Describing the mechanical behaviour of bone is an important part of developing finite element (FE) models among the biomechanics community. Several constitutive material models have been introduced in the last decades accounting for the arrangement of the trabecular architecture by linking the trabecular microstructure with the anisotropic response of bone to mechanical loads. Currently, fabric-elasticity or high-resolution FE models are the main approaches for characterising the anisotropic stiffness tensor in bone samples with a uniform trabecular distribution. However, due to the highly complex and heterogenous trabecular distribution in entire bone segments, the accuracy of these techniques in determining the mechanical anisotropy of whole bones remains somewhat unclear. Largevolume micro-computed tomography (micro-CT) scanners have been recently introduced for examining the microarchitecture in entire human bone segments rather than small bone samples harvested from strategic bone locations, offering the potential for investigating the mechanical effect of trabecular anisotropy at the organ level. Furthermore, the biomechanics community still needs to achieve an appropriate standard methodology for developing FE models of bones. Consequently, there is significant interlaboratory variability in predicting the mechanical behaviour of bone due to using different protocols. In addition, currently, experimental validations of the FE models are mainly limited to cortical bone measurement of strains, leaving the validity of internal bone predictions unclear. In this context, understanding the mechanical anisotropy of the proximal human femur by investigating the effect of bone microarchitecture on the load support capacity may have implications on protocols for modelling bone mechanics, overcoming some e current limitations.
This thesis aimed to understand the bone mechanics of proximal human femurs by investigating the anisotropic mechanical behaviour of bone due to its microarchitecture. To achieve this, the following questions need to be addressed: 1) what is the effect of employing two homogenization-based methodologies on determining the anisotropic stiffness tensor of trabecular bone in the entire proximal human femur? 2) what is the contribution of microstructural anisotropy to the load-bearing capacity of the entire human femur? 3) to what extent does the variability of different material constitutive models influence the prediction of internal bone strains in the human femur, and what are the qualitative differences compared to a selected model?
The starting point of this research was a unique dataset of micro-computed tomography (micro-CT) imaging of entire human femurs obtained at the Australian Synchrotron using a novel large-object time-elapsed micro-CT protocol developed by my supervisors. Taking advantage of this recently introduced high-resolution imaging modality, the 3D examination of bone segments allows for capturing relevant features of bone architecture, providing a deeper understanding of the role of trabecular microstructure in the mechanical behaviour and load support capacity at the organ level.
A software pipeline with semi-automatic image processing was developed to characterise the mechanical anisotropy of bone cubes using high-resolution images from a cohort of nine elderly woman donors. Contiguous 5-mm length cubes were virtually extracted by intersecting a 3D multigrid with the volumetric images. The anisotropic stiffness tensor was computed for each cube based on fabric measurements and subsequently compared against direct mechanical assessment using micro-FE analysis. Furthermore, this pipeline has been applied extensively across the entire volume of proximal human femurs to perform a comprehensive comparison between fabric and micro-FE methods for bone cubes with different trabecular microstructures. It is worth noting that the micro-FE and fabric-based approaches rely on the homogenisation assumption. Therefore, comparing the stiffness tensor between these methods will shed light on their respective applicability and inherent differences, even without direct measurements of reference. Regression analysis showed weak agreement between fabric- and micro-FE models (R2=0.57). Deviations between fabric-elasticity and micro-FE models were mapped onto micro-CT images, followed by an in-depth examination of their correlations with bone volume fraction providing valuable insights concerning the trabecular microstructure. While weak-moderate agreement was found between models in predicting stiffness tensor with deviations up to 100% for cubes extracted along the femur head and femur neck, high deviations up to 1000% were reported for samples extracted at the interface between cortical and trabecular bone, and from the inner bone regions having values of bone volume fraction lower than 18%.
The contribution of trabecular microstructure to mechanical support of the whole proximal femur was investigated by mapping fabric-based anisotropic material properties into continuum FE models and comparing the prediction of strain energy with the widest-used isotropic constitutive law. The investigation revealed that the majority of strain energy is accumulated within the trabecular bone, accounting for approximately 86-92% of the total energy. In contrast, the cortical bone contributed to a comparatively lower percentage, about 8-14%. Notably, when considering a threshold of 90% for the amount of external work, it was observed that this work was predominantly concentrated along the principal compressive trabeculae groups, highlighting their potential role in energy absorption and dissipation. Furthermore, a comparison of local differences in strain energy between isotropic and anisotropic models demonstrated a significant 60 ±40%, suggesting different energy transfer pathways associated with the modelling of mechanical anisotropy.
Finally, the variability in predicting strains, attributed to the lack of standardisation in modelling the bone material properties within the biomechanics community, was extended to the internal bone volume. Significant deviations in strain predictions, up to 50% of the yield strain, were observed in both cortical and inner bone regions. Although a preliminary qualitative comparison between measurements based on digital volume correlation and numerical FE predictions demonstrated good agreement in identifying regions with the most pronounced strains, a quantitative validation study is warranted to ensure the reliability and reproducibility of these findings.
In conclusion, in this thesis, a semi-automated methodology for characterising the mechanical anisotropy of trabecular bone based on high-resolution volumetric images was introduced, providing a better understanding of the mechanics of the entire proximal human femur, with the following findings: 1) large deviations between fabric- and micro-FE based models in determining the anisotropic stiffness tensor in entire proximal human femur analysis; 2) a better understanding of the strain energy redistribution mechanism obtained by modelling the mechanical anisotropy due to trabecular microstructure; 3) significant local differences in predicting internal strain between different material constitutive models. Further investigation is required to validate inner strain predictions and address anisotropic FE models for clinical settings. Deep learning algorithms can achieve this by translating the insights from micro-CT images into clinical images. The integration of advanced imaging techniques with cutting-edge machine learning methodologies represents an exciting avenue for future research and can potentially revolutionise the field of bone biomechanics and its clinical applications.