Hysteretic pinching of human secondary osteons subjected to torsion

Modeling of bending and torsional stiffnesses of bone at sub-microscale: Effect of curved mineral lamellae

Recent transmission electron microscopy images of transverse sections of human cortical bone showed that mineral lamellae (polycrystalline sheets of apatite crystals) form arcuate multi-radius patterns around collagen fibrils. The 3-6 nm thick mineral lamellae are arranged in stacks of 3-20 layers and curve around individual fibrils, few fibrils, and higher numbers of collagen fibrils. We evaluate the effect of these stacked mineral lamellae with various radius of curvature patterns on the elastic bending and torsional responses of bone at the sub-microscale using a finite element method. We find that the curved multi-radius stack patterns increased the bending and torsional stiffnesses by 7% and 23%, respectively, compared to when the stacks of mineral lamellae only encircle individual fibrils for the idealized geometric models considered. This study provides new insights into the structure-property relations for the bone ultrastructure.

Theoretical mathematics, polarized light microscopy and computational models in healthy and pathological bone

The needs of everyday life, such as counting and measuring, are roots of theoretical mathematics. I believe these roots are why mathematical ideas ground research so amazingly well within many scientific fields. Initially trained as a theoretical mathematician and having collaborated with non-mathematicians in the field of bone research, I address the advantages and challenges of collaborations across fields of research among investigators trained in different disciplines. I report on the mathematical ideas that have guided my research on the mechanics of bone tissue. I explain how the mathematical ideas of local vs. global properties influence my research. Polarized light microscopy (PLM) is a tool that I use consistently, in association with other microscopy techniques, to investigate bone in its healthy state and in the presence of bone disease, in humans and in animal models. I review the results that I and investigators around the world have obtained with PLM. Applied to thin bone sections, PLM yields extinct (black) and bright (white) signals that are interpreted in terms of the orientation of collagen type I, by means of other microscopy techniques. Collagen type I is an elementary component of bone tissue. Its orientation is important for the mechanical function of bone. Images obtained by PLM at a specific bone site yield big data sets regarding collagen orientation. Multiple data sets in respect of multiple sites are often needed for research because the bone tissue differs by location in response to the distinct forces acting on it. Mathematics, defined by philosophers as the theory of patterns, offers the backdrop for pattern identification in the big data sets regarding collagen orientation. I also discuss the computational aspect of the research, pursuant to which the patterns identified are incorporated in simulations of mechanical behaviors of bone. These mathematical ideas serve to understand the role of collagen orientation in bone fracture risk.

Mechanical Characterization of Bone: State of the Art in Experimental Approaches-What Types of Experiments Do People Do and How Does One Interpret the Results?

PURPOSE OF REVIEW

The mechanical integrity of bone is determined by the direct measurement of bone mechanical properties. This article presents an overview of the current, most common, and new and upcoming experimental approaches for the mechanical characterization of bone. The key outcome variables of mechanical testing, as well as interpretations of the results in the context of bone structure and biology are also discussed.

RECENT FINDINGS

Quasi-static tests are the most commonly used for determining the resistance to structural failure by a single load at the organ (whole bone) level. The resistance to crack initiation or growth by fracture toughness testing and fatigue loading offers additional and more direct characterization of tissue material properties. Non-traditional indentation techniques and in situ testing are being increasingly used to probe the material properties of bone ultrastructure. Destructive ex vivo testing or clinical surrogate measures are considered to be the gold standard for estimating fracture risk. The type of mechanical test used for a particular investigation depends on the length scale of interest, where the outcome variables are influenced by the interrelationship between bone structure and composition. Advancement in the sensitivity of mechanical characterization techniques to detect changes in bone at the levels subjected to modifications by aging, disease, and/or pharmaceutical treatment is required. As such, a number of techniques are now available to aid our understanding of the factors that contribute to fracture risk.

Collagen mutation causes changes of the microdamage morphology in bone of an OI mouse model

Previous studies have postulated that ultrastructural changes may alter the pattern and capacity of microdamage accumulation in bone. Using an osteogenesis imperfecta (OI) mouse model, this study was performed to investigate the correlation of collagen mutation with the microdamage morphology and the associated brittleness of bone. In this study, femurs from mild OI and wild type mice were fatigued under four-point bending to create microdamage in the specimens. Then, the microdamage morphology of these specimens was examined using the bulk-staining technique with basic fuchsin. Similar with the results of previous studies, it was observed that linear microcracks were formed more easily in compression, whereas diffuse damage was induced more readily in tension for both wild-type and mild-type mice. However, less diffuse damage was found in the tensile side of mild OI mouse femurs (collagen mutation) compared with those of wild type mice, showing that the microdamage morphology is correlated to the brittleness of bone. The results of this study provide direct evidence that supports the prediction made by the previous numerical simulation studies, suggesting that microdamage morphology in bone is significantly correlated with the integrity of the collagen phase.