The Theory Of Adaptive Elasticity (Hegedus And Cowin,1976) That Deals With Internal Bone Remodeling, Could Also Be Used In Order To Describe The Sur- Face Bone Remodeling.

Abstract

In the present paper we proved that the theory of the adaptive elasticity (Hegedus and Cowin, 1976) that deals with internal bone remodeling, can also be used in order to study the surface bone remodeling. Particularly we considered the problem of a long bone which is under an axial load. Our theoretical findings, predicts the results of the studies that describes the athrophy (Uhthoff and Jaworski, 1978; Jaworski , et., al.,1980) and the hypertrophy of the bone ( Woo, et., al., 1981; Clisouras, 1984; Kaplan, 1997, Monaco, 1997, Beck, 1998; Amendola, 1999,Walker,1999; Bouche,1999; Coutoure and Karlson, 2002; Magnusson, 2003, Hester, 2006, American Academy of Orthopaedic Surgeons, 2007) and comes to agreement with the classic theory of surface bo-ne remodeling, proposed by Cowin and Firoozbaksh (1981). INTRODUCTION Living bone is continually undergoing processes of growth, reinforcement and resorption, termed collectively remodeling. There are two kinds of bone remodeling: internal and surface (Frost, 1964). Hegedus and Cowin (1976) proposed a theory for internal remodeling, ter-med as “theory of adaptive elasticity” which has been used in various problems (Cowin and Van-Buskirk,1978; Tsili, 2000; Qin and Ye, 2004). The purpose of this work is to show that the theory of adaptive elasticity, can also be successfully used in order to study the surface remodeling of long bone. THE METHOD Initially, that is for t a(t) The diaphyseal crosssection area S(t) is given by : S(t) = π(b(t) ─ a(t)) >0. The inner and outer radius and the cross-section area in reference configuration, were ao, bo and So = π(bo 2─ao ) >0 respectively. The equations of the adaptive elasticity (Hegedus ─ Cowin, 1976) in cylindrical coordinates are, the rate re-modeling equation: Figure 1 the straindisplacement equations: Figure 2 the stress in equilibrium state: The Theory Of Adaptive Elasticity (Hegedus And Cowin,1976) That Deals With Internal Bone Remodeling, Could Also Be Used In Order To Describe The SurFace Bone Remodeling.