Required test duration for group comparisons in ligament viscoelasticity: A statistical approach

Abstract

The goal of this study was to determine the duration of time that ligaments from a study group need to be loaded in order to adequately determine their collective viscoelastic behavior. Rat ligaments were subjected either to creep or stress relaxation for 1,000 s or stress relaxation for 10,000 s to compare estimates of viscoelastic behavior for different test durations. Stresses versus time (relaxation) or strains versus time (creep) were fit with power law models (t^β where β is the rate of creep or relaxation on a log–log scale). Time intervals were separated by logarithmic decade and analyzed using a Random Coefficients approach to compute residual specimen error as a function of the number of decades of data analyzed. Standard Regression was also used for comparison. Results show that by testing for ≤100 s (i.e. two logarithmic decades of time) offers 1% less accuracy than testing for 1,000 seconds (i.e. three decades) when estimating the viscoelastic behavior of a specimen. These 100 s power law estimates are far more accurate than the between specimen dispersion of viscoelastic properties. Hence, a better way to compare viscoelastic behavior between study groups is to test more specimens for shorter durations. This reduces experimental time per sample and therefore increases efficiency.