Mechanics of Cellular Bone Remodeling
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Qin Biomedical Engineering 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 Remodeling Bone Cellular of Mechanics Mechanics of Cellular 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 Bone Remodeling 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 Coupled Thermal, Electrical, in response to external multifield loads. Topics include: and Mechanical Field Effects • 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. Qing-Hua Qin K16026 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 ISBN: 978-1-4665-6416-9 711 Third Avenue New York, NY 10017 90000 an informa business 2 Park Square, Milton Park www.taylorandfrancisgroup.com Abingdon, Oxon OX14 4RN, UK 9 781466 564169 www.crcpress.com K16026 cvr mech.indd 1 11/8/12 8:27 AM Mechanics of Cellular Bone Remodeling Coupled Thermal, Electrical, and Mechanical Field Effects Mechanics of Cellular Bone Remodeling Coupled Thermal, Electrical, and Mechanical Field Effects Qing-Hua Qin CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20120823 International Standard Book Number-13: 978-1-4665-6417-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. 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Contents Preface ......................................................................................................................xi The Author ........................................................................................................... xiii 1. Introduction to Bone Materials ...................................................................1 1.1 Introduction ...........................................................................................1 1.2 Types of Bones .......................................................................................1 1.2.1 Bone Types Based on the Macroscopic Approach ..............1 1.2.2 Bone Types Based on Microscopic Observation ..................3 1.2.3 Bone Types Based on Geometric Shape ................................3 1.3 Bone Functions ......................................................................................7 1.4 Bone Cells ...............................................................................................9 1.5 Osteoporosis ........................................................................................12 1.6 Bone Metabolism ................................................................................. 14 1.6.1 Parathyroid Hormone (PTH)................................................ 15 1.6.2 Vitamin D ................................................................................ 16 1.6.3 Calcitonin ................................................................................ 16 1.6.4 Insulin-Like Growth Factor .................................................. 17 1.6.5 Transforming Growth Factor ............................................... 17 1.6.6 Platelet-Derived Growth Factor ........................................... 18 1.6.7 Fibroblast Growth Factor ...................................................... 19 1.7 Introduction to Bone Remodeling .................................................... 19 References .......................................................................................................22 2. Basic Bone Remodeling Theory .................................................................25 2.1 Introduction .........................................................................................25 2.2 Adaptive Elastic Theory .....................................................................25 2.2.1 Two Kinds of Bone Remodeling ..........................................26 2.2.2 Surface Bone Remodeling .....................................................28 2.2.3 Internal Bone Remodeling ....................................................29 2.3 A Simple Theory of Surface Bone Remodeling .............................. 31 2.3.1 Basic Equations of the Theory .............................................. 31 2.3.2 Bone Remodeling of Diaphysial Surfaces ..........................33 2.3.3 Extension to Poroelastic Bone with Fluid ...........................36 2.4 A Simple Theory of Internal Bone Remodeling .............................40 2.4.1 Internal Remodeling Induced by Casting a Broken Femur ......................................................................40 2.4.2 Extension to Poroelastic Bone with Fluid ...........................42 References .......................................................................................................49 vii viii Contents 3. Multifield Internal Bone Remodeling ......................................................53 3.1 Introduction .........................................................................................53 3.2 Linear Theory of Thermoelectroelastic Bone..................................54 3.3 Analytical Solution of a Homogeneous Hollow Circular Cylindrical Bone ..................................................................................55 3.4 Semianalytical Solution for Inhomogeneous Cylindrical Bone Layers ..........................................................................................60 3.5 Internal Surface Pressure Induced by a Medullar Pin ..................64 3.6 Numerical Examples ..........................................................................66 3.6.1 A Hollow, Homogeneous Circular Cylindrical Bone Subjected to Various External Loads ........................ 67 3.6.2 A Hollow, Inhomogeneous Circular Cylindrical Bone Subjected to External Loads .......................................72 3.7 Extension to Thermomagnetoelectroelastic Solid ..........................72 References .......................................................................................................79 4. Multifield Surface Bone Remodeling .......................................................83 4.1 Introduction .........................................................................................83 4.2 Solution of Surface Modeling for a Homogeneous Hollow Circular Cylindrical Bone ..................................................................83 4.2.1 Rate Equation