Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects, 1st Edition (Paperback) book cover

Mechanics of Cellular Bone Remodeling

Coupled Thermal, Electrical, and Mechanical Field Effects, 1st Edition

By Qing-Hua Qin

CRC Press

320 pages | 100 B/W Illus.

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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


About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
MEDICAL / Biotechnology
MEDICAL / Orthopedics
MEDICAL / Surgery / General