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Contents
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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- Skeletal Function and Form
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- 18 December 2000, pp vii-x
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Frontmatter
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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- Skeletal Function and Form
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Appendix B - Structural Characteristics
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Strength of Materials Approach
The continuum material concepts of stress, strain, and material properties are critical to understanding the mechanical response of a structure to applied loads. In this section, we present a few examples of stress analyses of long bones subjected to axial, bending, and torsional loading. We use a method that is sometimes referred to as a strength of materials approach. This approach yields accurate estimates of deformations and stress and strain distributions for structures with simple shapes, material property distributions, and loading conditions. The solutions can also provide approximations of the mechanical response of slightly more complicated problems in structural mechanics.
First consider a long bone that is being compressed by forces (F) applied to both ends (Figure B.1). We assume here that the diaphysis of the bone is straight and that the force is directed through the centroid of the cross section of the mid-diaphysis. We further assume that the diaphysis is perfectly cylindrical with an endosteal inner radius of ri and periosteal outer radius ro. Let us now consider the distribution of stress on a transverse plane through the midshaft. Conceptionally, we can isolate a short section of the diaphysis of length L (Figure B.1). Since this region is far from the areas of force application, the axially oriented internal force will be spread over the entire section and the normal stress σzz at all points in the plane will be equal to F/A where A is the cross-sectional area of the mid-diaphysis. There will be no shear stress acting at the section (σzx = σzy = 0).
Chapter 9 - Mechanobiology in Skeletal Evolution
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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- Skeletal Function and Form
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Summary
In the preceding chapters we have described how mechanical loading histories regulate skeletal biology, with an emphasis on extant terrestrial mammals. The cellular and molecular mechanisms responsible for this control have not been addressed and for the most part remain unknown. These mechanisms, and thus the associated mechanobiological rules, have a genetic basis and are accordingly subject to basic evolutionary selection processes. This chapter addresses evolutionary questions associated with skeletal mechanobiology and the morphology of bones in different taxa. We seek, as did Roux, Wolff, and Thompson, a mechanistic and not a teleological explanation of the morphological differences among bones.
Genotypic variations in vertebrate cartilage and bone both permit and constrain the range of skeletal features that can appear in the skeleton (Moss and Moss-Salentijn, 1983). To understand the possible phylogenetic basis for differences in skeletal tissue response to mechanical stimuli, it is important first to understand the evolution of bone developmental processes that determine morphology. A broad view of the evolution of skeletal characteristics in different taxa was presented in Chapter 1, and the reader may wish to review that material before proceeding (Figure 1.6).
Consider two adult animals of different taxa but similar size and anatomical construction. Assume that the morphology of a particular bone, like a femur, is very different in these two animals. To explain the morphological differences between the two bones we could argue (1) that genetic positional information resulted in significant size and/or shape differences in the anlagen, or (2) that the bones developed under different mechanical conditions, or (3) that genetic differences in the cartilage and bone tissues of the two animals were manifested in different mechanobiological responses, thus resulting in different morphologies in the adult animals.
Skeletal Function and Form
- Mechanobiology of Skeletal Development, Aging, and Regeneration
- Dennis R. Carter, Gary S. Beaupré
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- 18 December 2000
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The intimate relationship between form and function inherent in the design of animals is perhaps nowhere more evident than in the musculoskeletal system. In the bones, cartilage, tendons, ligaments, and muscles of all vertebrates there is a graceful and efficient physical order. This book is about how function determines form. It addresses the role of mechanical factors in the development, adaptation, maintenance, ageing and repair of skeletal tissues. The authors refer to this process as mechanobiology and develop their theme within an evolutionary framework. They show how the normal development of skeletal tissues is influenced by mechanical stimulation beginning in the embryo and continuing throughout life into old age. They also show how degenerative disorders such as arthritis and osteoporosis are regulated by the same mechanical processes that influence development and growth. Skeletal Function and Form bridges important gaps among disciplines, providing a common ground for understanding, and will appeal to a wide audience of bioengineers, zoologists, anthropologists, palaeontologists and orthopaedists.
Chapter 6 - Cancellous Bone
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Biology and Morphology
Cancellous bone in the metaphyseal and epiphyseal regions is derived primarily through endochondral ossification. The endochondral ossification process described in Chapter 5 leads to the calcification of cartilage extracellular matrix around the hypertrophic chondrocytes. The spatial patterns of the terminal, hypertrophic chondrocytes in the matrix determine the textural pattern of matrix calcification. In humans, the newly calcified cartilage is quickly resorbed by chondroclasts, creating small erosion bays in which osteoblasts immediately form bony trabeculae. The initial architecture of the cancellous bone that is formed is thus dictated by the organization of the cells and calcified cartilage that precede bone formation.
The histomorphologic organization of the hypertrophic chondrocytes can vary considerably, and therefore the initial architecture of the cancellous bone can be quite different in different regions and in different taxa (as will be considered in Chapter 9). For example, the primary growth front in mammals tends to be organized into columns of maturing and hypertrophying chondrocytes. The hypertrophying chondrocytes around the secondary ossific nucleus, however, are relatively unorganized (Farnum and Wilsman, 1998). Consequently, the initial bone structure in the metaphysis is organized into fine columns of interconnecting trabeculae, and the initial cancellous bone in the epiphysis appears to have thicker trabeculae and a more random appearance. As the secondary ossification center expands and the subchondral growth front approaches the joint surface, the chondrocytes become more organized into columns. Newly formed subchondral cancellous bone therefore tends to be organized with a principal trabecular orientation that is perpendicular to the joint surface.
Chapter 1 - Form and Function
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Historical Foundation
The beautiful designs that can be observed in plants and animals have held a fascination for people throughout history. Intimate relationships between form and function inherent in many of these designs are perhaps nowhere as evident as in the musculoskeletal system. In the bones, cartilage, tendons, ligaments, and muscles of all vertebrates there is a gracefully efficient physical order that manifests itself on the organ, tissue, cell, and molecular levels. The existence of such a hierarchy of structural and kinematic harmony is not accidental but the result of unique and complex phylogenetic and ontogenetic histories in which genes and mechanical forces provide critical control. This book addresses the role of mechanical forces in regulating the biological processes that lead to the spatial order, size, shape, and histomorphological characteristics of the skeleton. Throughout this book we refer to this regulatory process as mechanobiology.
The fundamental questions that confront us have been faced by many investigators in the past. In the late eighteenth and early nineteenth centuries, the school of Naturphilosophie, championed by Lorenz Oken (Oken, 1809–1811), held that organic order was guided by a divine force that directed the creation of life forms with successively increasing degrees of sophistication and perfection (Gould, 1977). The final level of perfection was thought to be the human form. The Naturphilosophen deemphasized the specific mechanisms of development. The overwhelming consideration was the final organic form itself, and one could be content with the assumption that specific features exist for specific reasons. Those who ascribe to the view that all natural processes move toward a predetermined end are called teleologists or finalists.
Appendix A - Material Characteristics
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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- 18 December 2000, pp 267-282
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Summary
Stress
When forces are applied to a structure such as a femur, it will deform slightly from its original geometry, and interatomic distances will be changed throughout the bone. These changes in interatomic distances are associated with very complicated, spatially dependent distributions of local internal forces and deformations. Using continuum models of the femur articular cartilage, cancellous bone, and compact bone, we can conceptually define the intensity of internal forces and the magnitude of internal deformations by the stress and strain values at specified locations. The stresses (dimensions = force per unit area, MN/m2 or MPa) can be mathematically related to the strains (dimensions = length per length, mm/mm). The quantitative parameters used to define the relationships between stress and strain are the material properties of the tissue. Examples of material properties are the tissue elastic modulus and Poisson's ratio, which will be discussed later.
To fully define the state of stress at a point in a structure, one must specify the six independent values of the stress tensor. These six values are the normal stresses and shear stress on three independent planes passing through that point. The concept of stress and strain is simplified, however, when we restrict ourselves to the stress components that act on one specific plane through the point. Consider a femur that is exposed to a particular set of forces acting at a specific time (Figure A.1). The stresses act on a transverse plane at a point within the cortex of the mid-diaphysis. Using the coordinate system shown in Figure A.1, we can define the plane under consideration by z = constant.
Chapter 3 - Cartilage Differentiation and Growth
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Tendon Development and Fibrocartilage Metaplasia
The soft connective tissues can be considered both histomorphologically and mechanically as a broad range of tissues consisting of various amounts of proteoglycans, water, and structural proteins that are organized with specific ultrastructural arrangements. The composition and ultrastructural organization of these tissues are exquisitely matched to the loading histories to which they are exposed. In general terms, we find that the collagen fiber orientations in fibrous tissues correspond to the predominant direction of in vivo tensile stresses (Figure 3.1). In structures wherein compression is imposed in directions perpendicular to the direction of primary tensile loading, the cells and extracellular matrix manifest the more chondroid character of fibrocartilage. Articular cartilage, on the other hand, is exposed primarily to compressive loading from the joint surface. Since cartilage behaves as a nearly incompressible material at physiologic loading frequencies (1 hz), the adjacent cartilage material effectively provides a tangential compressive stress under the region of contact (Figure 3.1). High hydrostatic pressure is thereby created under the contact area (Figure 2.9). Significant developmental modulations in phenotype, tissue organization, and geometry are possible in tendon, ligaments, menisci, intervertebral discs, articular cartilage, and other soft connective tissue structures. The local mechanical loading history plays a major role in regulating these modifications and thereby “designing” tissues and structures that are matched to their mechanical environment.
To illustrate the role of mechanobiology in dense connective tissue, we can consider the development and adaptation of tendons. During growth and development, tendons will experience changes in both composition and geometry. In particular, progressive increases are observed in the volume fraction of collagen and the size of the tendons.
Chapter 5 - Endochondral Growth and Ossification
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Morphology and Biology
The cartilage growth that was considered in Chapter 3 is a nearly isometric growth in the relatively immature cartilage at the end of a cartilage rudiment. Most of the cartilage growth during development, however, is highly organized and directed at providing growth and ossification in specific directions. Although cartilage growth during development is generally thought of as providing an increase in bone length, complicated organized patterns of growth in various directions are observed in different regions. In the ends of long bones, in particular, three-dimensional growth patterns are observed that lead to the expanse of joint surfaces and trochanters. The directional variations in cartilage growth cause shape changes in developing bones and are responsible for the dramatic changes in skeletal appearance during development (Figures 1.9 and 1.10).
During endochondral growth and ossification, the chondrocytes undergo a characteristic process of proliferation, maturation, hypertrophy, and death. Growth is achieved by cell division, a net increase in the amount of extracellular matrix, and an increase in cell size. In the final stage of growth, the cells hypertrophy and die as the extracellular matrix calcifies. The calcified cartilage matrix is then resorbed and replaced by mineralized, well-vascularized bone tissue that is formed and maintained by bone cells. These phases of cartilage growth and ossification can be observed wherever and whenever endochondral ossification occurs. These phases can be identified in the primary growth center of the cartilage rudiment, the primary growth front of the fetal long bone, secondary growth centers, growth plates, subchondral growth fronts under articular cartilage, and healing fracture calluses (Figure 5.1).
Chapter 8 - Articular Cartilage Development and Destruction
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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- 18 December 2000, pp 201-234
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Summary
Growth and Ossification Near Joint Surfaces
An appreciation of the mechanobiological factors influencing the development, adaptation, and repair of articular cartilage is critically important to understanding the joint pathologies that occur in the aging skeleton. Mechanically mediated endochondral growth and ossification proceed toward the articulations of developing bones. There the same factors that regulate endochondral ossification become involved in the histomorphological development and maintenance of articular cartilage. With advancing age, the articular cartilage destruction and the associated tissue reactions at joints are mediated by the same mechanobiological factors associated with endochondral ossification and skeletal regeneration (Carter, Rapperport, et al., 1987; Carter and Wong, 1990).
The mechanobiological factors regulating articular cartilage development at a typical joint can be illustrated by examining the developing anlagen of the hand. At birth, the ends of long bones in the hand have yet to ossify and the short bone rudiments, like the carpal bones in the wrist, are still entirely cartilaginous (Figure 8.1). At some long bone sites, such as the proximal 2–5 metacarpals and distal first phalanges, the primary ossification front will simply continue its advance toward the joint surface. A secondary ossific nucleus will not appear. As the ossification front approaches the articular surfaces at these locations, the rate of the advance diminishes. At maturity, the ossification front stabilizes under the articular cartilage, and further advance is so slow that it is usually considered negligible. The position at which the subchondral growth front stabilizes determines the thickness of the cartilage.
The rate of endochondral growth and ossification is determined by the baseline “biological growth rate” that is modified by local mechanobiological effects of the loading history.
Chapter 2 - Skeletal Tissue Histomorphology and Mechanics
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Cartilage
Cartilage is a phylogenetically primitive tissue and predates bone as the primary connective tissue of the skeleton. Cartilage appeared in the vertebral endoskeleton over 500 million years ago and may have an invertebrate origin (Moss and Moss- Salentijn, 1983). In the adult human, cartilage is present at the articulations between bones and is also found in the walls of the thorax, larynx, trachea, bronchi, nose, ears, and base of the skull (Moss and Moss-Salentijn, 1983). Like bone, cartilage consists of living cells that are embedded in fibrous extracellular matrix. However, cartilage is quite different from bone in its structure, chemical composition, vascularity, metabolism, growth and regeneration processes, and mechanical properties.
Young cartilage cells are called chondroblasts. They are relatively small cells that are often flat, and they are derived from mesenchymal stem cells. Mature cartilage cells, called chondrocytes, are larger, generally round in shape, and surrounded by an abundant extracellular matrix. Cartilage cells are characterized by their production of the extracellular structural protein, type II collagen. By way of contrast, bone, tendon, ligament, and skin cells produce predominantly type I collagen.
Cartilage grows by both interstitial and appositional mechanisms. Interstitial growth occurs by cell division, cell hypertrophy, and an increased production of extracellular matrix molecules. In addition, a chondrogenic fibrous sheath called the perichondrium envelops some regions of cartilage in the developing skeleton. Stem cells within this sheath can differentiate into chondroblasts that produce extracellular molecules that expand the size of the adjacent cartilage mass via an appositional mechanism. The young cartilage cells are then incorporated into the matrix as chondrocytes and can participate in further interstitial growth.
Index
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Chapter 10 - The Physical Nature of Living Things
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
The preceding chapters provide an introduction to the role of physical factors in the development and evolution of the vertebrate skeleton. We have endeavored to present a coherent picture of the mechanobiological aspects of osteogenesis that encourages an integrated scientific approach to skeletal biology. The models and explanations offered in the text are intentionally simple, since the most direct models and explanations often provide the fundamental basis for understanding. Future refinements, extensions, and corrections by us and by others will surely follow.
Because our understanding of mechanobiology has progressed faster in the skeletal tissues than in other systems, this text has solely addressed the mechanobiology of skeletal development. However, skeletal tissues are not the only biological systems significantly impacted by mechanobiological principles. Other animal tissues and organ systems are also influenced in ways that may not be directly obvious. Currently, investigators are involved in studies on the role mechanical factors play in the development, adaptation, and aging of muscle and cardiovascular tissues. The application of mechanobiology in the study of plant development has also begun to provide a basis for understanding pattern formation throughout nature. It is safe to assume that virtually all cells and tissues respond biologically to mechanical influences to some degree. The tissues that perform a mechanical function or are exposed to significant forces seem to be the most significantly affected.
Current research in the life sciences is strongly based in cell and molecular biology. In these studies the chemical environment and response are a focus of intense interest, but insufficient attention has been given to the impact of physical factors.
Appendix C - Failure Characteristics
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
A Simplification of Material Behavior
In Appendix C we present the concepts of mechanical energy, stress and strain histories, failure characteristics, and fatigue damage in skeletal tissues. These topics by themselves are extremely complicated, and we could easily devote a significant portion of the book to their consideration. We and other investigators have addressed the mechanical properties of bone and other tissues extensively in other publications (Carter and Spengler, 1978; Cowin, 1989; Woo, An, et al., 1994; Mow and Hayes, 1997), and the interested reader is referred to these works for a more in-depth treatment of bone and cartilage mechanics.
In the text we discuss tissue mechanics using a very simplified approach. We present a highly idealized view of cartilage and bone, which in the first approximation are isotropic, linear elastic materials. Bone is often viewed here as having approximately the same strength in tension and compression. Cartilage is viewed, in the first approximation, as a single-phase continuum material that is nearly incompressible.
The simplified view of tissue mechanics that we take allows more attention to be given to fundamental aspects of the tissue loading history which are important in skeletal mechanobiology. We believe that our simplifications convey fundamental concepts without distortion. A presentation using more complete tissue characterizations is certainly possible. However, future investigations using more complicated material models will, we believe, build on the ideas that are used here.
Monotonic Material Failure Criteria
When increasingly high forces are applied to a structure such as a bone, the stresses and strains throughout the structure increase. When critically high levels of stress or strain at any location are reached, material failure and fracture will occur at that location.
Chapter 4 - Perichondral and Periosteal Ossification
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Bone Formation
The flat bones of the skull and face are formed by intramembranous ossification within a condensation of cells derived from the neural crest. In the limb bones and most of the postcranial skeleton, however, mesenchymal cell condensations chondrify, creating the endoskeletal cartilage anlagen. These cartilage rudiments form the templates of the future skeleton and subsequently, in the process of growth, undergo a bony transformation.
The anlagen of the skeleton in early development are small, avascular rudiments consisting of chondrocytes surrounded by an extracellular matrix (Figure 3.13). The largest and most mature chondrocytes in most rudiments are found in the central region of the diaphysis. The cells in the center are surrounded by more extracellular matrix than those at the rudiment ends, leading to a low cell density. In most rudiments this area becomes the center of growth and ossification.
Cartilage growth occurs by mitosis, a net increase in the amount of extracellular matrix, and an increase in cell size. In the end stages of growth in a cartilage region, the cells hypertrophy and die as the extracellular matrix is calcified and then replaced by well-vascularized bone tissue. The cartilage cells within the rudiments therefore undergo a characteristic process of cell proliferation, maturation, hypertrophy, and death, followed by matrix calcification and ossification. Variations in the cartilage growth and ossification rates in different directions within the anlage result in shape changes of developing bones.
Five different phases of cartilage growth and differentiation during long bone ossification were described by Streeter (Streeter, 1949) (Figure 4.1).
Chapter 7 - Skeletal Tissue Regeneration
- Dennis R. Carter, Stanford University, California, Gary S. Beaupré, VA Palo Alto Health Care System
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Summary
Biology and Mechanobiology
Bone fracture or damage triggers a complicated cascade of biological responses that lead to skeletal tissue regeneration. Regeneration is to be distinguished from tissue repair with scar formation since it involves de novo skeletal tissue formation that is accomplished by the proliferation and differentiation of pluripotential mesenchymal stem cells. The mechanobiological factors that regulate skeletal regeneration are similar to those involved in development (Carter, 1987). In this chapter we examine the mechanobiology of skeletal regeneration in four different contexts: (1) tissue differentiation at the interface of a surgical implant, (2) fracture healing, (3) distraction osteogenesis, and (4) neochondrogenesis in joint repair. In Chapter 8 we consider how the mechanobiology of tissue differentiation plays a role in the reparative processes associated with the late stages of osteoarthritis.
Skeletal regeneration is initiated by a traumatic episode that involves damage to the bone that often includes the periosteum, bone marrow spaces, and surrounding soft tissues. Trauma, such as fracture or surgical cutting and drilling, causes a physical disruption of the mineralized tissue matrix, death of many types of cells, and interruption of the local blood supply. Local fibrin clotting of blood follows, and additional necrosis around the trauma site results from the disruption of the vasculature. The necrotic cells release lysosomal enzymes and other products of cell death, thereby initiating the cell proliferation and differentiation processes associated with inflammation and skeletal regeneration.
The inflammatory response begins almost immediately as platelets, polymerphonuclear neutrophils, monocytes, and macrophages appear and fibroblasts and pluripotential mesenchymal cells appear shortly thereafter (Ostrum, Chao, et al., 1994).