Table Of Contentusculoskeletal
iomechanics
Paul Brinckmann
Wolfgang Frobin
Gunnar Leivseth
(§) Thieme
Musculoskeletal
Biomechanics
Paul Brinckmann, Ph. D.
Professor and Director
Institute for Experimental
Biomechanics
Universitatsklinikum Munster
Munster, Germany
Wolfgang Frobin, Ph. D.
Institute for Experimental
Biomechanics
Universitatsklinikum Munster
Munster, Germany
Gunnar Leivseth, M. D., Ph. D.
Professor
Department of Clinical Neurosciences
Faculty of Medicine
Norwegian University of
Science and Technology
Trondheim, Norway
Foreword by
2 NATIONAL INSTITUTES OF HEALTH Gunnar Andersson, M. D., Ph. D.
I? v* NIH LIBRARY
244 illustrations
m
JUL 2 0 2002
BLDG 10, 10 CENTER DR.
BETHESDA, MD 20892-1150
Thieme
Stuttgart • New York
Library of Congress Cataloging-in-Publication Data Important Note: Medicine is an ever-changing science
undergoing continual development. Research and clini¬
Brinckmann, Paul cal experience are continually expanding our knowl¬
[Orthopadische Biomechanik. English] edge, in particular our knowledge of proper treatment
Musculoskeletal biomechanics / Paul Brinckmann, and drug therapy. Insofar as this book mentions any dos¬
Wolfgang Frobin, Gunnar Leivseth. age or application, readers may rest assured that the au¬
p. : cm. thors, editors, and publishers have made every effort to
Includes bibliographical references and index. ensure that such references are in accordance with the
ISBN 3131300515 - ISBN 1-58890-080-0 state of knowledge at the time of production of the book.
1. Human mechanics. 2. Musculoskeletal system - Me¬ Nevertheless this does not involve, imply, or express
chanical properties. 3. Orthopedics. I. Frobin, W. II. Leiv¬ any guarantee or responsibility on the part of the pub¬
seth, Gunnar. III. Title. lishers in respect of any dosage instructions and forms
[DNLM: 1. Biomechanics. 2. Movement-physioloy. 3. Or¬ of application stated in the book. Every user is requested
thopedics. WE 103 B8580 2002] to examine carefully the manufacturers’ leaflets accom¬
QP303 B7513 2002 panying each drug and to check, if necessary in consul¬
612.7’6-dc21 2001058204 tation with a physician or specialist, whether the dosage
schedules mentioned therein or the contraindications
Title of the German edition: stated by the manufacturers differ from the statements
Orthopadische Biomechanik. made in the present book. Such examination is particu¬
Published and copyrighted 2000 larly important with drugs that are either rarely used or
by Georg Thieme Verlag, Stuttgart, have been newly released on the market. Every dosage
Germany. schedule or every form of application used is entirely at
the user’s own risk and responsibility. The authors and
publishers request every user to report to the publishers
any discrepancies or inaccuracies noticed.
Any reference to or mention of manufacturers or specific © 2002 Georg Thieme Verlag, RiidigerstralSe 14,
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Some of the product names, patents, and registered New York, NY 10001, USA.
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V
Foreword
Orthopedic surgeons use biomechanical theory plex; it can also - as in this text - be made simple
every day. It influences prevention, diagnosis, and and relevant. Its application in daily practice
treatment of most musculoskeletal injuries and should be intuitive. This requires that principles be
diseases. Consider advising a patient with back learned, not memorized.
pain about lifting, relating loss of range of motion Dr. Brinckmann and his coauthors have written
of a joint to an internal joint derangement, or op¬ a superior treatise on the subject. In striking an ap¬
erating on a fracture using internal fixation: All propriate balance, the book keeps you focused on
should be based on sound knowledge of biome¬ the principles, while providing the background
chanical principles. This book provides such basic theory. Orthopedic surgeons and other health pro¬
knowledge and more. Written by well-known bio¬ fessionals with an interest in biomechanics are for¬
mechanics experts with a long history of teaching tunate. Buy, read and enjoy.
and working with orthopedic surgeons and beau¬
tifully illustrated, it blends sound basic theory with Gunnar Andersson, M. D., Ph. D.
applied biomechanical principles. Chair, Department of Orthopedic Surgery
Most young orthopedic residents fear mathe¬ Rush-Presbyterian-St. Luke’s Medical Center
matical engineering theory. It can be made com¬ Chicago, Illinois
VI
Preface
Based on lectures, scientific papers, and publica¬ As stated above, simple calculations cannot be
tions, this book addresses readers from the disci¬ dispensed with when discussing mechanical as¬
plines of physiotherapy, rehabilitation, orthope¬ pects of the locomotor system. All calculations are
dics, and biomechanical research. Its aim is accu¬ explained step by step. It is quite conceivable that
rately to present the lines of thought and proce¬ some readers may find this too simple (sorry!) and
dures in orthopedic biomechanics, as well as the that others may find it takes some getting used to
current state of knowledge of mechanical effects (sorry again!). Vector algebra is explained because
on the human locomotor system, though with only the reader will come across it in scientific papers
minimal reference to physics and mechanics and and textbooks. When dealing with forces and mo¬
with the simplest possible mathematical calcula¬ ments, vector notation is not used consistently
tions. The insight into the structure and function throughout this book; preference is given to con¬
of the locomotor system gained from a mechanical veying the basic information as clearly as possible
aspect lays the foundation for understanding without forcing vector notation on to the reader.
mechanisms of primary mechanical impairment This will (hopefully) not result in confusion. Those
and dysfunction and for treatment and rehabili¬ who start performing calculations in the field of
tation concepts as well as for preventive mea¬ biomechanics will, in any case, soon get used to
sures. vector notation.
The book is divided into four parts. Chapters 2- Appendix A illustrates the specifically biome¬
7 form an introduction into the fundamental as¬ chanical standpoint and the interaction of mechan¬
pects of physics and mechanics. These fundamen¬ ical and non-mechanical factors with the examples
tals are reiterated only to the extent necessary for of currently (and controversially) discussed prob¬
an understanding of the chapters that follow. It lems of primary mechanical causes of disk pro¬
would not hurt to have college textbooks on phys¬ lapse, adaptation and remodeling of bones, and
ics, geometry, and trigonometry to hand (if, indeed, loading of the spine in standing compared to sit¬
anyone still has such books!). Proof is generally not ting. Appendix B deals with the mathematical de¬
provided for theorems in the field of mechanics or scription of translation and rotation in three-di¬
for mathematical formulae cited here. In such in¬ mensional space. The description of orientation
stances the reader will find the note “the proof is and location of objects is of interest in a number
not detailed here.” This indicates that the validity of biomechanical studies. New electromagnetic
of the theorems or formulae is not obvious (some¬ measurement devices, for example, deliver Euler
times far from obvious!), but has to be proven. (We angles to describe the orientation of a rigid body
trust such proof has been furnished correctly in the with respect to a reference coordinate system. This
past by competent authors.) topic (and the associated problems) thus deserve a
Chapters 8-15 deal with the function and load¬ comprehensive description. The chapters compris¬
ing of joints and the mechanical properties of mus¬ ing Appendix B are mathematically demanding.
cle, tendon, skin, and bone. Biomechanical discus¬ The aim is to provide the reader of the scientific
sions and model calculations are generally con¬ literature with a guideline, at least, even if he has
fined to two-dimensional problems and to systems no intention of using the mathematical apparatus
without accelerated masses and inertial forces. For himself. Appendix B concludes with a chapter on
many problems, the static, two-dimensional case errors. Consideration of error influences is an im¬
constitutes at least an acceptable approximation. portant, indispensable part of biomechanical re¬
The underlying mechanical facts usually come search.
across vividly as well. For a number of problems of At the end of each chapter, a list of textbooks and
practical interest, for example, joint loads or pres¬ review papers is recommended as further reading.
sure on articular surfaces, knowing the precise References to scientific papers cited in the text or
magnitude of the mechanical parameters is not of the figures are given without exception. The papers
prime interest. Often it is more interesting to ex¬ cited were selected because they were judged by
plore what changes can be induced by therapy, the authors to be exceptionally interesting or es¬
training, external aids, modified behavior, or ergo¬ pecially instructive. Thus, the selection is certainly
nomic improvements at the workplace. subjective, and no claim is made that the list of ref-
Preface VII
erences is comprehensive. If complete coverage is future commitment to biomechanical develop¬
needed, databases are easily accessible for this pur¬ ment and research.
pose nowadays. It must be kept in mind, however, The authors thank Mrs. Susan Griesbach, Muns¬
that scientific work described in books or in new, ter, for her expert help in editing the English trans¬
specialized journals may only be incorporated into lation of the German version of this book and
established databases with considerable delay, if at Mr. Charles Wolstenholme, Tromso, for the careful
all. (Studying the original publications rather than design of the illustrations. The authors also wish to
just their abstracts and extracting new, up-to-date thank the Thieme publishing house and acknowl¬
sources from their lists of references is thus neither edge the pleasant cooperation especially with the
outdated nor old-fashioned.) Executive Editor Mr. Clifford Bergman M. D. and
The authors hope that this book will help the the Production Director Mr. Gert A. Kruger in the
reader to understand past and current scientific preparation of this book.
work in the field of orthopedic biomechanics, to
judge the scientific and practical relevance of such Munster / Trondheim, January 2002
work, and to apply state-of-the-art knowledge in
solving practical problems in the fields of physio¬ Paul Brinckmann
therapy, rehabilitation, and orthopedics. Perhaps it Wolfgang Frobin
will also provide a stimulus for the reader’s own. Gunnar Leivseth
VIII
Contents
1 Musculoskeletal Biomechanics, an Elastic, viscoelastic, and plastic
Important and Interesting Discipline deformation.42
at the Interface between Medical Hardness.44
and Natural Sciences. 1 Friction.45
Fracture...45
2 Basic Concepts from Physics and
Mechanics. 4 7 Deformation and Strength of
Force. 4 Structures.48
Moment. 8 Experimental determination of
Pressure. 11 deformation and strength.49
Mechanical stress. 13 Deformation and strength of beam-like
Mechanical work, energy and power_ 14 structures.52
Stability and instability. 16 Deformation of a beam under tension
or compression.53
3 Vector Algebra. 17 Bending of a beam fixed at one end .... 53
The trigonometric functions sine, Torsion of a beam around its long axis.. 54
cosine, and tangent. 17
Representation of vectors. 19 8 Estimation of the Load Transmitted
Addition of vectors: graphical procedure by Joints of the Human Locomotor
in the two-dimensional case. 21 System by Means of a Biomechanical
Addition of vectors: numerical Model Calculation.57
procedure. 24 Calculation of a joint load in the static
Decomposition of a vector into vector case, illustrated with the example of
addends. 25 the elbow joint.58
Multiplication of vectors: scalar product Determination of the joint force in the
and vector product. 25 dynamic case, illustrated with the
example of the ankle joint.61
4 Translation and Rotation in a Plane.... 28 Determination of the joint force if more
Translation. 28 than one muscle or ligament force has
Rotation. 29 to be taken into account.66
Combined translation and rotation. 29
Instantaneous center of rotation. 31 9 Mechanical Aspects of the Hip Joint .... 69
Error influences when describing Load on the hip joint in the stance
amotion. 32 phase of slow gait.69
Influencing the load on the hip joint
5 Mechanical Equilibrium. 35 by gait technique, walking aids,
Conditions of static mechanical or surgical interventions.72
equilibrium. 35 Determination of the load on the hip
Example: calculation of an unknown joint by gait analysis.74
moment in the state of static Measurement of the load on the hip
equilibrium. 36 joint by instrumented joint replace¬
Example: calculation of an unknown ment.77
force in the state of static equilibrium ... 36 Determination of the stress distribution
Example: calculation of the joint force of on the surface of the hip joint.78
a beam balance in static equilibrium. 37 Measurement of the pressure distribution
on the surface of the hip joint.82
6 Material Properties of Solid Materials.. 40 Pressure on the articular surface as a
Elongation and compression. 40 primary cause of arthrosis of the hip
Shear. 42 joint.83
