Characterizing the non-linear mechanical behavior of native and biomimetic engineered tissues in 1D with physically meaningful parameters.

ABSTRACT

It is common practice to evaluate the mechanical performance of a scaffold for tissue engineering using concepts from linear elasticity theory (i.e. Young's modulus), or variations thereof, and uniaxial testing data. In some cases the non-linear nature of tissue stress-strain behavior has prompted development of empirical approaches to obtain a more comprehensive description of the observed mechanical behavior. Such approaches constitute improvements over singular stiffness measures but the lack of an appropriate non-linear theoretical foundation renders them somewhat arbitrary and potentially incomplete. Recently, a constitutive model for non-linear tissues was developed based on first principles in physics. The Freed-Rajagopal 1-D Fiber Model incorporates physically meaningful parameters that provide a unique and comprehensive characterization of non-linear tissue behavior for the class of tissues with strain limiting behavior in 1D. The physical interpretation that these parameters provide suggests they may serve as useful design targets for tissue engineering applications. In this study, the Freed-Rajagopal model is employed with conventional uniaxial mechanical testing data obtained from experiments with collagen scaffolds for hernia repair grafts and the healthy native tissue counterpart. Results from the Freed-Rajagopal analysis revealed that tissue-engineered constructs that qualify as "biomimetic" according to linear elasticity theory, or variations thereof, are not truly biomimetic, as they do not mimic the non-linear mechanical behaviors observed in their native tissue counterparts. Most importantly, the Freed-Rajagopal model was easy to employ (it can be done using a standard uniaxial testing system, with minimal additional effort) and revealed specific design improvements that could be targeted to improve the biofidelity of these constructs. A performance comparison with conventional non-linear models (including Fung's 1D Law and a one-dimensionalized version of the Holzapfel, Gasser, Ogden model), was then conducted and revealed the Freed-Rajagopal model produced results that correlated exceptionally well with experimental data and better describes material behavior at low strains as compared to competing models.