On the sufficiency conditions for the stability of bone remodeling equilibrium.
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 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.
Cowin
S C
SC
Department of Mechanical Engineering, School of Engineering, City College, City University of New York, NY 10031.
Luo
G M
GM
Sadegh
A M
AM
Harrigan
T P
TP
D000465:Algorithms; D015519:Bone Density; D016723:Bone Remodeling / Q000502:physiology*; D001842:Bone and Bones / Q000502:physiology*; D004548:Elasticity; D006801:Humans; D008954:Models, Biological; D013314:Stress, Mechanical