On the sufficiency conditions for the stability of bone remodeling equilibrium

S. C. Cowin; G. M. Luo; A. M. Sadegh; T. P. Harrigan

doi:10.1016/0021-9290(94)90207-0

On the sufficiency conditions for the stability of bone remodeling equilibrium

S. C. Cowin, G. M. Luo, A. M. Sadegh, T. P. Harrigan

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4 Scopus citations

Abstract

In this technical note a sufficiency condition is established for the stability of a strain-energy-based bone remodeling theory in the special case of a beam loaded by an axial force and a bending moment. In a previous report the same condition was shown to be a necessary condition for stability in the same situation. The remodeling scheme is one characterized by a remodeling stimulus equal to the strain energy density divided by the bulk or apparent density raised to an exponent m as well as an elastic modulus proportional to bulk or apparent density raised to an exponent n. In order for a remodeling scheme to be stable for an elastic beam loaded by an axial force and a bending moment, it is established that the condition that m must be greater than n is not only necessary, but also sufficient.

Original language	English (US)
Pages (from-to)	183-186
Number of pages	4
Journal	Journal of Biomechanics
Volume	27
Issue number	2
DOIs	https://doi.org/10.1016/0021-9290(94)90207-0
State	Published - Feb 1994
Externally published	Yes

ASJC Scopus subject areas

Biophysics
Orthopedics and Sports Medicine
Biomedical Engineering
Rehabilitation

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10.1016/0021-9290(94)90207-0

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AU - Cowin, S. C.

AU - Luo, G. M.

AU - Sadegh, A. M.

AU - Harrigan, T. P.

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N2 - In this technical note a sufficiency condition is established for the stability of a strain-energy-based bone remodeling theory in the special case of a beam loaded by an axial force and a bending moment. In a previous report the same condition was shown to be a necessary condition for stability in the same situation. The remodeling scheme is one characterized by a remodeling stimulus equal to the strain energy density divided by the bulk or apparent density raised to an exponent m as well as an elastic modulus proportional to bulk or apparent density raised to an exponent n. In order for a remodeling scheme to be stable for an elastic beam loaded by an axial force and a bending moment, it is established that the condition that m must be greater than n is not only necessary, but also sufficient.

AB - In this technical note a sufficiency condition is established for the stability of a strain-energy-based bone remodeling theory in the special case of a beam loaded by an axial force and a bending moment. In a previous report the same condition was shown to be a necessary condition for stability in the same situation. The remodeling scheme is one characterized by a remodeling stimulus equal to the strain energy density divided by the bulk or apparent density raised to an exponent m as well as an elastic modulus proportional to bulk or apparent density raised to an exponent n. In order for a remodeling scheme to be stable for an elastic beam loaded by an axial force and a bending moment, it is established that the condition that m must be greater than n is not only necessary, but also sufficient.

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On the sufficiency conditions for the stability of bone remodeling equilibrium

Abstract

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