A general model for the absorption of ultrasound by biological tissues and experimental verification

In this paper, a closed-form expression is derived for the absorption of ultrasound by biological tissues. In this expression, the viscothermal and viscoelastic theories of relaxation processes are combined. Three relaxation time distribution functions are introduced, and it is assumed that each of these distributions can be described by an identical and simple hyperbolic function. Several simplifying assumptions had to be made to enable the experimental verification of the derived closed-form expression of the absorption coefficient. The simplified expression leaves two degrees of freedom and it was fitted to the experimental data obtained from homogenized beef liver. The model produced a considerably better fit to the data than other, more pragmatic models for the absorption coefficient as a function of frequency that could be found in the literature. Scattering in beef liver was estimated indirectly from the difference between attenuation in in vitro liver tissue as compared to absorption in a homogenate. The frequency dependence of the scattering coefficient could be described by a power law with a power of the order of 2. A comparable figure was found in direct backscattering measurements, performed at our laboratory with the same liver samples [Van den Aarssen et al., J. Acoust. Soc. Am. (to be published)]. A model for scattering recently proposed by Sehgal and Greenleaf [Ultrason. Imag. 6, 60-80 (1984)] was fitted to the scattering data as well. This latter model enabled the estimation of a maximum scatterer distance, which appeared to be of the order of 25 micron.