Anatomy and Embryology

, Volume 181, Issue 6, pp 523–532 | Cite as

A theoretical model of endochondral ossification and bone architectural construction in long bone ontogeny

  • Marcy Wong
  • Dennis R. Carter


The role of mechanical stresses in the formation of endochondral ossification patterns and the construction of basic bone architecture in human long bones is investigated using a three-dimensional generalized model of long bone development. The distribution of mechanical stress which is created in developing bones as a result of intermittent mechanical loading is calculated using a computer model that mathematically represents the bone's geometry, material properties and loading conditions. The process of endochondral ossification is simulated by iteratively converting cartilaginous regions of the computer model to bone, based on the calculated intermittent hydrostatic and shear stress distributions. Once local regions of mineralized bone have formed, these regions are remodeled according to an algorithm which relates bone density to a mechanical stress stimulus. The results simulated the correct sequence of the appearance of morphological structures which are common to long bones in the human appendicular skeleton. These developmental structures include the site of the first endochondral bone and the secondary ossification center and the tubular nature of long bones. Our results suggest that mechanical loading histories may influence bone morphogenesis beginning from the early stages of endochondral ossification and continuing throughout life. The stress-based algorithms may be part of the ‘rules of construction’ or ‘developmental constraints’ which guide limb ontogeny.

Key words

Bone development Mechanical stress Limb bones Osteogenesis Remodeling 



Daily osteogenic index at jth day (MPa · day)


Peak cyclic octahedral shear stress (MPa)


Peak cyclic dilatational stress (MPa)


Empirical constant (= 0.5)


Peak tensor stress quantity


Osteogenic index constant (= 0.18)


Total maturation index after n days (MPa)


Daily maturation rate at jth day (MPa·day−1)


Baseline maturation rate (MPa·day−1) (= 20)


Number of loading conditions


Number of daily cycles of loading condition i


Daily mechanical stress stimulus (MPa·day−1)


effective stress (MPa)


Stress exponent (= 4.0)


Bone apparent density (g·cm−3)


Cortical bone apparent density (g·cm−3) (=1.92)


Daily mechanical stress stimulus to maintain cortical bone (MPa·day−1)(=17)


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Marcy Wong
    • 1
    • 2
  • Dennis R. Carter
    • 1
    • 2
  1. 1.Department of Mechanical Engineering, Design DivisionStanford UniversityStanfordUSA
  2. 2.Rehabilitation Research and Development Center, Veterans Administration Medical CenterPalo AltoUSA

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