The biomechanical behavior of the vascular system is a function of the viscoelastic properties of the vessel wall components. For a quantitative description of the vascular biomechanics and for identifying viscoelastic parameters we have chosen two mechanical models, known in physiology as Kelvin and Maxwell models. They are 3-element systems consisting of a viscous element (η) and two elastic elements (Es, and Ep,). The aim of this study was to identify viscoelastic moduli from incremental stress relaxation curves of cerebral arteries, to develop an adequate method for parameter identification and to compare the behavior of the Kelvin and Maxwell models. Three different curve fitting methods were used: linear, parabolic and direct exponential ones. The accuracy of fitting by the exponential method is much higher than that by other ones, thus the direct exponential fitting seems to be appropriate for identifying viscoelastic moduli using the 3-element model. Both models can be described by the same mathematical equation, consequently the global rheological behavior they characterize is the same. On the other hand, our results show that when changing the value of one selected element, the change in the shape of the stress relaxation curve is not the same in the Kelvin and in the Maxwell model. In this respect they are not equivalent.

Keywords: stress relaxation, vessel wall, viscoelasticity, Models