Download PDF
Vet Comp Orthop Traumatol 1988; 01(01): 7-17
DOI: 10.1055/s-0038-1633151
Short Communication
Schattauer GmbH

Structural Adaptations to Mechanical Usage. A Proposed “Three-Way Rule” for Bone Modeling

Part I
H. M. Frost
1   From the Southern Colorado Clinic, Purdue University, Pueblo, CO 81004, USA
› Author Affiliations
Further Information

Publication History

Publication Date:
22 February 2018 (online)

    Permissions and Reprints

A collection of fundamental structural adaptations is defined for how compacta and spongiosa respond to overloading in compression, tension and flexure, alone and in combinations. Those adaptations underlie most physiological tissue- and organ-level structural adaptations of healthy intact bones to mechanical usage, so explaining them is a major task for models of mechanical determinants of bone architecture. A biomechanical function called the Gamma function is then devised to predict from a structure's net end-loads and the strain history of any given small bone surface domain, whether mechanically induced formation, resorption or neither will occur in that domain. A separate function is devised to predict local rates of modeling from local strain histories. These functions correctly predict varied details of all of the fundamental adaptations and they also suggest new laws for the mechanical control of bone architecture, some of which are presented. The threeway rule is a new way to analyse the mechanical determinants of bone architecture that accounts for bone-biological realities learned after 1960.

Key words

Bone - Biomechanics - Bone architecture - Bone remodeling - Bone modeling - Wolff’s law - Intermediary organization
 

  • References

  • 1 Frost H M. Intermediary Organization of the Skeleton. Boca Raton: CRC Press; 1986
    Google Scholar
  • 2 Wolff J. Das Gesetz der Transformation der Knochen. Berlin: A Hirschwald; 1892
    Google Scholar
  • 3 Epker B N, Frost H M. Correlations of patterns of bone resorption and formation with physical behaviour of loaded bone. J Dent Res 1965; 44: 33-42.
    CrossrefPubMedGoogle Scholar
  • 4 Epker B N, O’Ryan F. Determinants of Class II dentofacial morphology: I: A biomechanical theory. In: Effects of Surgical Intervention on Craniofacial Growth. McNamara Jr J A, Carlson D S, Ribbens K A. (eds). Ann Arbor: Univ. Michigan; 1982: 169-205.
    Google Scholar
  • 5 Pauwels F. Biomechanics of the Locomotor Apparatus. Berlin: Springer-Verlag; 1986
    Google Scholar
  • 6 Frost H M. Laws of Bone Structure. Springfield: Charles C Thomas; 1964
    Google Scholar
  • 7 Frost H M. Bone Modeling and Skeletal Modeling Errors. Springfield: Charles C Thomas; 1973
    Google Scholar
  • 8 Frost H M. A chondral modeling theory. Calc Tiss Int 1979; 28: 181-200.
    CrossrefPubMedGoogle Scholar
  • 9 Frost H M. Mechanical determinants of bone modeling. J Met Bone Dis Rel Res 1983; 4: 217-30.
    PubMedGoogle Scholar
  • 10 Frost H M. The regional acceleratory phenomenon. A review. Henry Ford Hosp Med J 1983; 31: 3-9.
    PubMedGoogle Scholar
  • 11 Frost H M. The pathomechanics of osteoporoses. Clin Orthop Rel Res 1985; 200: 198-225.
    PubMedGoogle Scholar
  • 12 Frost H M. Osteogenesis imperfecta. The setpoint proposal. Clin Orthop Rel Res 1987; 216: 200-17.
    PubMedGoogle Scholar
  • 13 Frost H M. The mechanostat: A proposed pathogenetic mechanism of osteoporoses and the bone mass effects of mechanical and nonmechanical agents. Bone and Mineral 1987; 2: 73-85.
    PubMedGoogle Scholar
  • 14 Frost H M. Vital biomechanics. Proposed general concepts for skeletal adaptations to mechanical usage. Calc Tiss Int. 1987 (in press).
    PubMedGoogle Scholar
  • 15 Alexander R McN. Optimum strengths for bones liable to fatigue and accidental failure. J Theor Biol 1984; 109: 621-36.
    CrossrefPubMedGoogle Scholar
  • 16 Carter D R. Mechanical loading histories and cortical bone remodeling. Calc Tiss Int 1984; 36: S19-S24.
    CrossrefPubMedGoogle Scholar
  • 17 Cowin S C. Wolff’s Law of trabecular architecture at remodeling equilibrium. J Biomech Eng 1986; 108: 83-8.
    CrossrefPubMedGoogle Scholar
  • 18 Currey J D. The Mechanical Adaptations of Bones. Princeton: Princeton Univ Press; 1984
    Google Scholar
  • 19 Lanyon L E. Functional strain as a determinant for bone modeling. Calc Tiss Int 1984; 36: S56-S61.
    CrossrefPubMedGoogle Scholar
  • 20 Rubin C T. Skeletal strain and the functional significance of bone architecture. Calc Tiss Int 1984; 36: S11-S18.
    CrossrefPubMedGoogle Scholar
  • 21 Arnold J S. Focal excessive resorption in aging and senile osteoporosis. In: Osteoporosis. Barzel U S. (ed). New York: Grune and Stratton; 1970: 80-1.
    Google Scholar
  • 22 Parfitt A M, Matthews H E, Vallanueva A R, Kleerekoper M, Frame B, Rao D S. Relationship between surface, volume and thickness of iliac trabecular bone in aging and disease. J Clin Invest 1983; 72: 1396-409.
    CrossrefPubMedGoogle Scholar
  • 23 Courpron P. Bone tissue mechanisms underlying osteoporoses. Ortho Clin N Amer 1981; 12: 513-46.
    PubMedGoogle Scholar
  • 24 Enlow D H. Principles of Bone Remodeling. Springfield: Charles C Thomas; 1963
    Google Scholar
  • 25 Jaworski Z F G. Lamellar bone turnover system and its effector organ. Calc Tiss Int 1984; 36: S46-S55.
    CrossrefPubMedGoogle Scholar
  • 26 Jee W S S. The Skeletal tissues. In: Histology. ed. 5. Weiss L. (ed). New York: Elsevier-North Holland; 1983: 200-5.
    Google Scholar
  • 27 Weinmann J P, Sicher H. Bone and Bones. 2nd Ed.. St. Louis: C V Mosby Co; 1955
    Google Scholar
  • 28 Anderson W A D, Kissane J M. Pathology. 7th ed.. St. Louis: C V Mosby Co; 1977
    Google Scholar
  • 29 Jaffe H. Metabolic, Degenerative and Inflammatory Diseases of Bones and Joints. Philadelphia: Lea and Febiger; 1972
    Google Scholar
  • 30 Putschar W G J. General pathology of the musculoskeletal system. In: Handbuch der Allgemeinen Pathologie. Buchner F, Letterer E, Roulet F. (eds). Berlin: Springer-Verlag; 1960: 361-488.
    Google Scholar
  • 31 Uhthoff H. (ed). Current Concepts in Bone Fragility. Berlin: Springer-Verlag; 1986
    Google Scholar
  • 32 Parfitt A M. The cellular basis of bone remodeling: The quantum concept reviewed in the light of recent advances in the cell biology of bone. Calc Tiss Int 1984; 36: S38-S45.
    PubMedGoogle Scholar
  • 33 Recker R R. (ed). Bone Histomorphometry. Techniques and Interpretation. Boca Raton: C R C Press; 1983
    Google Scholar
  • 34 Reilly D T, Burstein A M. The mechanical properties of cortical bone. J Bone Jt Surg 1974; 56A: 1001-22.
    PubMedGoogle Scholar
  • 35 Bouvier M. Application of in vivo bone strain measurement techniques to problems of skeletal adaptations. Yearbook of Phys Anthrop 1985; 28: 237-48.
    PubMedGoogle Scholar
  • 36 Burr D B. Symposium on current theoretical and experimental perspectives on bone remodeling mechanisms: Introductory comments. Yearbook of Phys Anthrop 1985; 28: 207-9.
    PubMedGoogle Scholar
  • 37 Tschantz P, Rutishauser E. La surcharge mecanique de l’os vivant. Annales d’ Anat et Path 1967; 12: 223-48.
    PubMedGoogle Scholar
  • 38 Fyhrie D P, Carter D R. A unifying principle relating stress to trabecular bone morphology. J Orthop Res 1986; 4: 304-17.
    CrossrefPubMedGoogle Scholar
  • 39 Cochran G, Van B. A Primer of Orthopaedic Biomechanics. Edinburgh: Churchill-Livingstone; 1982
    Google Scholar
  • 40 Meade J B, Cowin S C, Klawitter J J, Van Buskirk W C, Skinner H R. Bone remodeling due to continuously applied loads. Calc Tiss Int 1984; 36: S25-S30.
    CrossrefPubMedGoogle Scholar