Free Surface Density Instead of Volume Fraction in the Bone Remodeling Equation: Theoretical Considerations

Gholamreza Rouhi¹, Walter Herzog^1,2 , Les Sudak¹ , Keikhosrow Firoozbakhsh³ and Marcelo Epstein¹*

¹Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive NW Calgary, Canada T2N 1N4
²Department of Kinesiology, Human Performance Laboratory, University of Calgary, 2500 University Drive NW Calgary, Canada T2N 1N4
³Department of Orthopaedics Health Sciences Center, University of New Mexico, Albuquerque NM 87131, U.S.A.
*E-mail address: mepstein@ucalgary.ca

(Received July 30, 2004; Accepted February 22, 2005)

Keywords: Remodeling, Adaptive Elasticity, Small Strain

Abstract. In this paper we propose a new set of constitutive equations for bone remodeling that uses the specific surface instead of volume fraction. The theory of small-strain adaptive elasticity proposed by COWIN and HEGEDUS and a surface remodeling equation are derived to develop the remodeling theory. A relationship between net bone cell activity, bone material property and mechanical stimuli is derived. For illustration, the rate of change of trabecular remodeling is derived for selected geometries. With this model, the effect of bone micro-structure and mechanical stimuli on the rate of remodeling can be studied.