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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)289-294
Number of pages6
JournalJournal of Biomechanics
Volume31
Issue number3
DOIs
Publication statusPublished - 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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