Features

Systematically discusses the bone remodeling process at both macro- and cellular level, providing derivations of the basic equations
Provides numerical simulations to model bone mechanics and dynamics during the remodeling process
Covers the response of bone materials to coupled thermo-magneto-electro-elastic fields
Presents experimental data and applications drawn from both the biomedical engineering and clinical perspectives
Summary

Research on bone remodeling has resulted in much new information and has led to improvements in design and biomedical practices. Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects presents a unified exploration of recent advances, giving readers a sound understanding of bone remodeling and its mathematical representation.

Beginning with a description of the basic concept of bone remodeling from a mathematical point of view, the book details the development of each of the techniques and ideas. From there it progresses to the derivation and construction of multifield and cellular bone remodeling and shows how they arise naturally in response to external multifield loads. Topics include:

Fundamental concepts and basic formulations for bone remodeling
Applications of formulations to multifield internal bone remodeling of inhomogeneous long cylindrical bone
Theory and solution of multifield surface bone remodeling
A hypothetical regulation mechanism on growth factors for bone modeling and remodeling under multifield loading
The RANK RANKL OPG pathway and formulation for analyzing the bone remodeling process
A model of bone cell population dynamics for cortical bone remodeling under mechanical and pulsed electromagnetic stimulus
Recent developments in experiments with bone materials
Readers will benefit from the thorough coverage of general principles for each topic, followed by detailed mathematical derivations and worked examples, as well as tables and figures where appropriate. The book not only serves as a reliable reference but is also destined to attract interested readers and researchers to a field that offers fascinating and technologically important challenges.

Table of Contents

Introduction to Bone Materials
Types of Bones
Bone Types Based on the Macroscopic Approach
Bone Types Based on Microscopic Observation
Bone Types Based on Geometric Shape
Bone Functions
Bone Cells
Osteoporosis
Bone Metabolism
Parathyroid Hormone (PTH)
Vitamin D
Calcitonin
Insulin-like Growth Factor
Transforming Growth Factor
Platelet-Derived Growth Factor
Fibroblast Growth Factor
Introduction to Bone Remodeling
Basic Bone Remodeling Theory
Adaptive Elastic Theory
Two Kinds of Bone Remodeling
Surface Bone Remodeling
Internal Bone Remodeling
A Simple Theory of Surface Bone Remodeling
Basic Equations of the Theory
Bone Remodeling of Diaphysial Surfaces
Extension to Poroelastic Bone with Fluid
A Simple Theory of Internal Bone Remodeling
Internal Remodeling Induced by Casting a Broken Femur
Extension to Poroelastic Bone with Fluid
Multifield Internal Bone Remodeling
Linear Theory of Thermoelectroelastic Bone
Analytical Solution of a Homogeneous Hollow Circular Cylindrical Bone
Semianalytical Solution for Inhomogeneous Cylindrical Bone Layers
Internal Surface Pressure Induced by a Medullar Pin
Numerical Examples
A Hollow, Homogeneous Circular Cylindrical Bone Subjected to Various External Loads
A Hollow, Inhomogeneous Circular Cylindrical Bone Subjected to External Loads
Extension to Thermomagnetoelectroelastic Solid
Multifield Surface Bone Remodeling
Solution of Surface Modeling for a Homogeneous Hollow Circular Cylindrical Bone
Rate Equation for Surface Bone Remodeling
Differential Field Equation for Surface Remodeling
Approximation for Small Changes in Radii
Analytical Solution of Surface Remodeling
Application of Semianalytical Solution to Surface Remodeling of Inhomogeneous Bone
Surface Remodeling Equation Modified by an Inserting Medullar Pin
Numerical Examples for Thermopiezoelectric Bones
Extension to Thermomagnetoelectroelastic Solid References
Theoretical Models of Bone Modeling and Remodeling
Hypothetical Mechanism of Bone Remodeling
Bone Growth Factors
Electrical Signals in Bone Remodeling
Bone Mechanostat
Adaptive Bone Modeling and Remodeling
A Mechanistic Model for Internal Bone Remodeling
Relationship between Elastic Modulus and Bone Porosity
Porosity Changes
BMU Activation Frequency
Rate of Fatigue Damage Accretion
Disuse
BMU Activation Frequency Response to Disuse and Damage
A Model for Electromagnetic Bone Remodeling
A Constitutive Model
Numerical Examples
Bone Surface Modeling Model Considering Growth Factors
Equations of Growth and Remodeling
Bone Remodeling Simulation
Bone Remodeling Induced by a Medullary Pin
The Solution of Displacements and Contact Force p(t)
A Constitutive Remodeling Model
Numerical Assessments
Effect of Parathyroid Hormone on Bone Metabolism
Structure of the Model and Assumption
Bone Remodeling Formulation
Results and Discussion
Cortical Bone Remodeling under Mechanical Stimulus
Development of Mathematical Formulation
RANK RANKL OPG Signaling Pathway
Mechanotransduction in Bone
Mathematical Model
Numerical Investigation
Parametric Study of the Control Mechanism
Bone Remodeling under Pulsed Electromagnetic Fields and Clinical Applications
Model Development
Effects of PEMF on Bone Remodeling
Mathematical Model
Numerical Investigation of the Model
Parametric Study of Control Mechanism of Bone Remodeling under PEMF
Effects of PEMF on Patients Undergoing Hip Revision
Basic Process
Clinical and Densitometric Evaluation
PEMF Stimulation
Discussion
Experiments
Removal of Soft Tissue from Bone Samples
Removal of Soft Tissues
Preparation of Thin Sections
Microstructural Analysis and Porosity Measurement
Standard Microhardness Indentation Testing
Results for the Samples after Removal of Soft Tissues
Change of Microstructure with Cleaning Procedure
Microindentation Testing of Dry Cortical Bone Tissues
Preparation of Bone Samples
Standard Microhardness Indentation Testing
Testing Results
Stretching Relaxation Properties of Bone Piezovoltage
Sample Preparation
Experimental Setup
Experimental Procedure and Characteristics of Piezovoltage
Results and Discussion
The Fitting Scheme for Stretched Exponential Function
Influence of Shear Stress on Bone Piezovoltage
Methods
Results
Discussion
Appendix A: Bone Types Based on Pattern of Development and Region
Index