Biomechanics - Principles and Applications - D. Schneck, J. Bronzino (CRC, 2003) WW

309 Pages·2003·7.66 MB·English

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PRINCIPLES
and APPLICATIONS
Biomechanics

Edited by
DANIEL J. SCHNECK
JOSEPH D. BRONZINO

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© 2003 by CRC Press LLC
This material was originally published in Vol. 1 of The Biomedical Engineering Handbook, 2nd ed.,
Joseph D. Bronzino, Ed., CRC Press, Boca Raton, FL, 2000.

No claim to original U.S. Government works
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Library of Congress Cataloging-in-Publication Data

Biomechanics : principles and applications / edited by Daniel Schneck and Joseph D. Bronzino.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-1492-5 (alk. paper)
1. Biomechanics. I. Schneck, Daniel J. II. Bronzino, Joseph D., 1937–

QH513 .B585 2002
571.4′3—dc21
2002073353

CIP

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Preface

ECHANICS IS THE ENGINEERING SCIENCE that deals with studying, defining, and math-
ematically quantifying “interactions” that take place among “things” in our universe. Our
ability to perceive the physical manifestation of such interactions is embedded in the concept
of a force, and the “things” that transmit forces among themselves are classified for purposes of analysis
as being solid, fluid, or some combination of the two. The distinction between solid behavior and fluid
behavior has to do with whether or not the “thing” involved has disturbance-response characteristics
that are time rate dependent. A constant force transmitted to a solid material will generally elicit a discrete,
finite, time-independent deformation response, whereas the same force transmitted to a fluid will elicit
a continuous, time-dependent response called flow. In general, whether or not a given material will behave
as a solid or a fluid often depends on its thermodynamic state (i.e., its temperature, pressure, etc.).
Moreover, for a given thermodynamic state, some “things” are solid-like when deformed at certain rates
but show fluid behavior when disturbed at other rates, so they are appropriately called viscoelastic, which
literally means “fluid-solid.” Thus a more technical definition of mechanics is the science that deals with
the action of forces on solids, fluids, and viscoelastic materials. Biomechanics then deals with the time
and space response characteristics of biological solids, fluids, and viscoelastic materials to imposed systems
of internal and external forces.
The field of biomechanics has a long history. As early as the fourth century B.C., we find in the works
of Aristotle (384–322 B.C.) attempts to describe through geometric analysis the mechanical action of
muscles in producing locomotion of parts or all of the animal body. Nearly 2000 years later, in his famous
anatomic drawings, Leonardo da Vinci (A.D. 1452–1519) sought to describe the mechanics of standing,
walking up and down hill, rising from a sitting position, and jumping, and Galileo (A.D. 1564–1643)
followed with some of the earliest attempts to mathematically analyze physiologic function. Because of
his pioneering efforts in defining the anatomic circulation of blood, William Harvey (A.D. 1578–1657) is
credited by many as being the father of modern-day biofluid mechanics, and Alfonso Borelli (A.D.
1608–1679) shares the same honor for contemporary biosolid mechanics because of his efforts to explore
the amount of force produced by various muscles and his theorization that bones serve as levers that are
operated and controlled by muscles. The early work of these pioneers of biomechanics was followed up
by the likes of Sir Isaac Newton (A.D. 1642–1727), Daniel Bernoulli (A.D. 1700–1782), Jean L. M. Poiseuille
(A.D. 1799–1869), Thomas Young (A.D. 1773–1829), Euler (whose work was published in 1862), and others
of equal fame. To enumerate all their individual contributions would take up much more space than is
available in this short introduction, but there is a point to be made if one takes a closer look.
In reviewing the preceding list of biomechanical scientists, it is interesting to observe that many of the
earliest contributions to our ultimate understanding of the fundamental laws of physics and engineering
(e.g., Bernoulli’s equation of hydrodynamics, the famous Young’s modulus in elasticity theory, Poiseuille
flow, and so on) came from physicians, physiologists, and other health care practitioners seeking to study
and explain physiologic structure and function. The irony in this is that as history has progressed, we
have just about turned this situation completely around. That is, more recently, it has been biomedical
engineers who have been making the greatest contributions to the advancement of the medical and
physiologic sciences. These contributions will become more apparent in the chapters that follow that
address the subjects of biosolid mechanics and biofluid mechanics as they pertain to various subsystems
of the human body.
Since the physiologic organism is 60 to 75% fluid, it is not surprising that the subject of biofluid
mechanics should be so extensive, including—but not limited to—lubrication of human synovial joints
(Chapter 4), cardiac biodynamics (Chapter 11), mechanics of heart valves (Chapter 12), arterial macro-
circulatory hemodynamics (Chapter 13), mechanics and transport in the microcirculation (Chapter 14),

M

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venous hemodynamics (Chapter 16), mechanics of the lymphatic system (Chapter 17), cochlear mechan-
ics (Chapter 18), and vestibular mechanics (Chapter 19). The area of biosolid mechanics is somewhat
more loosely defined—since all physiologic tissue is viscoelastic and not strictly solid in the engineering
sense of the word. Also generally included under this heading are studies of the kinematics and kinetics
of human posture and locomotion, i.e., biodynamics, so that under the generic section on biosolid
mechanics in this Handbook you will find chapters addressing the mechanics of hard tissue (Chapter 1),
the mechanics of blood vessels (Chapter 2) or, more generally, the mechanics of viscoelastic tissue,
mechanics of joint articulating surface motion (Chapter 3), musculoskeletal soft tissue mechanics
(Chapter 5), mechanics of the head/neck (Chapter 6), mechanics of the chest/abdomen (Chapter 7), the
analysis of gait (Chapter 8), exercise physiology (Chapter 9), biomechanics and factors affecting mechani-
cal work in humans (Chapter 10), and mechanics and deformability of hematocytes (blood cells) (Chapter
15). In all cases, the ultimate objectives of the science of biomechanics are generally twofold. First,
biomechanics aims to understand fundamental aspects of physiologic function for purely medical pur-
poses, and, second, it seeks to elucidate such function for mostly nonmedical applications.
In the first instance above, sophisticated techniques have been and continue to be developed to monitor

physiologic function, to process the data thus accumulated, to formulate inductively theories that explain
the data, and to extrapolate deductively, i.e., to diagnose why the human “engine” malfunctions as a result
of disease (pathology), aging (gerontology), ordinary wear and tear from normal use (fatigue), and/or
accidental impairment from extraordinary abuse (emergency medicine). In the above sense, engineers
deal directly with causation as it relates to anatomic and physiologic malfunction. However, the work
does not stop there, for it goes on to provide as well the foundation for the development of technologies
to treat and maintain (therapy) the human organism in response to malfunction, and this involves
biomechanical analyses that have as their ultimate objective an improved health care delivery system.
Such improvement includes, but is not limited to, a much healthier lifestyle (exercise physiology and
sports biomechanics), the ability to repair and/or rehabilitate body parts, and a technology to support
ailing physiologic organs (orthotics) and/or, if it should become necessary, to replace them completely
(with prosthetic parts). Nonmedical applications of biomechanics exploit essentially the same methods
and technologies as do those oriented toward the delivery of health care, but in the former case, they
involve mostly studies to define the response of the body to “unusual” environments—such as subgravity
conditions, the aerospace milieu, and extremes of temperature, humidity, altitude, pressure, acceleration,
deceleration, impact, shock and vibration, and so on. Additional applications include vehicular safety
considerations, the mechanics of sports activity, the ability of the body to “tolerate” loading without failing,
and the expansion of the envelope of human performance capabilities—for whatever purpose! And so,
with this very brief introduction, let us take somewhat of a closer look at the subject of biomechanics.

Free body diagram of the foot.

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Contributors

Editors

Daniel J. Schneck
Virginia Polytechnic Institute
and State University
Blacksburg, Virginia

Joseph D. Bronzino
Trinity College
Hartford, Connecticut

Kai-Nan An
Biomechanics Laboratory
The Mayo Clinic
Rochester, Minnesota

Gary J. Baker
Stanford University
Stanford, California

Thomas J. Burkholder
Georgia Institute
of Technology
Atlanta, Georgia

Thomas R. Canfield
Argonne National Laboratory
Argonne, Illinois

Roy B. Davis
Motion Analysis Laboratory
Shriners Hospitals for Children
Greenville, South Carolina

Peter A. DeLuca
Gait Analysis Laboratory
Connecticut Children’s Medical
Center
Hartford, Connecticut

Philip B. Dobrin
Hines VA Hospital and Loyola
University Medical Center
Hines, Illinois

Cathryn R. Dooly
University of Maryland
College Park, Maryland

Jeffrey T. Ellis
Georgia Institute of Technology
Atlanta, Georgia

Michael J. Furey
Virginia Polytechnic Institute
and State University
Blacksburg, Virginia

Wallace Grant
Virginia Polytechnic Institute
and State University
Blacksburg, Virginia

Alan R. Hargen
University of California
San Diego and NASA Ames
Research Center
San Diego, California

Robert M. Hochmuth
Duke University
Durham, North Carolina

Bernard F. Hurley
University of Maryland
College Park, Maryland

Arthur T. Johnson
University of Maryland
College Park, Maryland

J. Lawrence Katz
Case Western Reserve University
Cleveland, Ohio

Kenton R. Kaufman
Biomechanics Laboratory
The Mayo Clinic
Rochester, Minnesota

Albert I. King
Wayne State University
Detroit, Michigan

Jack D. Lemmon
Georgia Institute of Technology
Atlanta, Georgia

Richard L. Lieber
University of California and
Veterans Administration
Medical Centers
San Diego, California

Andrew D. McCulloch
University of California
San Diego, California

Sylvia Ounpuu
Gait Analysis Laboratory
Connecticut Children’s Medical
Center
Hartford, Connecticut

Roland N. Pittman
Virginia Commonwealth
University
Richmond, Virginia

Aleksander S. Popel
The Johns Hopkins University
Baltimore, Maryland

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Carl F. Rothe
Indiana University
Indianapolis, Indiana

Charles R. Steele
Stanford University
Stanford, California

Richard E. Waugh
University of Rochester
Rochester, New York

Geert Schmid-Schönbein
University of California
San Diego, California

Jason A. Tolomeo
Stanford University
Stanford, California

Ajit P. Yoganathan
Georgia Institute of Technology
Atlanta, Georgia

Artin A. Shoukas
The John Hopkins University
Baltimore, Maryland

David C. Viano
Wayne State University
Detroit, Michigan

Deborah E. Zetes-Tolomeo
Stanford University
Stanford, California

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Contents

1
Mechanics of Hard Tissue
J. Lawrence Katz................................................................ 1

2
Mechanics of Blood Vessels
Thomas R. Canfield & Philip B. Dobrin.................... 21

3
Joint-Articulating Surface Motion
Kenton R. Kaufman & Kai-Nan An................ 35

4
Joint Lubrication
Michael J. Furey................................................................................ 73

5
Musculoskeletal Soft Tissue Mechanics
Richard L. Lieber &
Thomas J. Burkholder.......................................................................................................... 99

6
Mechanics of the Head/Neck
Albert I. King & David C. Viano........................... 107

7
Biomechanics of Chest and Abdomen Impact
David C. Viano &
Albert I. King...................................................................................................................... 119

8
Analysis of Gait
Roy B. Davis, Peter A. DeLuca, & Sylvia Ounpuu...................... 131

9
Exercise Physiology
Arthur T. Johnson & Cathryn R. Dooly.................................. 141

10
Factors Affecting Mechanical Work in Humans
Arthur T. Johnson &
Bernard F. Hurley ............................................................................................................... 151

11
Cardiac Biomechanics
Andrew D. McCulloch ......................................................... 163

12
Heart Valve Dynamics
Ajit P. Yoganathan, Jack D. Lemmon, & Jeffrey T. Ellis... 189

13
Arterial Macrocirculatory Hemodynamics
Baruch B. Lieber .............................. 205

14
Mechanics and Transport in the Microcirculation
Aleksander S. Popel &
Rolan N. Pittman............................................................................................................... 215

15
Mechanics and Deformability of Hematocytes
Richard E. Waugh &
Robert M. Hochmuth......................................................................................................... 227

16
The Venous System
Artin A. Shoukas & Carl F. Rothe.......................................... 241

17
Mechanics of Tissue and Lymphatic Transport
Alan R. Hargen &
Geert W. Schmid-Schönbein ............................................................................................. 247

18
Cochlear Mechanics
Charles R. Steele, Gary J. Baker, Jason A. Tolomeo, &
Deborah E. Zetes-Tolomeo ................................................................................................ 261

19
Vestibular Mechanics
Wallace Grant ........................................................................ 277

Index............................................................................................................................................. 291

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0-8493-1492-5/03/$0.00+$.50
© 2003 by CRC Press LLC

1

Mechanics of

Hard Tissue

1.1
Structure of Bone.................................................................1
1.2
Composition of Bone...........................................................2
1.3
Elastic Properties..................................................................4
1.4
Characterizing Elastic Anisotropy.....................................10
1.5
Modeling Elastic Behavior.................................................10
1.6
Viscoelastic Properties .......................................................11
1.7
Related Research.................................................................14

Hard tissue, mineralized tissue, and calcified tissue are often used as synonyms for bone when describing
the structure and properties of bone or tooth. The hard is self-evident in comparison with all other
mammalian tissues, which often are referred to as soft tissues. Use of the terms mineralized and calcified
arises from the fact that, in addition to the principle protein, collagen, and other proteins, glycoproteins,
and protein-polysaccherides, comprising about 50% of the volume, the major constituent of bone is a
calcium phosphate (thus the term calcified) in the form of a crystalline carbonate apatite (similar to
naturally occurring minerals, thus the term mineralized). Irrespective of its biological function, bone is
one of the most interesting materials known in terms of structure–property relationships. Bone is an
anisotropic, heterogeneous, inhomogeneous, nonlinear, thermorheologically complex viscoelastic mate-
rial. It exhibits electromechanical effects, presumed to be due to streaming potentials, both in vivo and
in vitro when wet. In the dry state, bone exhibits piezoelectric properties. Because of the complexity of
the structure–property relationships in bone, and the space limitation for this chapter, it is necessary to
concentrate on one aspect of the mechanics. Currey [1984] states unequivocally that he thinks, “the most
important feature of bone material is its stiffness.” This is, of course, the premiere consideration for the
weight-bearing long bones. Thus, this chapter will concentrate on the elastic and viscoelastic properties
of compact cortical bone and the elastic properties of trabecular bone as exemplar of mineralized tissue
mechanics.

1.1
Structure of Bone

The complexity of bone’s properties arises from the complexity in its structure. Thus it is important to
have an understanding of the structure of mammalian bone in order to appreciate the related properties.
Figure 1.1 is a diagram showing the structure of a human femur at different levels [Park, 1979]. For
convenience, the structures shown in Fig. 1.1 will be grouped into four levels. A further subdivision of
structural organization of mammalian bone is shown in Fig. 1.2 [Wainwright et al., 1982]. The individual
figures within this diagram can be sorted into one of the appropriate levels of structure shown in Fig. 1.1
as described in the following. At the smallest unit of structure we have the tropocollagen molecule and

J. Lawrence Katz

Case Western
Reserve University

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