Biomechanics Principles and Applications - Schneck and Bronzino
.pdfBiomechanics
PRINCIPLES
and APPLICATIONS
Edited by
DANIEL J. SCHNECK
JOSEPH D. BRONZINO
CRC PR E S S
Boca Raton London New York Washington, D.C.
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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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.
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Preface
MECHANICS IS THE ENGINEERING SCIENCE that deals with studying, defining, and mathematically 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 macrocirculatory hemodynamics (Chapter 13), mechanics and transport in the microcirculation (Chapter 14),
venous hemodynamics (Chapter 16), mechanics of the lymphatic system (Chapter 17), cochlear mechanics (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 mechanical 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 purposes, 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.
Contributors
Editors
Daniel J. Schneck |
Joseph D. Bronzino |
Virginia Polytechnic Institute |
Trinity College |
and State University |
Hartford, Connecticut |
Blacksburg, Virginia |
|
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
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
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
Cathryn R. Dooly |
J. Lawrence Katz |
Aleksander S. Popel |
University of Maryland |
Case Western Reserve University |
The Johns Hopkins University |
College Park, Maryland |
Cleveland, Ohio |
Baltimore, Maryland |
Carl F. Rothe |
Charles R. Steele |
Richard E. Waugh |
Indiana University |
Stanford University |
University of Rochester |
Indianapolis, Indiana |
Stanford, California |
Rochester, New York |
Geert Schmid-Schönbein |
Jason A. Tolomeo |
Ajit P. Yoganathan |
University of California |
Stanford University |
Georgia Institute of Technology |
San Diego, California |
Stanford, California |
Atlanta, Georgia |
Artin A. Shoukas |
David C. Viano |
Deborah E. Zetes-Tolomeo |
The John Hopkins University |
Wayne State University |
Stanford University |
Baltimore, Maryland |
Detroit, Michigan |
Stanford, California |
Contents
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mechanics of Hard Tissue J. Lawrence Katz................................................................ |
|
1 |
Mechanics of Blood Vessels Thomas R. Canfield & Philip B. Dobrin .................... |
21 |
|
Joint-Articulating Surface Motion Kenton R. Kaufman & Kai-Nan An ................ |
35 |
|
Joint Lubrication Michael J. Furey................................................................................ |
|
73 |
Musculoskeletal Soft Tissue Mechanics Richard L. Lieber & |
|
|
Thomas J. Burkholder .......................................................................................................... |
|
99 |
Mechanics of the Head/Neck Albert I. King & David C. Viano........................... |
107 |
|
Biomechanics of Chest and Abdomen Impact |
David C. Viano & |
|
Albert I. King...................................................................................................................... |
|
119 |
Analysis of Gait Roy B. Davis, Peter A. DeLuca, & Sylvia Ounpuu...................... |
131 |
|
Exercise Physiology Arthur T. Johnson & Cathryn R. Dooly.................................. |
141 |
|
Factors Affecting Mechanical Work in Humans |
Arthur T. Johnson & |
|
Bernard F. Hurley ............................................................................................................... |
|
151 |
Cardiac Biomechanics Andrew D. McCulloch ......................................................... |
|
163 |
Heart Valve Dynamics Ajit P. Yoganathan, Jack D. Lemmon, & Jeffrey T. Ellis... |
189 |
|
Arterial Macrocirculatory Hemodynamics Baruch B. Lieber .............................. |
205 |
|
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
17
The Venous System Artin A. Shoukas & Carl F. Rothe .......................................... |
241 |
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 |
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 |
|
J. Lawrence Katz |
1.5 |
Modeling Elastic Behavior ................................................. |
10 |
|
Case Western |
1.6 |
Viscoelastic Properties ....................................................... |
11 |
|
1.7 |
Related Research |
14 |
||
Reserve University |
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 material. 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
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