Micro and macro rheology of planar tissues

Tissues are intrinsically non-linear, anisotropic, viscoelastic, and undergo a process of mechanical adaptation (preconditioning). Previous constitutive laws considered one or two of these response aspects, often resulting in inadequate fit to data. Here we developed a general constitutive formulation encompassing the entire set of features. To exemplify this novel approach, constitutive equation for the skin was developed by stochastic incorporation of the fibers' orientation and undulation distributions. Predictions were contrasted with biaxial data of rabbit skin. The significance of each micro-feature was examined by sensitivity analysis. The results show that micro-structure based rheological characterization provides reliable representation under multiple biaxial protocols. Parametric investigation points to the essential roles of the fibers' orientation distributions (elastin and collagen) and waviness (collagen), their respective stress-strain relationship, and their viscoelasticity and preconditioning adaptation. The effect of ground substance is small but significant for model-to-data fit. Although the collagen is two order of magnitude stiffer, the contribution of elastin is predominant at low strains, and still significant (up to 20%) at high strains at which collagen carries the major load. The results are consistent with collagen preconditioning steming from stretch induced increase in the reference length, while in elastin it is the Mullins effect (strain softening). The most important impact of the study is that for the first time the entire scope of multi-axial tissue properties are unified in a single constitutive formulation. The potential implications are on the procedures of tissues characterization and on the design and analysis of artificial tissue scaffolds.