessment of biomaterials by time-lapsed in vivo micro-computed tomography

Thorough preclinical evaluation of functionalized biomaterials for treatment of large bone defects is essential prior to clinical application. Using in vivo micro-computed tomography (micro-CT) and mouse femoral defect models with different defect sizes, we were able to detect spatio-temporal healing patterns indicative of physiological and impaired healing in three defect sub-volumes and the adjacent cortex. The time-lapsed in vivo micro-CT-based approach was then applied to evaluate the bone regeneration potential of functionalized biomaterials using collagen and bone morphogenetic protein (BMP-2). Both collagen and BMP-2 treatment led to distinct changes in bone turnover in the different healing phases. Despite increased periosteal bone formation, 87.5% of the defects treated with collagen scaffolds resulted in non-unions. Additional BMP-2 application significantly accelerated the healing process and increased the union rate to 100%. This study further shows potential of time-lapsed in vivo micro-CT for capturing spatio-temporal deviations preceding non-union formation and how this can be prevented by application of functionalized biomaterials. This study therefore supports the application of longitudinal in vivo micro-CT for discrimination of normal and disturbed healing patterns and for the spatio-temporal characterization of the bone regeneration capacity of functionalized biomaterials