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Bone and Cartilage

  • Chapter
Biomechanics

Abstract

Bone works in the small strain range; yet its biology is very sensitive to the strain level. Its constitutive equation is linear with respect to the strain, and the strain-displacement relationship is also linear; but the relationship is anisotropic. In this chapter the mechanical properties of bone are described with an emphasis on biology.

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References

  • Amtmann, E. (1968) The distribution of breaking strength in the human femur shaft. J. Biomech. 1, 271–277.

    Article  PubMed  CAS  Google Scholar 

  • Amtmann, E. (1971) Mechanical stress, functional adaptation, and the variation of structure of the human femur diaphysis. Ergebnisse Anat. Entwicklungsgeschichte 44, 7–89.

    Google Scholar 

  • Amtmann, E and Schmitt, H. P. (1968) Über die Verteilung der Corticalisdichte im menschlichen Femurschaft und ihre Bedeutung für die Bestimung der Knochenfestigkeit. Z. Anat. u. Entwickl.-ges. 127, 25–41.

    Article  Google Scholar 

  • Basset, C. A. L. and Pawlick, R. J. (1964) Effect of electrical currents on bone in vivo. Nature 204, 652–653.

    Article  Google Scholar 

  • Becker, R. O. and Murray D. G. (1970) The electrical control system regulating fracture healing in amphibians. Clin. Orthopedics 73, 169–198.

    CAS  Google Scholar 

  • Boume, G. H. (ed.) (1972) The Biochemistry and Physiology of Bone, 2nd edition, Vol. 1: Structure. Vol. 2: Physiology and Pathology. Vol. 3: Development and Growth. Academic Press, New York.

    Google Scholar 

  • Brânemark, P.-I., Hansson, B. O., Breine, U., Lindström, J., Hallén, O., and Öhman, A. (1977) Osseointegrated Implants in the Treatment of the Edentulous Jaw. Almquist and Wiksell, Stockholm, 132 pp.

    Google Scholar 

  • Brannan, E. W., Rockwood, C. A., and Potts, P. (1963) The influence of specific exercises in the prevention of debilitating musculoskeletal disorders. Aerospace Med. 34, 900–906.

    Google Scholar 

  • Brookes, M. (1971) The Blood Supply of Bone. An Approach to Bone Biology. Butter-worths, London.

    Google Scholar 

  • Carter, D. R. and Hayes, W. C. (1977) The compressive behavior of bone as a two-phase porous material. J. Bone Joint Surg. 49A, 954–962.

    Google Scholar 

  • Carter, D. R., Harris, W. H., Vasu, R., and Caler, W. E. (1981) The mechanical and biological response of cortical bone to in vivo strain histories. In Mechanical Properties of Bone, S. Cowin ed. AMD Vol. 45, American Society of Mechanical Engineering, New York, pp. 81–92.

    Google Scholar 

  • Carter, D. R., Fyhrie, D. P., and Whalen, R. T. (1987) Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy. J. Biomech. 20, 785–794.

    Article  PubMed  CAS  Google Scholar 

  • Carter, D. R. (1987) Mechanical loading history and skeletal biology. J. Biomech. 20, 1095–1109.

    Article  PubMed  CAS  Google Scholar 

  • Carter, D. R., Orr, T. E., Fyhrie, D. P., and Schurman, D. J. (1987) Influences of mechanical stress on prenatal and postnatal skeletal development. Clin. Orthopaedics 219, 237–250.

    Google Scholar 

  • Carter, D. R. and Wong, M. (1988) Mechanical stresses and endochondralossification in the chondroepiphysis. J. Orthopaedic Res. 6, 148–154.

    Article  CAS  Google Scholar 

  • Cassidy, J. J. and Davy, D. T. (1985) Mechanical and architectural properties in bovine cancellous bone. Trans. Orthopaedic Res. Soc. 31, 354.

    Google Scholar 

  • Churches, A. E. and Howlett, C. R. (1981) The response of mature cortical bone to controlled time-varying loading. In Mechanical Propoerties of Bone S. Cowin (ed.) AMD Vol. 45. American Society of Mechanical Engineering, New York, pp. 69–80.

    Google Scholar 

  • Cowin, S. C. and Hegedus, D. M. (1976) Bone remodeling. J. Elasticity 6, 313–325, 337–352.

    Google Scholar 

  • Cowin, S. C and Nachlinger, R. R. (1978) Bone remodeling III. J. Elasticity 8, 285–295.

    Article  Google Scholar 

  • Cowin, S. C. and Van Buskirk, W. C. (1978) Internal bone remodeling induced by a medullary pin. J. Biomech. 11, 269–275.

    Article  PubMed  CAS  Google Scholar 

  • Cowin, S. C. and Van Buskirk, W. C. (1979) Surface remodeling induced by a medullary pin. J. Biomech. 12, 269–276.

    Article  PubMed  CAS  Google Scholar 

  • Cowin, S. C. (ed.) (1981) Mechanical Properties of Bone, ASME Publication No. AMD Vol. 45.

    Google Scholar 

  • Cowin, S. C. (1983) The mechanical and stress adaptive properties of bone. Ann. Biomed. Eng. 2, 263–295.

    Article  Google Scholar 

  • Cowin, S. C. (1984) Modeling of the stress adaptation process in bone. Cal. Tissue Int. 36 (Suppl.), S99 - S104.

    Google Scholar 

  • Cowin, S. C., Hart, R. T., Balser, J. R., and Kohn, D. H. (1985) Functional adaptation in long bones: Establishing in vivo values for surface remodeling rate coefficients. J. Biomech. 18, 665–684.

    Article  PubMed  CAS  Google Scholar 

  • Cowin, S. C. (1986) Wolff’s law of trabecular architecture at remodeling equilibrium. J. Biomech. Eng. 108, 83–88.

    Article  PubMed  CAS  Google Scholar 

  • Cowin, S. C and Van Buskirk, W. C. (1986) Thermodynamic restrictions on the elastic constants of bone. J. Biomech. Eng. 108, 83–88.

    Article  PubMed  CAS  Google Scholar 

  • Cowin, S. C., Van Buskirk, W. C., and Ashman, R. B. (1987) Properties of bone. In Handbook of Bioengineering, R. Skalak and S. Chien (eds.) McGraw-Hill, New York, pp. 2. 1–2. 27.

    Google Scholar 

  • Cowin, S. C. (1988) Strain assessment by bone cells. In Tissue Engineering, R. Skalak and C. F. Fox (eds.) Alan Liss, New York, pp. 181–188.

    Google Scholar 

  • Cowin, S. C., Sadegh, A. M., and Luo, G. M. (1992) An evolutionary Wolff’s law for trabecular architecture. J. Biomech. Eng. 114, 129–136.

    Article  PubMed  CAS  Google Scholar 

  • Crowningshield, R. D. and Pope, M. H. (1974) The response of compact bone in tension at various strain rates. Ann. Biomed. Eng. 2, 217–225.

    Article  Google Scholar 

  • Culmann, C. ( 1866 and 1875) Die Graphische Statik. 1st edition, Meyer und Zeller, Zurich.

    Google Scholar 

  • Currey, J. D. (1964) Three analogies to explain the mechanical properties of bone. Biorheology 2, 1–10.

    Google Scholar 

  • Dietrick, J. E., Whedon, G., and Shorr, E. (1948) Effects of immobilization upon various metabolic and physiological functions of normal man. Am. J. Med. 4, 3–36.

    Article  Google Scholar 

  • Dintenfass, L. (1963) Rheology of synovial fluid and its role in joint lubrication. Proc. Int. Congress Rheolog. 4, 489.

    Google Scholar 

  • Dowson, D., Longfield, M., Walker, P., and Wright, V. (1968) An investigation of the friction and lubrication in human joints. Proc. Institution Mech. Eng. (London) 181, Part 3J, 45–54.

    Google Scholar 

  • Dowson, D. and Whoms, T. L. (1968) Effect of surface quality upon the traction characteristics of lubricated cylindrical contacts. Proc. Institution Mech. Eng. (London) 182, Part 1, 292–299.

    Google Scholar 

  • Evans, F. G. (1957) Stress and Strain in Bones. Their Relation to Fractures and Osteogenesis. C. C. Thomas, Springerfield, I I.

    Google Scholar 

  • Evans, F. G. (1969) The mechanical properties of bone. Artificial Limbs 13, 37–48.

    PubMed  CAS  Google Scholar 

  • Evans, F. G. (1973) Mechanical Properties of Bone. Charles C. Thomas, Springfield, IL.

    Google Scholar 

  • Fein, R. S. (1967) Are synovial joints squeeze film lubricated? Proc. Inst. Mech. Eng. 181, 125–128.

    Google Scholar 

  • Firoozbakhsh, K. and Cowin, S. C. (1980) Devolution of inhomogeneities in bone structure— Predictions of adpative elasticity theory. J. Biomech. Eng. 102, 287–293.

    Article  PubMed  CAS  Google Scholar 

  • Frost, H. M. (1964) The Laws of Bonre Structure. Charles C. Thomas, Springfield, IL.

    Google Scholar 

  • Fukada, E. and Yasuda, I. (1957) Piezoelectric effect of bone. J. Physical. Soc. Jpn. 12, 1158–1162.

    Article  Google Scholar 

  • Fukada, E. (1968) Mechanical deformation and electrical polarization in biological substances. Biorheology 5, 199–208.

    PubMed  CAS  Google Scholar 

  • Fung, Y. C. (1972) Stress-strain history relations of soft tissues in simple elongation. In Biomechanics: Its Foundations and Objectives. Prentice-Hall, Englewood Cliffs, NJ, pp. 181–208.

    Google Scholar 

  • Fung, Y. C. (1990) Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag, New York.

    Google Scholar 

  • Fyhrie, D. P. and Carter, D. R. (1985) A unifying principle relating stress state to trabecular bone morphology. Trans. Orthopaedic Res. Soc. 31, 337.

    Google Scholar 

  • Gjelsvik, A. (1973) Bone remodeling and piezoelectricity. I and II. J. Biomech. 6, 69–77, 187–193.

    Google Scholar 

  • Glücksmann, A. (1938) Studies on bone mechanics in vitro. I. Influence of pressure on orientation of structure. Anat. Record 72, 97–115.

    Article  Google Scholar 

  • Glücksmann, A. (1939) II. Role of tension and pressure in chodrogenesis. Anat. Record 73, 39–55.

    Article  Google Scholar 

  • Glücksmann, A. (1942) The role of mechanical stress in bone formation in vitro. J. Anat. 76, 231–239.

    PubMed  Google Scholar 

  • Ham, A. W. (1969) Histology, 6th edition. Lippincott, Philadelphia.

    Google Scholar 

  • Harrigan, T. and Mann, R. W. (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19, 761–767.

    Article  CAS  Google Scholar 

  • Hayes, W. C. and Snyder, B. (1981) Toward a gnemtitative formulation of Wolff’s law in trabecular bone. In Mechanical Properties of Bone, S. C. Cowin ed. AMD Vol. 45. American Society of Mechanical Engineers, New York.

    Google Scholar 

  • Hegedus, D. H. and Cowin, S. C. (1976) Bone remodeling II • Small strain adaptive elasticity. J. Elasticity 6, 337–352.

    Article  Google Scholar 

  • Hert, J. A., Liskova, M., and Landa, J. (1971) Reaction of bone to mechanical stimuli. Part 1. Continuous and intermittent loading of tibia in rabbit. Folia Morphol. 19, 290–317.

    CAS  Google Scholar 

  • Hert, J., Sklenska, A., and Liskova, M. (1971) Reaction of bone to mechanical stimuli. Part 5. Effect of intermittent stress on the rabbit tibia after resection of the pripheral nerves. Folia Morphol. 19, 378–387.

    CAS  Google Scholar 

  • Hoffman, 0. (1967) The brittle strength of orthotropic materials. J. Composite Mater. 1, 200–207.

    Article  Google Scholar 

  • Holmes, M. H. (1986) Finite deformation of soft tissue: Analysis of a mixture model in uniaxial compression. J. Biomech. Eng. 108, 372–381.

    Article  PubMed  CAS  Google Scholar 

  • Hong, S. Z., Wu, Z. K., and Zu, C. M. (1987) Experiments on human vertebrae cervical. Chin. J. Biomed. Eng. 6, 75–83.

    Google Scholar 

  • Johnson, M. W. and Katz, J. L. (1987) Electromechanical effects in bone. In Handbook of Bioengineering, R. Skalak and S. Chien (eds.) McGraw-Hill, New York, pp. 3. 1–3. 11.

    Google Scholar 

  • Jones, H. H., Priest, J. D., Hayes, W. C., Tichemor, C. C., and Nagel, D. A. (1977) Humeral hypertrophy in response to exercise. J. Bone Joint Surg. A 59, 204–208.

    CAS  Google Scholar 

  • Justus, R. and Luft, J. H. (1970) A mechanochemical hypothesis for bone remodeling induced by mechanical stress. Calcified Tissue Res. 5, 222–235.

    Article  CAS  Google Scholar 

  • Katz, J. L. and Mow, V. C. (1973) Mechanical and structural criteria for orthopaedic implants. Biomat. Med. Dev. Art. Organs 1, 575–638.

    CAS  Google Scholar 

  • Kazarian, L. E. and van Gierke, H. E. (1969) Bone loss as a result of immobilization and chelation. Clin. Orthopedics 65, 67–75.

    CAS  Google Scholar 

  • Knese, K.-H. (1972) Knochenstruktur als Verbundbau. G. Thieme, Stuttgart.

    Google Scholar 

  • Kummer, B. K. F. (1972) Biomechanics of bone: Mechanical properties, functional structure, and functional adaptation. In Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker (eds.) Prentice-Hall, Englewood Cliffs, NJ, pp. 237–271.

    Google Scholar 

  • Kwan, M. K., Lai, W. M., and Mow, V. C. (1984) Fundamentals of fluid transport through cartilage in compression. Ann. Biomedical Eng. 12, 537–558.

    Article  CAS  Google Scholar 

  • Kwan, M. K., Lai, W. M. and Mow, V. C. (1990) A finite deformation theory for cartilage and other soft hydrated connective tissues. I. Equilibrium results. J. Biomechanics. 23, 145–155.

    Article  CAS  Google Scholar 

  • Lai, W. M., Hou, J. S., and Mow, V. C. (1991) A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113, 245–258.

    Article  PubMed  CAS  Google Scholar 

  • Lakes, R. S., Katz, J. L., and Sternstein, S. (1979) Viscoelastic properties of wet cortical bone—I. Torsional and biaxial Studies. J. Biomech. 12, 657–678.

    Article  PubMed  CAS  Google Scholar 

  • Lakes, R. S. and Katz, J. L. (1979) Viscoelastic properties of wet cortical bone. II. Relaxation mechanisms. III. A nonlinear constitutive equation. J. Biomech. 12, 679–687, 689–698.

    Google Scholar 

  • Lanyon, L. B. and Baggott, D. G. (1976) Mechanical function as an influence on the structure and form of bone. J. Bone Joint Surg. B 58, 436–443.

    Google Scholar 

  • Lew, H. S. and Fung, Y. C. (1970) Formulation of a statistical equation of motion of a viscous fluid in an anisotropic nonrigid porous solid. Int. J. Solids Struct. 6, 1323–1340.

    Article  Google Scholar 

  • Linn, F. C. (1967) Lubrication of animal joints: I. The arthrotripsometer. J. Bone Joint Surg. A 49, 1079–1098.

    CAS  Google Scholar 

  • Linn, F. C. and Radin, E. L. (1968) Lubrication of animal joints: III. The effect of certain chemical alterations of the cartilage and lubricant. Arth. Rheum. 11, 674–682.

    Article  CAS  Google Scholar 

  • Lotz, J. C., Gerhart, T. N., and Hayes, W. C. (1991) Mechanical properties of metaphysical bone in the proximal femur. J. Biomech. 24, 317–329.

    Article  PubMed  CAS  Google Scholar 

  • Lotz, J. C., Cheal, E. J., and Hayes, W. D. (1991) Fracture prediction for the proximal femur using finite element models. Part I: Linear analysis. Part II: Nonlinear analysis. J. Biomech. Eng. 113, 353–365.

    Article  PubMed  CAS  Google Scholar 

  • MacConaill, M. A. (1932) The function of intra-articular fibrocartilages, with special reference to the knee and inferior radio-ulnar joints. J. Anat. 66, 210–227.

    PubMed  CAS  Google Scholar 

  • Mack, P. B., La Change, P. A., Vost, G. P., and Vogt, F. B. (1967) Bone demineralization of the foot and hand of Gemini IV, V, and VII astronauts during orbital flight. Am. J. Roentgenol. 100, 503–511.

    CAS  Google Scholar 

  • Mak, A. F. (1986) The apparent viscoelastic behavior of articular cartilage—The contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J. Biomech. Eng. 108, 123–130.

    Article  PubMed  CAS  Google Scholar 

  • Malcom, L. L. (1976) Frictional and deformational responses of articular cartilage interfaces to static and dynamic loading. Ph.D. thesis, University of California, San Diego, La Jolla, California.

    Google Scholar 

  • Maroudas, A. (1967) Hyaluronic acid films. Proc. Inst. Mech. Eng. 181, 122–124.

    Google Scholar 

  • Martin, B. (1972) The effects of geometric feedback in the development of osteoporosis. J. Biomech. 5, 447–455.

    Article  PubMed  CAS  Google Scholar 

  • Martin, R. B. (1984) Porosity and specific surface of bone. CRC Crit. Rev. Biomed. Eng. 10, 179–222.

    CAS  Google Scholar 

  • McCutchen, C. W. (1959) Mechanism of animal joints. Nature 184, 1284–1285.

    Article  Google Scholar 

  • McCutchen, C. W. (1962) The frictional properties of animal joints. Wear 5, 1.

    Article  Google Scholar 

  • McCutchen, C. W. (1967) Lubrication and wear in living and artificial joints. Proc. Inst. Mech. Eng. 181, 55, Part 3J.

    Google Scholar 

  • Merz, W. A. and Schenk, R. K. (1970) Quantitative structural analysis of human cancellous bone. Acta Anat. 75, 54–66.

    Article  PubMed  CAS  Google Scholar 

  • Mow, V. C. (1969) The role of lubrication in biomechanical joints. J. Lubr. Technol. Trans. ASME 91, 320–329.

    Article  Google Scholar 

  • Mow, V. C., Lipschitz, H., and Glimcher, M. J. (1977) Mechanisms of stress relaxation in articular cartilage Trans. Ortho. Res. Soc. 2, 75.

    Google Scholar 

  • Mow, V. C., Kuei, S. C., Lai, W. M., and Armstrong, C. G. (1980) Biphasic creep and stress relaxation of articular cartilage in compression: Theory and experiments. J. Biomech. Eng. Trans. ASME 102, 73–84.

    Article  CAS  Google Scholar 

  • Mow, V. C. and Lai, W. M. (1980) Recent developments in synovial joint biomechanics. SIAM Rev. 22, 275–317.

    Article  Google Scholar 

  • Mow, V. C., Ratcliffe, A., and Woo, S. L.-Y. (eds.) (1991) Biomechanics of Diarthroidal Joints, Vols. 1 and 2. Springer-Verlag, New York.

    Google Scholar 

  • Mow, V. C. and Hayes, W. C. (1991) Basic Orthopaedic Biomechanics. Raven Press, New York.

    Google Scholar 

  • Oda, M. (1976) Fabrics and their effects on the deformation behaviors of sand. Department of Foundation Engineering, Saitama University.

    Google Scholar 

  • Oda, M., Konishi, J., and Nemat-Nasser, S. (1980) Some experimentally based fundamental results on the mechanical behavior of granular materials. Geotechnique 30, 479–495.

    Article  Google Scholar 

  • Ogston, A. G. and Stanier, J. E. (1953) The physiological function of hyaluronic acid in synovial fluid: Viscous, elastic, and lubrication properties. J. Physiol. 119, 244–252, 253–258.

    Google Scholar 

  • Patwardham, A. G., Bunch, W. H., Meade, K. P., Vanderby, R., and Knight, G. W. (1986) A biomechanical analog of curve progression and orthotic stabilization in idiopathic scoliosis. J. Biomech. 19, 103–117.

    Article  Google Scholar 

  • Pauwels, F. (1948) Die Bedeutung der Bauprinzipien der Stütz-und Bewegungs- apparatus für die Beanspruchung der Röhrenknochen. Z. Anat. 114, 129–166.

    Article  CAS  Google Scholar 

  • Pauwels, F. (1950) Die Bedeutung der Muskelkräfte für der Regelung der Beanspruchung des Röhrenknochens während der Bewegung der Glieder. Z. Anat. 115, 327–351.

    Article  Google Scholar 

  • Pauwels, F. (1968) Gesammelte Abhandlungen zur funktionellen Anatomie des Bewegungsapparates. Springer-Verlag, New York.

    Google Scholar 

  • Powell, M. J. D. (1965) A method for minimizing a sum of species of nonlinear functions without calculating derivatives. Computer J. 7, 303–307.

    Article  Google Scholar 

  • Radin, E. L., Swann, D. A., and Weisser, P. A. Separation of a hyaluronate—free lubricating factor from synovial fluid. (1970) Nature 228, 377.

    CAS  Google Scholar 

  • Reilly, D. T. and Burstein, A. H. (1974) The mechanical properties of cortical bone. J. Bone Joint Surg. A 56, 1001–1022.

    CAS  Google Scholar 

  • Rhinelander, F. W. (1972) Circulation of bone. In The Biochemistry and Physiology of Bone, 2nd edition, G. H. Bourne (ed.) Academic, New York, pp. 2–78.

    Google Scholar 

  • Roux, W. (1895) Gasammelte Abhandlungen über Entwicklungsmechanik der Organismen Vols. I and I I. Engelmann, Leipzing.

    Google Scholar 

  • Rydevik, B., Bränemark, P.-I., and Skalak, R. (eds.) (1990) International Workshop on Osseointegration in Skeletal Reconstruction and Joint Replacement. Institute for Applied Biotechnology, Göteborg, Sweden.

    Google Scholar 

  • Schmitt, H. P. (1968) Über die Beiehungen zwischen Dichte und Festigkeit des Knochens am Beispiel des menschlichen Femur. Z. Anat. 127, 1–24.

    Article  CAS  Google Scholar 

  • Sedlin, E. (1985) A rheological model for cortical bone. Suppl. 83, Acta Scand. Ortho. 36.

    Google Scholar 

  • Skalak, R. and Chien, S. (eds.) (1987) Handbook of Bioengineering. McGraw-Hill, New York.

    Google Scholar 

  • Skalak, R. and Fox, C. F. (eds.) (1988) Tissue Engineering. Alan Liss, New York.

    Google Scholar 

  • Spilker, R. L., Jakobs, D. M., and Schultz, A. B. (1986) Material constants for a finite element model of the intervertebral disk with a fiber composite amulus. J. Biomech. Eng. 108, 1–11.

    Google Scholar 

  • Stone, J. L., Beaupre, G. S., and Hayes, W. O. (1983) Multiaxial strength characteristics of trabecular bone. J. Biomech. 16, 743–752.

    Article  PubMed  CAS  Google Scholar 

  • Stone, J. L., Snyder, B. D., Hayes, W. C., and Strang, G. L. (1984) Three-dimensional stress morphology analysis of trabecular bone. Trans. Orthopedic Res. Soc. 30, 199.

    Google Scholar 

  • Tencer, A. F., Ahmed, A. M., and Burke, D. C. (1982) Some static mechanical properties of the lumbar intervertebral joint, intact and injured. J. Biomech. Eng. 104.

    Google Scholar 

  • Torino, A. J., Davidson, C. L., Klopper, P. J., and Lindau, L. A. (1976) Protection from stress in bone and its effects: Experiments with stainless steel and plastic plates in dogs. J. Bone Joint Surg. B 58, 107–113.

    Google Scholar 

  • Torzilli, P. A. and Mow, V. C. (1972) On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function, parts I and II. J. Biomech. 9, 541–522 (this is in error), 587–606.

    Google Scholar 

  • Turner, C. H. (1989) Yield behavior of bovine cancellous bone. J. Biomech. Eng. 11, 257–260.

    Google Scholar 

  • Unsworth, A., Dowson, D., and Wright, V. (1975) The frictional behavior of human synovial joints—Part I: Natural joints. J. Lub. Tech. Trans. ASME 97, 369–376.

    Article  Google Scholar 

  • Walker, P. S., Dowson, D., Longfield, M. D., and Wright, V. (1968) “Boosted lubrication” in synovial joints by fluid entrapment and enrichment. Ann. Rheum. Dis. 27, 512–520.

    Google Scholar 

  • Wertheim, G. (1847) Memoire sur l’elasticité et la cohésion des principaux tissus du corps humain. Ann. Chim. Phys. 21, 385–414.

    Google Scholar 

  • Whitehouse, W. J. (1974) The quantitative morphology of anisotropic trabecular bone. J. Microsc. 101, 153–168.

    Article  PubMed  CAS  Google Scholar 

  • Whitehouse, W. J. and Dyson, E. D. (1974) Scanning electron microscope studies of trabecular bone in the proximal end of the human femur. J. Anat. 118, 417–444.

    PubMed  CAS  Google Scholar 

  • Wolff, J. (1869) Über die bedeutung der Architektur der spongiösen Substanz. Zentralblatt für die medizinische Wissenschaft. VI. Jahrgang. pp. 223–234.

    Google Scholar 

  • Wolff, J. (1870) Über die innere Architektur der Knochen und ihre Bedeutung für die Frage vom Knochenwachstum. Arch. pathol. Anat. Physiol. klinische Medizin (Virchovs Arch.) 50 389–453.

    Google Scholar 

  • Wolff, J. (1884) Das Gesetz der Transformation der inneren Architektur der Knochen bei pathologischen Veränderungen der äusseren Knochenform. Sitz, Ber. Preuss. Akad. Wiss. 22. Sitzg., phys.-math. Kl.

    Google Scholar 

  • Wolff, J. (1892) Das Gesetz der Transformation der Knochen. Hirschwald, Berlin.

    Google Scholar 

  • Wonder, C. C., Briney, S. R., Kral, M., and Skavgstad, C. (1960) Growth of mouse femurs during continual centrifugation. Nature 188, 151–152.

    Article  Google Scholar 

  • Woo, S. L.-Y., Akeson, W. H., Coutts, R. D., Rutherford, L., Doty, D., Jemmott, G. F., and Amiel, D. (1976) A comparison of cortical bone atrophy secondary to fixation with plates with large differences in bending stiffness. J. Bone Joint Surg. A 58, 190–195.

    CAS  Google Scholar 

  • Woo, S. L.-Y., Simon, B. R., Kuei, S. C., and Akeson, W. H. (1979) Quasi-linear viscoelastic properties of normal articular cartilage. J. Biomech. Eng. 102, 85–90.

    Article  Google Scholar 

  • Woo, S. L.-Y., Gomez, M. A., Woo, Y.-K., and Akeson, W. H. (1982) Mechanical properties of tendons and ligaments. II. The relationships of immobilization and exercise on tissue remodeling. Biorheology 19, 397–408.

    PubMed  CAS  Google Scholar 

  • Woo, S. L.-Y. and Buckwalter, J. A. (eds.) (1988) The Injury and Repair of Musculoskeletal Soft Tissues. American Academy of Orthopedic Surgeons, Park Ridge, IL.

    Google Scholar 

  • Woo, S. L.-Y. and Seguchi, Y. (eds.) (1989) Tissue Engineering. ASME BIO Vol. 14. American Society of Mechanical Engineers, New York.

    Google Scholar 

  • Woo, S. L.-Y., and Wayne, J. S. (1990). Mechanics of the anterior cruciate ligament and its contribution to knee kinematics. Appl. Mech. Rev. 43, 5142–5149.

    Article  Google Scholar 

  • Yamada, H. (1970) Strength of Biological Materials, translated by F. G. Evans. Williams and Wilkins, Baltimore.

    Google Scholar 

  • Young, J. Z. (1957) The Life of Mammals. Oxford University Press, London.

    Google Scholar 

  • Young, J. T., Vaishnav, R. N., and Patel, D. J. (1977). Nonlinear anisotropic viscoelastic properties of canine arterial segments. J. Biomech. 10, 549–559.

    Article  PubMed  CAS  Google Scholar 

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© 1993 Springer Science+Business Media New York

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Fung, YC. (1993). Bone and Cartilage. In: Biomechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2257-4_12

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  • DOI: https://doi.org/10.1007/978-1-4757-2257-4_12

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