Validity of viscoelastic models of blood vessel wall

Quantitative description of biomechanical behaviour of the blood vessel wall is needed for understanding normal and pathologic functions of the vascular system. In this study we investigated the stress relaxation of blood vessels. Strips were cut from the vessel wall and they were stretched in a stepwise manner until they tore. The mechanical stress (approximately 10(5)-10(6) Pa) induced in the strips was determined. This showed an initial steep rise and then a slow, near exponential decay (stress relaxation) after each step of stretch. For the mathematical description we used two technical models (the Maxwell and the Kelvin model--they are built of two elastic elements and of one viscous element), as well as a one-dimensional continuum mechanical model. The moduli of the models were identified with a curve fitting method. Our aim was to compare these models in order to elucidate, which one describes the rheological behaviour of the blood vessel more correctly. The results of our analysis show that the corresponding moduli diverge from each other in the Maxwell and Kelvin models: that is, they depend on the mode of the assumed connection between the mechanical units. In contrast, moduli of the continuous model are unambiguous. We conclude that the continuous model properly describes the stress relaxation of the vascular wall. Its advantage over the technical models is that moduli describing the viscoelastic behaviour of the tissue do not depend on the not wholly well-known structure of the wall components.