Absorption of longitudinal and shear waves and generation of heat in soft tissues

The author analysed the oblique incidence of a longitudinal plane wave and the generation of a shear wave at a boundary between a soft tissue and a gas, considering a viscoelastic model (Voigt solid) of the medium. From the data measured by Frizzell et al. (J. Acoust. Soc. Am. 60, 1409-1411) for shear waves, the average velocity 30 m/s and the average absorption coefficient 7.7 X 10(3) cm-1 at the frequency of 5 MHz were assumed for calculations. The amplitude and the intensity of the generated shear wave were obtained and hence the rate of heat production per unit volume was determined. At the boundary, this quantity was found to be of the same order of magnitude for the generated shear wave as for the incident longitudinal wave. In the case of the shear wave, which propagates almost perpendicularly to the boundary, it decreases rapidly with the distance. Therefore, the temperature increase caused by shear waves was negligible in respect to longitudinal waves in spite of the extremely high absorption coefficient. This conclusion could be confirmed by solving the inhomogeneous equation of heat conductivity for the case under consideration.