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 the initial mineralization of soft tissues is presented and used to derive a limit of the allowable strain in tissue engineered biomaterials. The model incorporates the mechanical energy in calcified tissue due to time-varying loads into the more commonly used energetic arguments for 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 developed to assess the effect of an imposed overall material strain on mineralization. A rate equation based on strain energy was used to model the kinetics of mineralization, and the stability of the rate equation was assessed, leading to a limit on overall material strain based on the specific energy for mineralization of soft tissues. The result depended on the stiffness of the material in series with the mineralizing tissue. Taking the stiffness of the material in series with the tissue as infinite lead to a prediction of critical strain for mineralization in the calcifying biological tissue which was the same on the Reuss and Voight models. The interaction of this theoretical model with biological factors and some clinical implications of the model are discussed.