1. Basic Anatomy INTRODUCTION Mechanically, the healthy human skeleton is an optimal structure which has adapted its form in response to its function. In order to perform any biomechanical analysis of the musculoskeletal system, it is necessary to understand the underlying anatomy since this comprises the geometry, material properties, and some of the boundary conditions of the problem. Our approach will be to learn enough anatomy to enable us to perform our analyses. Depending on the goal of the particular analysis, a more detailed treatment of the anatomy may be necessary. For example, in some cases, it may be sufficient to model the femoral diaphysis as a hollow circular cylinder, in other cases it may be necessary to account for its non-circular, asymmetric cross-section. This decision is up to the analyst and that decision making process is a major challenge to the bioengineer. Treating the musculoskeletal system as a biomechanical system, we begin with a brief overview of the four main functions of the skeleton. Second, we examine the structure of the skeleton, those regions that will be of special interest to us, and the four main classifications of bones. Once we have developed a basic understanding of the skeletal system, we will describe some important anatomic terms and the anatomic planes, the various types of joints, the structure of the hip, knee, and spine, and some of the important muscle groups. Students requiring a more in-depth treatment of this subject should consult an anatomy text. THE FUNCTIONS OF THE SKELETON The skeletal system consists of bone, the passive soft tissues (tendon, ligament, cartilage, meniscus, joint capsules), muscles, and nerves. It has four main functions, the first two of which are mechanical in nature, the second two, physiological: • support and motion • protection of the vital organs • mineral storage • hematopoiesis. Support and Motion: Probably the most important function of the skeleton from an evolutionary perspective, the relatively rigid bones which articulate at the synovial joints enable the body to move quickly and in a relatively agile manner. The bones and joints operate together as levers, with the muscles providing the active torque about the joint. When the muscles contract they produce forces which cause a bone or an entire limb to rotate about a joint, thereby generating movement. For example, when the biceps contract, the lower arm rotates about the elbow joint, an action known as flexion. Since muscles are

usually attached (or inserted) quite close to the joint, there is a mechanical disadvantage at most joints, i.e. the muscle must pull with a force that is much larger than the external load. However, the advantage of this is that small contractions of the muscle will produce large motions at the end of the limb, which may be advantageous from an evolutionary perspective. Protection of the vital organs: In order to protect the vital organs such as the brain, heart, spinal cord and lungs, the skeleton has developed various structures that allow it to absorb large amounts of energy yet remain lightweight. For example, the cranial bones of the skull have a sandwich construction consisting of a stiff cortical shell surrounding a relatively compliant trabecular bone core (Figure 1.1). The outer cortical shell distributes external forces evenly to the underlying trabecular bone which absorbs most of the energy on compression. The ribs and sternum protect the lungs and heart in a similar manner as do the spine and pelvis their respective soft tissue organs.

Figure 1.1: Cross-sectional view of the human skull (Atlas of the Human Body. Harper Perennial, 1989). Mineral Storage: The skeletal system also has an important physiological function in that it acts as a mineral bank, especially for calcium and phosphorous. Bone is made up primarily of a mixture of collagen (a compliant and ductile protein polymer) and hydroxyapatite (a brittle calcium phosphate ceramic). Approximately 99% of the calcium in the human body is stored in the skeleton. One of the ways that the body regulates the level of these minerals in the bloodstream is by a continuous process of remodeling (the resorption and formation of bone tissue). If the body falls short of its daily calcium intake via the gut, it will turn to the bones to get what it needs. Thus, individuals with calcium deficient diets are at risk of losing bone mass, which in turn would lead to weakening of their bones. Since calcium absorption decreases with aging, elderly people are advised to increase their daily intake of calcium to help reduce the risk of osteoporotic bone fractures. Hematopoiesis: Finally, trabecular bone, the spongy highly porous bone found at the ends of the long bones, the vertebrae, and several other locations (skull, pelvis, sternum)

provides sites for the formation of red blood cells, a process known as hematopoiesis. This occurs only in the red bone marrow. Yellow bone marrow, which is found in the middle (or diaphysis) of most long bones, serves primarily as a storage area for fat cells. BONES There are 206 bones in the human skeleton (Figure 1.2a). Eighty of these bones are found in the axial skeleton (torso) while the remaining 126 comprise the appendicular skeleton (head and limbs). These bones are often divided into four categories based on their shape: long, short, flat, and irregular. The long bones include the femur, tibia, and humerus. The metacarpals and vertebral bodies are short bones. The ilium, cranium, and scapula are flat bones. Irregular bones are those that do not fit neatly into the first three categories and include the wrist bones (carpals) and the posterior vertebral elements. Many of our analyses will deal with the mechanics of long bones. These bones are extremely important in the study of fracture fixation and total joint replacements. We will also examine in detail the vertebral body, a short bone, since it plays a major role in osteoporosis of the spine. Another bone of particular interest is the irregularly-shaped top (or proximal) part of the femur, since it is also important in age-related hip fractures. Because the spine is an important area of concern in orthopaedic biomechanics, some basic knowledge of the vertebral column is necessary. The spine consists of 33 vertebrae (Figure 1.2b) in three sections: seven in the cervical spine (the neck), 12 vertebrae in the thoracic spine (surrounding the chest and rib cage), five in the lumbar spine (the lower back), five in the sacral spine (fused to the pelvis), and four vertebrae are in the coccygeal region, which is the tail for many animals. Usually the sacral and coccygeal vertebrae are fused, i.e. allow no relative motion. Consequently they are seldom injured and we concern ourselves only with the cervical, thoracic, and lumbar regions. These latter regions have limited ability to articulate via the intervertebral disk on the front (or anterior) side, and the facet joints on the back (or posterior) side. Most of the compressive load goes through the disk, i.e. the facet joints allow twisting motions and limit our ability to bend backwards (extension of the spine).

a:

b:

Figure 1.2: a: the human skeleton; b: the vertebral column (Netter, Frank H. The CIBA Collection of Medical Illustrations. Vol. 8, Part 1, 1987). ANATOMIC TERMS AND PLANES OF MOTION When we discuss the bones of the human skeleton it is often useful to distinguish between different regions of the bone. Thus, the following terms are frequently used: • Proximal aspect: Nearest to the top of the body. Usually only used in conjunction with the bones of the appendicular skeleton. Thus, we talk of the proximal femur, which is at the hip joint. • Distal aspect: The opposite of proximal: nearest the bottom of the body. Again, this term is normally used in conjunction with the bones of the appendicular skeleton. This distal femur, for example, is at the knee joint. • Inferior: Beneath or lower. Used to denote the bottom or underside of a tissue or structure. Especially important when discussing bones of the axial skeleton. • Superior: Opposite of inferior; same rules of usage. • Lateral: The part closest to the outside of the body or furthest from the body’s midline. So the lateral aspect of the femur is on the outside of your (left or right) thigh. • Medial: Opposite of lateral: the part closest to the inside or midline of the body. Note lateral and medial are referenced to the mid-line of the body, not to either the left or right sides.

• •

Anterior: Before or in front. Posterior: Behind or in back.

The above terms allow us to describe structures of the skeleton. In order to describe motions of the body we must first define the anatomic position and the three anatomic planes. In the anatomic position, the individual is standing with head and palms facing forward. The frontal (coronal) plane divides the skeleton front-back, the sagittal plane divides the skeleton left-right and the transverse plane divides the skeleton top-bottom. For example, a biceps curl is a motion in the sagittal plane; twisting one’s head to the side is a motion in the transverse plane. In order to describe motions in these planes we use the following terms: •

• • • • • •

• • •

Flexion: A folding movement in which the anterior angle between two bones is decreased (except the knee and toes in which case the angle is measured posteriorly). It generally means that you are moving a bone closer to the body with respect to its anatomical position. Extension: The opposite of flexion: an increase in the anterior angle between two bones (except the knee and toes in which case the angle is measured posteriorly). Abduction: Movement away from the midline of the body, usually in the frontal plane. Adduction: Movement towards the midline of the body, usually in the frontal plane. Hyperextension: Continuation of motion beyond the anatomic position. Lateral flexion: Movement of the spine to the right or left, in the frontal plane. Supination: A movement of the forearm to rotate the hand into the anatomic position. For example, this would be a clockwise rotation of the right forearm (looking down the arm). Pronation: Opposite of supination: a movement of the forearm to rotate the hand so that the palm faces backwards. Dorsiflexion: Rotation of the ankle about a transverse axis so that the toes move upwards (away from the ground) in the sagittal plane. Used only for the ankle. Plantar flexion: Opposite of dorsiflexion: rotation of the ankle so that the toes move toward the ground. Used only for the ankle.

JOINTS OF THE BODY There are two ways to classify joints, functionally, and structurally. The functional classification is based on the amount of relative motion permitted by the joint. One that allows no relative motion between the bones is called synarthrosis. If the joint allows slight motion, it is called an amphiarthrosis. Finally, a joint which allows large relative motions is called a diarthrosis or a diarthrodial joint. Because we will focus on the mechanics of various types of joints, it is often more useful to employ the structural classifications. Fibrous joints and cartilaginous joints are held together by fibrous connective tissue or cartilage as their names imply. For analysis of

most human motion and the design of total joint replacements, the joints of most interest are the synovial joints, a subset of diarthrodial joints. The bones forming a synovial joint are held together by a fibrous joint capsule which may contain connective ligaments. The joint also contains a cavity which is filled with synovial fluid, a highly viscous fluid that helps provide lubrication between the bones in the joint. The synovial fluid is secreted by a thin layer of synovial cells (the synovium) that line the inside of the joint capsule. Human synovial joints possess an extremely small coefficient of friction, lower in fact than virtually any man-made bearing surfaces (Table 1.1). The other main characteristic of synovial joints is that each end of the bone is covered with a thin layer of articular cartilage. Table 1.1: Coefficients of Friction for Various Joints and Common Bearing Materials (Mow, V.C. et al. “Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures.” Biomaterials. Vol. 13, No. 2, pp. 67-97, 1992). Joint / Materials Coefficient of Investigator Friction Human knee 0.005-0.02 J. Charnley (1960) Human hip 0.01-0.04 A. Unsworth (1975) Canine ankle 0.005-0.01 F.C. Linn (1968) Porcine Shoulder 0.02-0.35 C.W. McCutchen Bovine Shoulder 0.002-0.03 L.L. Malcolm (1976) Gold on gold 2.8 Aluminum on aluminum 1.9 Silver on silver 1.5 Steel on steel 0.6-0.8 Brass on steel 0.35 Glass on glass 0.9 Wood on wood 0.25-0.5 Nylon on nylon 0.2 Graphite on steel 0.1 o Ice on ice at 0 C 0.01-0.1 Deterioration of the joints occurs to some degree in nearly all individuals. Osteoarthritis occurs when some combination of mechanical wear and biochemical degradation erodes the cartilage on each covering each bone. It is a localized effect and is most common in the knee and hip since these joints bear the largest loads in the skeleton. Rheumatoid arthritis is a systemic condition where the immune system attacks the joints. The articular cartilage swells, deteriorates, limits mobility, and puts pressure on the nerve endings in the underlying bone. Surrounding soft tissues such as the ligaments and tendons are also affected. Typically this disease starts in the hands and spreads to the back and limbs.

THE HIP Both the hip and knee joints are synovial joints. The hip joint is a relatively simple balland-socket joint in which the head of the femur rotates relative to the fixed acetabulum (Figure 1.4). The most common reason for hip replacements is to restore the range of motion and eliminate the pain caused by osteoarthritis. When the head of the femur is replaced, the natural load transfer paths are interrupted and we must examine the stresses in various regions of the bone. The easiest place to start is the diaphysis because it can often be approximated by a hollow circular beam. The metaphysis (the region where the shaft starts to expand, remember “meta” means “change”) is more difficult to analyze since the load transfer to the surrounding bone is more complicated and we must often resort to finite element studies. Also important to the load distribution and overall mechanical analysis are the ephiphysis and the linea aspera. The ephiphyses (one at each end of the bone) contain spongy trabecular bone and are two of the principal sites for hematopoiesis. All bone growth during maturation occurs at the epiphyseal plate, a soft cartilaginous tissue that eventually fuses and turns into bone. Fractures across the epiphyseal plate in children are therefore dangerous since they can interrupt or even terminate bone growth. The linea aspera is a raised bony ridge on the posterior side of the femur to which many of the muscle groups attach. The reason for the raised ridge will become apparent when we discuss the adaptation of bone to applied loads (bone remodeling). Other examples of specialized muscle attachment points are the greater and lesser trochanters on the proximal femur (Figure 1.3) and the calcaneus, which forms the part of the ankle joint. Biomechanically, these ridges create an increased moment arm for the muscles with respect to the joint center.

Figure 1.3: The right femur. (a): anterior view; (b): posterior view. THE KNEE The knee joint (Figure 1.4) is a condyloid joint that allows the femur and tibia to rotate, twist, and slide relative to one another. Each type of motion is important to the stability of the joint and must be reproduced in an artificial knee replacement. Otherwise abnormal forces can develop on the cartilage or in the ligaments, which can lead to their deterioration. This intimate relationship between the kinematics and loads is a characteristic of most synovial joints. Among the most important structures in the knee are the medial collateral ligament (MCL), the lateral collateral ligament (LCL), quadriceps tendon, patellar ligament, anterior cruciate ligament (ACL), and the posterior cruciate ligament (PCL). Athletes, especially football players and gymnasts, are well acquainted with the MCL, LCL, ACL, and the pain associated with injuries to these structures. The ACL and PCL lie within the joint capsule; the other ligaments are outside. The ACL attaches at the anterior side of the proximal tibia and the middle, bottom surface of the distal femur. Similarly, the PCL connects the posterior side of the proximal tibia and the middle, bottom surface of the distal femur (Figure 1.4b). It should be noted here that there is an inherent difference between ligaments and tendons. Ligaments connect one bone to another while tendons connect bone to muscle. Another important structure in the knee is the meniscus. This crescent-shaped pad helps distribute the loads from the femoral condyles evenly over the surface of the tibia.

a:

b:

Figure 1.4: (a) Side and (b) anterior views of the knee joint. Note that the fibular collateral ligament is also known as the lateral collateral ligament and runs along the lateral aspect of the joint. (Tortora, G. J. Principles of Human Anatomy. Harper and Row, Publishers, New York, 1983.) THE SPINE One of the few cartilaginous joints that we will study is the anterior part of the intervertebral joint (Figure 1.5a). In fact the connective tissue is not cartilage but a fibrocartilage structure known as the intervertebral disc. The disc is analogous to an inflated tire and is the largest avascular tissue in the body (Figure 1.5b). The outside is a concentric ring of collagen sheets (the annulus fibrosis) while the center is filled with a highly viscous gel (the nucleus pulposis). With aging, this gel solidifies, which can have significant biomechanical consequences. This particular joint allows small motions between the bones comprising it and is often injured, hence its significance to the orthopaedic biomechanics community. On the posterior side, there is the synovial type facet joint. This controls lateral twisting and helps limit extension in the spine.

a:

b:

Figure 1.5: The intervertebral joints (a) and disk (b). (Tortora, G. J. Principles of Human Anatomy. Harper and Row, Publishers, New York, 1983.) Figure 6 provides two views of a lumbar vertebra, the largest and strongest in the vertebral column. The principal load bearing region is the vertebral body. The cortex is only 200-350 mm thick and the interior is comprised of some of the lowest density trabecular bone in the body, particularly in the elderly. The articular processes (also known as facet joints) connect the spinous process of one vertebral body to those above and below. The foramen (derived from the Latin for “hole”) houses the spinal cord. The entire structure then, serves to support the upper body and protect the spinal cord from trauma. When analyzing the mechanics of the lower spine it is often assumed that the back muscles (the erector spinae among others) act at a distance of 5 cm posterior to the center of the vertebral body, although this tends to be an oversimplification. The center of rotation of the joint for sagittal bending is within the disk, although this can vary with aging.

Figure 1.6: Lumbar vertebra: superior (A) and right lateral (B) views.

MAJOR MUSCLE GROUPS There are approximately 700 different muscles in the human body and they are divided into three different types, skeletal, cardiac, and smooth or visceral muscles. Skeletal muscle is voluntary and striated and makes up approximately 36% of the total body weight in women and 42% in men. The cardiac muscle is also striated but is an involuntary muscle. Smooth muscle tissue involuntary and is not striated. We will be concerned almost exclusively with skeletal muscles and because many common movements are coordinated by muscles acting in groups, we will often consider them as such. For instance, the quadriceps (the “thigh muscles”) are made up of the rectus femoris, vastus medialis, vastus lateralis, and the vastus intermedius, but they all act together to extend the knee. The main condition for lumping muscles together in this fashion is that they all have a common insertion point on the bone, thereby creating no moment about that point. For example, the quadriceps all come together at the patella via the single quadriceps tendon and both the long and short heads of the biceps attach to the radius through a single tendon. A summary of the major muscles or muscle groups is provided in Table 1.2 along with the action that they effect. Table 1.2: Major muscle groups and their actions on the knee, hip, lumbar spine, and elbow. Joint Knee

Action Muscles/ Muscle Groups Flexion Hamstrings* Extension Quadriceps** Hip Flexion Iliacus, Psoas Major Extension Hamstrings*, Gluteus Maximus Abduction Abductors Adduction Adductors Lumbar Spine Flexion Rectus Abdominis, Internal and External Obliques Extension Erector Spinae Elbow Flexion Brachialis, Biceps Brachii Extension Triceps Brachii * The hamstrings consists of three different muscles, the semitendinosus, semimembranosus, and biceps femoris. ** The quadriceps consists of four different muscles, the rectus femoris, vastus lateralis, vastus medialis, and vastus intermedius. Acknowledgements: Written with Eric Nauman, Ph.D. REFERENCES Charnley, J. The lubrication of animal joints. In: Symposium on Biomechanics, pp. 12-22 Institute of Mechanical Engineers, London, 1959.

Linn, F. C. Lubrication of animal joints: II. The mechanism. J. Biomech., 1: 193-205, 1968. Malcolm, L. L. An experimental investigation of the frictional and deformational responses of articular cartilage interfaces to static and dynamic loading. Ph.D. Thesis, University of California, San Diego, 1976. McCutchen, C.W. The frictional properties of animal joints. Wear, 5: 1-17, 1962. Netter, Frank H. The CIBA Collection of Medical Illustrations. Vol. 8, Part 1, 1987 Atlas of the Human Body. Harper Perennial, 1989 Tortora, G. J. Principles of Human Anatomy. Harper and Row, Publishers, New York, 1983 Unsworth, A., Dowson, D. and Wright, V. The frictional behavior of human synovial joints: I. Natural joints. J. Lubr. Technol., 97:360-376, 1975.

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