Instantaneous and Equilibrium Responses of the Brain Tissue by Stress Relaxation and Quasi-Linear Viscoelasticity Theory

Document Type : Article


1 Mechanical Engineering Department, North Dakota State University, Fargo, ND. 58108-6050, USA

2 Department of Physiology and Biomedical Engineering, Mayo Clinic, 200 First Street, S.W., Rochester, MN 55905, USA


Human brain and brainstem tissues have viscoelastic characteristics and their behaviours are functions of strains, as well as strain rates. Determination of the equilibrium and instantaneous stresses happening at low and high strain rates provide insights into a better understanding of the behaviour of such tissues. In this manuscript we present the results of a series of stress relaxation tests, at six 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 are measured from long-term responses of the stress relaxation test. The instantaneous stresses at high strain rates are determined using Quasi-Linear Viscoelasticity (QLV) theory at six strains. The results show that the instantaneous stresses are much larger (almost 11 times) than the equilibrium stresses and across all the strains. It can be concluded that the instantaneous response can be reasonably estimated from the long-term response which can be easily measured experimentally. The experimental results also show that the reduced relaxation moduli, estimated from the QLV theory, vary for the six strains tested.