Impendant method for determining the reduction of hydraulic resistance in large arterial vessels with permafle walls

During the contraction of the heart from the heart along the walls of the blood vessels, a wave of pressure propagates, which is called a pulse wave. As the wave moves away from the heart, this wave gradually weakens and practically fades in the capillaries. The speed of the pulse wave propagation depends on many factors, among which, for example, the elastic-viscous properties of the vessel wall, blood pressure, its density, viscosity, permeability of the vessel wall, etc. can be noted. In most works,1‒6 the main attention is paid to determining the propagation of a pulse pressure wave taking into account the elasticity of the vessel wall, and its permeability is not taken into account anywhere. However, the permeability of the wall significantly affects the propagation of the pulse pressure wave and its damping. The branching of the arterial tree is modelled by introducing a “permeability” of the wall with volume outflows of transverse velocity to the walls. In fact, this velocity is a strongly discontinuous function of the coordinate, when using the model of a permeable tube this function is always smoothed by the wall surface. Apparently, the idea of modelling an artery in the form of a permeable tube was first expressed in7 and is developed further in.8 The most complete study of such a model is contained in,9 where the system of blood circulation of a dog is modelled. Unlike other works,2‒6 to determine the hydraulic resistance in the central arterial vessel, the formulation of the problem of pulsating blood flow in the arterial channel was considered in,10,11 where the outflow of blood is mathematically modelled as a permeable wall of blood vessels. It should be noted that in addition to wave flows, it is advisable to study the steady flow of blood in a vessel with permeable walls. However, this case does not follow from the solution for wave fluxes as the limit as the frequency tends to zero, so the stationary problem should be considered in a separate formulation.