Several constitutive theories have been proposed in the literature to model the viscoelastic response of soft tissue, including widely used rheological constitutive models. These models are characterized by certain parameters (“time constants”) that define the time scales over which the tissue relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open.
As a step towards answering this question, we develop an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback-Leibler divergence. Tissue is modeled as a standard linear solid and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback-Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain.