The adaptation of bone apparent density to applied load

David P Fyhrie, M. B. Schaffler

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


A phenomenological theory of bone remodeling was developed with improved spatial stability compared to some of the more standard formulations. The improved stability was created by changing the nature of the remodeling differential equation to have an exponential character. As a result, the theoretical predictions are consistent with the experimental observation that changes in bone density during disuse, after hip surgery, during growth and during aging are all consistent with an exponential dependence of density on time. The new theory and the standard theory were both used to model the time course of bone changes in two animal models of bone loss during disuse. The new theory was better able to model the results of the experiments than the standard theory. The basic continuum theory underlying the remodeling theory was presented in some detail. This presentation was used to motivate the development of the new theory, as the standard theories can predict non-smooth distributions of bone density rather than the expected smooth distributions. It was shown that these non-smooth distributions are a violation of the continuum assumption, one of the bases for the theory of finite element stress analysis. The new model's stability was investigated using example problems and shown to be improved compared to the standard model.

Original languageEnglish (US)
JournalJournal of Biomechanics
Issue number2
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Biophysics
  • Biomedical Engineering
  • Orthopedics and Sports Medicine
  • Rehabilitation


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