Mathematical Model of Pulse Wave

Abstract

A mathematical model of the pulse wave has been developed taking into account the absence of adhesion conditions at the blood-vessel wall interface. This condition is inherent only in living organisms. The condition of adhesion at the wall-liquid interface, which is usual for inanimate nature, would lead to the formation of plaques, blood clots and, ultimately, to the death of the organism. Although blood is a non-Newtonian fluid, i.e. having a threshold nature, in the case of modeling the hemodynamics of large blood vessels in most modern works, and in ours in particular, blood is assumed to be a Newtonian fluid. Unlike existing models, this work took into account the presence of a background blood flow, the disturbance of which leads to the formation of a pulse wave. Of course, a linearized system of equations was solved. The solution was sought in cylindrical coordinates. To take into account sliding along the contact surface, a viscous friction coefficient was introduced, which should be determined empirically. An equation for vortex transfer is obtained, although in this work we do not consider vortex motions. In our consideration, the movement is potential in nature, although it has been experimentally established that helical movement is observed in large blood vessels. The dispersion relation was obtained. It is shown that the wave propagates relative to the background flow (Doppler effect). It has been established that the larger the radius of the capillary, the lower the frequency of the pulse wave.