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Biomechanics PRINCIPLES and APPLICATIONS

Edited by

DANIEL J. SCHNECK JOSEPH D. BRONZINO

CRC PR E S S Boca Raton London New York Washington, D.C.

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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

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 0-8493-1492-5/01/$0.00+$.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com © 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 International Standard Book Number 0-8493-1492-5 Library of Congress Card Number 2002073353 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

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Preface

M

ECHANICS 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),

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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.

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Contributors Editors Daniel J. Schneck

Joseph D. Bronzino

Virginia Polytechnic Institute and State University Blacksburg, Virginia

Trinity College Hartford, Connecticut

Kai-Nan An

Jeffrey T. Ellis

Kenton R. Kaufman

Biomechanics Laboratory The Mayo Clinic Rochester, Minnesota

Georgia Institute of Technology Atlanta, Georgia

Biomechanics Laboratory The Mayo Clinic Rochester, Minnesota

Gary J. Baker

Virginia Polytechnic Institute and State University Blacksburg, Virginia

Stanford University Stanford, California

Thomas J. Burkholder Georgia Institute of Technology Atlanta, Georgia

Thomas R. Canfield Argonne National Laboratory Argonne, Illinois

Roy B. Davis

Michael J. Furey

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

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

Motion Analysis Laboratory Shriners Hospitals for Children Greenville, South Carolina

Robert M. Hochmuth

University of California San Diego, California

Peter A. DeLuca

Duke University Durham, North Carolina

Sylvia Ounpuu

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

Philip B. Dobrin

Bernard F. Hurley University of Maryland College Park, Maryland

Arthur T. Johnson

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

Roland N. Pittman

University of Maryland College Park, Maryland

Virginia Commonwealth University Richmond, Virginia

Cathryn R. Dooly

J. Lawrence Katz

Aleksander S. Popel

University of Maryland College Park, Maryland

Case Western Reserve University Cleveland, Ohio

The Johns Hopkins University Baltimore, Maryland

Hines VA Hospital and Loyola University Medical Center Hines, Illinois

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Carl F. Rothe

Charles R. Steele

Richard E. Waugh

Indiana University Indianapolis, Indiana

Stanford University Stanford, California

University of Rochester Rochester, New York

Geert Schmid-Schönbein

Jason A. Tolomeo

Ajit P. Yoganathan

University of California San Diego, California

Stanford University Stanford, California

Georgia Institute of Technology Atlanta, Georgia

Artin A. Shoukas

David C. Viano

Deborah E. Zetes-Tolomeo

The John Hopkins University Baltimore, Maryland

Wayne State University Detroit, Michigan

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

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