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Chapter 1. The structure of tissues (40 pp., 33 figs.)

• 1.1 Introduction
• 1.2 The adaptation of tissues in the species and in the individual
• 1.3 Tissue types
• 1.4 The structure and function of cells
• 1.5 The hierarchical structure of tissues
• 1.6 Plans for the structure of a tissue
• 1.7 Structural materials for the tissue
• 1.8 Assembly of the tissue structure
• 1.9 References

Chapter 2. Mechanical modeling of biological structures (51 pp., 40 figs., 2 tables)

• 2.1 Introduction
• 2.2 Models and the real physical world
• 2.3 Guidelines for modeling biological tissues and solving biomechanics problems
• 2.4 The types of models used in biomechanics
• 2.5 The particle model
• 2.6 The rigid object model
• 2.7 The deformable continuum model
• 2.8 Lumped parameter models
• 2.9 Statistical models
• 2.10 Cellular automata
• 2.11 The limits of reductionism
• 2.12 References
• Appendix 2A Laplace Transform Refresher
• Appendix 2B First Order Differential Equations
• Appendix 2C Electrical analogs of the spring and dashpot models

Chapter 3. Basic continuum kinematics (26 pp., 10 figs.)

• 3.1 The deformable material model, the continuum
• 3.2 Rates of change and the spatial representation of motion
• 3.3 Infinitesimal motions
• 3.4 The strain conditions of compatibility

Chapter 4. Continuum formulations of conservation laws (23 pp., 10 figs.)

• 4.1 The conservation principles
• 4.2 The conservation of mass
• 4.3 The state of stress at a point
• 4.4 The stress equations of motion
• 4.5 The conservation of energy

Chapter 5 Modeling material symmetry (30 pp., 14 figs., 4 tables)

• 5.1 Introduction
• 5.2 The representative volume element (RVE)
• 5.3 Crystalline materials and textured materials
• 5.4 Planes of mirror symmetry
• 5.5 Characterization of material symmetries by planes of symmetry
• 5.6 The forms of the 3D symmetric linear transformation A
• 5.7 The forms of the 6D symmetric linear transformation
• 5.8 Curvilinear anisotropy
• 5.9 Symmetries that permit chirality
• 5.10 Relevant literature

Chapter 6. Formulation of constitutive equations (22 pp, 2 figs.)

• 6.1 Guidelines for the formulation of constitutive equations
• 6.2 Constitutive ideas
• 6.3 Localization
• 6.4 Invariance under rigid object motions
• 6.5 Determinism
• 6.6 Linearization
• 6.7 Coordinate invariance
• 6.8 Homogeneous versus inhomogeneous constitutive models
• 6.9 Restrictions due to material symmetry
• 6.10 The symmetry of the material coefficient tensors
• 6.11 Restrictions on the coefficients representing material properties
• 6.12 Summary of results
• 6.13 Relevant literature

Chapter 7. Four linear continuum theories (47 pp., 11 figs., 2 tables)

• 7.1 Formation of continuum theories
• 7.2 The theory of fluid flow through rigid porous media
• 7.3 The theory of elastic solids
• 7.4 The theory of viscous fluids
• 7.5 The theory of viscoelastic materials
• 7.6 Relevant literature

Chapter 8 Modeling material microstructure (26 pp., 8 figs.)

• 8.1 Introduction
• 8.2 The representative volume element (RVE)
• 8.3 Effective material parameters
• 8.4 Effective elastic constants
• 8.5 Effective permeability
• 8.6 Structural gradients
• 8.7 Tensorial representations of microstructure
• 8.8 Relevant literature

Chapter 9. Poroelasticity (45 pp., 8 figs., 2 tables)

• 9.1 Poroelastic materials
• 9.2 The stress-strain-pore pressure constitutive relation
• 9.3 The fluid content-stress-pore pressure constitutive relation
• 9.4 Darcy’s law
• 9.5 Matrix material and pore fluid incompressibility constraints
• 9.6 The undrained elastic coefficients
• 9.7 Expressions of mass and momentum conservation
• 9.8 The basic equations of poroelasticity
• 9.9 The basic equations of incompressible poroelasticity
• 9.10 Some example isotropic poroelastic problems
• 9.11 An example: the unconfined compression of an anisotropic disc
• 9.12 Relevant literature

Chapter 10. Collagen (32 pp., 51 figs., 3 tables)

• 10.1 Introduction
• 10.2 The extracellular matrix (ECM).
• 10.3 The amino acid composition sequence
• 10.4 The procollagen and collagen molecules
• 10.5 Experimental and theoretical deduction of collagen structure
• 10.6 The axial Young’s modulus of a collagen molecule
• 10.7 The many types and classes of collagens
• 10.8 Collagen structural hierarchy
• 10.9 Supramolecular assembly
• 10.10 Assembly of a tendon
• 10.11 References

Chapter 11. Bone tissue (43 pp., 22 figs., 8 tables)

• 11.1 Introduction
• 11.2 The types of bone tissue
• 11.3 Bone interfaces, porosities and fluids
• 11.4 Bone cells
• 11.5 The elastic symmetry of cortical bone
• 11.6 The poroelastic model for cortical bone
• 11.7 Electrokinetic effects in bone
• 11.8 Cortical bone strength
• 11.9 Cancellous bone architecture
• 11.10 The elastic properties of cancellous bone
• 11.11 Relevant literature

Chapter 12. Bone tissue adaptation (44 pp., 16 figs., 0 tables)

• 12.1 Introduction
• 12.2 Four animal experiments
• 12.3 Representation of the stimulus to bone remodeling
• 12.4 A phenomenological theory of surface adaptation
• 12.5 Estimating remodeling parameters
• 12.6 Prediction of the surface adaptation due to the bending of bone
• 12.7 Summary of surface remodeling results
• 12.8 A one-dimensional phenomenological bone stress adaptation model
• 12.9 Three-dimensional phenomenological bone stress adaptation theories
• 12.10 Possible cellular mechanisms for bone tissue adaptation
• 12.11 Relevant literature

Chapter 13 Modeling electrical effects in tissues, mixtures and charges (62 pp., 9 figs., 1 table)

• 13.1 Introduction
• 13.2 Kinematics of mixtures
• 13.3 The conservation laws for mixtures
• 13.4 A statement of irreversibility in mixture processes
• 13.5 Donnan equilibrium and osmotic pressure
• 13.6 Continuum model for a charged porous medium; the governing equations
• 13.7 Linear irreversible thermodynamics and the four constituent mixture
• 13.8 Modeling swelling and compression experiments on the intervertebral disc
• 13.9 Relevant literature

Chapter 14. Cartilage mechanics (37 pp., 25 figs., 2 tables)

• 14.1 Introduction
• 14.2 Hyaline cartilage
• 14.3 Elastic cartilage
• 14.4 Fibrocartilage
• 14.5 The perichondrium
• 14.6 Common properties of the three tissues; intervertebral disc, articular cartilage and the meniscus
• 14.7 The intervertebral disc (IVD)
• 14.8 Articular cartilage
• 14.9 Lubrication in synovial joints
• 14.10 The mechanical modeling of articular cartilage behavior
• 14.11 Menisci
• 14.12 Relevant literature

Chapter 15. Kinematics and mechanics of large deformations (57 pp., 26 figs.)

• 15.1 Large deformations
• 15.2 Large homogeneous deformations
• 15.3 Polar decomposition of the deformation gradients
• 15.4 The strain measures for large deformations
• 15.5 Measures of volume and surface change in large deformations
• 15.6 Stress measures
• 15.7 Finite deformation elasticity
• 15.8 The isotropic finite deformation stress-strain relation
• 15.9 Finite deformation hyperelasticity
• 15.10 Incompressible elasticity
• 15.11 Fung’s exponential strain energy function for tissues
• 15.12 Strain energy functions for tissues
• 15.13 Fung's quasi-linear viscoelasticity (QLV)
• 15.14 Relevant literature

Chapter 16. Tendon and ligament mechanics (28 pp., 14 figs., 3 tables)

• 16.1 Introduction
• 16.2 The constituents of tendons and ligaments
• 16.3 The cells and cell systems of the tendon
• 16.4 The arrangement of collagen fibers in tendons and ligaments
• 16.5 The lubrication system in tendons
• 16.6 The mechanical properties of tendons and ligaments
• 16.7 Constitutive equations for tendons and ligaments
• 16.8 Interstitial fluid flow
• 16.9 The insertions of tendons and ligaments
• 16.10 Structural adaptation

Appendix A. Matrices and tensors (74 pp., 5 figs)

• A.1 Introduction and rationale
• A.2 Definition of square, column and row matrices
• A.3 The types and algebra of square matrices
• A.4 The algebra of n-tuples
• A.5 Linear transformations
• A.6 Vector spaces
• A.7 Second rank tensors
• A.8 The moment of inertia tensor
• A.9 The alternator and vector cross products
• A.10 Connection to Mohr’s circles
• A.11 Special vectors and tensors in six dimensions
• A.12 The gradient operator and the divergence theorem

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