Biomechanics Textbook

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<p>This page intentionally left blankIntroductory BiomechanicsFrom Cells to OrganismsIntroductory Biomechanics is a new, integrated text written specically forengineering students. It provides a broad overview of this important branch of therapidly growing eld of bioengineering. A wide selection of topics is presented,ranging from the mechanics of single cells to the dynamics of human movement.No prior biological knowledge is assumed and in each chapter, the relevantanatomy and physiology are rst described. The biological system is thenanalyzed from a mechanical viewpoint by reducing it to its essential elements,using the laws of mechanics, and then linking mechanical insights back tobiological function. This integrated approach provides students with a deeperunderstanding of both the mechanics and the biology than that obtained fromqualitative study alone. The text is supported by a wealth of illustrations, tables,and examples, a large selection of suitable problems and many current references,making it an essential textbook for any biomechanics course.C. Ross Ethier is a Professor of Mechanical and Industrial Engineering, theCanada Research Chair in Computational Mechanics, and the Director of theInstitute of Biomaterials and Biomedical Engineering at the University of Toronto,with cross-appointment to the Department of Ophthalmology and Vision Sciences.His research focuses on biomechanical factors in glaucoma and on blood ow andmass transfer in the large arteries. He has taught biomechanics for over 10 years.Craig A. Simmons is the Canada Research Chair in Mechanobiology and anAssistant Professor in the Department of Mechanical and Industrial Engineering atthe University of Toronto, with cross-appointments to the Institute of Biomaterialsand Biomedical Engineering and the Faculty of Dentistry. His research interestsinclude cell and tissue biomechanics and cell mechanobiology, particularly as itrelates to tissue engineering and heart valve disease.Cambridge Texts in Biomedical EngineeringSeries EditorsProfessor Mark Saltzman Yale UniversityProfessor Shu Chien University of California, San DiegoProfessor William Hendee Medical College of WisconsinProfessor Roger Kamm Massachusetts Institute of TechnologyProfessor Robert Malkin Duke UniversityProfessor Alison Noble Oxford UniversityCambridge Texts in Biomedical Engineering provides a forum for high-quality,accessible textbooks targeted at undergraduate and graduate courses in biomedicalengineering. It will cover a broad range of biomedical engineering topics fromintroductory texts to advanced topics including, but not limited to, biomechanics,physiology, biomedical instrumentation, imaging, signals and systems, cellengineering, and bioinformatics. The series will blend theory and practice, aimedprimarily at biomedical engineering students but will be suitable for broadercourses in engineering, the life sciences and medicine.Introductory BiomechanicsFrom Cells to OrganismsC. Ross Ethier and Craig A. SimmonsUniversity of Toronto, CanadaCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So PauloCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKFirst published in print formatISBN-13 978-0-521-84112-2ISBN-13 978-0-511-27360-5 C. R. Ethier and C. A. Simmons 20072007Information on this title: www.cambridge.org/9780521841122This publication is in copyright. Subject to statutory exception and to the provision ofrelevant collective licensing agreements, no reproduction of any part may take placewithout the written permission of Cambridge University Press.ISBN-10 0-511-27360-6ISBN-10 0-521-84112-7Cambridge University Press has no responsibility for the persistence or accuracy of urlsfor external or third-party internet websites referred to in this publication, and does notguarantee that any content on such websites is, or will remain, accurate or appropriate.Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orghardbackeBook (EBL)eBook (EBL)hardbackTo my family, who make it all worthwhile.c. ross ethi erTo Deborah,and to my parents, who inspired my love of learning.crai g a. si mmonsContentsAbout the cover page xiiPreface xv1 Introduction 11.1 A brief history of biomechanics 31.2 An outline of this book 12References 152 Cellular biomechanics 182.1 Introduction to eukaryotic cellular architecture 182.2 The cells energy system 222.3 Overview of the cytoskeleton 232.3.1 Actin laments 252.3.2 Intermediate laments 282.3.3 Microtubules 282.4 Cellmatrix interactions 292.5 Methods to measure the mechanical properties of cellsand biomolecules 352.5.1 Atomic force microscopy 352.5.2 Optical trapping (optical tweezers) 412.5.3 Magnetic bead microrheometry 422.5.4 Micropipette aspiration 432.6 Models of cellular biomechanical behavior 532.6.1 Lumped parameter viscoelastic model of the cell 542.6.2 Tensegrity model of the cytoskeleton 602.6.3 Modeling actin laments as a foam 692.6.4 Computational model of a chondrocyte in its matrix 722.7 Mechanotransduction: how do cells sense and respond tomechanical events? 762.7.1 Mechanoreceptors 762.7.2 Intracellular signal transduction 782.7.3 Cellular response to mechanical signals 80viii Contents2.8 Techniques for mechanical stimulation of cells 802.8.1 Compressive loading 812.8.2 Stretching 822.8.3 Fluid ow 862.9 Summary of mechanobiological effects on cells inselected tissues 902.9.1 Endothelial cells in the vascular system 912.9.2 Smooth muscle cells in vascular tissue 932.9.3 Chondrocytes in articular cartilage 942.9.4 Osteoblasts and osteocytes in bone 952.10 Problems 99References 1113 Hemodynamics 1193.1 Blood rheology 1193.1.1 Blood composition 1213.1.2 Relationship between blood composition and rheology 1243.1.3 Constitutive equation for blood 1293.2 Large artery hemodynamics 1303.2.1 Physical characteristics of blood ow patterns in vivo 1303.2.2 Steady blood ow at low ow rates 1333.2.3 Unsteady ow in large vessels 1383.3 Blood ow in small vessels 1423.3.1 FahraeusLindqvist effect 1433.3.2 Inverse FahraeusLindqvist effect 1463.4 Problems 147References 1614 The circulatory system 1644.1 Anatomy of the vasculature 1644.2 The heart 1694.2.1 Gross anatomy of the heart 1714.2.2 Qualitative description of cardiac pumping 1724.2.3 Cardiac pumping power and ventricular function 1754.3 Arterial pulse propagation 1794.3.1 Systolic and diastolic pressure 1794.3.2 Windkessel model 1804.3.3 Arterial wall structure and elasticity 1834.3.4 Elastic waves 1864.3.5 Pressureow relationships: purely oscillatory ow 194ix Contents4.3.6 Pressureow relationships: mean ow effects 1974.3.7 Pressureow relationships: deviations from ideality 1984.4 The capillaries 2044.4.1 Capillary ltration: the experiments of Landis 2074.4.2 Osmotic pressure 2094.4.3 Quantitative analysis of capillary leakage 2114.5 The veins 2124.6 Scaling of hemodynamic variables 2134.7 Problems 218References 2355 The interstitium 2405.1 Interstitial uid ow 2405.1.1 Darcys law 2415.1.2 Clearance of edema 2425.2 Problems 248References 2496 Ocular biomechanics 2506.1 Ocular anatomy 2506.2 Biomechanics of glaucoma 2516.2.1 Tonometry 2526.2.2 Drainage of aqueous humor in normal and glaucomatous eyes 2576.2.3 Aqueous humor circulation in the anterior chamber 2636.2.4 Optic nerve head biomechanics 2646.3 Ocular blood ow 2716.4 Problems 274References 2767 The respiratory system 2827.1 Gross anatomy 2827.1.1 The conducting airways and pulmonary vasculature 2827.1.2 Associated structures 2857.2 Biomechanics of breathing 2877.3 Lung elasticity and surface tension effects 2887.4 Mass transfer 2947.4.1 Blood-side acinar mass transfer 2957.4.2 Air-side acinar mass transfer 3077.4.3 Whole lung mass transfer 3087.5 Particle transport in the lung 313x Contents7.6 Problems 316References 3298 Muscles and movement 3328.1 Skeletal muscle morphology and physiology 3338.1.1 Isotonic versus isometric contraction 3398.2 Muscle constitutive modeling 3438.3 Whole muscle mechanics 3518.3.1 Parallel versus pinnate muscle types 3518.4 Muscle/bone interactions 3538.4.1 Foreleg motion in two species 3538.4.2 Flexion of the elbow 3558.4.3 Biomechanics of the knee 3658.5 Problems 369References 3769 Skeletal biomechanics 3799.1 Introduction to bone 3799.2 Composition and structure of bone 3829.2.1 Cortical bone 3849.2.2 Trabecular bone 3849.3 Biomechanical properties of cortical and trabecular bone 3879.3.1 Cortical bone mechanics 3889.3.2 Trabecular bone mechanics 3899.3.3 Trabecular bone mechanics: density dependence 3909.3.4 Trabecular bone mechanics: unit cell models 3939.4 Bone fracture and failure mechanics 3959.4.1 Fast fracture 3979.4.2 Fatigue fracture 4039.5 Functional adaptation and mechanobiology 4079.6 The design of bone 4099.7 Introduction to soft connective tissues 4119.8 Structure of collagen 4129.9 Structure of ligament, tendon, and cartilage 4149.9.1 Ligament 4149.9.2 Tendon 4169.9.3 Cartilage 4189.10 Biomechanical properties of ligament, tendon, and cartilage 4199.10.1 Structural properties 4209.10.2 Material properties 4239.10.3 Material properties: tension 425xi Contents9.10.4 Material properties: compression 4269.10.5 Material properties: viscoelasticity 4289.10.6 Material properties: biphasic mixture theory of cartilage 4359.11 Problems 436References 43910 Terrestrial locomotion 44410.1 Jumping 44410.1.1 Standing jump 44410.1.2 Running jumps 44810.2 Description of walking and running 45110.2.1 Walking 45110.2.2 Running 45910.3 Gait analysis 46110.3.1 Kinematics 46310.3.2 Anthropometry 46810.3.3 Kinetics 47110.4 Problems 480References 487Appendix The electrocardiogram 489Index 498Color plate section between pages 118 and 119About the coverThe cover contains images that together represent the broad scope of modernbiomechanics. The gures are as follows:r Main image: A uorescent immunohistochemical image of an endothelial cellisolated fromthe surface of a pig aortic heart valve and grown in culture. Withinthe cell, the nucleus is stained blue and vimentin laments are stained green.Vimentin is an intermediate lament protein of the cellular cytoskeleton thatplays an important role in cellular mechanics.r Left top: An intermediate stage from a simulation of the forced unfolding ofrepeats 4 and 5 of chain Aof the protein lamin. Filamin is an actin cross-linkingprotein and therefore plays a role in the biomechanics of the cytoskeleton. Thesimulation was based on the crystal structure of part of lamin [1], and wascarried out in NAMD [2] and visualized using the VMD package [3]. (Imagecourtesy of Mr. Blake Charlebois.)r Left middle: A sketch by the Swiss anatomist Hermann von Meyer of theorientation of trabecular bone in the proximal human femur. This sketch wasaccompanied in the original article by a sketch of the principal stress trajectoriesin a crane having a shape similar to the femur. Together these sketches arebelieved to have inspired Wolffs Law of bone remodelling. From [4].r Left lower: The distributionof mass transfer rates fromowingbloodtoculturedvascular endothelial cells. The contoured quantity (the Sherwood number) wascomputedbyrst measuringthe topographyof the endothelial cells usingatomicforce microscopy and then solving the convection-diffusion equation in theblood owing over the cells. Mass transfer from blood to endothelial cells isimportant in cell-cell signalling. (Image courtesy of Mr. Ji Zhang.)References1. G. M. Popowicz, R. Muller, A. A. Noegel, M. Schleicher, R. Huber and T. A. Holak.Molecular structure of the rod domain of dictyostelium lamin. Journal of MolecularBiology, 342 (2004), 16371646.xiii About the cover2. L. Kale, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N. Krawetz et al. NAMD2:Greater scalability for parallel molecular dynamics. Journal of Computational Physics,151 (1999), 283312.3. W. Humphrey, A. Dalke and K. Schulten. VMD: Visual Molecular Dynamics. Journalof Molecular Graphics, 14 (1996), 3338.4. J. Wolff. Uber die innere Architectur der Knochen und ihre Bedeutung f ur die Fragevom Knochenwachsthum. Archiv f ur Pathologische Anatomie und Physiologie und f urKlinische Medicin, 50 (1870), 389450.PrefaceFor some years, we have taught an introductory course in biomechanics withinthe Department of Mechanical and Industrial Engineering at the University ofToronto. We have been unable to nd a textbook suitable for the purpose of intro-ducing engineers and others having a hard science background to the eld ofbiomechanics. That is not to say that excellent books on biomechanics do not exist;in fact, there are many. However, they are typically at a level that is too advancedfor an introductory course, or they cover too limited a subset of topics for purposesof an introductory course.This book represents an attempt to ll this void. It is not meant to be an extensivetreatise on any particular branch of biomechanics, but rather to be an introductionto a wide selection of biomechanics-related topics. Our hope is that it will aid thestudent in his or her introduction to the fascinating world of bioengineering, andwill lead some to pursue the topic in greater detail.In writing this book, we have assumed that the reader has a background inengineering and mathematics, which includes introductory courses in dynamics,statics, uid mechanics, thermodynamics, and solid mechanics. No prior knowl-edge of biology, anatomy, or physiology is assumed, and in fact every section beginswith a reviewof the relevant biological background. Each chapter then emphasizesidentication and description of the essential aspects of the related biomechanicsproblems. Because of the introductory nature of this book, this has led in somecases to a great deal of simplication, but in all instances, we have tried to maintaina rm link to biological reality.We wish to thank Professor David F. James, of the Department of Mechanicaland Industrial Engineering, University of Toronto. He rst developed the introduc-tory course in biomechanical engineering at the University and his course notesprovided the inspiration for parts of this book. Professors James E. Moore Jr.and Takami Yamaguchi provided important material for Ch. 1. We have benetedgreatly from interactions with our students, who sometimes are the best teachers,and our colleagues and mentors.We shall be most grateful to students who, upon discovering errors in...</p>