An experimental comparison of different methods of measuring wave propagation in viscoelastic tubes

In this work the values of wave attenuation and phase velocity in a 6 x 9 latex rubber tube closed at the distal end were measured by means of different equations, and varying the distance between transducers. Three equations are based on two simultaneous pressure measurements and on the knowledge of the terminal reflection coefficient (two-point methods). The fourth equation is based on three simultaneous pressure measurements (three-point method). In all cases small amplitude pressure signals (20 mmHg peak-to-peak) were employed. The results of our experiments were then compared with those computed using a classic linear model of wave propagation, and with the high-frequency asymptotic values obtained experimentally using an original method recently developed by the authors. The results obtained with 40 cm between transducers demonstrate that phase velocity (about 15 m/s) and wave attenuation (about 0.003 Neper/cm at 10 Hz) are in agreement with the predictions of classic linear theories in the frequency range 1-15 Hz, provided wall tethering and viscoelasticity are taken into account. Only at certain critical frequencies, which depend on the particular equation employed, does the estimation of wave attenuation become inaccurate owing to an insufficient signal-to-noise ratio. Moreover, wave propagation measurements become inaccurate also at very low frequencies (< 1 Hz). The results obtained using a small distance between transducers (10 cm) demonstrate that the two-point methods maintain greater accuracy than the three-point one. In particular, when reducing the separation between transducers, the three-point attenuation values become 3-4 times greater than the attenuation obtained using the two-point equations. This finding might explain the large differences between propagation values observed in recent in vivo experiments. Finally, asymptotic estimations of the high-frequency phase velocity and attenuation per wave-length turn out rather robust and insensitive to a reduction in the transducer distance. These estimations might, therefore, be usefully adopted during in vivo experiments performed in difficult conditions.