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Table of contents
1 Introduction
1.1 Context and motivation
1.2 Hierarchical structure of bone
1.3 Importance of cortical bone and its elasticity
1.4 Assessment of cortical bone elasticity
1.4.1 Linear elasticity and Hooke’s law
1.4.2 Methods to measure bone mesoscopic elasticity
1.4.3 Methods to measure bone microelastic properties
1.5 MULTIPS project
1.6 Objectives of the thesis
1.7 Outline of the thesis
2 Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone
2.1 Introduction
2.2 RUS theory
2.3 Measurements
2.3.1 Specimens
2.3.2 Bone elasticity measurements by RUS
2.3.3 Specimen geometry
2.4 Simulation of the errors due to uncertainties on resonant frequencies and dimensions
2.4.1 Method
2.4.2 Results
2.5 Simulation of the errors due to imperfect specimen geometry
2.5.1 Method
2.5.2 Results
2.6 Discussion and conclusion
3 Relative contributions of microstructural and compositional properties to cortical bone stiffness at millimeter-scale
3.1 Introduction
3.2 Materials and methods
3.2.1 Specimens
3.2.2 Bone stiffness measurements
3.2.3 Bone microstructure
3.2.4 Degree of mineralization of bone
3.2.5 Fourier transform infrared microspectroscopy
3.2.6 Biochemical measurements
3.2.7 Statistics
3.2.8 Micromechanics modeling
3.3 Results
3.3.1 Descriptive statistics
3.3.2 Univariate correlation analysis
3.3.3 Multivariate regression model
3.3.4 Comparison between micromechanics model and experimental data
3.4 Discussion
3.5 Conclusion
4 Role of microstructure on the anisotropic elasticity of human cortical bone
4.1 Introduction
4.2 Materials and methods
4.2.1 Specimens
4.2.2 Stiffness measurements with resonant ultrasound spectroscopy
4.2.3 Bone microstructure
4.2.4 Numerical model and method of solution
4.2.5 Model with idealized microsstructure
4.2.6 Calibration of bone matrix stiffness
4.2.7 Data analysis
4.3 Results
4.3.1 Calibration of the model
4.3.2 Effect of pore shape
4.3.3 Descriptive statistics
4.3.4 Correlations between synthetic bone stiffness and microstructural variables
4.3.5 Effects of microstructure on bone stiffness
4.3.6 Effects of the simplified bone microstructure on bone stiffness
4.4 Discussion
4.5 Conclusion
5 Bone tissue anisotropic elastic properties determined by an inverse homogenization method and resonant ultrasound spectroscopy
5.1 Introduction
5.2 Materials and methods
5.2.1 Specimens
5.2.2 Bone elasticity measurements
5.2.3 Bone microstructure
5.2.4 Degree of mineralization of bone
5.2.5 Forward problem
5.2.6 Inverse problem
5.2.7 Error propagation analysis
5.2.8 Microstrain on bone matrix
5.3 Results
5.3.1 Experimental data and computation efficiency
5.3.2 Error propagation analysis
5.3.3 Comparison of the stiffness constants
5.3.4 Comparison between bone matrix elasticity and DMB
5.3.5 The variation of the microstrain
5.4 Discussion
5.5 Conclusion
6 Cortical bone elasticity measured by resonant ultrasound spectroscopy is not altered by defatting and synchrotron X-ray imaging
6.1 Introduction
6.2 Materials and methods
6.2.1 Specimens
6.2.2 Elasticity measurements by resonant ultrasound spectroscopy
6.2.3 Bone defatting
6.2.4 Synchrotron radiation microtomography
6.2.5 Experimental Protocol
6.2.6 Statistics
6.3 Results
6.4 Discussion
6.5 Conclusion
7 Assessment of trabecular bone tissue elasticity with resonant ultrasound spectroscopy
7.1 Introduction
7.2 Method
7.2.1 Specimens
7.2.2 Image acquisition and processing
7.2.3 RUS measurements
7.2.4 μ-FE and model frequency calculation
7.3 Results
7.4 Discusion
7.5 Conclusion
8 Critical assessment of ultrasonic bulk wave velocity method in bone elasticity measurements
8.1 Introduction
8.2 Theory
8.3 Method
8.3.1 Specimens
8.3.2 Ultrasonic velocity measurements
8.3.3 Resonant Ultrasound Spectroscopy
8.3.4 Data analysis
8.4 Results
8.5 Discussion
8.6 Conclusion
9 A comparison study of human cortical bone elasticity at multiple skeletal sites
9.1 Introduction
9.2 Materials and method
9.2.1 Specimens
9.2.2 Bone stiffness and porosity measurements
9.2.3 Statistics
9.3 Results
9.4 Discussion
9.5 Conclusion
