Global asymptotic stability of bone remodeling theories: A new approach based on non-linear dynamical systems analysis

Angelo Cappello; Marco Viceconti; Fabrizio Nanni; Giuseppe Catania

doi:10.1016/S0021-9290(98)00010-4

Global asymptotic stability of bone remodeling theories: A new approach based on non-linear dynamical systems analysis

Angelo Cappello, Marco Viceconti, Fabrizio Nanni, Giuseppe Catania

Istituti Ortopedici Rizzoli

Research output: Contribution to journal › Article

Abstract

Mathematical tools for the analysis of nonlinear dynamical systems are applied to the study of stability of bone remodeling theories. As a practical application, the same problem studied by Harrigan and Hamilton and Cowin et al. is analysed using these tools, and their findings on the necessary and sufficient conditions to ensure local asymptotic stability are easily confirmed. Using a general approach based on Lyapunov's method the same condition has been found to be necessary and sufficient also for the global asymptotic stability, thus confirming a result obtained by Harrigan and Hamilton (1994) by variational methods applied to finite-element models. The proof is based on the discretization of the spatial domain but the results for the continuum can be easily extrapolated.

Original language	English
Pages (from-to)	289-294
Number of pages	6
Journal	Journal of Biomechanics
Volume	31
Issue number	3
DOIs	https://doi.org/10.1016/S0021-9290(98)00010-4
Publication status	Published - Dec 19 1997

Keywords

Bone
Bone mechanical properties
Bone remodeling
Global stability
Nonlinear dynamics

ASJC Scopus subject areas

Orthopedics and Sports Medicine

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10.1016/S0021-9290(98)00010-4

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Cappello, A., Viceconti, M., Nanni, F., & Catania, G. (1997). Global asymptotic stability of bone remodeling theories: A new approach based on non-linear dynamical systems analysis. Journal of Biomechanics, 31(3), 289-294. https://doi.org/10.1016/S0021-9290(98)00010-4

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