Pulsatile Flow in Vessels whose Distensibility and Size vary with Site

A theoretical treatment is given for pulsatile flow in large vessels (in which viscosity is neglected) where there may exist built-in geometric taper and also `mechanical taper' - or change of distensibility along the vessel. The solution for the combined pressure-and-flow wave and its propagation is complicated and includes attenuation factors that are different for the pressure (e−A1x/2) and for the cross-sectionally averaged velocity e(k1−A1)x/2. These have similar dependence on geometric taper and different dependence on the mechanical taper. The possible solutions include those of two wave modes, sinusoidal and exponential, whose possible existence depends on the magnitude of a dimensionless parameter β=(2A1+k1) c0/4ω in a somewhat general case. The exponential mode is the only one possible when this magnitude exceeds unity (as it can in some arteries), and the possible transition between the mode types at certain types of vessel sites is also treated, as is the ratio between the pressure and flow amplitudes.