297

Index

aABAQUS 90abrasive wear 148acetabulum 183active transporters 34ADAM17 see tumor necrosis factor-alpha

converting enzyme (TACE)adaptive bone remodeling 77adenine 4adhesive wear 148adipose tissue 239afferent nerve fibers 30α-amino acids 46–47α-carbon 47α-chains 48α-form 48amide bond 46amine–carboxylic acid coupling strategy

201amino acids 3, 47– protein 46–48amphiphile 32– molecule 33animal cell 32anisotropy 114, 116, 131, 171, 186– bone remodeling 130ankle joint replacement 216–217, 229antibody-tagged magnetic nanoparticles

targeting 202apatites, in bone 18–21arbitrary stress state 176Aristotle of Stageira 2arterial supply system– dynamics 236–237– overview 234–236– in small animals and humans 238–239– transcortical arterial hemodynamics

237–238

arterioles 237, 239, 240articular calcified cartilage 14articular lamella 17articulations 17artificial joint 77, 154aseptic loosening 267, 271asymmetry, of living bodies 3atomic force microscopy (AFM) 104, 194,

195, 196auxin 11Avanta Soft Skeletal Implant 220

bball-and-strut model 185–186base pair (bp) 4basic invariants 162, 163, 175, 176, 179Bernal spiral 52, 53β-form 48Biaxial wrist implant 222, 223bidimensional simulations 78bilinear model 84biological apatite 106biological fibers architecture 58biological systems 9biomaterials, for joint replacement implants

209–211biomechanical behavior of bone implant, and

stem geometry 268biomechanical testing– living tissue, tribological testing of

152–154– orthopedic implants, tribological testing of

145–152– theoretical analysis, of tribological issues

154–155biomineralization 2Biot poroelastic formalism 253Birmingham hip 214

Biomechanics of Hard Tissues: Modeling, Testing, and Materials.Edited by Andreas Ochsner and Waqar AhmedCopyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32431-6

298 Index

bisphosphonates 43blood pressure 248, 261body environment 145, 150, 152, 155Boerdijk–Coxeter (B–C) helix 52, 53bonded bone 79, 89, 97– see also ingrowth under bonebone 1, 2, 77, 183– apatite in 18–21– body structure and 16–17– cells 31–39 see also magnetic cell

stimulation; mechanical cellstimulation

– cement 217–218– collagen and 48–52– deformation 233– density distribution 92, 95, 96, 130, 131– fluids 237– general microscopic structure of 22–24– growth of 13–15, 125– ingrowth 83, 93, 94, 95, 218, 268, 272,

290, 294– innervation 28–31– long 235, 236– loss 213–214, 292– marrow 8, 14, 29, 124, 237– mechanical loading of 233– mineral 18– modeling 42– osteons 24–27– osteoprotegerin (OPG) and 39, 40–41– polymer thermodynamics 55–63– porosity levels 244–247– protein amino acids and 46–48– RANK/RANKL and 41–42– regeneration see magnetic cell stimulation;

mechanical cell stimulation– resorption 38, 39, 45, 124, 132– of skeleton 17– structure of 21–22– tissue 17, 18– triple helix geometry and 52–55– tumor necrosis factor-alpha converting

enzyme (TACE) and 42– see also individual entriesbone fracture healing 125–126– application to 133–134– mechanistic models of 134–137, 136– model application examples, to implant

design 137–140bone lining cells 25, 36, 124bone lymphatics and blood vessel

trans-wall transport 241–244bone mineral density test 182bone morphogenetic proteins (BMPs) 35

bone multicellular unit (BMU) 24bone remodeling 42–46, 77, 124–125, 127,

193– application examples, to implant design

128–132– constitutive models 80–90– – bone model 80–81– – interface model 82–85– – interfacial adaptation model 89–90– – periprosthetic adaptation model 85–89– mechanical adaptations 79–80– mechanistic models of 126–128– microstructure orientation after 97– model 290–294, 292, 293– numeric examples 90–97– objective function for 276–277– phenomenological models of 126– see also bone fracture healingbone salt 2boundary lubrication 146–147, 148, 150, 222bovine serum lubrication 150, 151BOX 217Bragg–Nye bubble raft experiment 4, 5bulk compressibility 254

ccalcitonin gene-related peptide (CGRP) 31calcium carbonate CaCO3 18calcium hydroxyphosphate, Ca5(PO4)3OH

18callus 135, 139canaliculi 26, 36, 37–38canal system, in bones 24cancellous bone 181, 182, 186– porosity 246capillary network 238, 240carbohydrate cellulose 6cartilage 2, 14, 17, 183Cauchy elasticity 165cell-cultured flexure see four-point bendingcell membrane 32–34– transport 34–35cell metabolism 8–9cell stimulation see magnetic cell stimulation;

mechanical cell stimulationcell theory 4– see also individual entriescellular plastics and metals 183–188cellulose 58cemented stems 267, 269–270cementless implants 267, 271– hip stem, design requirements for– – implant stability 272– – stress shielding effect 272–273

Index 299

cementless prosthesis see under boneceramics 212– alumina 210Charnley hip stem 212chirality 3cholesterol 34chondrichthyes 14chondrification 2, 14chondrocytes 2, 14cobalt chrome molybdenum alloy 215,

217, 221, 222collagen 4, 18, 47, 48–52– elasticity 60–63– fibers 11–12, 22, 24, 25, 58, 59–60, 103,

106, 112–113– interaction with minerals 104– macromolecule 48– material properties of 105– microfibril 48, 50, 58, 60– molecular structure 51–52– three-chain configuration for 49,

50, 51collagen–apatite porosity 243collagen–hydroxyapatite porosity 244, 245,

247, 252, 253compact bone 21, 23, 38, 181– adult 102– decalcified cross section of 26– ground cross section of 27– osteons 24– see also cortical bonecompliance matrix 172, 173, 174composite material, bone as 101– elastic modulus 108–111– implications 117–118– macroscopic effects 111–112– microscale effects 112–113– mineral phase, of bone 103–104,

106–107– organic phase, of bone 103, 105–106– physical structure of bone material 104– water, in bone 104–105, 107compression loading systems 195compressive stimulation 197computational biomechanics and tools, for

implant designs see implant designs,optimization methods for 267

computational mechanobiology 129, 137,140

computational model, for boneimplant design 277

– finite element model 280–281, 281– optimization algorithm 278–280, 279concentric lamellae 24

connective tissue (CT) 1, 2, 6, 13, 18constitutive equations– linear elastic behavior– – generalized Hooke’s law, for isotropic

materials 165–171, 169, 171– – generalized Hooke’s law, for orthotropic

materials 171–173– – generalized Hooke’s law, for transverse

isotropic materials 173–174– – plastic behavior, failure, and limit surface

174–181constitutive models 80–90constraint modulus 168contact 146–147– kinematic conditions of 146– stresses 272continuum mathematical model, of bone

healing process 136cortical bone– see also compact bonecounterface wear 148Coxeter helix 52cubic block model 187, 188cubic plate model 186, 187cubic strut model 186cushion form joint, for hip 214cylindrical hexagonal lattice 53cytokines 40cytoplasm 7cytosine 4cytoskeleton 31, 39

ddead volume 186degenerative arthritis see osteoarthritisdendrites 36dense bone see compact boneDescartes–Euler theorem 12–13deviatoric strain 133diaphysis 15, 235diastase 34differentiation theory 135diffusion 2dimer formation 6dissymmetry 3distal interphalangeal (DIP) joints 219distraction osteogeneis 139DNA polymers 4Duocel 184dynamic compression 197

eE-cadherins receptors 204efferent nerves 29

300 Index

efflux pumps 34elastic constants 168, 169, 171– conversion of 166elastic indentation modulus 116elasticity– of collagen 60–63– and modulus 108–111– tensor 165– see also linear elastic behaviorelastohydrodynamic lubrication 146, 154electrokinetic effects in bone 252–254embryogenesis 2, 14endochondral ossification 14, 15endosteum 246endothelial cells 240enzymes 34– kinetics 34epiphyseal plates 15equivalent model 84error-driven models 78E-selectins receptors 204essential amino acids 47eukaryotic cells 31, 34Exeter prosthesis 132experiment-based numerical analysis 155external fixator 138external remodeling 79extracellular matrix (ECM), of bone

2, 13, 14, 48extracellular signal-regulated

kinase (ERK) 6

ffailure mode and effect analysis 227femur 215– head of 182, 211, 228– human 21, 30, 93, 96– stress shielding effect and 273FE simulation 129, 130fibroblastic growth factors (FGFs) 125fibroblasts 13fibrous tissue 79, 80, 82–83, 89–90,

93, 97finger joint replacement 219–222finite difference method 136finite element analysis (FEA) 124, 226finite element method (FEM) 154, 159,

185, 187, 268finite element model 135, 270, 271,

280–281, 281– poroelastic 138fixation methods 217–218Flexspan 219

fluid-film lubrication see hydrodynamiclubrication

fluid pressures in long bones, and interstitialfluid 248–249

fluid shear systems 195fluorapatite 19, 20Food and Drug Administration (FDA) 223FORTRAN 90four-point bending 195fractures 42, 45– molecular 58– osteoporotic 21fragile bone 182

ggasket element, spatial representation of 83Gaussian chain model see ideal chain modelgelatin sugar 47gliding 146glycine 47, 48glycocalyx 253glycocolle see glycineglycolipids 34gradient projection (GP) method 278Green elastic material 165ground substance 13growth 39– of bone 13–15, 21, 42, 44– of organism 4, 9–11growth-associated protein (GAP-43) 30, 31guanine 4Gumbel number 147

hHaigh–Westergaard coordinates 176Halpin–Tsai relationships 109–110Hashin–Shtrikman (H–S) bounds 109Haversian canal 24, 25, 26, 27, 239, 240,

244, 257Haversian system see osteonshelical structure 3Helmholtz free energy 55, 56hematopoiesis 8hemopoietic tissue 239, 240hemostasis 80Henri–Michaelis–Menten kinetics 35hexagonal model, of columnar structure

186, 187Hintegra total ankle prosthesis 218hip replacement– and interface layer 82– joint 211–215hip resurfacing implants 214hip resurfacing prostheses 130–132

Index 301

histology 7histomorphology, of oblique

pseudarthrosis 137‘‘Hodge–Petruska’’ gaps 104homeostatic equilibrium state 78homogenization 164homoplasy 6, 32Hooke’s law, generalized 175– for isotropic materials 165–171,

169, 171– for orthotropic materials 171–173– for transverse isotropic materials

173–174horizontal magnetic pulling 202, 203Howship’s lacunae 38human mesenchymal stem cells (hMSCs)

197, 198human patella 187hyaluronic acid (HA) 150, 154hydrodynamic lubrication 146, 148,

213hydrodynamic methods 58hydrostatic stress 161, 168, 175, 180,

245hydroxyapatite see hydroxylapatitehydroxylapatite 18, 103hydroxyproline 47, 48, 51

iideal chain model 56–57implant designs, optimization methods

for 267– cemented stems 269–270– computational model 277– – finite element model 280–281, 281– – optimization algorithm 278–280,

279– design requirements for cementless hip

stem 271– – implant stability 272– – stress shielding effect 272–273– long-term performance 289–294– multicriteria formulation 273– – bone remodeling, objective function

for 276–277– – design variables and geometry

274–275– – interface displacement, objective

function for 275– – interface stress, objective

function for 275–276– – and objective function 277– optimal geometry 281– – multicriteria 286–289

– – for normal contact stress 283–284– – for remodeling 284–285– – for tangential interfacial displacement

282–283– uncemented stems 270–271India ink 243in-plane substrate distension 195integrin receptors 204interface constitutive model 82–85interface stress 272interfacial adaptation model 89–90interfragmentary strain (IS) 133intermedullary pressure 241internalization, of nanoparticles 203internal remodeling 79interstitial fluid movement, in cortical bone

tissue 233– arterial supply system– – dynamics 236–237– – overview 234–236– – in small animals and humans 238–239– – transcortical arterial hemodynamics

237–238– bone lymphatics and blood vessel trans-wall

transport 241–244– bone porosity levels– – cancellous bone porosity 246– – collagen–hydroxyapatite porosity 245– – interfaces 246–247– – lacunar–canalicular porosity (PLC)

245– – vascular porosity 244–245– electrokinetic effects in bone 252–254– fluid pressures in long bones and

248–249– and mechanosensation 249–252– microvascular network 239–241– permeability determination implications

262– poroelastic model 254–257– vascular and lacunar–canalicular

porosities, interchange of fluid between257–261

– venous drainage of bone 241intramedullary pressure 248intramembranous ossification 14invertase 34iron oxide particles 199isotropic bone remodeling 129–130isotropic material– generalized Hooke’s law for 165–171,

169, 171– with penalization (SIMP) 81

302 Index

jjigs 217joint 17– prostheses 145, 148, 150, 155joint replacement implants 209– biomaterials for 209–211– design 223–229, 224– – changes 229– – feasibility 225– – manufacture 228– – transfer 229– – validation 228–229– – verification 226–227– for finger joint replacement 219–222– for weight-bearing joints– – ankle joint replacement 216–217– – fixation methods 217–218– – hip joint replacement 211–215– – knee joint replacement 215–216– for wrist joint replacement 222–223

kkinases 6kinematic conditions, of contact 146knee cap see human patellaknee joint replacement 215–216kneepan see human patellaknee simulator 228Knoop microindentation testing 114Kratky–Porod model see wormlike chain

(WLC) model

llacunae 26, 27, 36lacunar–canalicular porosity (PLC)

234, 243, 247, 248, 250, 252, 255, 256,257, 258, 262

Lagrangian stationarity condition 86–87lamellae 17, 24Leeuwenhoek 24Leishmania 8ligaments 17linear elastic behavior– generalized Hooke’s law, for isotropic

materials 165–171, 169, 171– generalized Hooke’s law, for orthotropic

materials 171–173– generalized Hooke’s law, for transverse

isotropic materials 173–174linear irreversible thermodynamics 253living organisms– growth of 8–12– planarity of biological structures 12–13– structure of 7–8

load cases 280– spatial distribution of 91longitudinal stretch systems 195lubrication 146lymph 242

mmacrophage colony-stimulating factor

(M-CSF) 42macroscopic constitutive equations 164magnetic cell stimulation 204– and nanoparticles 199– – functionalization 201– – limitations 203– – properties 199–201– and pulling systems 201–202– for tissue regeneration 204– twisting system 202–203, 203Malpighi 7marrow cavity pressure 249material principal axes 171material properties 246– averaging 164material symmetries 165Mayo stem 271MC3T3 45–46MC3T3-E1 46mean normal stress see hydrostatic stressmechanical cell stimulation 193, 194– mechanical loading application techniques

195–196– mechanotransduction 196–197– on stem cell 197–198mechanobiological models, for bone tissue

123– bone fracture healing 125–126– – application to 133–134– – mechanistic models of 134–137, 136– – model application examples, to implant

design 137–140– see also bone remodelingmechano-regulation model 80mechanosensation 249–252mechanotransduction 196–197, 256Medical Device Directive 223medullary ischemia 238meiosis 4meniscus 215meristems 9–10– lateral 9mesenchymal stem cells (MSCs) 35, 124,

197, 198, 204mesenchyme 36mesoderm 2, 13

Index 303

metacarpophalangeal (MCP) joints219, 221

metacarpus 16metals, for joint replacement implants

209–210, 210metaphysis 15, 21–22metatarsal bones 16method of moving asymptotes (MMA)

278microelectromechanical system (MEMS)

106microfilaments 31microneedle indentation see

nanoindentationmicroparticles, magnetic 200microphotographs 27microscopic constitutive

equations 164microvascular network 239–241milieu interieur 247mineral apatite 18mineralized tissues, compositions of

111–112mineral phase, of bone 18, 103–104,

106–107mitosis 4mixed lubrication 147, 148, 213monocytes 36monomers 4, 56M-Pore 184multidirectional motions

149, 150Mus musculus 46

nnanoindentation 195, 196, 245– testing 114, 116nanoparticles, magnetic 199, 200– functionalization of 201– limitations 203– properties of 199–201nested porosities 255–256Neuflex finger joint 220–221, 220nucleic acids 4, 7nucleotides 4

ooctahedral plane 175, 176, 178, 180open-cell structures, idealizations of 186optical tweezers 193, 195, 196optimal geometry 281– multicriteria 286–289– for normal contact stress 283–284– for remodeling 284–285

– for tangential interfacial displacement282–283

optimization algorithm 278–280, 279‘‘order-from-disorder’’ principle 3organic phase, of bone 103, 105–106orthogonal plywood model 26orthopedic implants 145–152Ortron 90 210osmotic pressure 237osseointegration 82, 268, 271, 272, 291ossification 12, 14, 42osteoarthritis 183osteoblasts 14, 36, 40, 103, 124, 193, 204– evolution 139osteoclastogenesis inhibitory factor

(OCIF) 41osteoclasts 36, 38–39, 40, 124, 127osteocytes 6, 8, 26, 36, 37, 124, 197, 233– lacuno-canalicular network 36–37osteocytic osteolysis 36osteogenesis criterium 90osteoid 36osteolysis 124, 213, 217– osteocytic 36osteomyelitis 7, 15osteons 5, 24–27, 235, 243, 257– classes of 25– collagen fibers in human 59–60– elements of 24– structure 25osteopetrosis 114osteopontin 197osteoporosis 114, 125, 182, 256osteoprogenitors 35osteoprotegerin (OPG) 39, 40–41, 42,

44, 45out-of-plane distension systems 195overlap 59oxidized zirconium see OxiniumOxinium 210, 212oxygen concentration 152

ppacking geometry 9, 13paracrine signaling 6parenchymal cells 8pendulum testing 153pentagonal dodecahedron 188peptides 46periimplant repair 79–80periosteal network of veins 241periosteum 246periprosthetic adaptation model 85–89permeases 35

304 Index

PFC sigma fixed bearing knee system216

p-glycoprotein 34phenomenological models see macroscopic

constitutive equationsphospholipids 33, 34phyllotaxis 9pin-on-disc configuration test 149, 150pin-on-plate wear test 148, 150plant cell 33plasticity– and behavior, failure, and limit surface

174–181– cellular plastics and metals 183–188plastic multiplier 181plastic potential 181platelet-derived growth factors

(PDGF) 125pleiotropy 34plowing friction 149Poisson’s ratio 165, 168, 172, 174polyethylene 148, 149–152polyhedral cell model 188polymers 4– thermodynamics 55–63polymethylmethacrylate 217polyurethane foams 183pore fluid pressure 249, 257,

259–261, 262pore size porosity and nesting 255poroelastic model 254–257porosity, in bone 105, 116preclinical testing, of joint replacement

implants 228preosteoblasts 193primary ossification centers 15primordium 9, 10principal invariants 162, 163principal stress 175, 176, 269products 34prokaryotes 31proline 47, 48, 51prosthesis 123– tissue differentiation around 97protease 34protein gene product (PGP) 9.5 30, 31proteins 7– amino acids 46–48– membrane transport 35proximal interphalangeal (PIP) joints 219pseudarthrosis 137pulling magnetic systems 201–202Pyrocarbon Total Joint 221Python 90

rrapid prototyping 227real geometry 184–185receptor activator of nuclear factor-kappaB

(RANK) 39–40– ligand (RANKL) 39, 41–42, 43, 44, 45, 46red marrow see hemopoietic tissueregular polygon 52relative displacement 268, 270, 272, 273Re-motion 222representative volume element (RVE) 184resorption lacuna 39revision surgery 213–214, 217, 222rheumatoid arthritis 221risk analysis, of joint replacement implants

227rolling 146rotated plywood 27Royal Society of London 24ruffled border 38–39rule-of-mixtures approach 108

sscanning acoustic microscopy (SAM)

107scanning electron microscopy (SEM) 27scientific hip prostheses 269screw fixation 218secondary ossification 15sensory fibers 29–30shear strain, definition of 167shear stress 161, 168, 290Sherman–Morrison formula 171shoot apical meristem (SAM) 9, 11silicone 211silicone implants 221silicone spacer, single-piece 219, 220simulation 145, 150, 151, 153, 155single cells 7skeletal system 14sliding 146solid mechanical modeling, of engineering

materials 164sphere-on-flat sliding test 153spiral phyllotaxis 9, 10spongy bone 22SRTM 221Staphylococcus aureus 7stem cell, mechanical stimulation on

197–198stem geometry 268stiffness 101, 102, 105, 118, 172, 173, 174,

290, 291– of cellular material 185

Index 305

– coefficient 114– values 113stochastic constitutive equations 164strain cycling experiments 61strain-generated potentials (SGPs) 252,

253–254stress Lode angle 176, 177stress shielding effect 268, 269, 272–273,

276stress–strain curves 159, 160– of collagen 61stress tensor decomposition 160–161Stribeck curve 147stroma 8Styrofoam 183substance P (SP) 30, 31substrates 34sucrase 34Sutter implant 220Swanson finger implant 219–220, 227Swanson wrist implant 222symmetry, in plants 9synchrotron X-ray scattering experiments,

in situ 61synovial fluid 150, 151, 154synovial joints 209, 211, 215

ttachykinin peptides 30tachykinins 30telopeptide 60tetrahedron 54tetrahelix 53tetrakaidecahedron 188thermodynamics 55–56– limit 57thigh pain 267, 268, 272three-dimensional printing 227three-sphere fibrations 54–55thymine 4tissue differentiation 80, 89– models, and bone fracture healing

133–134, 134– and prosthesis 97tissue regeneration, magnetic cell stimulation

for 204titanium alloy 210titanium grommets 220, 222titanium nitride 210tobacco mosaic virus (TMV) 7total hip arthroplasty (THA) 77, 78, 82, 267,

273total hip replacement (THR) 129, 130,

132, 268

– joint 183, 228Total Metacarpophalangeal Replacement

TMPRTM 221trabecular bone 21– idealized microstructure of 81trabecular bone and constitutive

modeling 159– invariants 161–163– linear elastic behavior 165–174– – generalized Hooke’s law, for isotropic

materials 165–171, 169, 171– – generalized Hooke’s law, for orthotropic

materials 171–173– – generalized Hooke’s law, for transverse

isotropic materials 173–174– plastic behavior, failure, and limit surface

174–181– stress tensor decomposition 160–161– structure and modeling approaches 181– – cellular plastics and metals 183–188transcortical arterial hemodynamics

237–238transforming growth factor beta

(TGF-β) 125translation 46transmission electron microscopy (TEM) 104transmural pressure 237, 248transport proteins 35triangulated helical polyhedron (THP) 53tribology see under biomechanical testingTri-Lock stem 271, 274, 275triple helix 48, 51– geometry of 52–55tropocollagen (TC) 4– helix 53– molecules 55, 58, 59tumor necrosis factor (TNF) 39tumor necrosis factor-alpha converting

enzyme (TACE) 42, 44tumor necrosis factor receptor

(TNFR) 39tumor necrosis factor-related

activation-induced cytokine (TRANCE)see receptor activator of nuclearfactor-kappaB (RANK)

turnover 10, 36, 45twisted plywood model 26‘‘twisting’’ technique 199twisting magnetic system 202–203, 203

uultrahigh molecular weight polyethylene

(UHMWPE) 148, 151, 210, 215, 222– acetabular parts 212, 213

306 Index

uncemented stems 270–271uniaxial stress–strain curves 159,

160unicondylar implant 216unidirectional reciprocating motion 149Universal 2 222

vvascularization, of marrow 237, 239vascular porosity (PV) 162, 234, 239, 242,

244–245, 247, 248, 255, 256, 257,258, 259, 260, 261

venous drainage of bone 241vertical magnetic pulling 202, 203viruses 7Voigt–Reuss (V–R) bounds 108Volkmann canals 26, 27, 235, 239,

240, 244

wwater, in bone 104–105, 107wear debris 213wear joint simulation test 151wear mechanisms 148

weight-bearing joints, joint replacementimplants for

– ankle joint replacement 216–217– fixation methods 217–218– hip joint replacement 211–215– knee joint replacement 215–216Wolff’s law 126, 273wood–bone structure analogy 32wormlike chain (WLC) model 57–58wrist joint replacement 222–223wrist simulator 229

xX-ray diffraction 48, 49, 104

yyellow marrow see adipose tissueyield criterion 175yield surface 175Young’s modulus 165, 166, 168, 172

zzirconia 210zoledronic acid (ZOL) 43, 44