Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects

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ISBN 9781466564169
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    • 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


    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
    Bone Metabolism
    Parathyroid Hormone (PTH)
    Vitamin D
    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
    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
    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

    Appendix A: Bone Types Based on Pattern of Development and Region

    Author Bio(s)

    Qing-Hua Qin received his bachelor of engineering degree in mechanical engineering from Chang An University, China in 1982, and his master of science and Ph.D. degrees in applied mechanics from Huazhong University of Science and Technology (HUST), China in 1984 and 1990, respectively. He is currently working as a professor in the Research School of Engineering at the Australian National University, Canberra, Australia. He was appointed a guest professor at HUST in 2000 and was a recipient of the J. G. Russell Award from the Australian Academy of Science. He has published over 200 journal papers and 6 monographs.