The role of the arterial prestress in blood flow dynamics

Blood flowing in a vessel is modelled using one-dimensional equations derived from the Navier-Stokes theory on the base of long pressure wavelength. The vessel wall is modelled as an initially highly prestressed elastic membrane, which slightly deforms under the blood pressure pulses. On the stressed configuration, the vessel wall undergoes, even in larger arteries, small deformation and its motion is linearized around such initial prestressed state. The mechanical fluid-wall interaction is expressed by a set of four partial differential equations. To account for a global circulation features, the distributed model is coupled with a six compartments lumped parameter model which provide the proper boundary conditions by reproducing the correct waveforms entering into the vessel and avoid unphysical reflections. The solution has been computed numerically: the space derivatives are discretized by a finite difference method on a staggered grid and a Runge-Kutta scheme is used to advance the solution in time. Numerical experiments show the role of the initial stresses in the flow dynamics and the wall deformation.