Transformation of the viscoelastic functions of calcified tissues and interfacial biomaterials into a common representation

Abstract

Since both connective and calcified tissues are markedly viscoelastic in nature, an understanding of the behavior of these tissues intrinsically as materials on their own, as well as in composite formation with synthetic implants, is of prime importance in order to predict and anticipate materials' design and function. Thus considerable interest has developed in recent years with respect to measurements of the viscoelastic properties of biological materials. However, attempts to characterize the viscoelasticity of calcified tissues have involved many different experimental procedures; hence results appear in terms of different functions, e.g. relaxation modulus, creep compliance. Since this diversity precludes a simple useful comparison of the results, the present study was initiated so that measured functions could be cast into a common representation, and thus compared. Linear viscoelasticity theory implies definite exact relationships between the functions. Using these relations, experimental results on bone, dentin and implant materials presently used to interface to the natural tissues, e.g. polymethyl methacrylate and high density linear polyethylene, were transformed into the complex dynamic modulus representation. Analysis shows that the results of experiments on bone are not in agreement as to dispersion (i.e. change of modulus with frequency) and its variation with strain. Further, analysis of the internal consistency of some experiments demonstrates a violation of the Boltzmann integral which indicates that linear viscoelasticity (almost invariably assumed by workers in the field) fails for bone in compression. It is concluded that the dynamic behavior of bone is not as well understood as has been thought heretofore; direction is given for future experiments.