Instantaneous and equilibrium responses of the brain tissue by stress relaxation and quasi-linear viscoelasticity theory

Human brain and brainstem tissues have viscoelastic characteristics and their behaviors are functions of strains as well as strain rates. Determination of the equilibrium and instantaneous stresses happening at low and high strain rates provides insights into a better understanding of the behavior of such tissues. In this manuscript, we present the results of a series of stress relaxation tests at 0 different values of strains conducted on porcine brainstem tissue samples to indirectly measure the equilibrium and instantaneous stresses. The equilibrium stresses at low strain rates were measured from long-term responses to the stress relaxation test. The instantaneous stresses at high strain rates were determined using Quasi-Linear Viscoolasticity (QLV) theory at 6 strains. The results showed that the instantaneous stresses were much larger (almost I I times) than the equilibrium stresses across all t he strains. It. was concluded that the instantaneous response could reasonably be estimated from the long-term response, which could easily be measured in an experimental manner. The experimental results also showed that the reduced relaxation moduli, estimated by the QLV theory, varied for the 0 strains tested.