Three-dimensional lattice continuum model of cancellous bone for structural and remodeling simulation

JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

Volumn 42, Issue 3, 1999, Pages 470-480

  Adachi, Taiji ^a   Tomita, Yoshihiro ^a   Tanaka, Masao ^b  

^a KOBE UNIVERSITY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Adaptation; Biomechanics; Bone Remodeling; Cancellous Bone; Lattice Continuum; Residual Stress

Indexed keywords

BIOMECHANICS; COMPUTER SIMULATION; CONTINUUM MECHANICS; MATHEMATICAL MODELS; RESIDUAL STRESSES; STRESS ANALYSIS; VOLUME FRACTION;

REMODELING SIMULATIONS; THREE-DIMENSIONAL LATTICE CONTINUUM MODELS;

BONE;

EID: 0033185290     PISSN: 13447653     EISSN: None     Source Type: Journal    
DOI: 10.1299/jsmec.42.470     Document Type: Article

References (35)

1. Wolff, J., The Law of Bone Remodeling, (Translated by Maquet, P. and Furlong, R.), (1986), Springer.
2. Roesler, H., The History of Some Fundamental Concepts in Bone Biomechanics, J. Biomech., Vol. 20, No. 11/12 (1987), p. 1025-1034.
3. Chamay, A. and Tschantz, P., Mechanical Influences in Bone Remodeling : Experimental Research on Wolff's Law, J. Biomech., Vol. 5, (1972), p. 173-180.
4. Goodship, A.E., Lanyon, L.E. and McFie, H., Functional Adaptation of Bone to Increased Stress : An Experimental Study, J. Bone Jt. Surg., Vol. 61A, No. 4 (1979), p. 539-546.
5. Lanyon, L.E. and Rubin, C.T., Static vs. Dynamic Loads as an Influence on Bone Remodeling, J. Biomech., Vol. 17, No. 12 (1984), p. 897-905.
6. Cowin, S.C. and Hegedus, D.H., Bone Remodeling I : Theory of Adaptive Elasticity, J. Elasticity, Vol. 6, No. 3 (1976), p. 313-326.
7. Carter, D.R., Fyhrie, D.P. and Whalen, R.T., Trabecular Bone Density and Loading History : Regulation of Connective Tissue Biology by Mechanical Energy, J. Biomech., Vol. 20, No. 8 (1987), p. 785-794.
8. Huiskes, R., Weinans, H., Grootenboer, H.J., Dalstra, M., Fudala, B. and Slooff, T.F., Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis, J. Biomech., Vol. 20, No. 11/12, (1987), p. 1135-1150.
9. Cowin, S.C., Bone Stress Adaptation Models, Trans. ASME, J. Biomech. Eng., Vol. 115 (1993), p. 528-533.
10. Cowin, S.C., Moss-Salentijn, L. and Moss, M.L., Candidates for the Mechanosensory System in Bone, Trans. ASME, J. Biomech. Eng., Vol. 113, No. 2 (1991), p. 191-197.
11. Parfitt, A.M., Osteonal and Hemi-Osteonal Remodeling : The Spatial and Temporal Framework for Signal Traffic in Adult Human Bone, J. Cellular Biochem., Vol. 55 (1994), p. 273-286.
12. Gibson, L.J., The Mechanical Behavior of Cancellous Bone, J. Biomech., Vol. 18, No. 5 (1985), p. 317-328.
13. Turner, C.H., Cowin, S.C., Rho, J.Y., Ashman, R. B. and Rice, J.C., The Fabric Dependence of the Orthotropic Elastic Constants of Cancellous Bone, J. Biomech., Vol. 23, No. 6 (1990), p. 549-561.
14. Hollister, S.J., Fyhrie, D.P., Jepsen, K.J. and Goldstein, S.A., Application of Homogenization Theory to the Study of Trabecular Bone Mechanics, J. Biomech., Vol. 24, No. 9 (1991), p. 825-839.
15. Hollister, S.J., Brennan, J.M. and Kikuchi, N., A Homogenization Sampling Procedure for Calculating Trabecular Bone Effective Stiffness and Tissue Level Stress, J. Biomech., Vol. 27, No. 4 (1994), p. 433-444.
16. Cowin, S.C., Sadegh, A.M. and Luo, G.M., An Evolutionary Wolff's Law for Trabecular Architecture, Trans. ASME, J. Biomech. Eng., Vol. 114 (1992), p. 129-136.
17. Mullender, M.G., Huiskes, R., and Weinans, H., A Physiological Approach to the Simulation of Bone Remodeling as a Self-Organizational Control Process, J. Biomech., Vol. 27, No. 11 (1994), p. 1389-1394.
18. Adachi, T., Tomita, Y., Sakaue, H. and Tanaka, M., Simulation of Trabecular Surface Remodeling Based on Local Stress Nonuniformity, JSME Int. J., Vol. 40C, No. 4 (1997), p. 782-792.
19. Tanaka, M., Adachi, T. and Tomita, Y., Mechanical Remodeling of Bone with Tissue Structure Considering Residual Stress, JSME Int. J., Vol. 39A, No. 3 (1996), p. 297-305.
20. Adachi, T., Tomita, Y. and Tanaka, M., Computational Simulation of Deformation Behavior of 2D-Lattice Continuum, Int. J. Mech. Sci., Vol. 40, No. 9 (1998), p. 857-866.
21. Tanaka, M. and Adachi, T., Residual Stress in Bone Structure : Experimental Observation and Model Study with Uniform Stress Hypothesis, In : Biomechanics - Functional Adaptation and Remodeling, (Eds. Hayashi, K., Kamiya, A. and Ono, K.), (1996), p. 169-184, Springer.
22. Adachi, T., Tanaka, M. and Tomita, Y., Uniform Stress State in Bone Structure with Residual Stress, Trans. ASME, J. Biomech. Eng., Vol. 120, No. 3 (1998), p. 342-347.
23. Mindlin, R.D., Influence of Couple-Stresses on Stress Concentrations, Exp. Mech., Vol. 3 (1963), p. 1-7.
24. Koiter, W.T., Couple-Stress in the Theory of Elasticity, Proc. K. Ned. Akad. Wet., Vol. B-67 (1964), p. 17-44, North-Holland Publishing.
25. Adachi, T., Tomita, Y. and Tanaka, M., Skew Lattice Continuum Model for Cancellous Bone, In : Continuum Models and Discrete Systems, (Ed: Markov, K.Z.), (1996), p. 342-349, World Scientific.
26. Tanaka, M., Adachi, T. and Tomita, Y., Simulation Model of Surface Remodeling in Cancellous Bone by Lattice Continuum Concept, In : Simulations in Biomedicine IV, (Eds : Power, H., Brebbia, C.A., and Kenny, J.), (1997), p. 189-198, Computational Mechanics Publications, Southampton.
27. Dalstra, M., Huiskes, R., Odgaard, A. and Van Erning, L., Mechanical and Textural Properties of Pelvic Trabecular Bone, J. Biomech., Vol. 26, No. 4/5 (1993), p. 523-535.
28. Tanaka, M., Adachi, T. and Tomita, Y., Lattice Continuum as Computational Model of Bone with Microstructure : Mechanical Characteristics and Structural Parameter, In : Computer Simulations in Biomedicine, (Eds : Power, H. and Hart, R.T.), (1995), p. 277-284, Computational Mechanics Publications, Southampton.
29. Tateishi, T., Shirasaki, Y. and Miyanaga, Y., A Mechanical Model of Bone as a Porous Composite Material with Application to the Human Upper Tibia, Theor. Appl. Mech., Vol. 25, (1977), p. 279-298.
30. Carter, D.R. and Hayes, W.C., The Compressive Behavior of Bone as a Two-Phase Porous Structure, J. Bone Jt. Surg., Vol. 59A, (1977), p. 954-962.
31. Tanaka, M. and Adachi, T., Preliminary Study on Mechanical Bone Remodeling Permitting Residual Stress, JSME Int. J., Vol. A37, No. 1 (1994), p. 87-95.
32. Fung, Y.C., Biodynamics : Circulation, (1984), p. 64, Springer.
33. Takamizawa, K. and Hayashi, K., Strain Energy Density Function and Uniform Strain Hypothesis for Arterial Mechanics, J. Biomech., Vol. 20, No. 1 (1987), p. 7-17.
34. Cowin, S.C., Wolff's Law of Trabecular Architecture at Remodeling Equilibrium, Trans. ASME, J. Biomech. Eng., Vol. 108 (1986), p. 83-88.
35. Miyamoto, H., Shiratori, M. and Miyoshi, T., Analysis of Stress and Strain Distribution at the Crack Tip by Finite Element Method, In : Recent Advances in Matrix Methods of Structural Analysis and Design, (Eds : Gallagher, R.H., Yamada, Y. and Oden, J.T.), (1971), p. 317-341.