Wave motions in viscoelastic tubes. Forced oscillations

Abstract

A characteristic of small blood and lymphatic vessels is the capacity of the wall to change its rheological properties and lumen by active contraction of the annular muscle cells contained in it [1–3]. A model of flow in the vessels taking this feature into account has been proposed in [4, 5], where a linear stability analysis is also given. A consequence of wall activity is the existence of auto-oscillatory flow conditions [6–8], which have also been discovered in the numerical solutions of the corresponding problems [9, 10]. Up to the present time flows have only been studied under steady conditions at the ends of the vessel and in the environment. The wall of an actual blood vessel is subject to various actions, frequently of a periodic nature: pressure pulsations at entry and rhythmically changing external forces applied from the surrounding tissues. Data exist on the sensitivity of vessels to transient actions [11–13], in particular on the relationship of their hydraulic resistance to frequency and amplitude of the action. There has been frequent discussion of the hypothesis that bv contraction of muscles in its walls or by external compression the vessel can act as a valveless pump [14, 15]. Within the framework of the quasione-dimensional approximation given below [4] the movement of liquid along a viscoelastic tube in the presence of small amplitude periodic external actions has been studied. A general solution of the problem has been constructed and concrete examples are given illustrating the features of forced wave motions in a tube having passive and active properties.