New suggestions for the mechanical control of bone remodeling.

Bone is constantly renewed over our lifetime through the process of bone (re)modeling. This process is important for bone to allow it to adapt to its mechanical environment and to repair damage from everyday life. Adaptation is thought to occur through the mechanosensitive response controlling the bone-forming and -resorbing cells. This report shows a way to extract quantitative information about the way remodeling is controlled using computer simulations. Bone resorption and deposition are described as two separate stochastic processes, during which a discrete bone packet is removed or deposited from the bone surface. The responses of the bone-forming and -resorbing cells to local mechanical stimuli are described by phenomenological remodeling rules. Our strategy was to test different remodeling rules and to evaluate the time evolution of the trabecular architecture in comparison to what is known from micro-CT measurements of real bone. In particular, we tested the reaction of virtual bone to standard therapeutic strategies for the prevention of bone deterioration, i.e., physical activity and medications to reduce bone resorption. Insensitivity of the bone volume fraction to reductions in bone resorption was observed in the simulations only for a remodeling rule including an activation barrier for the mechanical stimulus above which bone deposition is switched on. This is in disagreement with the commonly used rules having a so-called lazy zone.

Mechanical behavior of idealized, stingray-skeleton-inspired tiled composites as a function of geometry and material properties.

Tilings are constructs of repeated shapes covering a surface, common in both manmade and natural structures, but in particular are a defining characteristic of shark and ray skeletons. In these fishes, cartilaginous skeletal elements are wrapped in a surface tessellation, comprised of polygonal mineralized tiles linked by flexible joints, an arrangement believed to provide both stiffness and flexibility. The aim of this research is to use two-dimensional analytical models to evaluate the mechanical performance of stingray skeleton-inspired tessellations, as a function of their material and structural parameters. To calculate the effective modulus of modeled composites, we subdivided tiles and their surrounding joint material into simple shapes, for which mechanical properties (i.e. effective modulus) could be estimated using a modification of traditional Rule of Mixtures equations, that either assume uniform strain (Voigt) or uniform stress (Reuss) across a loaded composite material. The properties of joints (thickness, Young's modulus) and tiles (shape, area and Young's modulus) were then altered, and the effects of these tessellation parameters on the effective modulus of whole tessellations were observed. We show that for all examined tile shapes (triangle, square and hexagon) composite stiffness increased as the width of the joints was decreased and/or the stiffness of the tiles was increased; this supports hypotheses that the narrow joints and high tile to joint stiffness ratio in shark and ray cartilage optimize composite tissue stiffness. Our models also indicate that, for simple, uniaxial loading, square tessellations are least sensitive and hexagon tessellations most sensitive to changes in model parameters, indicating that hexagon tessellations are the most "tunable" to specific mechanical properties. Our models provide useful estimates for the tensile and compressive properties of 2d tiled composites under uniaxial loading. These results lay groundwork for future studies into more complex (e.g. biological) loading scenarios and three dimensional structural parameters of biological tilings, while also providing insight into the mechanical roles of tessellations in general and improving the design of bioinspired materials.

Modelling the role of surface stress on the kinetics of tissue growth in confined geometries.

In a previous paper we presented a theoretical framework to describe tissue growth in confined geometries based on the work of Ambrosi and Guillou [Ambrosi D, Guillou A. Growth and dissipation in biological tissues. Cont Mech Thermodyn 2007;19:245-51]. A thermodynamically consistent eigenstrain rate for growth was derived using the concept of configurational forces and used to investigate growth in holes of cylindrical geometries. Tissue growing from concave surfaces can be described by a model based on this theory. However, an apparently asymmetric behaviour between growth from convex and concave surfaces has been observed experimentally, but is not predicted by this model. This contradiction is likely to be due to the presence of contractile tensile stresses produced by cells near the tissue surface. In this contribution we extend the model in order to couple tissue growth to the presence of a surface stress. This refined growth model is solved for two geometries, within a cylindrical hole and on the outer surface of a cylinder, thus demonstrating how surface stress may indeed inhibit growth on convex substrates.

Intrafibrillar plasticity through mineral/collagen sliding is the dominant mechanism for the extreme toughness of antler bone.

The inelastic deformability of the mineralised matrix in bones is critical to their high toughness, but the nanoscale mechanisms are incompletely understood. Antler is a tough bone type, with a nanostructure composed of mineralised collagen fibrils ∼100nm diameter. We track the fibrillar deformation of antler tissue during cyclic loading using in situ synchrotron small-angle X-ray diffraction (SAXD), finding that residual strain remains in the fibrils after the load was removed. During repeated unloading/reloading cycles, the fibril strain shows minimal hysteresis when plotted as a function of tissue strain, indicating that permanent plastic strain accumulates inside the fibril. We model the tensile response of the mineralised collagen fibril by a two - level staggered model - including both elastic - and inelastic regimes - with debonding between mineral and collagen within fibrils triggering macroscopic inelasticity. In the model, the subsequent frictional sliding at intrafibrillar mineral/collagen interfaces accounts for subsequent inelastic deformation of the tissue in tension. The model is compared to experimental measurements of fibrillar and mineral platelet strain during tensile deformation, measured by in situ synchrotron SAXD and wide-angle X-ray diffraction (WAXD) respectively, as well as macroscopic tissue stress and strain. By fitting the model predictions to experimentally observed parameters like the yield point, elastic modulus and post-yield slope, extremely good agreement is found between the model and experimental data at both the macro- and at the nanoscale. Our results provide strong evidence that intrafibrillar sliding between mineral and collagen leads to permanent plastic strain at both the fibril and the tissue level, and that the energy thus dissipated is a significant factor behind the high toughness of antler bone.

Trabecular bone remodelling simulated by a stochastic exchange of discrete bone packets from the surface.

Human bone is constantly renewed through life via the process of bone remodelling, in which individual packets of bone are removed by osteoclasts and replaced by osteoblasts. Remodelling is mechanically controlled, where osteocytes embedded within the bone matrix are thought to act as mechanical sensors. In this computational work, a stochastic model for bone remodelling is used in which the renewal of bone material occurs by exchange of discrete bone packets. We tested different hypotheses of how the mechanical stimulus for bone remodelling is integrated by osteocytes and sent to actor cells on the bone's surface. A collective (summed) signal from multiple osteocytes as opposed to an individual (maximal) signal from a single osteocyte was found to lead to lower inner porosity and surface roughness of the simulated bone structure. This observation can be interpreted in that collective osteocyte signalling provides an effective surface tension to the remodelling process. Furthermore, the material heterogeneity due to remodelling was studied on a network of trabeculae. As the model is discrete, the age of individual bone packets can be monitored with time. The simulation results were compared with experimental data coming from quantitative back scattered electron imaging by transforming the information about the age of the bone packet into a mineral content. Discrepancies with experiments indicate that osteoclasts preferentially resorb low mineralized, i.e. young, bone at the bone's surface.

Cortical bone composition and orientation as a function of animal and tissue age in mice by Raman spectroscopy.

Important aspects of bone tissue quality include the physicochemical properties of its main constituents, the organic matrix and the mineral crystals. One of the most commonly reported measurements of Raman analysis of bone is the mineral to matrix ratio, obtained from the ratio of the integrated areas of any of the phosphate and amide peaks which depend on both tissue organization and composition. Cube-like samples of normal mouse cortical bone taken from the diaphysis and metaphysis of the femur were investigated within different age groups (2, 4, 8 and 12 weeks) by Raman microspectroscopy. Anatomically identical bone in both longitudinal and transverse directions was analyzed, enabling the discrimination between orientation and composition changes both as a function of animal age, and tissue age within the same animal. The results of the present study indicate that there is a parallel evolution of both orientation and chemical composition as a function of animal age, as well as tissue age within the same specimen. Our tissue age modified ratio of the carbonate to phosphate Raman peaks suggests that the bone mineral crystallite maturity remains relatively constant with animal age. Comparisons of polarized and depolarized experiments in the transversal plane of the diaphysis show a lack of orientation effects as a function of tissue age within the same animal, but exhibit differences as a function of animal age. In the metaphysis, the orientation effect is evident too, albeit less pronounced. This is most likely due to either the age difference between the two tissues within the same specimen in the long bone axis, as metaphyseal bone is generally younger than diaphyseal, or the more random orientation of the tissue collagen itself.