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

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

ISBN 9781138033719
Published October 12, 2017 by CRC Press
320 Pages 100 B/W Illustrations

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Book Description

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

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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.