Constitutive equations for ligament and other soft tissue: evaluation by experiment

Ligaments, tendons and other soft tissues are nonlinearly viscoelastic. To discriminate among various constitutive equations which may be used to describe the tissue, appropriate experimental modalities are requisite. Ideally, testing should span physiologic ranges for load (or strain), load history (recovery and reloading), and load onset and duration, and a robust model will fit all data. Methods to expand the experimental window of time for relaxation and creep are presented and evaluated. The role of ramp, relaxation and recovery protocols is studied in the context of viscoelasticity describable by linear, quasilinear (QLV), nonlinear superposition, Schapery, and multiple integral formulations. The advantages associated with testing protocols that expand the time windows for creep or relaxation are presented. 3 INTRODUCTION Like other soft tissues in the body, tendons and ligaments exhibit viscoelastic, or time-dependent, behavior. When these tissues are held at a constant strain level, stress in the tissues decrease, a phenomenon called stress relaxation. Conversely, when held at a constant stress level, strain in the tissues increase, known as creep. Creep and relaxation are important components of tissue behavior, and investigation of such behavior takes careful consideration. An optimal experiment extracts the maximum amount of useful information from the specimen being tested. This may often require performing multiple phases in the experiment, such as testing at various strain levels or strain rates, to robustly capture the true behavior. As an example, performing a single stress relaxation test on a specimen at one specific strain level will give information about the time-dependent nature of the specimen, but it fails to give any insight about linearity. Performing relaxation tests at multiple strain levels would be required to determine any nonlinear viscoelastic properties. It may also be necessary to perform viscoelastic tests at various strain rates, as any stress-strain curve generated will depend on the strain rate utilized during data collection. While a concave-up stress-strain curve is an indication of nonlinear behavior, a concave-down curve could be due to nonlinearity or to time dependence or both. Careful planning is also required in order to determine which constitutive equation provides the best representation of the data. The purpose of this paper is not only to present constitutive equations for the modeling of soft tissues such as tendon and ligament, but also to suggest the means by which to evaluate the best choice of constitutive model by experimentation. In addition, methods to expand the time window …