A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of wolff

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 2, Issue 2, 1999, Pages 125-138

  Fernandes, P ^a   Rodrigues, H ^a   Jacobs, C ^b  

^a Instituto Superior Tecnico Institute for Mechanical Engineering   (Portugal)

^b PENN STATE COLLEGE OF MEDICINE   (United States)

Author keywords

Bone adaptation; Femur; Finite element modelling; Homogenisation; Optimisation; Three dimensions

Indexed keywords

BONE ADAPTATION; FEMUR; FINITE ELEMENT MODELLING; HOMOGENISATION; OPTIMISATIONS; THREE-DIMENSIONS;

COST ACCOUNTING; FINITE ELEMENT METHOD; GLOBAL OPTIMIZATION; MICROSTRUCTURE; STIFFNESS; STRESSES; STRUCTURAL OPTIMIZATION; TISSUE;

BONE;

EID: 0001352989     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255849908907982     Document Type: Article

References (28)

1. Cowin, S. C. and Hegedus, D. H. (1976). Bone Remodeling I: theory of adaptive elasticity. Journal of Elasticity, 6, 313-326.
2. Weinans, H., Huiskes, R. and Grootenboer, H. J. (1992). The Behavior of adaptive bone-remodeling simulation models. Journal of Biomechanics, 25, 1425-1441.
3. 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.
4. 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.
5. Jacobs, C., Simo, C., Beauprć, G. and Carter, D. (1997). Adaptive Bone Remodelling Incorporating Simultaneous Density and Anisotropy Considerations, Journal of Biomechanics, 30, 603-613.
6. Fyhrie, D. and Carter, D. (1986). A Unifying Principle Relating Stress to Trabecular Bone Morphology, Journal of Orthopaedic Research, 4, 304-317.
7. Hollister, S., Kikuchi, N. and Goldstein, S. (1993). Do Bone Ingrowth Processes Produce a Globally Optimized Structure?, Journal of Biomechanics, 26, 391-407.
8. Wolff, J. (1986). The law of bone remodelling (Das Gesetz der Transformation der Knochen, Hirschwald, 1892). Translated by Maquet P. and Furlong R. Springer, Berlin.
9. Bendsøe, 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.
10. Bendsøe, M. P. (1995). Optimisation of Structural Topology, Shape, and Material, Springer-Verlag.
11. 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.
12. Sanchez-Palencia, E. (1980). Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, 127, Springer, Berlin.
13. Gibson, L. J. and Ashby, M. F. (1988). Cellular Solids-Structure and properties, Pergamon Press, Oxford.
14. 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.
15. Pedersen, P. (1990). Bounds on Elastic Energy in Solids of Orthotropic Materials, Structural Optimisation, 2, 55-62.
16. 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.
17. Cowin, S. C. (1994). Optimisation of the Strain Energy Density in Linear Anisotropic Elasticity, Journal of Elasticity, 34, 45-68.
18. 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.
19. Kuiper, J. H. (1993). Numerical Optimisation of Artificial Joint Designs. Ph.D. Thesis, Kathoiieke Universiteit Nijmegen.
20. Currey, J. (1984). The Mechanical Adaptation of Bones. Princeton University Press.
21. 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.
22. 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.
23. Orr, E. (1990). The Role of Mechanical Stresses in Bone Remodeling. PhD Thesis, Stanford University.
24. Diaz, A. and Bendsøe, M. (1992). Shape Optimisation of Structures for Multiple Loading Conditions Using a Homogenisation Method, Structural Optimisation 4. pp. 17-22.
25. Hert, J. (1992). A new explanation of the cancellous bone architecture. Functional Development and Morphology, 2, 17-24.
26. Murray, P. D. F. (1936). Bones. A study of the development and structure of the vertebrate skeleton. Cambridge University Press, Cambridge.
27. 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.
28. 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.