The Assumption of a Negligible Preload on the Determination of Viscoelastic Properties Based on the Quasi-linear Viscoelastic (QLV) Theory

When performing a stress-relaxation test of soft tissues, a small preload is usually applied to the specimen to remove slack and provide a gauge length. This preload is generally assumed to be negligible. However, for tissues with a low stiffness, such as healing ligaments and tendons, the preload, which corresponds to a prestress, may be a significant percentage of its peak stress. In this study, the effects of such an assumption on the parameters describing the viscoelastic behavior of soft tissue based on the quasi-linear viscoelastic (QLV) theory were evaluated. Simulated data were generated by inputting a single set of constants into the QLV theory and adjusting the strain rate. With the ramp time held constant, seven different strain rates were inputted to yield data sets with 7 different peak stresses. A prestress of 0.5 MPa was applied to each data set. Two different approaches were then utilized to curve-fit the simulated data to determine the values of the inputted constants -I) a strain history approach which does not account for the preload, and 2) a preload approach which includes a modification to the strain history approach to account for the preload. The constants determined by both approaches were compared with the inputted values and the percent error reflected the bias caused by assuming a negligible preload. In the strain history approach, the preload had a significant effect on the estimation of the viscoelastic properties when the ratio of prestress caused by preload to peak stress is higher than 0.01. However, the modification made in the preload approach improved the estimation providing an accurate determination, i.e. within 10%, of the inputted constants for all data sets. The results suggest that the preload should be to taken into account when charactering the viscoelastic behavior of tissues with a low stiffness and that the preload approach presented in this study provides an accurate estimate of the constants describing the QLV theory.