Characterizing microcrack orientation distribution functions in osteonal bone samples.

Prefailure microdamage in bone tissue is considered to be the most detrimental factor in defining its strength and toughness with respect to age and disease. To understand the influence of microcracks on bone mechanics it is necessary to assess their morphology and three-dimensional distribution. This requirement reaches beyond classic histology and stereology, and methods to obtain such information are currently missing. Therefore, the aim of the study was to develop a methodology that allows to characterize three-dimensional microcrack distributions in bulk bone samples. Four dumbbell-shaped specimens of human cortical bone of a 77-year-old female donor were loaded beyond yield in either tension, compression or torsion (one control). Subsequently, synchrotron radiation micro-computed tomography (SRµCT) was used to obtain phase-contrast images of the damaged samples. A microcrack segmentation algorithm was developed and used to segment microcrack families for which microcrack orientation distribution functions were determined. Distinct microcrack families were observed for each load case that resulted in distinct orientation distribution functions. Microcracks had median areas of approximately 4.7 µm2 , 33.3 µm2 and 64.0 µm2 for tension, compression and torsion. Verifying the segmentation algorithm against a manually segmented ground truth showed good results when comparing the microcrack orientation distribution functions. A size dependence was noted when investigating the orientation distribution functions with respect to the size of the volume of interest used for their determination. Furthermore, a scale separation between tensile, compressive and torsional microcracks was noticeable. Visual comparison to classic histology indicated that microcrack families were successfully distinguished. We propose a methodology to analyse three-dimensional microcrack distributions in overloaded cortical bone. Such information could improve our understanding of bone microdamage and its impact on bone failure in relation to tissue age and disease.

Multi-scale in silico and ex silico mechanics of 3D printed cochlear implants for local drug delivery.

The currently available treatments for inner ear disorders often involve systemic drug administration, leading to suboptimal drug concentrations and side effects. Cochlear implants offer a potential solution by providing localized and sustained drug delivery to the cochlea. While the mechanical characterization of both the implants and their constituent material is crucial to ensure functional performance and structural integrity during implantation, this aspect has been mostly overlooked. This study proposes a novel methodology for the mechanical characterization of our recently developed cochlear implant design, namely, rectangular and cylindrical, fabricated using two-photon polymerization (2 PP) with a novel photosensitive resin (IP-Q™). We used in silico computational models and ex silico experiments to study the mechanics of our newly designed implants when subjected to torsion mimicking the foreseeable implantation procedure. Torsion testing on the actual-sized implants was not feasible due to their small size (0.6 × 0.6 × 2.4 mm³). Therefore, scaled-up rectangular cochlear implants (5 × 5 × 20 mm³, 10 × 10 × 40 mm³, and 20 × 20 × 80 mm³) were fabricated using stereolithography and subjected to torsion testing. Finite element analysis (FEA) accurately represented the linear behavior observed in the torsion experiments. We then used the validated Finite element analysis models to study the mechanical behavior of real-sized implants fabricated from the IP-Q resin. Mechanical characterization of both implant designs, with different inner porous structures (pore size: 20 µm and 60 µm) and a hollow version, revealed that the cylindrical implants exhibited approximately three times higher stiffness and mechanical strength as compared to the rectangular ones. The influence of the pore sizes on the mechanical behavior of these implant designs was found to be small. Based on these findings, the cylindrical design, regardless of the pore size, is recommended for further research and development efforts.

Extrafibrillar matrix yield stress and failure envelopes for mineralised collagen fibril arrays.

Bone metabolic diseases such as osteoporosis constitute a major socio-economic challenge. A detailed understanding of the structure-property relationships of bone's underlying hierarchical levels has the potential to improve diagnosis and the ability to treat those diseases, especially with regards to the onset of failure. Therefore, elastic and yield properties of mineralised turkey leg tendon (MTLT), a mineralised tissue that is similar to bone but has a simpler multiscale structure, were investigated. Elastic properties were identified using a multiscale micromechanical model. The input parameters include constituent mechanical properties, volume fractions and inclusion aspect ratios and these were obtained from a wide variety of literature sources. The determined elastic properties were used to formulate micromechanically informed yield surfaces and to identify yield properties of MTLT at the nanometre length scale where failure is first reported to occur. This was done in conjunction with experimental results from the compression of micropillars extracted from individual mineralised collagen fibres. This data was then used to identify micromechanically informed failure envelopes. The shear yield stress of the extrafibrillar matrix, associated with interfibrillar sliding, was identified as 137.65 MPa. The ratio between tensile and compressive yield stress in the Drucker-Prager yield criterion was 0.65. For both criteria apparent yield stress of the mineralised collagen fibril decreased to 25.3-31.4% when varying fibril orientation from 0° to 90°. This study identified yield properties of extrafibrillar matrix using an aligned mineralised tissue. The ability to obtain yield stress data and unloading stiffness from micropillar compression tests of MTLT at the level of the mineralised collagen fibril array and downscaling these into the EM mitigates against possible errors associated with macroscopic stiffness predictions and proved to be an invaluable advantage compared to similar modelling approaches. Results may help to improve computational models that may then be used in pre-clinical testing or development of personalised treatment strategies.

Experimental validation of a nonlinear µFE model based on cohesive-frictional plasticity for trabecular bone.

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of µFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly.

The growing incidence of skeletal fractures poses a significant challenge to ageing societies. Since a major part of physiological loading in the lower limbs is carried by cortical bone, it would be desirable to better understand the structure-mechanical property relationships and scale effects in this tissue. This study aimed at assessing whether microindentation properties combined with chemical and morphological information are usable to predict macroscopic elastic and strength properties in a donor- and site-matched manner. Specimens for quasi-static macroscopic tests in tension, compression, and torsion and microindentation were prepared from a cohort of 19 male and 20 female donors (46 to 99 years). All tests were performed under fully hydrated conditions. The chemical composition of the extra-cellular matrix was investigated with Raman spectroscopy. The results of the micro-mechanical tests were combined with morphological and compositional properties using a power law relationship to predict the macro-mechanical results. Microindentation properties were not gender dependent, remarkably constant over age, and showed an overall small variation with standard deviations of approximately 10 %. Similar results were obtained for chemical tissue composition. Macro-mechanical stiffness and strength were significantly related to porosity for all load cases (p<0.05). In case of macroscopic yield strain and work-to-failure this was only true in torsion and compression, respectively. The correlations of macro-mechanical with micro-mechanical, morphological, and chemical properties showed no significance for cement line density, mineralisation, or variations in the microindentation results and were dominated by porosity with a moderate explanatory power of predominately less than 50 %. The results confirm that age, with minor exceptions gender, and small variations in average mineralisation have negligible effect on the tissue microindentation properties of human lamellar bone in the elderly. Furthermore, our findings suggest that microindentation experiments are suitable to predict macroscopic mechanical properties in the elderly only on average and not on a one to one basis. The presented data may help to form a better understanding of the mechanisms of ageing in bone tissue and of the length scale at which they are active. This may be used for future prediction of fracture risk in the elderly.

Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone.

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

An anisotropic elastic-viscoplastic damage model for bone tissue.

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain [Formula: see text] , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales.

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker-Prager, Tsai-Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai-Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

Fabric-mechanical property relationships of trabecular bone allografts are altered by supercritical CO2 treatment and gamma sterilization.

Tissue grafts are implanted in orthopedic surgery every day. In order to minimize infection risk, bone allografts are often delipidated with supercritical CO2 and sterilized prior to implantation. This treatment may, however, impair the mechanical behavior of the bone graft tissue. The goal of this study was to determine clinically relevant mechanical properties of treated/sterilized human trabecular bone grafts, e.g. the apparent modulus, strength, and the ability to absorb energy during compaction. They were compared with results of identical experiments performed previously on untreated/fresh frozen human trabecular bone from the same anatomical site (Charlebois, 2008). We tested the hypothesis that the morphology-mechanical property relationships of treated cancellous allografts are similar to those of fresh untreated bone. The morphology of the allografts was determined by µCT. Subsequently, cylindrical samples were tested in unconfined and confined compression. To account for various morphologies, the experimental data was fitted to phenomenological mechanical models for elasticity, strength, and dissipated energy density based on bone volume fraction (BV/TV) and the fabric tensor determined by MIL. The treatment/sterilization process does not appear to influence bone graft stiffness. However, strength and energy dissipation of the bone grafts were found to be significantly reduced by 36% to 47% and 66% to 81%, respectively, for a broad range of volume fraction (0.14