Bone remodeling is widely viewed as a dynamic process—maintaining bone structure through a balance between the opposed activities of osteoblast and osteoclast cells—in which the stability problem is often pointed out. By an analytical approach, we present a bone remodeling model applied to unit-elements in order to analyze the stationary states and the condition of their stability. In addition, this theory has been simulated in a computer model using the Finite Element Method (FEM) to show a relationship between the bone remodeling process and the stability analysis. [S0148-0731(00)01806-9]
Issue Section:
Technical Briefs
1.
Wolff, J. L., 1892, 1986, The Law of Bone Remodeling, Springer, Berlin (translated by Marquet et R. Furlong, 1986).
2.
Cowin
, S. C.
, 1993
, “Bone Stress Adaptation Models
,” ASME J. Biomech. Eng.
, 115
, pp. 528
–533
.3.
Taber
, L.
, 1995
, “Biomechanics of Growth, Remodeling, and Morphogenesis
,” Appl. Mech. Rev.
, 48
, No. 8
, pp. 487
–545
.4.
Cowin
, S. C.
, Moss-Salentijn
, L.
, and Moss
, M. L.
, 1991
, “Candidates for the Mechanosensory System in Bone
,” ASME J. Biomech. Eng.
, 113
, pp. 191
–197
.5.
Mullender
, M. G.
, Huiskes
, R.
, and Weinans
, H.
, 1994
, “A Physiological Approach to the Simulation of Bone Remodeling as Self Organizational Control Process
,” J. Biomech.
, 27
, No. 11
, pp. 1389
–1394
.6.
Cowin
, S. C.
, and Hegedus
, D. M.
, 1976
, “Bone Remodeling I: A Theory of Adaptive Elasticity
,” J. Elast.
, 6
, pp. 313
–325
.7.
Carter
, D. R.
, 1987
, “Mechanical Loading Histories and Skeletal Biology
,” J. Biomech.
, 20
, pp. 785
–794
.8.
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
, No. 1
, pp. 69
–81
.9.
Jacobs
, C. R.
, Levenston
, M. E.
, Beaupre´
, G. S.
, Simo
, J. C.
, and Carter
, D. R.
, 1995
, “Numerical Instabilities in Bone Remodeling Simulations: The Advantages of a Node-Based Finite Element Approach
,” J. Biomech.
, 28
, No. 4
, pp. 449
–459
.10.
Hart, R. T., 1995 “Review and Overview of Net Bone Remodeling.” Computer Simulations in Biomedicine, H. Power and T. Hart, eds., Computational Mechanics Publications, pp. 267–276.
11.
Fyhrie
, D. P.
, and Shaffler
, M. B.
, 1995
, “The Adaptation of Bone Apparent Density to Applied Load
,” J. Biomech.
, 28
, No. 2
, pp. 135
–146
.12.
Pettermann
, H. E.
, Reiter
, T. J.
, and Rammerstorfer
, F. G.
, 1997
, “Computational Simulation of Internal Bone Remodeling
,” Arch. Comput. Methods Eng.
, 4
, No. 4
, pp. 295
–323
.13.
Weinans
, H.
, Huiskes
, R.
, and Grootenboer
, H. J.
, 1992
, “The Behavior of Adaptive Bone Remodeling Simulation Models
,” J. Biomech.
, 25
, No. 12
, pp. 1425
–1441
.14.
Harrigan
, T. P.
, and Hamilton
, J. J.
, 1992
, “An Analytical and Numerical Study of the Stability of Bone Remodeling Theories: Dependence on Microstructural Stimulus
,” J. Biomech.
, 25
, pp. 447
–488
.15.
Capello
, A.
, Viceconti
, M.
, Nanni
, F.
, and Catania
, G.
, 1998
, “Global Asymptotic Stability of Bone Remodeling Theories: A New Approach Based on Non-Linear Dynamical Systems Analysis
,” J. Biomech.
, 31
, pp. 289
–294
.16.
Zidi
, M.
, and Ramtani
, S.
, 1999
, “Bone Remodeling Theory Applied to the Study of n Unit Elements Model
,” J. Biomech.
, 32
, No. 7
, pp. 743
–747
.17.
Zidi
, M.
, 1998
, “Contribution to Modelization of the Trabecular Bone Remodeling
,” C. R. Acad. Sci. Paris/T
, 326
, Se´rie II B, pp. 121
–128
.18.
Harrigan
, T. P.
, and Hamilton
, J. J.
, 1993
, “Finite Element Simulation of Adaptive Bone Remodeling: A Stability Criterion and a Time Stepping Method
,” Int. J. Numer. Methods Eng.
, 36
, pp. 8376
–854
.19.
Currey
, J. D.
, 1988
, “The Effect of Porosity and Mineral Content on the Young’s Modulus Elasticity of Compact Bone
,” J. Biomech.
, 21
, pp. 131
–139
.20.
Strang, G., 1986, Introduction to Applied Mathematics, Wellesley-Cambridge Press.
21.
Lindler
, J. F.
, and Ditto
, W. L.
, 1995
, “Removal, Suppression, and Control of Chaos by Nonlinear Design
,” Appl. Mech. Rev.
, 48
, No. 12
, pp. 795
–807
.Copyright © 2000
by ASME
You do not currently have access to this content.