MECHANICAL MODEL FOR CRITICAL STRAIN IN MINERALIZING BIOLOGICAL TISSUES - APPLICATION TO BONE-FORMATION IN BIOMATERIALS

A simple theoretical model for the role of strain energy density in th e initial mineralization of soft tissues is presented and used to deri ve a limit of the allowable strain in tissue engineered biomaterials. The model incorporates the mechanical energy in calcified tissue due t o time-varying loads into the more commonly used energetic arguments f or mineralization BY using the Voight (equal-strain) and Reuss (equal- stress) composite material models to relate the volumetric density of calcified tissue to overall material modules, two models were develope d to assess the effect of an imposed overall material strain on minera lization. A rate equation based on strain energy was used to model the kinetics of mineralization, and the stability of the rate equation wa s assessed, leading to a limit on overall material strain based on the specific energy for mineralization of soft tissues The result depende d on the stiffness of the material in series with the mineralizing tis sue. Taking the stiffness of the material in series with the tissue as infinite lead to a prediction of critical strain for mineralization i n the calcifying biological tissue which was the same on the Reuss and Voight models. The interaction of this theoretical model with biologi cal factors and some clinical implications Of the model are discussed. (C) 1997 Elsevier Science Limited.