Skip to main content
SpringerLink
Log in

Mechanics of Hard Tissues

  • Chapter
Integrated Biomaterials Science

Conclusions

The goal of this introduction to the mechanics of bone tissue has been to show the need for interdisciplinary approaches to understanding skeletal mechanics. In the first section, the experimental results were highlighted to demonstrate some of the complexities of bone tissue, including its structural complexity, its sensitivity to moisture, its inhomogeneity, its dependence upon loading rate, its viscoelastic response, its strength dependence upon loading type, and its response to repeated loading. In addition to complexity in mechanical behavior, some of the purely biological aspects of skeletal tissue were introduced with a focus upon the role of the bone cells in changing the material behavior and geometric structure of bone.

These complex mechanical and biological behaviors were employed to motivate the theoretical descriptions that are used to quantify behavior,bone’s behavior, although only the simplest linear elastic behavior was included. A number of ideas about how to simulate the adaptive response of bone tissue was introduced, and the role of numerical simulations in the study of bone and implants and in the study of the adaptive response was highlighted.

Despite the required brevity, this introduction has highlighted the need for a multidisciplinary approach to the study of skeletal mechanics that requires a team with competencies in clinical, mechanical, chemical, experimental, and numerical approaches. Future progress will be increasingly dependent upon collaboration, and hold the promise of prediction of bone responses, study of skeletal disease, and development and manipulation of therapeutic agents to repair, and to perhaps avoid, skeletal disease.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ashman, R.B. 1989. Experimental techniques, in: Bone Mechanics (S.C. Cowin, ed.), pp. 75–96, CRC Press, Inc., Boca Raton.

    Google Scholar 

  • Ashman, R.B., Rho, J.Y. 1988. Elastic moduli of trabecular bone material, J. Biomech. 21, 177.

    Article  Google Scholar 

  • Ashman, R.B., Rho, J.Y., Turner, C.H. 1989. Anatomical variation of orthotropic elastic moduli of the proximal human tibia, J. Biomech, 22, 895–900.

    Article  Google Scholar 

  • Beauprè, G.S., Orr, T.E., Carter, D.R. 1990. An approach for time-dependent bone modeling and remodeling — theoretical development, J. Orthop. Res. 8(5), 651–661.

    Google Scholar 

  • Bowman, S.M., Keaveny, T.M., Gibson, L.J., Hayes, W.C., McMahon, T.A. 1994. Compressive creep behavior of bovine trabecular bone, J. Biomech. 27, 301–310.

    Article  Google Scholar 

  • Carter, D.R., Hayes, W.C. 1977. The compressive behavior of bone as a two-phase porous structure, J. Bone Jt. Surg., Am. Vol. 59(7), 954–962.

    Google Scholar 

  • Carter, D.R., Caler, W.E., Spengler D.M., Frankel, V.H. 1981. Uniaxial fatigue of human cortical bone. The influence of tissue physical characteristics, J. Biomech. 14(7), 461–470.

    Google Scholar 

  • Carter, D.R., Fyhrie, D.P., Whalen, R.T. 1987. Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy, J. Biomech. 20(8), 785–794.

    Google Scholar 

  • Cowin, S.C. 1981. Mechanical Properties of Bone, Presented at the Joint ASME-ASCE Applied Mechanics, Fluids Engineering, and Bioengineering Conference, Boulder, Colorado, June 22–24, 1981, New York, N.Y. (345 E. 47th St., New York 10017), American Society of Mechanical Engineers.

    Google Scholar 

  • Cowin, S.C. 1986. Wolff’s of trabecular architecture at remodeling equilibrium J. Biomech Eng, 108(1), 83–88.

    Article  Google Scholar 

  • Cowin, S.C. 1989. The mechanical properties of cortical bone tissue, in: Bone Mechanics (S.C. Cowin, ed.), pp. 97–128, CRC Press, Inc., Boca Raton.

    Google Scholar 

  • Cowin, S.C. 1997. The false premise of Wolff’s lowForma 12, 247–262.

    Google Scholar 

  • Cowin, S.C., Hegedus, D.H. 1976. Bone remodeling I: Theory of adaptive elasticity, J. Elast. 6(3), 313–326.

    Article  MathSciNet  MATH  Google Scholar 

  • Cowin, S.C., VanBuskirk, W.C. 1979. Surface bone remodeling induced by a medullary pin, J. Biomech, 12(4), 269–276.

    Article  Google Scholar 

  • Cowin, S.C., Balser, J.R., Hart, R.T., Kohn, D.H. 1985. Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients, J. Biomech. 18(9), 665–684.

    Article  Google Scholar 

  • Cowin, S.C., Sadegh, A.M., Luo, G.M. 1992. An evolutionary Wolff’s law for trabecular architecture, J. Biomech. Eng. 114(1), 129–136.

    Google Scholar 

  • Currey, J.D. 1995. The validation of algorithms used to explain adaptive remodelling in bone, in: Bone Structure and Remodelling (A. Odgaard, H. Weinans, eds.), pp. 9–13, World Scientific, Singapore.

    Google Scholar 

  • Currey, J.D. 1997. Was Wolff correct?, Forma 12, 263–266.

    Google Scholar 

  • Dalstra, M., Huiskes, R., Odgaard, A., van Erning, L. 1993. Mechanical and textural properties of pelvic trabecular bone, J. Biomech. 26, 523–535.

    Article  Google Scholar 

  • Davy, D.T., Hart, R.T. 1983. A Theoretical Model for Mechanically Induced Bone Remodeling, American Society of Biomechanics, Rochester, MN.

    Google Scholar 

  • Eriksen, E.F., Kassem, M. 1992. Editorial, The cellular basis of bone remodeling, Triangle, Sandoz J. Med. Sci. 31, 45–57.

    Google Scholar 

  • Ford, C.M., Keaveny, T.M. 1996. The dependence of shear failure properties of trabecular bone on apparent density and trabecular orientation, J. Biomech. 29, 1309–1317.

    Article  Google Scholar 

  • Frost, H.A. 1964. Dynamics of bone remodeling, in: Bone Biodynamics (H.A. Frost, ed.), pp. 315–333, Little, Brown, Boston.

    Google Scholar 

  • Frost, H.M. 1964. The Laws of Bone Structure, C.C. Thomas, Springfield, IL.

    Google Scholar 

  • Frost, H.M. 1986. Intermediary Organization of the Skeleton, CRC Press, Boca Raton.

    Google Scholar 

  • Frost, H.M. 1990. Skeletal structural adaptations to mechanical usage (SATMU): 1. Redefining Wolff’s law, the bone modeling problem, Anat Rec. 226(4), 403–413.

    Google Scholar 

  • Fyhrie, D.P., Schaffler, M.B. 1994. Failure mechanisms in human vertebral cancellous bone,Bone 15, 105–109.

    Article  Google Scholar 

  • Galileo Galilei, 1744, Opere di Galileo Galilei divise in 4 tomi, Dialogo delle scienze nuove, Volume 3, pp. 63 and 87, Stamperia del Seminario, Padova.

    Google Scholar 

  • Gluer, C.C., Wu, C.Y., Genant, H.K. 1993. Broadband ultrasound attenuation signals depend on trabecular orientation: an in vitro study, Osteoporosis Int. 3, 185–191.

    Google Scholar 

  • Goldstein, S.A. 1987. The mechanical properties of trabecular bone: dependence on anatomic location and function, J. Biomech. 20, 1055–1061.

    Google Scholar 

  • Goulet, R.W., Goldstein, S.A., Ciarelli, M.J., Kuhn, J.L., Brown, M.B., Feldkamp, L.A. 1994. The relationship between the structural and orthogonal compressive properties of trabecular bone, J. Biomech. 27, 375–389.

    Google Scholar 

  • Hall, B.K. (ed.). 1990–1994, Bone, Volumes 1–9,The Telford Press, Inc., Caldwell, N.J., and CRC Press, Inc., Boca Raton.

    Google Scholar 

  • Hart, R.T. 1995. Review and overview of net bone remodeling, in: Computer Simulations in Biomedicine (H. Power, R.T. Hart, eds.), pp. 267–276, Com putational Mechanics Publications, Southampton, Boston.

    Google Scholar 

  • Hart, R.T., Rust-Dawicki, A.M. 1995. Computational simulation of idealized long bone realignment, in: Computer Simulations in Biomedicine (H. Power, R.T. Hart, eds.), pp. 341–350, Computational Mechanics Publications, Southampton, Boston.

    Google Scholar 

  • Hart, R.T., Fritton, S.P. 1997. Introduction to finite element based simulation of functional adaptation of cancellous bone, Forma 12, 277–299.

    Google Scholar 

  • Hart, R.T., Davy, D.T., Heiple, K.G. 1984. A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling, J. Biomech. Eng. 106, 342–350.

    Article  Google Scholar 

  • Hart, R.T., Hennebel, V.V., Thongpreda, N., Dulitz, D.A. 1990. Computer simulation of cortical bone remodeling, in: Science and Engineering on Supercomputers (E.J. Pitcher, ed.), pp. 57–66, 565–566, Computational Mechanics Publications, Southampton, Boston.

    Google Scholar 

  • Huiskes, R. 1995. The law of adaptive bone remodelling, A case for crying Newton?, in: Bone Structure and Remodelling (A. Odgaard, H. Weinans, eds.), pp. 15–24, World Scientific, Singapore.

    Google Scholar 

  • Huiskes, R., Weinans, H., Grootenboer, H.J., Dalstra, M., Fudala, B., Slooff, T.J. 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis, J. Biomech. 20(11–12), 1135–1150.

    Google Scholar 

  • Katz, J.L. 1995. Mechanics of hard tissue, in: The Biomedical Engineering Handbook (J.D. Bonzino, ed.), CRC Press, Inc., Boca Raton.

    Google Scholar 

  • Kuhn, J.L., nee Ku, J.L., Goldstein, S.A., Choi, K.W., Landon, M., Herzig, M.A., Matthews, L.S. 1987. The mechanical properties of single trabeculae, pp. 12–48, Trans. 33rd Annu. Meet. Orthop. Res. Soc.

    Google Scholar 

  • Langton, C.M., Njeh, C.F., Hodgskinson, R., Currey, J.D. 1996. Prediction of mechanical properties of the human calcaneus by broadband attenuation, Bone 18, 495–503.

    Article  Google Scholar 

  • Lanyon, L.E., Goodship, A.E., Pye, C.J., MacFie, J.H. 1982. Mechanically adaptive bone remodelling, J. Biomech. 15(3), 141–154.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mattheck, C., Huber-Betzer, H. 1991. CAO: Computer simulation of adaptive growth in bones and trees, in: Computers in Biomedicine (K.D. Held, C.A. Brebbia, R.D. Ciskowski, eds.), pp. 243–252, Computational Mechanics Publications, Southampton, Boston.

    Google Scholar 

  • McNamara, B.P., Prendergast, P.J., Taylor, D. 1992. Prediction of bone adaptation in the ulnar-osteotomized sheep’s forelimb using an anatomical finite element model, J. Biomed. Eng. 14(3), 209–216.

    Google Scholar 

  • Mente, P.L., Lewis, J.L. 1987. Young’smodulus of trabecular bone tissue, pp. 112–149, Trans. 33rd Annu. Meet. Orthop. Res. Soc.

    Google Scholar 

  • Meroi, E.A., Natali, A.N., Schrefler, B.A. 1998. A porous media approach to finite deformation behaviour in soft tissues, Comp. Meth. Biomech. Biomed. Eng. 2(2), 157–170.

    Google Scholar 

  • Natali, A.N. 1999. The simulation of load bearing capacity of dental implants, in: Computer Technology in Biomaterials Science and Engineering, John Wiley & Sons, New York.

    Google Scholar 

  • Natali, A.N., Meroi, E.A. 1990. Nonlinear analysis of intervertebral disk under dynamic load, ASME J. Biomech Eng. 112, 358–363.

    Google Scholar 

  • Natali, A.N., Meroi, E.A. 1993. The mechanical behaviour of bony endplate and annulus in prolapsed disc configuration, J. Biomed. Eng. 15, 235–239.

    Google Scholar 

  • Natali, A.N., Meroi, E.A. 1996. Biomechanical analysis of dental implant in its interaction with bone tissue, in: Ceramics, Cells and Tissues-Bioceramic Coatings for Guided Bone Growth, pp. 223–240, Irtec CNR, Faenza.

    Google Scholar 

  • Natali, A.N., Meroi, E.A. 1997. Numerical formulation of intervertebral joint with regard to ageing problems of soft and hard tissues, in: Ceramics, Cells and Tissues, pp. 101–108, Irtec CNR, Faenza.

    Google Scholar 

  • Natali, A.N., Meroi, E.A. 1998. Numerical formulation for biomechanical analysis of spinal motion segment, Proc. Mathematical Theory of Networks and Systems MTNS98-13th Int. Symp. on Math Theory of Networks and Systems, pp. 1051–1054.

    Google Scholar 

  • Natali, A., Trebacz, H. 1999. The ultrasound velocity and attenuation in cancellous bone samples from lumbar vertebra and calcaneus, Osteoporosis Int. 9(2), 99–105.

    Google Scholar 

  • Natali, A.N., Meroi, E.A., Donà, S.,1997a. Tissue-implant interaction phenomena for dental implants: a numerical approach, in: Ceramics, Cells and Tissues, pp. 93–100, Irtec CNR, Faenza.

    Google Scholar 

  • Natali, A.N., Meroi, E.A., Trebacz, H. 1997b. The influence of ageing on mechanical behaviour of intervertebral segment, Proc. 3rd Int. Symp. on Computer Methods in Biomechanics & Biomedical Engineering, pp. 323–330.

    Google Scholar 

  • Natali, A.N., Meroi, E.A., Williams, K.R., Calabrese, L. 1998. Investigation of the integration process of dental implants by means of a numerical analysis of dynamic response, Dent. Mater. 13(5), 325–337.

    Google Scholar 

  • Nicholson, P.H.F., Haddaway, M.J., Davie, M.W.J. 1994. The dependence of ultrasonic properties on orientation in human vertebral bone, Phys. Med. Biol. 39, 1013–1024.

    Article  Google Scholar 

  • Oden, Z.M., Hart, R.T., Forwood, M.R., Burr, D.B. 1995. A priori prediction of functional adaptation in canine radii using a cell based mechanistic approach, Trans. 41st Orthop. Res. Soc.

    Google Scholar 

  • Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M., Huiskes, R. 1997. Fabric and elastic principal directions of cancellous bone are closely related, J. Biomech. 30(5), 487–495.

    Article  Google Scholar 

  • Pugh, J.W., Rose, R.M., Radin, E.L. 1973. Elastic and viscoelastic properties of trabecular bone: dependence of structure, J. Biomech. 6, 475.

    Google Scholar 

  • Reilly, D.T., Burstein, A.H., Fankel, V.H. 1974. The elastic modulus for bone, J. Biomech. 7, 271–275.

    Article  Google Scholar 

  • Rice, J.C., Cowin, S.C., Bowman, J.A. 1988. On the dependence of the elasticity and strength of cancellous bone on apparent density, J. Biomech. 21, 155–161.

    Article  Google Scholar 

  • Roesler, H. 1981. Some historical remarks on the theory of cancellous bone structure (Wolff’s law), in: Mechanical Properties of Bone (S.C. Cowin, ed.), pp. 27–42, American Society of Mechanical Engineers, New York.

    Google Scholar 

  • Rubin, C.T., Lanyon, L.E. 1984. Dynamic strain similarity in vertebrates: an alternative to allometric limb bone scaling, J. Theor Biol. 107(2), 321–327.

    Google Scholar 

  • Runkle, J.C., Pugh, J.W. 1975. The micromechanics of cancellous bone. II. Determination of the elastic modulus of individual trabeculae by buckling analysis, Bull. Hosp. Jt. Dis. 36, 2.

    Google Scholar 

  • Ryan, S.D., Williams, J.L. 1986. Tensile testing of individual bovine trabeculae, Proc. 12th NE Bio-Engineering Conference, 35.

    Google Scholar 

  • Sadegh, A.M., Luo, G.M., Cowin, S.C. 1993. Bone ingrowth, an application of the boundary element method to bone remodeling at the implant interface, J. Biomech. 26(2), 167–182.

    Article  Google Scholar 

  • Townsend, P.R., Rose, R.M., Radin, E.L. 1975. Buckling studies of a single human trabecula, J. Biomech. 8, 199.

    Google Scholar 

  • Treharne, R.W. 1981. Review of Wolff’s proposed means of operation, Orthop. Rev. 10(1), 35–47.

    Google Scholar 

  • Turner, C.H. 1997. The relationship between cancellous bone architecture and mechanical properties at the continuum level, Forma 12, 225–233.

    Google Scholar 

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

    Google Scholar 

  • Williams, J.L., Lewis, J.L. 1982. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis, J Biomech. Eng. 104, 50.

    Article  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre of Mechanics of Biological Materials, Dipartimento di Costruzioni e Trasporti, UniversitàPadova, Via F. Marzolo 9, 35131, Padova, Italy

    Arturo N. Natali

  2. Department of Biomedical Engineering, Boggs Center, Suite 500, Tulane University, New Orleans, Louisiana, 70118, USA

    Richard T. Hart

Authors
  1. Arturo N. Natali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard T. Hart
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Interuniversity Research Center for Advanced Medical Systems (C.R.I.S.M.A.) Department of Chemical and Biosystem Sciences and Technologies, University of Siena, Siena, Italy

    Rolando Barbucci

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Natali, A.N., Hart, R.T. (2002). Mechanics of Hard Tissues. In: Barbucci, R. (eds) Integrated Biomaterials Science. Springer, Boston, MA. https://doi.org/10.1007/0-306-47583-9_15

Download citation

  • DOI: https://doi.org/10.1007/0-306-47583-9_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46678-6

  • Online ISBN: 978-0-306-47583-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation