2011, Number 1
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Rev Cubana Invest Bioméd 2011; 30 (1)
Some notes on the numerical integration of bone remodeling process
Garzón-Alvarado DA, Ramírez MAM, Linero SDL
Language: Spanish
References: 21
Page: 2-14
PDF size: 311.87 Kb.
ABSTRACT
In present paper the problem of bone remodeling process proposed by Weinans et
al is solved. To resolve the density equation the fourth order Euler, Heun and
Runge Kutta methods are used. To assess the mechanical stimulus and to estimate
density evolution two approaches are used: one based on the element and other
based on node. Results showed that Euler, Heun and Runge Kutta methods move
closer appropriately the bone remodeling problem, and for meshs and the passage
of time used there are not significant differences in the patterns obtained. On the
contrary, the use of the approach based on element and the based on node, there
are lack of continuities of "chessboard" type near of charge zone and well defined
columns far from it. In the approach based on node there is continuity in density
distribution. These patterns are well represented by solution methods for density
equation. Present study concludes that for steps of time and mesh used it doesn't
matter which temporal integral method be applied.
REFERENCES
Ganong WF. Fisiología médica. 20ma. edición. México: Editorial Manual Moderno; 2006.
Cowin S. Bone Mechanics Handbook. Second Edition. USA: CRC Press; 2001.
Jacobs C, Simo JC, Beaupré GS. Carter DR. Adaptative Bone Remodeling Incorporating simultaneous density and anisotropy considerations. Journal of Biomechanics. 1997;30(6):603-13.
Weinans H, Huiskes R, Grootenboer R. The Behavior of adaptive bone remodeling simulation models. Journal of Biomechanics. 1992;25(12):1425-41.
Wolff J. Das Gesetz der Transformation der Knochen. Berlin: Ediciones Hirschwald; 1892.
Frost HM. The laws of bon estructure. Springfield, IL., USA: Editorial Charles C. Thomas; 1964.
Frost HM. Mathematical elements of Lamellar Bone Remodeling. Springfield, IL. USA: Editorial Charles C. Thomas; 1964.
Frost HM. Vital Biomechanics. Proposed general concepts for skeletal adaptations to mechanical usage. Calcif Tissue Int. 1987;42:145-56.
Pauwels F. Gesammelte Abhandlungen zur Funktionelen Anatomie des Bewegungsapparates, Berlin: Springer; 1965.
Kummer BKF. Biomechanics of bone mechanical properties, functional structure, functional adaptation. En: Biomechanics: Its foundation and objectives. Edited by Fung YC, Perrone N, Anliker M, New Jersey, USA: Editorial Prentice Hall, Englewood Cliffs; 1972. p. 237-71.
Cowin SC. Wolff´s law of trabecular architecture at remodeling equilibrium. J Biomechanics Engineering. 1986;108:83-8.
Cowin SC, Hegedus DH. Bone remodeling I: A theory of adaptive elasticity. J Elasticity. 1976;6:313-26.
13] Cowin SC, Nachlinger RR. Bone remodeling III: uniqueness and stability inadaptive elasticity theory. J Elasticity. 1978;8:285-95.
14] Hegedus DH, Cowin SC. Bone remodeling II: small strain adaptive elasticity. J Elasticity. 1976;6:337-52.
Nackenhorst U. Numerical Simulation of Stress Stimulated Bone Remodeling.Technische Mechanik. 1997; 17(1):31-40.
Jacobs CR, Levenston ME, Beaupré GS, Simó JC Carter DR. Numerical Instabilities in bone remodeling simulations: The advantages of a node-based finite element approach. Journal of Biomechanics. 1995; 28:449-59.
Chen G, Pettet G, Pearcy M, McElwain DLS. Comparison of two numerical approaches for bone remodelling. Medical Engineering and Physics. 2007; 29:134- 39.
Hoffman JD. Numerical Methods for Engineers and Scientists, 2nd ed. New York: Mc Graw-Hill; 1992.
Oñate E. Structural Analysis with the Finite Element Method. Linear Statics: Volume 1: Basis and Solids. Barcelona, España: Springer; 2009.
Beaupre G, Orr T, Carter DR. An approach for time dependent bone modeling and remodeling-Theoretical Development. J Orthopedic Research. 1990;8:651-61.
Fernández JR, García-Aznar JM, Martínez R, Viaño J. Numerical analysis of astrain-adaptive bone remodelling problem. Comput Methods Appl Mech Engrg. 2010;199:1549-57.