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Biomechanics of Skeletal Muscles eBook

Biomechanics of Skeletal Muscles eBook

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    Richly illustrated and presented in clear, concise language, Biomechanics of Skeletal Muscles is an essential resource for those seeking advanced knowledge of muscle biomechanics. Written by leading experts Vladimir Zatsiorsky and Boris Prilutsky, the text is one of the few to look at muscle biomechanics in its entirety—from muscle fibers to muscle coordination—making it a unique contribution to the field.

    Using a blend of experimental evidence and mechanical models, Biomechanics of Skeletal Muscles provides an explanation of whole muscle biomechanics at work in the body in motion. The book first addresses the mechanical behavior of single muscles—from the sarcomere level up to the entire muscle. The architecture of human muscle, the mechanical properties of tendons and passive muscles, the biomechanics of active muscles, and the force transmission and shock absorption aspects of muscle are explored in detail. Next, the various issues of muscle functioning during human motion are addressed. The transformation from muscle force to joint movements, two-joint muscle function, eccentric muscle action, and muscle coordination are analyzed.

    This advanced text assumes some knowledge of algebra and calculus; however, the emphasis is on understanding physical concepts. Higher-level computational descriptions are placed in special sections in the later chapters of the book, allowing those with a strong mathematical background to explore this material in more detail. Readers who choose to skip over these sections will find that the book still provides a strong conceptual understanding of advanced topics.

    Biomechanics of Skeletal Muscles also contains numerous special features that facilitate readers’ comprehension of the topics presented. More than 300 illustrations and accompanying explanations provide an extensive visual representation of muscle biomechanics. Refresher sidebars offer brief reminders of mathematical and biomechanical concepts, and From the Literature sidebars present practical examples that illustrate the concepts under discussion. Chapter summaries and review questions provide an opportunity for reflection and self-testing, and reference lists at the end of each chapter provide a starting point for further study.

    Biomechanics of Skeletal Muscles offers a thorough explanation of whole muscle biomechanics, bridging the gap between foundational biomechanics texts and scientific literature. With the information found in this text, readers can prepare themselves to better understand the latest in cutting-edge research.

    Biomechanics of Skeletal Muscles is the third volume in the Biomechanics of Human Motion series. Advanced readers in human movement science gain a comprehensive understanding of the biomechanics of human motion as presented by one of the world’s foremost researchers on the subject, Dr. Vladimir Zatsiorsky. The series begins with Kinematics of Human Motion, which details human body positioning and movement in three dimensions; continues with Kinetics of Human Motion, which examines the forces that create body motion and their effects; and concludes with Biomechanics of Skeletal Muscles, which explains the action of the biological motors that exert force and produce mechanical work during human movement.


    A reference for biomechanists, motor development specialists, muscle physiologists, exercise and sport scientists, ergonomists, biomechanical and biomedical engineers, and rehabilitation specialists. A text for graduate-level courses in biomechanics.

    Table of Contents


    Part I. Muscle Architecture and Mechanics

    Chapter 1. Muscle Architecture
    Muscle Fascicles and Their Arrangements

    • Parallel Fibered and Fusiform Muscles
    • Pennate Muscles

      • Planar Models of Pennate Muscles
      • Pennation in Three Dimensions

    • Convergent and Circular Muscles

    Muscle Fascicle Curvature: Frenet Frames
    Fiber Architecture in the Fascicles
    Muscle as a Fiber-Reinforced Composite
    Fiber, Fascicle, and Muscle Length: Length–Length Ratios

    • Fiber and Fascicle Length
    • Length–Length Ratios

    Muscle Path: Muscle Centroids

    • Straight-Line Representation of Muscle Path
    • Centroid Model of Muscle Path
    • Curved and Wrapping Muscles
    • Twisted Muscles
    • Muscles Attaching to More Than Two Bones

    Cross-Sectional Area, Physiological and Anatomical
    Muscle Attachment Area
    Questions for Review
    Literature List

    Chapter 2. Properties of Tendons and Passive Muscles
    Biomechanics of Tendons and Aponeuroses

    • Elastic Behavior

      • Stress–Strain Relations

        • Stress–Strain Relations in the Toe Region
        • Stress–Strain Relations in the Linear Region

      • Tendon Forces
      • Tension and Elongation in Tendons and Aponeuroses
      • Constitutive Equations for Tendons and Ligaments

    • Viscoelastic Behavior of Tendons

      • Basic Concepts of Viscoelasticity
      • Viscoelastic Properties of Tendons

        • Computational Models of the Tendons
        • Factors Affecting Mechanical Properties of the Tendons

    • Tendon Interaction With Surrounding Tissues

      • Intertendinous Shear Force and Lateral Force Transfer
      • Interfinger Connection Matrices
      • Gliding Resistance Between the Tendons and Surrounding Tissues
      • Tendon Wrapping
      • Bowstringing
      • Tendon Properties and Muscle Function
      • Musculotendinous Architectural Indices

    Mechanical Properties of Passive Muscles

    • Muscle Tone: Equitonometry
    • Mechanical Properties of Relaxed Muscles

      • Elastic Properties
      • Viscoelastic Properties of Passive Muscles: Passive Mechanical Resistance in Joints

    On Joint Flexibility
    Questions for Review
    Literature List

    Chapter 3. Mechanics of Active Muscle
    Muscle Force Production and Transmission

    • Experimental Methods
    • Transition From Rest to Activity

      • Muscle Active State
      • Force Development in Humans: Rate of Force Development

    • Transition From Activity to Rest: Muscle Relaxation
    • Constancy of the Muscle Volume
    • Force Transmission and Internal Deformations (Strain)

      • Force Transmission in Muscle Fibers
      • Force Transmission in Muscles: Summation of Muscle Fiber Forces

        • Parallel-Fibered and Fusiform Muscles

          • Nonuniform Shortening of Muscle Fibers
          • Nonlinear Summation of Fiber Forces

        • Pennate Muscles

          • Force Transmission
          • Speed Transmission: Architectural Gear Ratio

    • Intramuscular Stress and Pressure

      • Specific Muscle Force
      • Stress Tensors
      • Intramuscular Fluid Pressure

        • Hydrostatic and Osmotic Pressure
        • Factors Affecting Intramuscular Pressure: Application of the Laplace Law
        • Biological Function of Intramuscular Pressure: The Compartment Syndrome

    • Functional RelationsForce-Length Relations

      • Force–Length Curves
      • Mechanisms Behind the Active Force–Length Curve
      • Problem of Muscle Stability
      • Submaximal Force–Length Curve
      • Muscle Lengths in the Body: Expressed Sections of the Force–Length Curve

    • Force–Velocity Relations

      • A Piece of History: Muscle Viscosity Theory and Heat Production
      • Hill’s Force–Velocity Curve
      • Other Types of the Force–Velocity Curves

        • Force–Velocity Relations in Single Movement
        • Nonparametric Force–Velocity Relations

      • Mathematical Description of the Force–Velocity Curve: The Hill Characteristic Equation
      • Power–Velocity Relations

    • Force–Length–Velocity Relations

    History Effects in Muscle Mechanics

    • Force Depression After Muscle Shortening
    • Effects of Muscle Release: Quick-Release and Controlled-Release Methods: Series Muscle Components

    Questions for Review
    Literature List

    Chapter 4. Muscles as Force and Energy Absorbers
    Muscle Mechanical Behavior During Stretch

    • Dynamic Force Enhancement

      • Force–Velocity Relation for Lengthening Muscle
      • Give Effects

    • Residual Force Enhancement

    Muscle Shortening After Stretch

    • Work and Power During Shortening After Stretch
    • Energy Consumption During Stretch and Efficiency of the Muscle Shortening After Stretch

    Dissipation of Energy
    Mechanical Muscle Models

    • Hill-Type Model
    • Model Scaling

    Questions for Review
    Literature List

    Part II Muscles in the Body

    Chapter 5. From Muscle Forces to Joint Moments
    Force Transmission: From Muscle to Bone

    • From Muscle to Tendon
    • From Tendon to Bone
    • Tendon Elasticity and Isometric Force–Length Relation

    Force Transmission Via Soft Tissue Skeleton (Fascia)

    • Structure of Fascia
    • Muscle–Tendon–Fascia Attachments
    • Fascia as Soft Tissue Skeleton (Ectoskeleton)

      • Plantar Fascia and the Windlass Mechanism
      • Fascia Lata and Iliotibial Tract

    Muscle Moment Arms

    • Muscle Moment Arm Vectors and Their Components

      • Moment Arms As Vectors
      • Muscle Moment Arms About Rotation Axes
      • Muscle Moment Arms About Anatomical Axes: Muscle Functions at a Joint
      • Moment Arms of Muscles With Curved Paths: Quadriceps Moment Arm
      • Moment Arms of Multijoint Muscles: Paradoxical Muscle Action

    • Methods for Determination of Muscle Moment Arms

      • Geometric Methods

        • Anatomical Geometric Methods

          • Planar Geometric Models
          • Three-Dimensional Geometric Models

        • Imaging Geometric Methods

      • Functional Methods

        • Tendon Excursion Method (Kinematic Method)
        • Load Application Method (Static Method)

    • Factors Affecting Muscle Moment Arm

      • Moment Arm as a Function of Joint Angles
      • Moment Arm as a Function of Exerted Muscle Force
      • Scaling of Moment Arms

    • Transformation of Muscle Forces to Joint Moments: Muscle Jacobian

    Questions for Review
    Literature List

    Chapter 6. Two-Joint Muscles in Human Motion
    Two-Joint Muscles: A Special Case of Multifunctional Muscles

    • Functional Features of Two-Joint Muscles
    • Anatomical and Morphological Features of Two-Joint Muscles

    Functional Roles of Two-Joint Muscles

    • Kinetic Analysis of Two-Joint Muscles: Lombard’s Paradox
    • Kinematic Analysis of Two-Joint Muscles: Solution of Lombard’s Paradox

    Mechanical Energy Transfer and Saving by Two-Joint Muscles

    • Tendon Action of Two-Joint Muscles

      • Illustrative Examples of Tendon Action of Two-Joint Muscles
      • Methods of Energy Transfer Estimation

        • Energy Generated by Joint Moment and Muscles at a Joint
        • Work Done by a Two-Joint Muscle at the Adjacent Joint

      • Tendon Action and Jumping Performance

    • Saving Mechanical Energy by Two-Joint Muscles

    Questions for Review
    Literature List

    Chapter 7. Eccentric Muscle Action in Human Motion
    Joint Power and Work as Measures of Eccentric Action

    • Negative Power and Work at a Joint
    • Total Negative Power and Work in Several Joints
    • Negative Power of Center of Mass Motion
    • Two Ways of Mechanical Energy Dissipation: Softness of Landing

    Negative Work in Selected Activities

    • Walking
    • Stair Descent and Ascent
    • Level, Downhill, and Uphill Running
    • Landing

    Joint Moments During Eccentric Actions

    • Maximal Joint Moments During Eccentric Actions
    • Force Changes During and After Stretch

      • Dynamic Force Enhancement
      • Short-Range Stiffness
      • Decay of Dynamic Force Enhancement

    • Residual Force Enhancement in Humans

    Muscle Activity During Eccentric Actions

    • Surface Electromyographic Activity During Eccentric Actions
    • Motor Unit Activity During Eccentric Actions
    • Electromechanical Delay

    Physiological Cost of Eccentric Action

    • Oxygen Consumption During Eccentric and Concentric Exercise
    • Fatigue and Perceived Exertion During Eccentric Action
    • Muscle Soreness After Eccentric Exercise

    Reversible Muscle Action: Stretch–Shortening Cycle

    • Enhancement of Positive Work and Power Production
    • Mechanisms of the Performance Enhancement in the SSC
    • Efficiency of Positive Work in SSC

    Questions for Review
    Literature List

    Chapter 8. Muscle Coordination in Human Motion
    Kinematic Redundancy and Kinematic Invariant Characteristics of Limb Movements

    • Straight-Line Limb Endpoint Trajectory
    • Bell-Shaped Velocity Profile8.1.3 Power Law
    • Fitts’ Law
    • Principle of Least Action

    Kinetic Invariant Characteristics of Limb Movements

    • Elbow–Shoulder Joint Moment Covariation During Arm Reaching
    • Minimum Joint Moment Change
    • Orientation and Shape of the Arm Apparent Stiffness Ellipses

    Muscle Redundancy

    • Sources of Muscle Redundancy
    • Invariant Features of Muscle Activity Patterns

    The Distribution Problem

    • Static Optimization

      • Problem Formulation
      • Cost Functions
      • Accuracy of the Static Optimization Methods: How Well Do the Methods Work?

    • Dynamic Optimization

      • Basic Concepts
      • Forward Dynamics Problem

    • Inverse Optimization
    • On Optimization Methods in Human Biomechanics and Motor Control

    Questions for Review
    Literature List

    About the Authors

    About the Author

    Vladimir M. Zatsiorsky, PhD, is a world-renowned expert in the biomechanics of human motion. He has been a professor in the department of kinesiology at Pennsylvania State University since 1991 and was a director of the university's biomechanics laboratory.

    Before coming to North America in 1990, Dr. Zatsiorsky served for 18 years as professor and chair of the department of biomechanics at the Central Institute of Physical Culture in Moscow. He has received several awards for his achievements, including the Geoffrey Dyson Award from the International Society of Biomechanics in Sports (the society's highest honor), Jim Hay’s Memorial Award from the American Society of Biomechanics, and the USSR's National Gold Medal for the Best Scientific Research in Sport in 1976 and 1982. For 26 years he served as consultant to the national Olympic teams of the USSR. He was also the director of the USSR's All-Union Research Institute of Physical Culture for three years.

    He has authored and coauthored more than 400 scientific papers and 15 books that are published in English, Russian, German, Italian, Spanish, Portuguese, Chinese, Japanese, Polish, Bulgarian, Romanian, Czech, Hungarian, and Serbo-Croatian. Dr. Zatsiorsky has been conferred doctor honoris causa degrees by the Academy of Physical Education (Poland, 1999) and the Russian State University of Physical Culture and Sport (2003). Among his books are Kinematics of Human Motion, Biomechanics in Sport: Performance Enhancement and Injury Prevention, Kinetics of Human Motion, and Science and Practice of Strength Training (coauthor).

    He and his wife, Rita, live in State College, Pennsylvania.

    Boris I. Prilutsky, PhD, is an associate professor in the School of Applied Physiology and director of biomechanics and motor control laboratory at the Georgia Institute of Technology in Atlanta, Georgia. Before that position, he was a senior research scientist in Georgia Tech’s Center for Human Movement Studies from 1998 to 2005.

    His research interests include muscle biomechanics, neural control of movements, and motor learning. His research contributed to the development of methods for quantifying mechanical energy transfer by two-joint muscles between body segments during locomotion and to the understanding of muscle coordination during human motion. Prilutsky has published more than 50 peer-reviewed research articles and five book chapters, and he is the author of six patents. His research is supported by the National Institutes of Health (NIH) and National Science Foundation (NSF).

    While living in the former Soviet Union, Prilutsky received a BS degree in physical education from the Central Institute of Physical Culture in Moscow and a BS degree in applied mathematics and mechanics from the Moscow Institute of Electronic Engineering. He received his PhD in biomechanics from the Latvian Research Institute of Traumatology and Orthopedics in Riga.

    From 1978 to 1992, he worked as a research scientist and lecturer in the department of biomechanics for the Central Institute of Physical Culture in Moscow. He was also a postdoctoral fellow in the department of kinesiology at the University of Calgary, Alberta, Canada (1992-1995), and at the department of health and performance sciences at Georgia Tech (1995-1998).

    Prilutsky is a member of the American Society of Biomechanics and a 1995 recipient of the organization’s Young Scientist Award. He is also a member of the International Society of Biomechanics, Society for Neuroscience, and the Neural Control of Movement Society. He serves as a reviewer for over 30 professional research journals and for the NIH, NSF, South Carolina Space Grant Consortium, Consiglio Nazionale delle Ricerche (CNR), and the Austrian Science Fund.Prilutsky resides in Duluth, Georgia, and enjoys mountain biking, reading, and traveling in his free time.


    "This is an excellent book for readers interested in building upon a basic understanding of biomechanics....In addition to the well-credentialed authors' expertise, important peer-reviewed research is presented throughout the book."

    --Doody's Book Review (5-star review)