A STRUCTURALLY BASED STRESS-STRETCH RELATIONSHIP FOR TENDON AND LIGAMENT

We propose a mechanical model for tendon or ligament stress-stretch be havior that includes both microstructural and tissue level aspects of the structural hierarchy in its formulation. Al the microstructural sc ale, a constitutive law for collagen fibers is derived based on a stra in-energy formulation. The three-dimensional orientation and deformati on of the collagen fibrils that aggregate to from fibers are taken int o consideration. Fibril orientation is represented by a probability di stribution function that is axisymmetric with respect to the fiber. Fi ber deformation is assumed to be incompressible and axisymmetric. The matrix is assumed to contribute to stress only through a constant hydr ostatic pressure term. At the tissue level, an average stress versus s tretch relation is completed by assuming a statistical distribution fo r fiber straightening during tissue loading. Fiber straightening stret ch is assumed to be distributed according to a Weibull probability dis tribution function. The resulting comprehensive stress-stretch law inc ludes seven parameters, which represent structural and microstructural organization, fibril elasticity, as well as a failure criterion. The failure criterion is stretch based. It is applied at the fibril level for disorganized tissues bur can be applied more simply at a fiber lev el for well-organized tissues with effectively parallel fibrils. The i nfluence of these seven parameters on tissue stress-stretch response i s discussed and a simplified form of the model is shown to characteriz e the nonlinear experimentally determined response of healing medial c ollateral ligaments. In addition microstructural fibril organizational data (Frank et al., 1991, 1992) are used to demonstrate holy fibril o rganization affects material stiffness according to the formulation. A simplified form, assuming a linearly elastic fiber stress versus stre tch relationship, is shown to be useful for quantifying experimentally determined nonlinear toe-in and failure behavior of tendons and ligam ents. We believe this ligament and tendon stress-stretch law can be us eful in the elucidation of the complex relationships between collagen structure, fibril elasticity, and mechanical response.