Section I Basic Biology

1 Integrated Bone Tissue Physiology: Anatomy and Physiology

1.1 Introduction

1.2 Morphology: Macroscopic and Microscopic Structures

1.2.1 Cortical and Cancellous Bone

1.2.2 Woven and Lamellar Bone

1.2.3 Composition of Bone

1.2.4 Vascular and Nervous Supply1,2,15

1.2.5 Bone Surfaces12013;3,5,8

1.2.6 Bone Structural Unit1–8

1.2.7 Cells of Bone12013;8,12,29,352013;39,442013;57

1.2.7.1 The Osteoclasts1–8,29–35

1.2.7.1.1 The Phenotype

1.2.7.1.2 Origin and Fate

1.2.7.1.3 Regulation

1.2.7.1.4 Function

1.2.7.2 The Osteoblasts12013;8,12,29,35,372013;39

1.2.7.2.1 The Phenotype

1.2.7.2.2 Origin and Fate

1.2.7.2.3 Regulation

1.2.7.2.4 Function

1.2.7.2.5 Linkage of Osteoblast and Osteoclast Development

1.2.7.3 The Bone-Lining Cells12013;6,82013;10,29,442013;52,148

1.2.73.1 The Phenotype

1.2.7.3.2 Origin and Fate

1.2.7.3.3 Function

1.2.7.4 The Osteocytes12013;6,82013;10,12,512013;57

1.2.7.4.1 The Phenotype

1.2.7.4.2 Origin and Fate

1.2.7.4.3 Function

1.3 Skeletal Development1,2

1.3.1 Intramembranous Ossification1–4

1.3.2 Endochondral Ossification1–4

1.3.3 Growth12013;4,7

1.3.4 Modeling12013;5,7,8,582013;67

1.3.5 Remodeling12013;8,34,40,68,69

1.3.6 Basic Multicellular Unit or Bone Remodeling Unit12013;8,34,35,40,151

1.3.6.1 Resting

1.3.6.2 Activation

1.3.6.3 Resorption

1.3.6.4 Reversal (Coupling)

1.3.6.5 Formation and Mineralization

1.3.6.6 Bone Turnover1,5,7

1.3.6.7 Remodeling Space2

1.3.6.8 Remodeling Map

1.3.6.9 Conservation and Disuse Mode Remodeling

1.3.6.10 Remodeling-Dependent Bone Gain

1.3.6.11 A Unifying Theory of Bone Remodeling

1.4 Development of a Typical Long Bone1

1.5 Skeletal Mass and Its Changes2,59

1.5.1 Skeletal Adaptation to Mechanical Usage1,2,8,772013;85

1.5.1.1 The Mechanostat

1.5.1.2 The Utah Paradigm of Skeletal Physiology

1.5.1.3 Animal Models of Skeletal Underloading (Immobilization)

1.5.1.4 Animal Models of Skeletal Loading

1.5.1.4.1 Aging and Exercise

1.5.1.4.2 Site-Specific Cancellous Bone Response in Growing Rats

1.5.1.4.3 Time Course Study of the Exercise Response

1.5.1.4.4 Exercise and Bone Strength

1.5.1.4.5 In Vivo Loading Models

1.5.1.4.6 Loading-Related Changes in Modeling

1.5.2 Osteoporosis1,2,59,87,88,91,1012013;110

1.5.2.1 Definition

1.5.2.2 Prevention and Treatment

1.5.2.3 Animal Models for in Vivo Experimentation in Osteoporosis Research167

1.5.3 Age-Related Bone Loss12013;3,36,1132013;118,127,128

1.5.4 Factors Influencing Age-Related Bone Loss and Fracture Risk552013;57,1132013;138,1402013;142

Dedication

Acknowledgments

References

2 Cell Biology of Bone

2.1 Introduction

2.2 Bone Cells and Their Lineages

2.3 Bone Cell Properties and Functions

2.3.1 Osteoblasts

2.3.1.1 Morphology

2.3.1.2 Matrix Synthesis and Secretion

2.3.1.3 Mineralization

2.3.2 Osteocytes

2.3.2.1 Morphology: Cell Connections and Gap Junctions

2.3.2.2 Function: Mechanosensation and Damage Recognition

2.3.3 Bone-Lining Cells

2.3.4 Osteoclasts

2.3.4.1 Morphology

2.3.4.2 Bone Mineral Dissolution

2.3.4.3 Bone Matrix Degradation

2.3.4.4 Osteoclast Integrins and Cytoskeleton

2.4 Bone Cell Life Cycles and Their Regulation

2.4.1 The Osteoblastic Lineage

2.4.1.1 Alternative Differentiation Pathways

2.4.1.2 Osteoblast-Specific Genes

2.4.1.3 Induction of Osteoblastic Differentiation

2.4.1.4 Control of Proliferation, Maturation, and Death

2.4.2 The Osteoclastic Lineage

2.4.2.1 Hematopoietic Stem Cells and Monocyte Precursors

2.4.2.2 Differentiation of Monocytes into Osteoclasts: Interactions with Stromal/Osteoblastic Cells

2.4.2.3 Osteoclast Death

2.5 Regulators of Bone Cell Function

2.5.1 Systemic Factors

2.5.1.1 G Protein-Associated Receptors: Parathyroid Hormone and Calcitonin

2.5.1.2 Steroid/Retinoid Receptors: l,25(OH)2D3, Glucocorticoids, Estrogens, Androgens

2.5.1.3 1,25(OH)2 vitamin D3

2.5.1.4 Glucocorticoids

2.5.1.5 Estrogens and Androgens125,126,135

2.5.2 Local Regulators: Growth Factors and Prostaglandins

2.5.2.1 G Protein-Associated Receptors: Prostaglandins

2.5.2.2 The TGF-β Superfamily: TGF-βs and BMPs

2.5.2.3 Receptor Tyrosine Kinases: Insulin-Like Growth Factors and Binding Proteins, Fibroblast Growth Factors, Platelet-Derived Growth Factors

2.5.2.4 Fibroblast Growth Factors102

2.5.2.5 Platelet-Derived Growth Factors101

2.5.2.6 Insulin-Like Growth Factors and IGF-Binding Proteins103

2.5.3 Local Regulators: Cytokines

2.5.3.1 Interleukin-1, Tumor Necrosis Factor164

2.5.3.2 gpl30-Associated Receptors: Interleukin-6, Leukemia Inhibitory Factor, Oncostatin-M, Interleukin-11, Ciliary Neurotrophic Factor167

2.5.4 Local Regulators: Adhesion-Based Signaling

2.5.4.1 Cell-Matrix Interactions: Integrins

2.5.4.2 Cell-Cell Interactions: Cadherins37,40

2.6 In Vitro Systems to Study Bone Cells178–181

2.6.1 Cell Culture vs. Organ Culture

2.6.1.1 Organ Cultures179,181

2.6.1.2 Cell Cultures178,180

References

3 Molecular Biology Techniques to Measure Skeletal Gene Expression

3.1 Introduction

3.2 Examination of Known (Previously Identified) Genes

3.2.1 Northern Blotting

3.2.2 Reverse Transcriptase-Polymerase Chain Reaction

3.2.3 In Situ Hybridization

3.2.4 RNase Protection Assay

3.2.5 Array Technology

3.3 Gene Discovery

3.3.1 Differential Display (DD), Subtractive Hybridization, and Representational Difference Analysis (RDA)

3.3.2 Serial Analysis of Gene Expression (SAGE)

3.3.3 Microchip Technology (DNA Chip)

3.4 Gene Transfer

3.4.1 Nonvirus-Based Gene Transfer

3.4.2 Adenovirus-Based Gene Transfer

3.4.3 Retrovirus-Based Gene Transfer

3.5 Inactivation of Specific Genes

3.5.1 Antisense: Oligonucleotides and Full-Length Constructs

3.5.2 Ribozymes

3.6 Summary

Acknowledgments

References

4 Creating Transgenic Mice to Study Skeletal Function

4.1 Introduction

4.2 Construction of Conventional Transgenic Mice

4.2.1 Ectopic Expression

4.2.2 Tissue-Specific Transgene Expression

4.2.3 Dominant Negative Transgenics

4.3 Construction of Gene-Targeted or Knockout Mice

4.3.1 DNA Preparation

4.3.2 Embryonic Stem Cells

4.3.3 Animal Husbandry

4.4 Examples of Transgenic Mice with Skeletal Phenotypes

4.5 Examples of Knockout Mice with Skeletal Phenotypes

4.6 New Frontiers: Designer Mice

4.6.1 Tissue-Specific Knockout Using Cre-recombinase

4.6.2 Point Mutations or Subtle Gene Alterations

4.6.3 From Knockout to Knockin

4.6.4 Inducible Gain of Function: Timing Is Everything

4.6.5 Tissue-Specific Gene Inactivation: Combining Space and Time

4.7 Summary

Acknowledgments

References

5 Bone Mineralization

5.1 Introduction

5.2 Analysis of Bone Mineral

5.2.1 Elemental Analysis

5.2.1.1 Gravimetric Analysis

5.2.1.2 ED AX and Related Methods

5.2.2 X-Ray Diffraction

5.2.3 Spectroscopic Methods

5.2.3.1 Infrared

5.2.3.2 Raman

5.2.3.3 NMR

5.2.4 Backscatter Electron Imaging and Tomographic Methods

5.2.5 Other Techniques of Mineral Analyses

5.3 Bone Mineral Is Not Always the Same

5.3.1 Age and Sex Differences

5.3.2 Diet and Bone Mineral Properties

5.3.3 Bone Diseases and Their Therapies

5.4 Bone Mineral Formation

5.4.1 A Digression: The Physical Chemistry of Crystal Formation

5.4.2 Factors Controlling Initial Bone Mineral Deposition

5.4.2.1 Ion Concentrations

5.4.2.2 Removal of Mineralization Inhibitors Facilitates Bone Mineral Deposition

5.4.2.3 Collagen—The Template for Mineral Deposition

5.4.2.4 Noncollagenous Proteins as Regulators of Mineral Deposition

5.4.2.4.1 Cell-Free Solution Studies

5.4.2.4.2 Cell Culture Studies

5.4.2.4.3 Studies of Animals with Genetic Defects

5.4.3 Regulation of Bone Mineral Crystal Size

5.4.4 Bone Development

References

Section II Techniques from Mechanics and Imaging

6 Mechanics of Materials★

6.1 Introduction

6.1.1 Bone and the Science of Mechanics

6.1.2 Objective and Organization

6.2 Force and Vectors

6.2.1 Force

6.2.2 Vectors

6.2.3 Mechanical Equilibrium

6.3 Stresses and Matrices

6.3.1 Normal Stresses and Shear Stresses

6.3.2 Matrix Notation

6.4 Strain

6.5 Axial Deformation

6.5.1 The Tensile Test

6.5.2 Poisson’s Ratios

6.6 Hooke’s Law for Orthotropic Materials

6.6.1 Orthotropic Symmetry

6.6.2 Multiaxial Loading

6.6.3 Hooke’s Law for Orthotropic Materials

6.6.4 Digression for a Point of Notation

6.6.5 Thermodynamic Restrictions on the Orthotropic Elastic Constants

6.7 Stresses in a Cylindrical Shaft

6.7.1 The Cylindrical Shaft

6.7.2 Centric Compressive Loading

6.7.3 Pure Bending

6.7.4 Eccentric Axial Loading

6.7.5 Torsion

6.8 The Displacement-Strain Relations

6.8.1 Position and Displacement

6.8.2 Derivatives and Gradients

6.8.3 Strain and Rotation

6.9 The Theory of Orthotopic Elasticity

6.9.1 The Stress Equations of Equilibrium

6.9.2 The Basic System of Equations

6.9.3 The Formulation of Boundary-Value Problems

References

7 Experimental Techniques for Bone Mechanics

7.1 Introduction

7.2 Specimen Handling and Considerations

7.2.1 Bone Hydration

7.2.2 Temperature

7.2.3 Strain Rate

7.3 Bone Density and Morphology Measurements

7.3.1 Direct Measurement of Bone Density

7.3.2 Cross-Sectional Moment of Inertia

7.3.3 Histomorphometry

7.3.3.1 Porosity

7.3.3.2 Collagen Orientation

7.4 Mechanical Testing Methods

7.4.1 Outcome Measures

7.4.2 Equipment

7.4.3 Tensile Testing

7.4.4 Compressive Testing

7.4.5 Bending Tests

7.4.6 Torsion Testing

7.4.7 Site-Specific Tests

7.4.8 Indentation Testing

7.4.9 Pure Shear Tests

7.4.10 Fracture Mechanics Testing

7.4.11 Fatigue Testing

7.4.12 Micro- and Nanotesting

7.4.13 Acoustic Tests

7.5 Animal Models for Biomechanical Testing

7.5.1 Choice of an Animal Model

7.5.2 Biomechanical Measurements for Mice

7.5.3 Evaluation of Drugs for Treatment of Osteoporosis

7.5.4 Evaluation of Drugs for Treatment of Osteoarthritis

7.5.5 Evaluation of Surgical Remedies

7.6 Quality Assurance

7.6.1 Experimental Protocols

7.6.2 Standard Operating Procedures

7.6.3 Equipment Calibration

7.6.4 Use of Testing Standards and Data Verification

7.6.5 Record Keeping

7.6.6 Archiving

References

8 In Vivo Measurement of Bone Deformations Using Strain Gauges

8.1 Introduction

8.2 The Development of Strain Gauge Procedures for Use with Bone

8.2.1 Development of the Bonded Resistance Strain Gauge

8.2.2 Early Bone Strain Gauge Studies

8.2.3 Types of Gauges Used

8.2.4 Waterproofing Strain Gauges

8.2.5 Bone Site Selection and Preparation

8.2.6 Attachment of Gauge to Bone

8.2.7 Wiring and Strain Relief

8.2.8 Verification of Gauge Attachment and Gauge Function

8.2.9 Dummy Gauges

8.2.10 Collection of Strain Gauge Data

8.2.11 Calculation of Principal Strains

8.2.12 Calculation of Normal and Shear Strains Across a Bone Section

8.3 Results of in Vivo Strain Gauge Experiments

8.3.1 Measurement of Peak Bone Strains and Strain Rates during Various Activities

8.3.1.1 Early Sheep and Dog Measurements

8.3.1.2 Human Measurements

8.3.1.3 Sheep Measurements

8.3.1.4 Horse Measurements

8.3.1.5 Pig Measurements

8.3.1.6 Dog Measurements

8.3.1.7 Measurements in the Dog, Horse, and Goat as a Function of Speed and Gait

8.3.1.8 Galago, Macaque, Gibbon, and Owl Monkey Measurements

8.3.1.9 Rabbit Measurements

8.3.1.10 Fish Measurements

8.3.1.11 Rat Measurements

8.3.1.12 Turkey Measurements

8.3.1.13 Growing Chicken and Rat Measurements

8.3.1.14 Rooster Measurements

8.3.1.15 Bat and Pigeon Measurements

8.3.1.16 Immature Alligator and Iguana Measurements

8.3.2 Quantifying the Daily Strain History of Bone

8.4 Alternative in Vivo Techniques to Measure Bone Strains

8.5 Summary

References

9 Imaging of Bone Structure

9.1 Introduction

9.1.1 About Bone Structure

9.1.2 About Spatial Resolution

9.2 Imaging Procedures

9.2.1 CT

9.2.2 Micro-CT

9.2.3 Synchrotron-CT

9.2.4 MRI

9.2.5 Micro-MRI

9.3 Structural Features Analyzed from Bone Images

9.3.1 Patient Examinations

9.3.2 Bone Samples

9.3.3 Small Laboratory Animals

9.4 Applications

9.4.1 Postmenopausal Osteoporosis

9.4.2 Simulated Bone Atrophy

9.4.3 Cellular-Level Bone Changes

9.5 Conclusions

References

Section III Mechanical and Architectural Properties of Bone

10 Mechanical Properties of Cortical Bone and Cancellous Bone Tissue

10.1 Introduction

10.2 Microstructural and Morphological Differences

10.3 Compositional Differences

10.4 Mechanical Properties of Cortical and Cancellous Bone Tissue

10.4.1 Mechanical Properties of Cortical Bone

10.4.2 Mechanical Properties of Cancellous Bone Tissue

10.4.2.1 Elastic/Inelastic Buckling

10.4.2.2 Uniaxial Tensile Testing

10.4.2.3 Bending Test

10.4.2.4 Ultrasonic Technique

10.4.2.5 Microindentation and Nanoindentation

10.4.2.6 Back-Calculation Using Finite Element Models

10.4.2.7 Fatigue Properties

10.5 Determinants of Cancellous Bone Tissue Modulus

10.6 Age-Related Changes

10.7 Summary

Acknowledgments

References

11 Viscoelastic Properties of Cortical Bone

11.1 Introduction: Viscoelastic Properties

11.2 Rationale: Why Is Bone Viscoelasticity of Interest?

11.3 Axial Properties of Bone

11.3.1 Linear Viscoelasticity

11.3.2 Nonlinear Viscoelasticity

11.4 Shear Properties of Bone

11.4.1 Linear Viscoelasticity

11.4.2 Nonlinear Viscoelasticity

11.5 Modeling

11.6 Structure and Causal Mechanisms

11.7 Comparisons with Other Materials

11.8 Summary

References

12 Composite Models of Bone Properties

12.1 Introduction

12.2 Composite Materials: An Introduction to Their Mechanical Characterization

12.3 Assessment of the Stiffness Parameters of Compact Bone

12.3.1 Review of the Older Literature6

12.3.2 Newer Theories

12.3.2.1 The Hierarchical Approach

12.3.2.2 The Global Approach

12.4 Approaches to the Viscoelastic and Failure Properties of Compact Bone

12.5 Interfacial Bonding between Organic and Mineral Phases

12.6 Conclusions

References

13 Dense Bone Tissue as a Molecular Composite

13.1 Introduction

13.2 The Mechanical Consequences of Changes in the Collagen Template

13.2.1 Cross-Links and Biomechanical Properties of Bone Collagen

13.2.2 Collagen Glycosylation

13.2.3 Osteogenesis Imperfecta

13.2.3.1 Mouse Models for Osteogenesis Imperfecta

13.2.3.1.1 The oim/oim Mouse

13.2.3.1.2 The Mov13 Mouse

13.2.3.1.3 The COLIA1 pro-alpha 1 Mutation

13.3 The Mechanical Consequences of Changes in the Mineral Phase

13.3.1 The Hydration Shell of Bone Mineral

13.3.2 Mineral Changes and Their Effects on Bone Biomechanical Properties

13.3.2.1 Effects of Ion Substitution

13.3.2.2 The X-Linked Hypophosphatemic Mouse (Hyp mouse)

13.4 The Role of Noncollagenous Proteins: Lessons from Gene-Targeted Models

13.4.1 Interfacial Bonding in the Engineering Sense: An Introduction

13.4.2 Noncollagenous Proteins and Proteoglycans Modulate the Properties of the Material “Bone”

13.4.2.1 Osteopontin

13.4.2.2 Osteonectin

13.4.2.3 Osteocalcin

13.4.2.4 Biglycan

13.4.2.5 Thrombospondin 2

13.5 Summary

References

14 Quantification of Cancellous Bone Architecture

14.1 Introduction

14.2 Stereological Methods

14.2.1 Volume Fraction

14.2.2 Surface Density

14.2.3 Star Volume

14.2.4 Connectivity

14.3 Three-Dimensional Methods

14.3.1 Anisotropy

14.3.1.1 Mean Intercept Length

14.3.1.2 Volume Orientation

14.3.1.3 Star Volume Distribution

14.3.2 Connectivity

14.3.3 Trabecular Dimensions

14.3.4 Other Measures

14.4 Traditional Histomorphometry

14.4.1 The Plate Model

14.5 Ad Hoc Methods

14.5.1 Trabecular Thickness

14.5.2 Connectivity

14.6 Concluding Remarks

References

15 Elastic Constants of Cancellous Bone

15.1 Introduction

15.2 Cancellous Bone Structural Characterization

15.3 Cancellous Bone Mechanical Characterization

15.3.1 Elastic Constants and Restrictions

15.3.2 Compressive and Tensile Mechanical Properties

15.4 Assessment of Cancellous Bone Elastic Constants

15.4.1 Experimental Assessment

15.4.2 Numerical Assessment from Structure Measurements

15.4.2.1 Micro-Finite-Element Analyses

15.4.2.2 Calculation of Stiffness Tensor and Mechanical Symmetries

15.5 The Anisotropic Elastic Properties of Cancellous Bone

15.5.1 Elastic Constants for Two Large Sets of Specimens

15.5.2 The Role of the Structure for Cancellous Bone Anisotropy

15.5.3 The Orthotropy Assumption

15.6 Cancellous Bone Elastic vs. Structural Parameters

15.6.1 Determination of Structure–Property Relationships

15.6.2 Structural Density Relationships

15.6.3 Other Structural Scalar Parameters

15.6.4 Relationships Based on Fabric Tensors

15.7 Dependency of Elastic Constants on Bone Tissue Properties

References

16 Strength of Trabecular Bone

16.1 Introduction

16.1.1 Terms and Definitions

16.2 Uniaxial Properties

16.2.1 Heterogeneity, Anisotropy, and Asymmetry

16.2.2 Strength-Density Relations

16.2.3 Tensile vs. Compressive Strengths

16.2.4 Failure Strains

16.2.5 Micromechanical Modeling

16.2.5.1 Cellular Solid Theory

16.2.5.2 Lattice-Type Finite-Element Modeling

16.2.5.3 High-Resolution Finite-Element Modeling

16.3 Multiaxial Behavior

16.3.1 Tsai-Wu Criterion

16.3.1.1 Derivation Using Strength-Density Relations—Triaxial Loading

16.3.1.2 Derivation Using Normalized Stresses—Axial-Shear Loading

16.3.1.3 Fabric-Based Formulation

16.3.2 Mechanistic Analysis

16.4 Post-Yield Behavior and Damage Mechanisms

16.4.1 Post-Yield Mechanical Behavior

16.4.2 Observations of Damage Mechanisms

16.5 Time-Dependent Behavior

16.5.1 Strain Rate Effects

16.5.2 Creep and Fatigue

16.6 Summary

Acknowledgments

References

17 Observations of Damage in Bone

17.1 Introduction

17.2 Mechanical Property Degradation as a Measure of Damage

17.2.1 Bone Inelasticity

17.2.2 The Mechanical Consequences of Damage

17.2.3 Methods of Experimental Study of Damage Mechanics

17.2.3.1 Measurement of Stiffness Degradation

17.2.3.2 Measurement of Strength Degradation

17.2.3.3 Other Mechanical Measures of Damage Accumulation

17.3 Histological Measures of Damage Accumulation

17.3.1 Histological Methods of Damage Characterization

17.3.2 In Vivo Damage Accumulation

17.3.3 Damage Induced during Laboratory Mechanical Tests

17.3.3.1 Damage Induced by Compressive Loading

17.3.3.2 Damage Induced by Tensile Loading

17.3.3.3 Damage Induced by Torsional Loading

17.3.3.4 Damage Induced in Trabecular Bone

17.3.4 The Relationship between Damage and Degradation

17.4 Acoustic Emission as a Measure of Damage Accumulation

17.5 Summary/Conclusions

References

18 Bone Damage Mechanics

18.1 Introduction

18.2 Basic Concepts of Continuum Damage Mechanics

18.3 Constitutive Models for Damaging Materials

18.3.1 State Variable Models

18.3.2 One-Dimensional Models

18.3.2.1 Damaging Elastic Model

18.3.2.2 Damaging Viscoelastic Model

18.3.2.3 Fondrk’s Viscoplastic Model

18.3.2.4 Elastic-Plastic and Elastic-Viscoplastic Models Incorporating Damage

18.3.2.5 Model of Zysset and Curnier

18.3.3 Fatigue Damage Models

18.4 Applications to Nonhomogeneous Loading

18.4.1 Symmetric Bending of a Prismatic Beam

18.4.2 Torsion of a Circular Cross Section

18.4.3 More General Problems, FEA Models

18.5 Micromechanical Models

18.6 Damage and Repair Models

18.7 Summary

References

19 Ontogenetic Changes in Compact Bone Material Properties

19.1 Introduction

19.1.1 The Development of Primary Bone

19.1.2 Mineralization

19.1.3 Remodeling

19.2 Changes in Mechanical Properties

19.2.1 Fetal Bone

19.2.2 Maturation and Aging

19.2.3 Pregnancy and Lactation

19.3 Are Youthful Changes Adaptive?

19.4 Adaptive Changes in Histology

19.5 Causes of Mechanical Decline

19.6 Ontogenetic Changes and Whole-Bone Behavior

19.6.1 Polar Bears

19.6.2 Gulls

19.7 Conclusions

References

20 Mechanical Effects of Postmortem Changes, Preservation, and Allograft Bone Treatments

20.1 Introduction

20.2 Postmortem Changes in Mechanical Properties

20.2.1 Postmortem Changes without Preservation

20.2.2 Changes in a Necrotic Bone that Remains in the Living Organism

20.2.3 Postmortem Changes in Unpreserved, Explanted Bones

20.3 The Mechanical Effects of Preserving Bone

20.3.1 Freezing

20.3.2 Chemical Preservation

20.3.2.1 Ethyl Alcohol

20.3.2.2 Formalin

20.3.2.3 Embalming

20.3.2.4 Summary

20.4 The Mechanical Effects of Storing and Treating Allograft Bone

20.4.1 Freeze-Drying

20.4.2 Irradiation

20.4.3 Methanol and Chloroform Treatment

20.4.4 Thermal Sterilization

20.4.5 Summary

Acknowledgments

References

Section IV Flow of Fluids in Bone

21 Blood Flow in Bone

21.1 Organization of Bone Vasculature

21.1.1 Circulatory Morphology

21.1.1.1 Afferent Vessels: Arteries and Arterioles

21.1.1.2 Efferent Vessels: Venules and Veins

21.1.1.3 Microvasculature

21.1.1.4 Lymphatics

21.1.2 Macrocirculation (Veins and Arteries) in a Typical Long Bone

21.1.2.1 Distribution of Blood Flow

21.1.2.2 Levels of Control of Macrocirculation

21 1.2.2.1 Direct Neuronal (Nervous) Control

21.1.2.2.2 Humoral Control

21.1.2.3 Local Control of Microcirculation

21.1.2.3.1 Local Chemical Regulation

21.1.2.3.2 Blood Element Regulation

21.1.2.3.3 Fluid Mechanical Regulation

21.2 Fluid Mechanical Aspects of Bone Blood Flow

21.2.1 Measurements of Convective Transport in Bone Vasculature as a Whole

21.2.1.1 Hydrostatic Pressure (P), Bone as a Starling Resistor

21.2.1.2 Axial Blood Flow

21.2.1.2.1 Q in Macroscopic Volumes of Bone

21.2.1.2.2 Q in Bone Microvasculature

21.2.1.3 Transmural Transport/Nutrient Exchange

21.2.1.3.1 Convective Transmural Transport

21.2.1.3.2 Diffusive Transport and Active Transport

Acknowledgments

References

22 Interstitial Fluid Flow

22.1 System Description

22.1.1 Basic Concept and Introduction

22.1.2 Tissue Composition

22.1.3 Levels of Porosity

22.1.4 Interstitial “Tissue” Fluid as Compared with Interstitial Fluid Component of Bone

22.1.5 Flow Pathways for Influx and Efflux of Interstitial Fluid to Bone Tissue

22.2 Molecular Transport Mechanisms in Bone

22.2.1 The Diffusion-Convection Equation

22.2.2 Diffusion or Transport in Bone Devoid of Mechanical Loading

22.2.2.1 Tracer Studies in “Quiescent” Bone: Elucidation of Transport Pathways and Barriers to Flow

22.2.2.2 Limiting Dimensions of Bone Spaces Relative to Tracer Sizes

22.2.3 Convection and Other Modes of Transport in Bone Subject to Loading

22.3 Biophysical Mechanisms of Fluid Movement

22.3.1 Active Transport by Osteocytes

22.3.2 Effects of Mechanical Loading

22.3.3 Pressure Gradients

22.3.3.1 Biot’s Theory of Poroelasticity

22.3.3.2 Application of Biot’s Theory to Bone

22.3.3.3 Interactions between the Medullary Canal and Capillary/Venous System

22.3.4 Electromechanical Effects

22.3.4.1 Piezoelectric Effects

22.3.4.2 Streaming Potentials: The Source of Strain Generated Potentials

22.3.5 Biochemical Mechanisms, Osmotic Pressure, Hydraulic Conductivity, and Interrelationships among Different Effects

22.4 Measurement of Interstitial Fluid Flow

22.4.1 Approximations Based on Theoretical Models

22.4.2 In Vitro Studies

22.4.3 Ex Vivo Studies

22.4.4 In Vivo Studies

22.5 Implications of Interstitial Fluid Flow for Bone Growth, Adaptation, and Repair

22.5.1 Mechanotransduction Effects

22.5.1.1 Direct Mechanical Effects on Cells

22.5.1.2 Enhancement of Transport

22.5.1.3 Electromechanical Effects

22.5.2 Bone Growth, Adaptation, and Repair

22.5.3 Proposal for a Transport-Based Theory of Bone Remodeling

References

23 Bone Poroelasticity

23.1 Introduction and Notation

23.1.1 Introduction

23.1.2 Notation

23.2 The Microstructure of the Bone Porosities

23.2.1 The Structures of Bone Associated with Bone Fluid

23.2.2 The Interfaces between the Levels of Bone Porosity

23.2.2.1 Periosteum

23.2.2.2 IC—The Cellular Interface, Including the Endosteum

23.2.2.3 ILC—The Interface Consisting of the Walls of the Lacunae and the Canaliculi

23.2.2.4 Cement Lines

23.2.3 The Porosities of Bone

23.2.3.1 Bone Fluid

23.2.3.2 PV—The Vascular Porosity

23.2.3.3 PLC—The Lacunar-Canalicular Porosity

23.2.3.4 PCA—The Collagen-Apatite Porosity

23.2.3.5 PIT—The Porosity of the Intertrabecular Space

23.3 Poroelasticity

23.3.1 The Approaches to Poroelasticity

23.3.2 Ideal Poroelasticity

23.3.3 Constitutive Equations for Ideal Poroelasticity

23.3.4 Field Equations for Ideal Poroelasticity

23.3.5 Solution Methods for the Poroelastic Equations

23.4 Poroelasticity Applied to Bone

23.4.1 Bone Poroelasticity Parameter Values

23.4.2 Applications of Single-Porosity Poroelasticity to Bone

23.4.3 Poroelastic Waves in Bone

23.4.4 The Two-Porosity Poroelastic Model for Bone

23.4.5 Strain-Generated Potentials in Bone

23.4.6 Anatomical Site of the Strain-Generated Potentials in Bone

23.4.7 Osteonal Strain-Generated Potentials in Bone: Experiment and Theory

23.5 Summary

References

24 Streaming Potentials in Bone

24.1 Streaming Potentials in Bone: A Historical Perspective

24.2 From Piezoelectricity to Streaming Potentials in Bone

24.2.1 Introduction

24.2.2 Electromechanical Measurements in Transition from Dry to Wet Bone

24.2.3 Summary of Early Streaming Potential Data

24.3 Microelectrode Studies of Streaming Potentials in Bone

24.4 Streaming Potentials in Living Bone

24.5 Review of Theoretical Models of Streaming Potentials in Bone: in Vitro Models

24.6 Theory Development in Live Bone

References

25 The Intrinsic Permeability of Cancellous Bone

25.1 Introduction

25.2 Permeability: Darcy’s Law

25.2.1 Units of Permeability

25.2.2 Limits of Validity

25.2.2.1 Upper Limit to Darcy’s Law

25.2.2.2 Lower Limit to Darcy’s Law

25.2.2.3 Other Non-Darcian Fluid Flows

25.3 Permeability Theories

25.3.1 Hydraulic Radius-Based Theories

25.3.1.1 Assumptions

25.3.1.2 Kozeny’s and Related Models (Carman’s Modification)

25.3.1.3 Anisotropic Extension of Kozeny-Carman Relation

25.3.2 Drag Theories

25.4 Cancellous Bone Permeability

25.4.1 Problems Associated with the Measurement of Cancellous Bone Permeability

25.4.1.1 Range of Porosity

25.4.1.2 Specimen Size

25.4.1.3 Shape of Fluid Channel

25.4.2 Results of Previous Investigations

25.5 Viscosity

25.6 Summary

References

Section V Bone Adaptation

26 Pathophysiology of Functional Adaptation of Bone in Remodeling and Repair in Vivo

26.1 Introduction

26.1.1 Functional Environment of the Skeleton

26.2 Bone Loss under Conditions of Reduced Loading

26.2.1 Reduced Functional Loading

26.2.1.1 Generalized Reduced Loading

26.2.1.2 Localized Loss of Bone

26.3 Adaptation of the Skeleton to Increased Functional Loading

26.3.1 Increased Physiological Exercise

26.3.2 Induced Overload of Skeletal Elements by Invasive Techniques

26.3.3 Induced Overload by Externally Applied Mechanical Stimuli

26.3.3.1 Application of Mechanical Stimuli by Means of Transcutaneous Implants

26.3.3.2 Application of Mechanical Stimuli by Noninvasive Techniques

26.3.3.3 Mechanically Induced Matrix Microdamage

26.3.4 Age-Related Modulation of Mechanically Induced Bone Formation

26.3.5 Hormonal Modulation of Mechanical Adaptation of Bone

26.3.6 Dietary Effects on Mechanical Adaptation of Bone

26.3.7 Modeling Changes in Bone Structure in Long-Term Adaptation

26.4 Transduction Pathways

26.4.1 Electrical and Electromagnetic Stimulation

26.4.2 Fluid Flow

26.4.3 Estrogen Mediation

26.4.4 Prostaglandins

26.4.5 Nitric Oxide

26.5 Mechanical Modulation of Bone Repair

26.5.1 Direct Fracture Repair

26.5.2 Indirect Fracture Repair

26.5.3 Mechanical Variables Influencing Healing

26.6 Conclusions

References

27 Devices and Techniques for in Vitro Mechanical Stimulation of Bone Cells

27.1 Introduction and Historical Background

27.2 Hydrostatic Compression

27.3 Direct Platen Contact

27.4 Longitudinal Substrate Distension

27.5 Substrate Bending

27.6 Axisymmetric Substrate Distension

27.7 Fluid Shear

27.8 Combined Stimuli

Acknowledgments

References

28 Experiments on Cell Mechanosensitivity: Bone Cells as Mechanical Engineers

28.1 Introduction

28.2 The Bone Cell Network

28.3 Mechanosensing Mechanism in Bone

28.4 Osteocyte Mechanosensitivity

28.5 The Lacuno-Canalicular Network and Bone Remodeling—a Hypothesis

References

29 Mechanosensory Mechanisms in Bone

29.1 Introduction

29.2 The Connected Cellular Network

29.3 Mechanosensation on the Ccn

29.3.1 Stimuli

29.3.2 Reception and Transduction

29.3.2.1 Stretch- and Voltage-Activated Ion Channels

29.3.2.2 Cyto-Matrix Sensation-Transduction Processes

29.3.2.3 Cyto-Sensation by Fluid Shear Stresses

29.3.2.4 Cyto-Sensation by Streaming Potentials

29.3.2.5 Exogenous Electric Field Strength

29.3.2.6 The Uniqueness of Osseous Mechanosensation

29.3.3 Signal Transmission

29.3.3.1 Cell-to-Cell Communication

29.3.3.2 Signal Processing and Integration

29.3.3.3 A Tentative Mechanotransduction Synthesis

29.4 Questions for Future Research; Socratic Questions

References

30 The False Premise in Wolffs Law

30.1 Introduction

30.2 The Problems with Wolff’s Law

30.2.1 the Origin of Wolff’s Law—The Culmann and von Meyer Drawings

30.2.2 Previous Critiques of Wolff’s Law

30.2.3 Stress Trajectories

30.2.4 The False Premise

30.3 Toward Resolution

30.3.1 The Resolution Length Restriction on the Trajectorial Theory

30.3.2 Abandoning the Use of Wolff’s Name or the Use of the Word Law or Both

References

31 Bone Modeling and Remodeling: Theories and Computation

31.1 Introduction

31.2 General Concepts and Assumptions for Adaptation Simulations

31.2.1 Control of the Adaptive Process

31.2.2 Mechanical Signaling to Initiate Adaptation

31.2.2.1 Site Dependence

31.2.2.2 Time Dependence

31.2.3 Transduction of the Mechanical Signals

31.2.4 Adaptive Effects: Closing the Feedback Loop

31.2.5 Model Classification: Optimization, Phenomenological, and Mechanistic

31.3 Mechanics and Computational Issues

31.3.1 General Assumptions and Equations: Linear Elasticity

31.3.2 Adaptation Models

31.3.2.1 Material Properties of Bone can Change over Time

31.3.2.2 Boundary Positions of Cortical Bone Surfaces Can Change over Time

31.3.3 Computational Implementation

31.4 Theoretical Models and Simulations: Cortical Bone

31.4.1 Flexure-Neutralization Theory and the Three-Way Rule

31.4.1.1 Example Application: Curvature Reduction

31.4.2 Adaptive Elasticity

31.4.2.1 Example Applications: Ulnar Osteotomy

31.4.3 Cell Dynamics Model

31.4.3.1 Constant Cellular Activity: A Simple Adaptive Elasticity Model

31.4.3.2 Example Application: Ulnar Osteotomy

31.4.4 Site-Dependent, Strain Energy Density Model

31.4.4.1 Example Application: “Stress-Shielding”

31.4.5 Homogeneous Stresses at the Surface

31.4.5.1 Example Application: Curvature Reduction

31.4.6 Strength Optimization: Fatigue Damage and Repair

31.4.6.1 Example Application: Ulnar Osteotomy

31.5 Theoretical Models and Simulations: Trabecular Bone

31.5.1 Adaptive Elasticity

31.5.1.1 Example Application: Fabric Reorientation

31.5.1.2 Trabecular Density and Orientation Models for Skeletal Morphogenesis

31.5.1.3 Example Applications: Trabecular Bone in the Femoral Head

31.5.2 Trabecular Density: Strain Energy Dependence

31.5.2.1 Example Applications: Discrete Structures

31.5.3 Trabecular Density and Orientation: Spatial Influence Function

31.5.3.1 Example Applications: Tissue-Level Adaptations

31.5.4 Boundary-Element Implementation

31.5.4.1 Example Applications: Mergers and Separations; Strain and Strain Rate

31.6 Discussion

Acknowledgments

References

32 Mechanics of Bone Regeneration

32.1 Introduction

32.2 Fracture Healing

32.3 Mechanobiological Models

32.3.1 Pauwels’ Theory

32.3.2 Interfragmentary Strain Theory

32.3.3 Deformation/Pressure Models

32.3.4 Models Including Fluid Flow

32.4 Future Directions

Acknowledgments

References

Section VI Clinically Related Issues

33 Applications of Bone Mechanics

33.1 Introduction

33.2 Parameters Related to Applied Loads

33.2.1 Proximal Femur

33.2.2 Spine

33.3 Ex Vivo Behavior and Imaging Parameters

33.3.1 Proximal Femur

33.3.2 Spine

33.4 In Vivo Fracture Risk and Imaging Parameters

33.4.1 Proximal Femur

33.4.2 Spine

33.5 Development of Models of Skeletal Structures

33.5.1 Proximal Femur

33.5.2 Spine

33.5.3 Future Trends in Modeling Skeletal Structures

References

34 Noninvasive Measurement of Bone Integrity

34.1 Introduction

34.2 X-Ray Densitometry

34.2.1 Absorptiometric Methods

34.2.1.1 Dual-Energy Methods

34.2.1.2 Single-Energy Methods

34.2.2 Quantitative Computed Tomography

34.2.3 Limitations of X-Ray Densitometry

34.3 Ultrasonic Techniques

34.3.1 Review of Ultrasound Theory

34.3.2 Tissue Characterization

34.3.2.1 Influences on Ultrasound Velocity

34.3.2.2 Influences on Ultrasound Attenuation

34.3.3 Review of Experimental and Clinical Studies

34.3.4 Computational Methods

34.3.5 Directions for Future Research

34.4 Alternative Techniques

34.4.1 Micro-CT and High-Resolution Magnetic Resonance Imaging

34.4.2 Vibrational Methods

34.4.3 Plain Radiographic Textural and Pattern Analyses

34.4.4 Other Methods

34.5 Summary

References

35 Bone Prostheses and Implants

35.1 Introduction

35.2 Biomaterials

35.2.1 Biocompatibility

35.2.2 Metals

35.2.3 Ceramics

35.2.4 Polymers

35.3 Design of Bone Prostheses

35.3.1 General Overview

35.3.2 Prosthesis and Implant Systems

35.3.2.1 Temporary and Resorbable Implants

35.3.2.1.1 Bone Fixation Systems

35.3.2.1.2 Bone Substitute Materials

35.3.2.2 Permanent Implants for Total Joint Arthroplasty

35.3.2.2.1 Hip Replacement Prostheses

35.3.2.2.2 Knee Replacement Prostheses

35.3.2.2.3 Shoulder Replacement Prostheses

35.3.2.2.4 Elbow Replacement Prostheses

35.3.2.2.5 Ankle Replacement Prostheses

35.3.2.2.6 Wrist Replacement Prostheses

35.3.2.3 Dental Implants

35.3.2.4 Middle-Ear Implants

35.4 Analysis and Assessment of Implants

35.4.1 Preclinical Tests

35.4.1.1 Analytical Methods

35.4.1.2 Finite Element Methods

35.4.1.3 Strain Measurement Methods

35.4.1.4 Simulators

35.4.1.4.1 Wear

35.4.1.4.2 Loosening

35.4.2 Clinical Assessment

35.4.2.1 Gait Analysis

35.4.2.2 Radiographic Assessment

35.4.2.3 Roentgen Stereophotogrammetry Analysis

35.4.2.4 Retrieval Analysis

35.4.2.5 Outcome Analysis

35.4.2.6 Survival Analysis

35.5 Future Directions

Acknowledgments

References

36 Design and Manufacture of Bone Replacement Scaffolds

36.1 Introduction

36.2 Designing Bone Scaffolds

36.3 Fabricating Bone Scaffolds

36.4 Bone Scaffolds: An Example from Design to Testing

36.5 Conclusion

References

Index