Bone is a dynamic organ, which performs a multitude of essential tasks in the physiology of human being. At the microscale, trabecular bone is composed of the so-called trabeculae, that are rod and plate-like structures which build up the trabecular bone network. Each trabecula is composed of bone packets, where collagen, hydroxyapatite crystals and water are the main constituents. The mechanical properties of bone are strictly related to bone material composition even though their relationship in the post-yield region is not yet fully understood. This knowledge is an essential step towards modelling individual’s mechanical performance, for instance by mean of finite element microstructural models, as well as improving diagnosis and prevention of diseases. A growing evidence of the importance in the post-yield region of collagen, its structure and the bone matrix organization has been shown in recent research. The general aim of this thesis is to investigate the mechanical properties of trabecular bone at the tissue level, specifically focusing on the inelastic region of the mechanical response, and in the characterization of the effects of the material composition. Three aims were specifically identified: (i) the development and validation of the system to mechanically test single trabeculae in bending and tension and to acquire the material composition data; (ii) the experimental measurement of the compositional and the postyield and failure properties in bending and tension of human bone tissue and (iii) the statistical modeling of the influence of collagen content on the mechanical properties of a single trabecula.
According to the first aim, a new device for measuring the material composition and the mechanical properties of single trabeculae in the post-yield region for both tensile and bending tests was developed and validated. Material composition was assessed for each single trabecula by calibrated µCT scans (TMD, average tissue mineral density) and Raman spectroscopy (MMR, mineral-to-matrix ratio; CPR, B-type carbonate substitution ratio; CCL, collagen cross-link ratio and total amount of collagen). Mechanical properties were calculated by means of a direct experimental testing on single trabeculae in tension and bending combined with reverse finite element analysis. The newly designed testing setup made use of a new optical strain tracking and real geometry acquisition and was validated by quantifying accuracy error (0.3%) and precision error (2.7%), thus demonstrating high reliability for accurate and reproducible measurements.
The newly designed setup was used to identify material and mechanical parameters of human trabecular bone at the tissue level. Beyond the elastic limit, an exponential hardening law characterised by the yield stress, postyield hardening stress and exponential hardening exponent was assumed. Absolute values and deviation were investigated at the tissue level up to failure for two different deformation modes, tension and bending and for two donors, a healthy and an osteoporotic one. A complete set of mechanical parameters (elastic modulus, yield stress, yield strain, ultimate stress, ultimate strain, exponential hardening coefficient, post-yield hardening stress, elastic work and post-yield work (PYW)) was reported, that can be used as a reference for modelling trabecular bone human tissue. High within-subject variability was found, for both the healthy and the osteoporotic donor. Nevertheless, the two donors could be separated by ultimate strain and post-yield work, as well as CCL and CPR.
Finally, the knowledge gained in the previous steps was used to statistically evaluate the influence of the physiological intra-donors variation of the material properties on the mechanical performance at the tissue level. By means of hierarchical multivariate regression analysis, for the first time it was reported that both the CCL and CPR are independent predictors of ultimate strain and PYW, explaining a significant amount of their variability. This finding indicates that bone matrix quality (CCL and CPR - mineral and collagen organization) play a dominant role in the determination of the local failure resistance of trabecular bone tissue, while the absolute value of mineral density or collagen concentration is of minor relevance. Principal component analysis (PCA) extracted three independently varying regions that explained 86% of the total variance, representing elastic, yield and ultimate components, named according to the parameters included in each component. PCA showed that CCL and CPR variation were included in the ultimate component. The high correlation between material properties and ultimate properties and the possibility to separate the mechanical behavior into three regions could allow implementing the results of the regression model as part of a constitutive model when predicting patient-specific bone failure. This finding suggests that a strain-based model could be the most appropriate one to predict tissue failure, modeled as a function of structure of the collagen fibers and the bone matrix composition.
In conclusion, the project presented in this thesis showed that a novel research approach, which makes use of multiple techniques including experimental mechanical testing, FE-reverse modeling and spectroscopy/µCT material analysis, is a promising method to provide the knowledge required for bone tissue constitutive modelling. The combination of these multiple techniques with this novel research approach is expected to provide a deeper understanding of the correlation between material and mechanical properties and to drive towards the implementation into bone failure predictive models.