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Original Articles

A Model of Bone Adaptation Using a Global Optimisation Criterion Based on the Trajectorial Theory of Wolff

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Pages 125-138 | Received 16 Apr 1998, Accepted 12 Sep 1998, Published online: 15 Mar 2007

References

  • Cowin , S. C. and Hegedus , D. H. (1976) . Bone Remodeling I theory of adaptive elasticity . Journal of Elasticity , 6 , 313 – 326 .
  • Weinans , H. , Huiskes , R. and Grootenboer , H. J. (1992) . The Behavior of adaptive bone-remodeling simulation models , Journal of Biomechanics , 25 , 1425 – 1441 .
  • Harrigan , T. P. and Hamilton , J. R. (1993) . Finite Element Simulation of Adaptive Bone Remodelling A Stability Criterion and a Time Stepping Method , International Journal for Numerical Methods in Engineering , 36 , 837 – 854 .
  • Mullender , M. G. , Huiskes , R. and Weinans , H. (1994) . A Physiological Approach to the simulation of Bone Remodeling as a Self-Organisational Control Process , Journal of Biomechanics . 27 , 1389 – 1394 .
  • Jacobs , C. , Simo , C. , Beaupré , G. and Carter , D. (1997) . Adaptive Bone Remodelling Incorporating Simultaneous Density and Anisotropy Considerations , Journal of Biomechanics , 30 , 603 – 613 .
  • Fyhrie , D. and Carter , D. (1986) . A Unifying Principle Relating Stress to Trabecular Bone Morphology , Journal of Orthopaedic Research , 4 , 304 – 317 .
  • Hollister , S. , Kikuchi , N. and Goldstein , S. (1993) . Do Bone Ingrowth Processes Produce a Globally Optimized Structure? , Journal of Biomechanics , 26 , 391 – 407 .
  • Wolff , J. (1986) . The law of bone remodelling (Das Gesetz der Transformation der Knochen, Hirsehwald, 1892). Translated by Maquet P. and Furlong R. Springer , Berlin .
  • Bends⊘e , M. P. and Kikuchi , N. (1988) . Generating Optimal Topologies in Structural Design using a Homogenisation Method , Computer Methods in Applied Mechanics and Engineering , 71 , 197 – 224 .
  • Bends⊘e , M. P. (1995) . Optimisation of Structural Topology, Shape, and Material , Springer-Verlag .
  • Beaupré , G. S. , Orr , T. E. and Carter , D. R. (1990) . An Approach for Time-Dependent Bone Modeling and Remodeling — Theoretical Development , Journal of Orthopaedic Research , 8 , 651 – 661 .
  • Sanchez-Palencia , E. (1980) . Non-Homogeneous Media and Vibration Theory , Lecture Notes in Physics , 127 , Springer , Berlin .
  • Gibson , L. J. and Ashby , M. F. (1988) . Cellular Solids — Structure and properties , Pergamon Press , Oxford .
  • Guedes , J. M. and Kikuchi , N. (1990) . Preprocessing and Postprocessing for Materials based on the Homogenisation Method with Adaptive Finite Elements Methods , Computer Methods in Applied Mechanics and Engineering , 83 , 143 – 198 .
  • Pedersen , P. (1990) . Bounds on Elastic Energy in Solids of Orthotropic Materials , Structural Optimisation , 2 , 55 – 62 .
  • Rovati , M. and Taliercio , A. (1991) . Optimal Orientation of the Symmetry Axes of Orthotropic 3-D Materials , In Proc. Int. Conf Engng. Optimisation in Design Processes , (ed. Eschenauer H. A. , Mattheck C. and Olhoff N. ) Karlsruhe ; Lecture Notes in Engineering, Springer Verlag, Berlin, 63, 127–134 .
  • Cowin , S. C. (1994) . Optimisation of the Strain Energy Density in Linear Anisotropic Elasticity , Journal of Elasticity , 34 , 45 – 68 .
  • Pidaparti , R. M. V. and Turner , C. H. (1997) . Cancellous bone architecture advantages of nonorthogonal trabecular alignment under multidirectional joint loading . J. Biomechanics , 10 . 979 – 983 .
  • Kuiper , J. H. (1993) . Numerical Optimisation of Artificial Joint Designs , Ph.D. Thesis, Katholieke Universiteit Nijimegen .
  • Currey , J. , (1984) . The Mechanical Adaptation of Bones . Princeton University Press .
  • Carter , D. R. , Orr , T. E. and Fyhrie , D. P. (1989) . Relationships Between Loading History and Femoral Cancellous Bone Architecture , Journal of Biomechanics , 22 , 231 – 244 .
  • Subbarayan , G. and Bartel , D. L. (1989) . Fully stressed and minimum mass structures in bone remodeling . In 1989 Biomechanics Symposium , AMD , New York , 173 – 176 .
  • Orr , E. (1990) . The Role of Mechanical Stresses in Bone Remodeling . PhD Thesis , Stanford University .
  • Díaz , A. and Bends⊘e , M. (1992) . Shape Optimisation of Structures for Multiple Loading Conditions Using a Homogenisation Method , Structural Optimisation 4 , pp. 17 – 22 .
  • Hert , J. (1992) . A new explanation of the cancellous bone architecture . Functional Development and Morphology , 2 , 17 – 24 .
  • Murray , P. D. F. (1936) . Bones. A study of the development and structure of the vertebrate skeleton . Cambridge University Press , Cambridge .
  • Kuo , A. D. and Carter , D. R. (1991) . Computational methods for analyzing the structure of cancellous bone in planar sections . Journal of Orthopaedics Research , 9 , 918 – 931 .
  • Bacon , G. E. , Bacon , P. J. and Griffiths , R. K. (1984) . A neutron diffraction study of the bones of the foot . Journal of Anatomy ., 139 , 265 – 273 .

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