LINEAR ~ROPA~AT~O~ OF PULSAT~LE WAVES IN VISCOELASTIC TUBES

An experimental and theoretical analysis is made of pulsatile wave propagation in deformable Iatex tubes as a model of the propagation of pressure pulses in arteries. A quasi one-dimensional linear model is used in which, in particular, attention is paid to the viscous phenomena in fluid and tube wall. The agreement between experimental and theoretical results is satisfactory. It appeared that the viscoelastic behaviour of the tube wall dominates the damping of the pressure pulse. Several linear models are used to describe the wall behaviour. No significant differences between the results of these models were found. The study of wave propagation in liquid-filled deform- able tubes is often motivated by its application to arterial blood flow. The full pi-symmetric~ linear approach is based on the work of Morgan and Kiely (1954) and Womersley (i957) which is later extended by several authors with regard to material properties: viscoelasticity, prestressing, tethering and anisotropy of the tube wall. Examples of a detailed linear study are Klip et al. (1967) and Kuiken (1984). An overview is given by Pedley (1980) and Milnor (1982). Ling and Atabek (1972) have included nonlinearities in their two-dimensional model. The work of Gerrard (1985) is mentionable as an attempt to verify experimentally a full axi-symmetrical linear theory. The inclusion of non-linearities and the extension to more complex geometries in two-dimensjonal models is difficult. Furthermore, typical two-dimensional phenomena such as higher order modes, are hardly observed in an in viva situation (Milnor, 1982). Many authors therefore choose a quasi one-dimensional approach in these cases. A description of the basic linear, elastic, nonvi~ous theory is given by LighthilI (1978). Similar models are developed in which in some way fluid viscosity, wall viscoelasticity, reflections or non-linearities are included (e.g. Anliker et ai., 1971; Gally et al., 1979; Holenstein et al., 1984; Abo-Ismail and Wassef, 1983; Van Steenhoven and Van Dongen, 1986). They show that in some applications the one- dimensional approach is a sensible one. The damping by fluid and wall viscosity appears to be an important factor in pulse propagation. Quantitative exper- imental results, however, are scarcely available. Men- tionable is the work of Newman et al. (1981, 1982, 1983) as a relatively simple, but quantitative exper- Dongen, 1986). The aim of the present paper was to study the validity of different models for the viscous behaviour of fluid and tube wall. A coupled analysis is presented in which both a frequency dependent wall shear stress and viscoelastic wall models are included. A quasi one-dimensional linear approach is chosen. Such an approach can be advantageous because of its simplicity and its ability to incorporate several differ- ent constitutive relations. The experimental condi- tions will be chosen such that non-linearities are small. The biomechanical relevance of the work is that a detailed analysis, apart from gaining more funda- mental insight in the damping of waves in arteries, may contribute to the development of a detection method for atherosclerosis at an early stage. With increasing age the flexibility of the vessel wall reduces and the local diameter can be reduced by stenotic lesions (Reneman et al., 1985). These changes will alter the behaviour of the arteries with respect to both pulse propagation in the vessels and pulse reflection at the branches. Our approach may be useful in combination with the use of small artificial high-frequency pressure waves, as proposed by Anliker et al. (1968). Hence, for a quantitative diagnosis it is necessary to have reliable and well-tested information about the inthtence of the properties of the vessel wall on the wave phenomena observed.