Jakob Schwiedrzik

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.

Fabric-based Tsai–Wu yield criteria for vertebral trabecular bone in stress and strain space

Osteoporosis related vertebral fractures are an increasing clinical problem in ageing societies. The prediction of vertebral fracture load from QCT-based anatomy-specific finite element simulations could be very useful in the management of patients with osteoporosis, especially with regard to a possible fracture prevention or treatment optimisation. A key property in finite element analysis is the yield surface for the trabecular bone material. This study is aimed at identifying continuum-level yield criteria for vertebral trabecular bone using micro-finite element models subjected to uni-axial, shear, and tri-axial loading. A fabric-dependent, orthotropic Tsai-Wu yield criterion is proposed in both stress and strain spaces. Nonlinear micro-finite element models of cubic vertebral trabecular bone samples with 5.62 mm edge length were generated from μCT-scans. Kinematic boundary conditions were imposed and the specimen was loaded force controlled beyond yield in 17 different load cases (six uni-axial, three shear and eight multi-axial). The proposed yield criteria were fitted to the resulting yield data. Yield strains on-axis were significantly lower (10% in tension and 6% in compression) than in the transverse directions. Average yield strains were 0.7% in tension, 1.1% in compression, 1.0% in shear and ranged from 0.6% to 1.1% under multi-axial loading. In axial direction, maximum yield stress was 2.6 MPa in tension and 4.7 MPa in compression. Lowest shear stress was found in the transverse plane with 1.3 MPa. Multi-axial yield stresses ranged between values for uni-axial tension and compression. Yield stresses depended significantly and substantially on both volume fraction and fabric. Yield strains depended also significantly on both bone volume fraction and fabric, but only weakly on the former. The standard error of the estimate and the concordance correlation coefficient of the yield surface were 5.47% and 0.93 in strain space and 13.58% and 0.96 in stress space. The results of this study are not only consistent with experimental data from the literature but also extend the current knowledge of yield to multi-axial load cases that can hardly be realised in a biomechanical experiment. The presented yield data and criteria will help improving the prediction of vertebral ultimate load using anatomy-specific finite element models.

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.

Comparison of proximal femur and vertebral body strength improvements in the FREEDOM trial using an alternative finite element methodology.

Denosumab reduced the incidence of new fractures in postmenopausal women with osteoporosis by 68% at the spine and 40% at the hip over 36 months compared with placebo in the FREEDOM study. This efficacy was supported by improvements from baseline in vertebral (18.2%) strength in axial compression and femoral (8.6%) strength in sideways fall configuration at 36 months, estimated in Newtons by an established voxel-based finite element (FE) methodology. Since FE analyses rely on the choice of meshes, material properties, and boundary conditions, the aim of this study was to independently confirm and compare the effects of denosumab on vertebral and femoral strength during the FREEDOM trial using an alternative smooth FE methodology. Unlike the previous FE study, effects on femoral strength in physiological stance configuration were also examined. QCT data for the proximal femur and two lumbar vertebrae were analyzed by smooth FE methodology at baseline, 12, 24, and 36 months for 51 treated (denosumab) and 47 control (placebo) subjects. QCT images were segmented and converted into smooth FE models to compute bone strength. L1 and L2 vertebral bodies were virtually loaded in axial compression and the proximal femora in both fall and stance configurations. Denosumab increased vertebral body strength by 10.8%, 14.0%, and 17.4% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Denosumab also increased femoral strength in the fall configuration by 4.3%, 5.1%, and 7.2% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Similar improvements were observed in the stance configuration with increases of 4.2%, 5.2%, and 5.2% from baseline (p≤0.0007). Differences between the increasing strengths with denosumab and the decreasing strengths with placebo were significant starting at 12 months (vertebral and femoral fall) or 24 months (femoral stance). Using an alternative smooth FE methodology, we confirmed the significant improvements in vertebral body and proximal femur strength previously observed with denosumab. Estimated increases in strength with denosumab and decreases with placebo were highly consistent between both FE techniques.

Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup.

Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation.

An experimentally validated finite element method for augmented vertebral bodies

BACKGROUND Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies. METHODS Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments. FINDINGS The finite element models were able to predict apparent stiffness (R(2)>0.86) and apparent strength (R(2)>0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R(2)>0.48) and qualitative agreement with the experiments. INTERPRETATION The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

Post-yield and failure properties of cortical bone

Ageing and associated skeletal diseases pose a significant challenge for health care systems worldwide. Age-related fractures have a serious impact on personal, social and economic wellbeing. A significant proportion of physiological loading is carried by the cortical shell. Its role in the fracture resistance and strength of whole bones in the ageing skeleton is of utmost importance. Even though a large body of knowledge has been accumulated on this topic on the macroscale, the underlying micromechanical material behaviour and the scale transition of bones mechanical properties are yet to be uncovered. Therefore, this review aims at providing an overview of the state-of-the-art of the post-yield and failure properties of cortical bone at the extracellular matrix and the tissue level.

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.

Identification of polymer matrix yield stress in the wood cell wall based on micropillar compression and micromechanical modelling

Based on a combination of micropillar compression experiments and modelling of the secondary cell wall (cw) using continuum micromechanics, the shear yield stress of the polymer matrix is identified for both normal and compression wood of Norway spruce. It is shown that the model is able to capture the differences in mechanical properties between the two tissues based on the knowledge of composition of the samples, microfibril angle, as well as phase properties on the nanometer scale. By testing an isolated piece of the cell wall with a homogeneous and uniaxial stress field on the micrometer scale and using the micromechanical model to determine average stress fields on the nanometer scale, it is possible to identify the shear yield stress of the polymer matrix in wood, which was found to be in the range of 14.9–17.5 MPa for normal and compression wood. It was shown that this corresponds to a stress in the lignin phase of approx. 17 MPa. This combined study thus demonstrates a new approach for validating multiscale models predicting yield properties with uniaxial experiments at the microscale and measuring phase properties of inhomogeneous materials by a combination of modelling and experimental approaches.

Loss of bone strength in HLA-B27 transgenic rats is characterized by a high bone turnover and is mainly osteoclast-driven

OBJECTIVE Although osteopenia is frequent in spondyloarthritis (SpA), the underlying cellular mechanisms and association with other symptoms are poorly understood. This study aimed to characterize bone loss during disease progression, determine cellular alterations, and assess the contribution of inflammatory bowel disease (IBD) to bone loss in HLA-B27 transgenic rats. METHODS Bones of 2-, 6-, and 12-month-old non-transgenic, disease-free HLA-B7 and disease-associated HLA-B27 transgenic rats were examined using peripheral quantitative computed tomography, μCT, and nanoindentation. Cellular characteristics were determined by histomorphometry and ex vivo cultures. The impact of IBD was determined using [21-3 x 283-2]F1 rats, which develop arthritis and spondylitis, but not IBD. RESULTS HLA-B27 transgenic rats continuously lost bone mass with increasing age and had impaired bone material properties, leading to a 3-fold decrease in bone strength at 12 months of age. Bone turnover was increased in HLA-B27 transgenic rats, as evidenced by a 3-fold increase in bone formation and a 6-fold increase in bone resorption parameters. Enhanced osteoclastic markers were associated with a larger number of precursors in the bone marrow and a stronger osteoclastogenic response to RANKL or TNFα. Further, IBD-free [21-3 x 283-2]F1 rats also displayed decreased total and trabecular bone density. CONCLUSIONS HLA-B27 transgenic rats lose an increasing amount of bone density and strength with progressing age, which is primarily mediated via increased bone remodeling in favor of bone resorption. Moreover, IBD and bone loss seem to be independent features of SpA in HLA-B27 transgenic rats.