Table Of ContentIUTAM SYMPOSIUM ON SYNTHESIS IN BIO SOLID MECHANICS
SOLID MECHANICSAND ITSAPPLICATIONS
Volume69
Series Editor: G.M.L. GLADWELL
Solid Mechanics Division, Faculty ofEngineering
University ofWaterloo
Waterloo, Ontario, CanadaN2L3GI
Aims and Scope ofthe Series
The fundamental questions arising in mechanics are: Why?, How?, andHowmuch?
The aim ofthis series is to provide lucid accounts written bij authoritative researchers
giving vision and insight in answering these questions on the subject of mechanics as
itrelates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it includes
the foundation of mechanics; variational formulations; computational mechanics;
statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and
structures; dynamical systems and chaos; the theories of elasticity, plasticity and
viscoelasticity; composite materials; rods, beams, shells and membranes; structural
control and stability; soils, rocks and geomechanics; fracture; tribology; experimental
mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are
monographs defining the current state of the field; others are accessible to final year
undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
IUTAM Symposium on
Synthesis in
Bio Solid Mechanics
Proceedings of the IUTAM Symposium
held in Copenhagen, Denmark,
24-27May 1998
Edited by
PAULI PEDERSEN
Department ofSolid Mechanics,
Technical University of Denmark,
Lyngby, Denmark
and
MARTINP. BENDSØE
Department of Mathematics,
TechnicaI University ofDenmark,
Lyngby, Denmark
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CONTENTS*
PREFACE ix
REMODELLINGANDEXPERIMENTS(Chairman:S.C.Cowin,USA)
T.C.Lee,L.Noelke,G.T.McMahon,J.P.MulvilleandD.Taylor
“FunctionalAdaptationinBone” 1–10
M.D. Roberts and R.T. Hart
“MechanicalandHormonalMechanismsInfluencing
SkeletalForm” 11–20
N. Inou, T. Uesugi, K. Todoroki and S. Ujihashi
“Self–organization of Topological Structures
by a Cellular Automaton ” 21 –32
MICROMECHANICS OFBONES (Chairman: H. Rodrigues, Portugal)
A. Odgaard, J. Kabel, B. van Rietbergen and R. Huiskes
“Architectural3–DParameters
andAnisotropicElasticPropertiesofCancellousBone” 33–42
M.TanakaandT. Adachi
“Lattice Continuum Modelfor Bone Remodeling Considering
Microstructural Optimality of Trabecular Architecture” 43 – 54
LOADS AND IMPLANTS (Chairman:I.Knets,Latvia)
L.R.Rakotomanana,A.Terrier,N.A.RatmanirakaandP.–F.Leyvraz
“Anchorage of Orthopedic Prostheses: Influence of
BoneProperties andBone-Implant Mechanics” 55–66
P.Vena,R.Contro,R.PietrabissaandL.Ambrosio
“Design of Materials Subject to
Bio-Mechanical Compatibility Constraints” 67 – 78
J. Rasmussen, M. Damsgaard and M. Voigt
“Joint Load Identification During Cyclic Movements ” 79 – 92
*AuthornamesinboldfontindicateparticipationintheSymposium.
vi
BASIC EVOLUTION QUESTIONS (Chairman: R.T.Hart,USA)
J.D.Currey
“Whyaren’tSkeletalTissuesPerfect?” 93–102
J.H.Heegaard
“Dynamics ofJointMorphogenesis” 103–114
J.E.Taylor
“Optimal Modification and Evolution
of Elastic Continuum Structures” 115–128
CREEPAND EXPERIMENTS(Chairman:S.Hollister,USA)
I.Knets,A.MelnisandM.Dobelis
“Effect of TimeDependenceon theMechanicalBehaviorof
CompactBoneTissue” 129–138
S.Tadano andM.Todoh
“Anisotropic Residual Stress Measurements in Compact Bone
Using Polychromatic X-rayDiffraction” 139 – 150
R.G.M. Breuls, E.M.H. Bosboom, C.W.J. Oomens,
C.V.C. Bouten and J.D. Janssen
“A 3–D Finite Element Model
ofthe Rat Tibialis Anterior Muscle” 151–162
HEALING AND CRACKS (Chairman: R. Contro, Italy)
S.J. Hollister, T.M. Chu, R.E. Guldberg, P.K. Zysset,
R.A. Levy,J.W.HalloranandS.E.Feinberg
“Image Based Design and Manufacture of
Scaffoldsfor Bone Reconstruction ” 163–174
D. Taylor
“Fatigue Damage in Bone: Links toAdaptation” 175–186
G.N.Duda,M. Heller,J.–E.Hoffmann,M.Pohl,K.Eckert–Hübner,
L.ClaesandN.Haas
“Fracture Gap Movement as a Function of Mimulo-Skeletal
Loading Conditions During Gait” 187–198
vii
MATERIAL AND MICROSTRUCTURE(Chairman: T.Adachi,Japan)
R.Lakes,C.Swan,E.Garner,T.LeeandK.Stewart
“ExperimentalMicromechanicsand Viscoelasticity
of Biological and Bioprotective Materials” 199–208
H.Rodrigues,C.Jacobs,J.M.GuedesandM.P.Bendsøe
“Globaland LocalMaterialOptimizationModels
AppliedtoAnisotropicBoneAdaption” 209–220
O.Sigmund
“On the Optimality of Bone Microstructure ” 221–234
MATHEMATICS OF REMODELLING(Chairman:J.Taylor,USA)
L.Trabucho
“An Existence Result in Bone Remodelling” 235 – 246
A. CherkaevandE.Cherkaev
“Structural Optimization and Biological “Designs” ” 247 –264
T.Lekszycki
“On Simple Model of Self–adapting Bone Muterial ” 265 – 276
EYE, FIBERORIENTATION AND MATERIAL SYMMETRY
(Chairman:R. Lakes, USA)
F. Jouve and K. Hanna
“Computer Simulations of Refractive Surgery
and Accommodation Mechanisms” 277 – 284
P.H.M. Bovendeerd, J. Rijcken, D.H. van Campen,
A.J.G. Schoofs, K. Nicolay and T. Arts
“Optimization of Left Ventricular Muscle Fiber Orientation ” 285 – 296
S.C. Cowin and G. Yang
“Optimization of Material Symmetry” 297–308
viii
REMODELLING AS A DYNAMIC PROCESS
(Chairman: R.Huiskes,TheNetherlands)
T.Adachi,K.TsubotaandY.Tomita
“Surface Remodeling Simulation ofTrabecular Bone Using
Microstructural Finite Element Models” 309–320
P.J.PrendergastandH.Weinans
“TissueAdaptationasaDiscrete–Dynamical
ProcessinTimeandSpace” 321–332
M.Bagge
“Time Simulation ofBone Adaptation” 333–348
G.H.vanLentheand R.Huiskes
“CantheMechanicalTrabecularBoneQualitybeEstimatedReliably
fromMeanInterceptLengthorOtherMorphologicalParameters?” 349–360
DAMAGEANDBONEEVOLUTION
(Chairman:D.H.vanCampen,TheNetherlands)
D.T. Davy,K.J.Jepsen,D.J.KrzypowandM.T.Fondrk
“Nonlinear Stress-StrainBehaviorDuetoDamage
Accumulationin CorticalBone” 361–372
R.SaxenaandT.S.Keller
“A VolumetricFiniteElementSchemeto Investigatethe
Mechanical Properties of Normal and Osteoporotic Trabecular Bone” 373 – 386
D. Tortorelli andP. Pedersen
“Similarities in Bone Remodelling and Damage Evolution” 387 – 400
R.LiptonandB.Vernescu
“Boundsfor Cell Wall Permeabilities” 401–406
LIST OF PARTICIPANTS 407 – 410
PREFACE
This book contains the edited version of invited lectures presented at the IUTAM-Sympo-
sium Synthesis in Bio Solid Mechanics, held at Hotel Frederiksdal, Virum (Copenhagen),
Denmark, May 24 to May 27, 1998. The symposiumwas attendedby48 scientistfrom 14
countries.
Biomechanics has been a very active research area in the last 25 years and covers a very
broad class of problems. The present symposium concentrated on the solid mechanics do-
main of biomechanics, where important problems of synthesis presently are an active and
challenging part.
Characteristics of biomechanical materials are not only the inhomogeneity and anisotropy,
but also the capability to change in relation to actual use. These living materials call for new
methods of analysis and also new methods for synthesis. By the synthesis in this context
is meant design of implants or artificial control of material growth.
Bone mechanics is closely related to recentwork on analysis and design ofmicrostructural
anisotropic materials. Also, recent work in shape design can to some extent be useful in the
more complicated problems of biomechanics. Here interface problems play an essential
role.
The symposium brought together scientists from mechanics, mathematics and medicine.
The cooperation between these groups made it possible to focus on the comparison of re-
sults frommodels andexperiments.Thus thisvolumeisorganizedinelevenparts,each one
representing a session ofthe workshop and addressing a sub–field ofthe area ofbio solid
mechanics with an emphasis on the mechanics ofbone. Thefields range overexperimental
issues, models of bone remodelling, micromechanics of bone, analogies between optimal
design models and bone remodelling, to mathematical issues of the various models seen in
this exciting area.
ix
x
Without the sponsorship and financial support from the International Union of Theoretical
and Applied Mechanics – IUTAM, the Villum Kann Rasmussen Foundation, and the Joint
Committee of the Nordic Natural Science Research Councils, the symposium and this book
would not have been possible. The financial support of the Department of Mathematics and
the Department of Solid Mechanics, Technical University of Denmark, is also gratefully
acknowledged.
The editors are indebted to the members of the Scientific Committee, Professor S.C. Cowin,
Professor D.H. van Campen, Professor S.J. Hollister, Professor R. Huiskes, Professor I.
Knets, Professor F.G. Rammerstorfer, Professor H.C. Rodrigues, and Professor M.A.
Hayes, fortheiradviceandhelpin organizing the symposium. Theorganizationofthesym-
posium was a shared effort between the Department of Mathematics and the Department
of Solid Mechanics, Technical University of Denmark, and the smooth running of this
shared effortis greatly attributed tothecompetentworkofOleSigmund andRobertZetter-
lund.
Lyngby,September 1998
Pauli Pedersen
MartinP.Bends¢e
