Computational simulation of internal bone remodeling

Archives of Computational Methods in Engineering

Volumn 4, Issue 4, 1997, Pages 295-323

  Pettermann, H E ^a   Reiter, T J ^a,b   Rammerstorfer, F G ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b VAI   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0004918276     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02737117     Document Type: Article

References (76)

1. Ashman, R.B., Rho J.Y. (1988), "Elastic Modulus of Trabecular Bone Material", J. Biomech., 21, pp. 177-181.
2. Beaupré, G.S. and Hayes W.C. (1985), "Finite Element Analysis of a Three-Dimensional Open-Cell Model for Trabecular Bone", J. Biomed. Engng., 107, pp. 249-256.
3. Beaupré, G.S., Orr T.E. and Carter D.R. (1990), "An Approach for Time-Dependent Bone Modeling and Remodeling - Theoretical Development", J. Orthop. Res., 8, pp. 651-661.
4. Bucháček, K. (1990), "Nonequilibrium Bone Remodelling: Changes of Mass Density and of the Axes of Anisotropy", Int. J. Engng. Sci, 28, pp. 1039-1044.
5. Büchter, N. and Ramm, E. (1992), "Large Rotations in Structural Mechanics - Overview", In Nonlinear Analysis of Shells by Finite Elements, F.G. Rammerstorfer (Ed.), pp. 1-13, Springer-Verlag, Wien.
6. Carter, D.R. and Hayes, W.C. (1977), "The Compressive Behavior of Bone as a Two-Phase Porous Structure", J. Bone Jt. Surg., 59-A, pp. 954-962.
7. Carter, D.R., Fyhrie, D.P. and Whalen, R.T. (1987), "Trabecular Bone Density and Loading History: Regulation of Connective Tissue Morphology by Mechanical Energy", J. Biomech., 20, pp. 785-794.
8. Carter, D.R., Orr, T.E. and Fyhrie, D.P. (1989), "Relationship between Loading History and Femoral Cancellous Bone Architecture", J. Biomech., 22, pp. 231-244.
9. Christensen, R.M. (1986), "Mechanics of Low Density Materials", J. Mech. Phys. Solids, 34, pp. 563-578.
10. Cowin, S.C. and Hegedus, D.H. (1976), "Bone Remodeling I: Theory of Adaptive Elasticity", J. Elasticity, 6, pp. 313-326.
11. Cowin, S.C. and Nachlinger, R.R. (1978), "Bone Remodeling III: Uniqueness and Stability in Adaptive Elasticity Theory", J. Elasticity, 8, pp. 285-295.
12. Cowin, S.C. (1985), "The Relationship between the Elasticity Tensor and the Fabric Tensor", Mechanics of Materials, 4, pp. 137-147.
13. Cowin, S.C. (1987), "Bone Remodeling of Diaphysial Surfaces by Torsional Loads: Theoretical Predictions", J. Biomech., 20, pp. 1111-1120.
14. Cowin, S.C., Sadegh A.M. and Luo, G.M. (1992), "An Evolutionary Wolff's Law for Trabecular Architecture", J. Biomech. Engng., 114, pp. 129-136.
15. Currey, J.D. (1964), "Three Analogies to Explain the Mechanical Properties of Bone", Biorheology, 2, pp. 1-10.
16. Firoozbakhsh, K. and Aleyaasin, M. (1989), "The Effect of Stress Concentration on Bone Remodeling: Theoretical Predictions", J. Biomech. Engng., 111, pp. 355-360.
17. Firoozbakhsh, K., Aleyaasin, M. and Moneim, M.S. (1992), "Evolution of Bone Inhomogeneity Around a Hole in an Orthotropic Plate of Bone: Theoretical Predictions", J. Biomech., 25, (4), pp. 387-394.
18. Frost, H.M. (1964), "The Laws of Bone Structure", Charles C. Thomas, Springfield, IL.
19. Fyhrie, D.P. and Carter, D.R. (1986), "A Unifying Principle Relating Stress to Trabecular Bone Morphology", J. Orthop. Res., 4, pp. 304-317.
20. Gibson, L.J. (1985), "The Mechanical Behavior of Cancellous Bone", J. Biomech., 18, pp. 317-328.
21. Gibson, L.J. and Ashby, M.F. (1988), "Cellular Solids: Structure and Properties", Pergamon Press, Oxford.
22. Goldstein, S.A., Wilson, D.L., Sonstegard, D.A. and Matthews, L.S. (1983), "The Mechanical Properties of Human Tibial Trabecular Bone as a Function of Metaphyseal Location", J. Biomech., 16, pp. 965-969.
23. Goulet, R.W., Goldstein, S.A., Ciarelli, M.J., Kuhn, J.L., Brown, M.B. and Feldkamp, L.A. (1994), "The Relationship Between the Structural and Orthogonal Compressive Properties of Trabecular Bone", J. Biomech., 27, pp. 375-389.
24. Harrigan, T.P. and Hamilton, J.J. (1992a), "An Analytical and Numerical Study of the Stability of Bone Remodeling Theories: Dependence on Microstructural Stimulus", J. Biomech., 25, pp. 477-488.
25. Harrigan, T.P. and Hamilton, J.J. (1992b), "Optimality Conditions for Finite Element Simulation of Adaptive Bone Remodeling", Int. J. Solids Struct., 29, pp. 2897-2906.
26. Harrigan, T.P. and Hamilton, J.J. (1993), "Finite Element Simulation of Adaptive Bone Remodelling: A Stability Criterion and a Time Stepping Method", Int. J. Num. Meth. Eng., 36, pp. 837-854.
27. Hart, R.T. and Davy, D.T. (1989), "Theories of Bone Modeling and Remodeling", In Bone Mechanics, S.C. Cowin (Ed.), CRC Press, Boca Raton, FL, pp. 253-277.
28. Hayes, W.C. and Snyder, B. (1989), "Toward a Quantitative Formulation of Wolff's Law of Trabecular Bone", In Mechanical Properties of Bone, S.C. Cowin (Ed.), AMD, 45, ASME, New York, NY, pp. 43-68.
29. Hegedus, D.H. and Cowin, S.C. (1976), "Bone Remodeling II: Small Strain Adaptive Elasticity", J. Elasticity, 6, pp. 337-352.
30. Hogan, H.A. (1989), "Micromechanics Modeling of Haversian Cortical Bone Properties", J. Biomech., 22, pp. 549-556.
31. Hollister, S.C., Kikuchi, N., Borodkin, J.L. and Goldstein, S.A. (1990), "A Study of Microstructural Analysis Methods: Implications for Modeling Trabecular Bone Microstructure", In Advances in Bioengineering, S.A. Goldstein (Ed.), BED, Vol. 17, ASME, New York, NY, pp. 387-390.
32. Hollister, S.J., Fyhrie, D.P., Jepsen, K.J. and Goldstein, S.A. (1991), "Application of Homogenization Theory to the Study of Trabecular Bone Mechanics", J. Biomech., 24, pp. 825-839.
33. Hollister, S.J., Brennan, J.M. and Kikuchi, N. (1994), "A Homogenization Sampling Procedure for relating Trabecular Bone Effective Stiffness and Tissue Level Stress", J. Biomech., 27, pp. 433-444.
34. Huiskes, R., Weinans, H., Grootenboer, H.J., Dalstra, M., Fudala, B. and Sloof, T.J. (1987), "Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis", J. Biomech., 22, pp. 1135-1150.
35. Jacobs, C.R., Simo, J.C., Beaupré, G.S. and Carter, D.R. (1995), "Comparing an Optimal Global Efficiency Assumption to a Principal Stress-Based Formulation for the Simulation of Anisotropic Bone Adaptation to Mechanical Loading", In Proc. of the 1995 Bioengineering Conference, R.M. Hochmuth et al. (Eds.), BED, Vol. 29, ASME, New York, NY, pp. 447-478.
36. Katz, J.L. (1971), "Hard Tissue as a Composite Material I. Bounds on the Elastic Behavior", J. Biomech., 4, pp. 455-473.
37. Katz, J.L. (1981), "Composite Material Models for Cortical Bone", In Mechanical Properties of Bone, S.C. Cowin (Ed.), AMD, Vol. 45, ASME, New York, NY, pp. 171-184.
38. Katz, J.L. and Meunier, A. (1990), "A Generalized Method for Characterizing Elastic Anisotropy in Solid Living Tissues", J. Mat. Sci. Mater. in Med., 1, pp. 1-8.
39. Krach, W., Reiter, T.J., Rammerstorfer, F.G. and Zenz, P. (1995), "Computerunterstützte Vorhersage des Knochenumbaus am Beispiel von Knieendoprothesen", In Proc. d. 19. Jahrestagung der österr. Biomedizinischen Technik, Biomedizinische Technik Band 40, Ergänzungsband 2, Schiele & Schön, Berlin, GFR, pp. 78-80.
40. Kummer, B.K.F. (1972), "Biomechanics of Bone: Mechanical Properties, Functional Structure, Functional Adaptation", In Biomechanics: Its Foundation and Objectives, Y.C. Fung (Ed.), Prentice-Hall, Englewood Cliffs, NJ, pp. 237-271.
41. Lees, S. and Davidson, C.L. (1977), "The Role of Collagen in the Elastic Properties of Calcified Tissues", J. Biomech., 10, pp. 473-486.
42. Lipson, S.F. and Katz, J.L. (1984), "The Relationship Between Elastic Properties and Microstructure of Bovine Cortical Bone", J. Biomech., 17, pp. 231-240.
43. Martin, R.B. and Burr, D.B. (1989), "Structure, Function and Adaptation of Compact Bone", Raven Press, New York, NY.
44. Martin, R.B. (1984), "Porosity and Specific Surface of Bone", In CRC Critical Reviews in Biomedical Engng., 10, CRC Press, Boca Raton FL, pp. 179-222.
45. McElhaney, J.H., Alem, N. and Roberts, V. (1970), "A Porous Block Model for Cancellous Bone", ASME Publication 70-WA/BHF-2, pp. 1-9.
46. Misra, J.C. and Samanta, S. (1987), "Effect of Material Damping on Bone Remodeling", J. Biomech., 20(3), pp. 241-249.
47. Müller, R. (1994), "3D Assessment and Analysis of Trabecular Bone Architecture", PhD. Thesis, ETH Zürich, Zurich.
48. Pauwels, F. (1965), "Gesammelte Abhandlungen zur funktionellen Anatomie des Bewegungsapparates", Springer-Verlag, Berlin.
49. Pedersen, P. (1989), "On Optimal Orientation of Orthotropic Materials", Struct. Opt., 1, pp. 101-106.
50. Pettermann, H. (1993), "Entwicklung eines Simulationsalgorithmus der natürlichen Anpassung des orthotropen Knochenmaterials", Diploma Thesis, Vienna University of Technology, Vienna.
51. Pettermann, H.E., Reiter, T.J. and Rammerstorfer, F.G. (1995), "Ein Simulationsalgorithmus der natürlichen Anpassung des orthotropen Knochenmaterials", In Proc. d. 19. Jahrestagung der österr. Biomedizinischen Technik, Biomedizinische Technik Band 40, Ergänzungsband 2, Schiele & Schön, Berlin, GFR, pp. 127-129.
52. Piekarski, K. (1973), "Analysis of Bone as a Composite Material", Int. J. Engng. Sci., 11, pp. 557-565.
53. Prendergast, P.J. and Taylor, D. (1992), "Design of Intramedullary Prostheses to Prevent Bone Loss: Predictions Based on Damage-Stimulated Remodelling", J. Biomed. Engng., 14, pp. 499-506.
54. Pugh, J.W., Rose, R.M. and Radin, E.L. (1973), "Elastic and Viscoelastic Properties of Trabecular Bone: Dependence on Structure", J. Biomech., 6, pp. 475-485.
55. Reilly, D.T., Burstein, A.H. and Frankel, V.H. (1974), "The Elastic Modulus for Bone", J. Biomech., 7, pp. 271-275.
56. Reiter, T.J., Rammerstorfer, F.G. and Böhm, H.J. (1990), "A Numerical Algorithm for the Simulation of Bone Remodeling", In Advances in Bioengineering, S.A. Goldstein (Ed.), BED, 17, ASME, New York, NY, pp. 181-184.
57. Reiter, T.J. and Rammerstorfer, F.G. (1993), "Simulation of Natural Adaptation of Bone Material and Appli-cation in Optimum Composite Design", Optimal Design with Advanced Materials, P. Pedersen (Ed.), Elsevier, Amsterdam, pp. 25-36.
58. Reiter, T.J., Rammerstorfer, F.G. and Böhm, H.J. (1993a), "Computation of Biomechanical Effects in Bone Caused by Implants", In Computer Methods in Mechanics, Vol. II, W. Gilewski and L. Chodor (Eds), Kielce University of Technology, Kielce, pp. 799-806.
59. Reiter, T.J., Rammerstorfer, F.G. and Böhm, H.J. (1993b), "Structural Design Improvement by Functional Adaptation", In Proc. of Structural Optimization 93, J. Herskovits (Ed.), Rio de Janeiro, pp. 361-368.
60. Reiter, T.J., Böhm, H.J., Krach, W., Pleschberger, M. and Rammerstorfer, F.G. (1994a), "Some Applications of the Finite Element Method in Biomechanical Stress Analysis", Int. J. Comput. Appl. Technol., 7, pp. 233-241.
61. Reiter, T.J., Pettermann, H.E. and Rammerstorfer, F.G. (1994b), "Simulation of Bone Remodeling with Respect to Bone Anisotroy", In Proc. of the 8th International Conference on Biomedical Engineering, J.C.H. Goh and A. Nather (Eds), Singapore, pp. 201-203.
62. Reiter, T.J. (1995), "Knochen - eine selbstoptimierende Struktur?", In Evolution und Optimierung: Strategien in Natur und Technik, U. Kull and E. Ramm and R. Reiner (Eds), S. Hierzel Wissenschaftliche Verlagsgesellschaft Stuttgart, GFR, pp. 121-135.
63. Reiter, T.J. (1996), "Functional Adaptation of Bone and Application in Optimal Structural Design", VDI-Berichte, Reihe 17, Nr. 145, VDI-Verlag, Düsseldorf, GFR.
64. Rho, J.Y., Ashman, R.B. and Turner, Ch.H. (1993), "Young's Modulus of Trabecular and Cortical Bone Material: Ultrasonic and Microtensile Measurements", J. Biomech., 26, pp. 111-119.
65. Rice, J.C., Cowin, S.C. and Bowman, J.A. (1988), "On the Dependence of the Elasticity and Strength, of Cancellous Bone on Apparent Density", J. Biomech., 21, pp. 155-168.
66. Van Rietbergen, B., Weinans, H., Huiskes, R. and Odgaard, A. (1995), "A New Method to Determine Trabecular Bone Elastic Properties and Loading Using Micromechanical Finite Element Models", J. Biomech., 28, pp. 69-81.
67. Starke, G.R., Mercer, C.D., Spirakis, A., Martin, J.B. and Learmonth, I.D. (1992), "Some Aspects of Adaptive Bone Growth as a Result of Total Hip Joint Replacement", In Proc. 1992 ABAQUS Users' Conference, HKS Inc., Providence, RI, pp. 483-496.
68. Suquet, P.M. (1990), "Une méthode simplifiée pour le calcul des proprietés élastiques de matériaux hétérogènes à structure périodique", C. R. Acad. Sci. Paris, série II, 311, pp. 769-774.
69. Townsend, P.R., Raux, P., Rose, R.M., Miegel, R.E. and Radin E.L. (1975), "The Distribution and Anisotropy of the Stiffnesses of Cancellous Bone in the Human Patella", J. Biomech., 8, pp. 363-367.
70. Turner, C.H., Cowin, S.C., Rho, J.Y., Ashman, R.B. and Rice, J.C. (1990), "The Fabric Dependence of the Orthotropic Elastic Constants of Cancellous Bone", J. Biomech., 23, pp. 549-561.
71. Van Buskirk, W.C. and Ashman, R.B. (1981), "The Elastic Moduli of Bone", In The Mechanical Properties of Bone, S.C. Cowin (Ed.), AMD, 45, ASME, New York, pp. 131-143.
72. Viceconti, M. and Seireg, A. (1990), "A Generalized Procedure for Predicting Bone Mass Regulation by Mechanical Strain", Calcif. Tiss. Int., 47, pp. 296-301.
73. Whalen, R.T., Carter, D.R. and Steele, C.R. (1988), "Influence of Physical Activity on the Regulation of Bone Density", J. Biomech., 21, pp. 825-837.
74. Williams, J.L. and Lewis, J.L. (1982), "Properties of an Anisotropic Model of Cancellous Bone from the Proximal Tibial Epiphysis", J. Biomech. Engng., 104, pp. 50-56.
75. Wolff, J. (1892), Das Gesetz der Transformation der Knochen, Hirschwald, Berlin.
76. Zysset, P.K. and Curnier, A. (1995), "An Alternative Model for Anisotropic Elasticity of Trabecular Bone", In Proc. of the 1995 Bioengineering Conference, R.M. Hochmuth et al. (Eds), BED, 29, ASME, New York, NY, pp. 359-360.