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Biomechanics of Joints

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JOINTS, BIOMECHANICS OF George (Yiorgos) Papaioannou, Ph.D. and *Yener N. Yeni, Ph.D.JOINTS, BIOMECHANICS OF Yiorgos Papaioannou, Ph.D. and *Yener N. Yeni, Ph.D. George Papaioannou Ph.D Assistant Professor Director of Advanced Biomechanics Laboratory Department of Biomedical Engineering School of Engineering The Catholic University of America Rm 123 Pangborn 621 Michigan Ave NE Washington DC 20064 Phone: (202) 319 5891 Fax: (202) 319-4287 E_mail: [email protected] Yener N. Yeni, Ph.D. Head, Section of Biomechanics Bone and Joint Center Henry Ford Hospital 2799 West Grand Boulevard Detroit, Michigan, 48202 USA *For correspondence: Yener N. Yeni, Ph.D. Head, Section of Biomechanics Bone and Joint Center Henry Ford Hospital 2799 West Grand Boulevard, E&R 2015 Detroit, Michigan, 48202 USA Phone: (313) 916 7592 Fax: (313) 916 8964 E_mail: [email protected] Bones in the skeleton join to form segments or links which provide for the attachment of muscles, ligaments, tendons etc. Altogether, these systems of bones and soft tissues, called joints, produce movement for the organism. Joint biomechanics traditionally is a division of biomechanics that studies the effect of forces on the joints of living organisms. Like all other organs, joints are subject to trauma and disease. Development of treatments, devices and exercise regimes for healthy joints, as well as learning from the great variety of naturally existing joints for the purpose of nature-inspired technology, requires a fundamental understanding of the mechanics of joints and joint tissues, and their interaction with the underlying biological mechanisms. At the current state of the art, the definition of joint biomechanics can be broadened to encompass these complex interactions and the relevant technology. It is the purpose of this chapter to introduce a current understanding of joint biomechanics with an emphasis on the structure, kinematics, kinetics, modeling and joint stability of human joints. A detailed consideration of the mechanics of artifical joints and that of the tissues forming a joint is left for other chapters. Keywords: Joints, biomechanics, joint mechanics, structure, kinematics, kinetics, modeling, joint stability, motion, joint health, experimental analysis, human joints, joint tissues. CONTENTS 1. Introduction 1.1 Articular anatomy, joint types and their function 1.2 Articular cartilage 1.3 Effects of motion and external loading on joints 2. Kinematics of joints 2.1 General comments 2.2 Characterization of the generic mechanical joint system- Terminology and definitions 2.3 Degrees of freedom 2.4 Planar motion 2.5 Instantaneous Center of Rotation-ICR 2.6 Analytical methods 2.6.1 Data collection 2.6.2 Data Analysis 2.6.2.1 Coordinate Systems and Transformation 2.6.2.2 Translation in three-dimensional space 2.6.2.3 Rotations about the coordinate Axes 2.6.2.4 Combined rotations as a result of a sequence of rotations 2.6.2.5 Euler and Bryant-Cardan angles 2.6.2.6 Parameters of the motion of a body observed in a laboratory coordinate system 3. Kinetics of joints 3.1 Equations of motion 3.2 Motion and forces on diarthroidal joints 4. Mathematical and mechanical models of joints 4.1 Assessment of mechanical factors associated with joint degeneration-Limitations and future work4.2 From experimental to advanced theoretical analysis in joint mechanics 4.3 Theoretical analysis of joint mechanics 4.4 Surface modeling 4.5 The joint distribution problem 4.5.1 Phenomenological joint models 4.5.2 Anatomical models 4.5.3 The reduction method 4.5.4 The optimization method 4.5.5 The forward analysis 4.5.6 Finite element analysis (FEA) of human joints 4.5.7 Towards Patient-Specific and Task dependent Morphological FE models 5. Joint Stability 5.1 The hip joint 5.2 The knee joint 5.3 The foot structure; the ankle joint 5.4 The spine 5.5 The shoulder 5.6 The elbow 5.7 The wrist 6. Overview 7. References FIGURES Figure 1. Basic structure and components of a synovial joint (also called diarthroses). Figure 2. Zones of articular cartilage (from F. Nelson (1)) Figure 3. Points S and S’ as well as Q and Q’ lie on the arcs of circles around the center of rotation ICR (used synonymously with CR after section 2.5). If lines SS’ and QQ’ are bisected perpendicularly, the center of rotation CR is located at the intersection of these perpendicular bisectors. This construction assumes that the perpendicular bisectors are differently orientated but a special case arises if the bisectors are identically oriented. Then the points S, Q and the center of rotation ICR lie on a straight line. Figure 4. Changing the coordinate systems, transformation of point coordinates from one coordinate system to another. Figure 5. A rigid body (shoebox) moves parallel to itself. The radius vectors from O to P and from O to P’ are designated by r and r’ so that r’ = r + t where t is the difference vector. Figure 6. Rotation about the z-axis of the coordinate system. Figure 7. General rotation composed of three partial rotations. The first rotation according to the Bryant-Cardan convention (above). The first of the general rotations using Euler as the selection of the axes and angles of rotation (below). Figure 8. Motion of a rigid body: minimum configuration of three reference points in order to determine the parameters describing the spatial motion. Figure 9. Interpretation of the motion as helical motion. Motion of a rigid body and interpretation of the general motion as helical motion (Chasles Theorem). The necessary number of reference points is fixed on a rigid body (not shown here). From the spatial location of the reference points in the initial and final state, the locations of the geometric centers S(rs) andS’(r’s), as well as the rotation matrix D are determined. The change in location of the respective geometric centers is described by ts = r’s - rs . The axis of rotation n and the angle of rotation ϕ can be determined from the rotation matrix. The translation tp in direction of the helical axis is defined by projection from n and ts. The location of the axis of rotation relative to the initial and final position of the object (segment) is set by points A and M. M is the midpoint of the line SS’. The vector f directed from M to A is perpendicular to n and ts. The radius R and the radius vector rA can be calculated by means of the unit vectors e, n, and f (adopted from Brinckmann et al.,


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