Residual stresses reduce pulse wave velocity in arteries

In this note, we develop simple analytical formulas to estimate the effect of residual stresses on the pulse wave velocity in blood vessels. We combine these formulas with three constitutive models of the arterial wall: the Fung model and two models accounting for the dispersion of collagen fibers via 8 and 16 structure tensors accordingly. The residual stresses come into play with a description of the initial kinematics - the opening angle. Our numerical examples reveal that residual stresses reduce the pulse wave velocity. The latter effect becomes especially pronounced at high values of blood pressure.