A Reconciliation of Local and Global Models for Bone Remodeling Through Optimization Theory

[+] Author and Article Information
G. Subbarayan

Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427 e-mail: ganesh@colorado.edu

D. L. Bartel

Cornell Hospital Program in Biomechanical Engineering, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

J Biomech Eng 122(1), 72-76 (Sep 01, 1999) (5 pages) doi:10.1115/1.429633 History: Received February 18, 1998; Revised September 01, 1999
Copyright © 2000 by ASME
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Cowin,  S. C., and Hegedus,  D. H., 1976, “Bone Remodelling—I: Theory of Adaptive Elasticity,” J. Elast., 6, p. 313.
Cowin,  S. C., and Hegedus,  D. H., 1976, “Bone Remodelling—II: Small Strain Adaptive Elasticity,” J. Elast., 6, p. 337.
Cowin,  S. C., and Nachlinger,  R. R., 1978, “Bone Remodelling—III: Uniqueness and Stability in Adaptive Elasticity Theory,” J. Elast., 8, pp. 285–295.
Cowin, S. C., 1981, “Continuum Models of the Adaptation of Bone to Stress,” Cowin, S. C., ed., Mechanical Properties of Bone, ASME AMD-Vol. 45, pp. 27–42.
Fyhrie,  D. P., and Carter,  D. R., 1986, “A Unifying Principle Relating Stress to Trabecular Bone Morphology,” J. Orthop. Res., 4, pp. 304–317.
Carter,  D. R., Fyhrie,  D. P., and Whalen,  R. T., 1987, “Trabecular Bone Density and Loading Hisotry: Regulation of Connective Tissue Biology by Mechanical Energy,” J. Biomech., 20, pp. 785–794.
Huiskes,  R., Weinans,  H., Grootenboer,  H. J., Dalstra,  M., Fudala,  B., and Slooff,  T. J., 1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic-Design Analysis,” J. Biomech., 20, pp. 1135–1150.
Weinans, H., Huiskes, R., and Grootenboer, H. J., 1989, “Convergence and Uniqueness of Adaptive Bone Remodeling,” Proc. 35th Annual Meeting, Orthopaedic Research Society.
Hart, R. T., and Davy, D. T., 1988, “Theories of Bone Modeling and Remodeling,” Bone Mechanics, Chap. 11, CRC Press, Melbourne, FL.
Umetani, Y., and Hirai, S., 1975, “An Adaptive Shape Optimization Method for Structural Material Using the Growing-Reforming Procedure,” Proc. 1975 Joint JSME–ASME Applied Mechanics Western Conference, pp. 359–365.
Wolff, J., 1892, Das Gesetz der Transformation der Knochen, A. Hirchwald, Berlin.
Alexander,  R. M., 1981, “Factors of Safety in the Structure of Animals,” Sci. Prog. (New Haven), 67, pp. 119–140.
Snyder, B., Strang, G., Hayes, W. C., and Norris, G., 1983, “Application of Structural Geometry Optimization Techniques in Microstructural Remodeling of Trabecular Bones,” Advances in Bioengineering, ASME BED.
Michell,  A. G. M., 1904, “The Limit of Economy of Material in Frame Structures,” Philos. Mag., 8, pp. 589–597.
Philpott, A., and Strang, G., 1984, Numerical & Biological Shape Optimization, Chap. 14, North-Holland Mathematics Studies, Elsevier Science Publishers B. V.
Haftka, R. T., and Gürdal, Z., 1992, Elements of Structural Optimization, Kluwer Academic Publishers, Boston.
Razani,  R., 1965, “Behavior of Fully Stressed Design of Structures and Its Relationship to Minimum Weight Design,” AIAA J., 3, pp. 2262–2268.
Subbarayan, G., 1991, “Bone Construction and Reconstruction: A Variational Model and Its Applications,” Ph.D. thesis, Cornell University, Ithaca, NY.
Subbarayan, G., and Bartel, D. L., 1991, “Bone Remodeling Around a Hole: A Comparison of Theoretical and Experimental Results,” Proc. 37th Annual Meeting, Orthopaedic Research Society.
Stadler, W., 1988, “Natural Structural Shapes (A Unified Optimal Design Philosophy),” Stadler, W., ed., Multi Criteria Optimization in Engineering and the Sciences, Plenum Press, New York.
Stadler, W., 1988, Multi Criteria Optimization in Engineering and the Sciences, Plenum Press, New York.
Reddy, J. N., 1984, Energy and Variational Methods in Applied Mechanics, Wiley, New York.
Dems,  K., and Mroz,  Z., 1983, “Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis—Part I: Variation of Material Parameters,” Int. J. Solids Struct., 19, pp. 677–692.
Carter,  D. R., and Hayes,  W. C., 1977, “Compressive Behavior of Bone as a Two-Phase Porous Structure,” J. Bone Jt. Surg., 59, pp. 954–962.
Bartel,  D. L., and Marks,  R. W., 1974, “The Optimum Design of Mechanical Systems With Competing Design Objectives,” ASME J. Eng. Ind., 96, pp. 171–178.
Dems,  K., and Mroz,  Z., 1984, “Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis—Part II: Structure Shape Variation,” Int. J. Solids Struct., 20, pp. 527–552.
Harrigan,  T. P., and Hamilton,  J. J., 1994, “Bone Remodeling and Structural Optimization,” J. Biomech., 27, pp. 323–328.
Yang, R. J., and Botkin, M. E., 1986, “The Relationship Between the Variational Approach and the Implicit Differentiation Approach to Shape Design Sensitivities,” Bennett, J. A., and Botkin, M. E., eds., The Optimum Shape: Automated Structural Design, Plenum Press, New York.
Haug, E. J., Choi, K. K., and Komkov, V., 1986, Design Sensitivity Analysis of Structural Systems, Academic Press, New York.
Jacobs,  C. R., Simo,  J. C., Beaupré,  G. S., and Carter,  D. R., 1997, “Adaptive Bone Remodeling Incorporating Simultaneous Density and Anisotropy Considerations,” J. Biomech., 30, pp. 603–613.





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