Inhomogeneous Media Including Gas Bubbles

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When the propagation medium is not a homogeneous fluid, mechanisms other than the structural or thermal relaxation of its molecular constituents may contribute to the excess absorption (Morfey 1968). In addition to scattering the sound waves (covered in Chapter 6), inhomogeneities in the inertial or elastic properties of the medium can be responsible for the extraction of the acoustic wave energy by either viscous or thermal processes.4 Viscous damping results from the relative motion that occurs, between a suspended structure and the embedding medium, when the density of the inhomogeneity is different from that of the medium. If the density of the inhomogeneity is uniform, it will simply attempt to move back and forth along the axis of sound propagation. If the density is not uniform, there will also be a tendency for relative rotational motion to occur. In either case absorption of acoustic wave energy occurs when the velocity amplitude of the relative motion is diminished because of the viscosity of the suspending medium. The process of thermal damping results when, during the cyclic pressure changes of the sound field, alternate compressions and expansions take place and heat is conducted (at a finite rate) between the suspending medium and the inhomogeneity. O'Donnell and Miller (1979) have found, by calculation from estimates of the principal inhomogeneities in specific tissues, that thermal losses appear to be dominated (in the 1 to 10 MHz frequency range) by viscous relative motion losses over a wide range of postulated sizes of inhomogeneity. The ratios of thermal to viscous losses calculated by these authors were of the order of 2% for heart muscle and much less for skin and blood. In applications of the theory of viscous relative motion McQueen (1977) has attempted to explain various experimentally observed phenomena (e.g. the rupture of blood capillaries in rat spinal cord by pulsed ultrasound) of the interaction of ultrasound and soft tissues. Unlike O'Donnell and Miller (1979), who follow a previously used assumption of a suspension of roughly spherical 'particles', McQueen treats the case of a fibrous network permeating a viscous medium; a possibly more realistic starting point for modelling certain tissues.

Another mechanism by which particle suspensions may attenuate ultrasound has been identified by Kol'tsova et al. (1980). If the particles have a high surface activity, then particle ensembles may form which have a mobile structure that responds to the sound pressure fluctuations in a manner that results in ultrasonic absorption of the structural relaxation kind. For particles of silica (~ 16 nm diameter) in water this contribution to the absorption is about 50 times as great as that from viscous, thermal and scattering losses combined, for the 1 to 10 MHz frequency range. It is not known whether similar processes exist for biologic media.

Since viscous and thermal damping processes involve the cyclic transfer respectively of momentum and heat between the suspended structures and the medium, which takes place at a finite rate, it is perhaps not surprising to find that the equations that describe them may be formulated as relaxation-type expressions. Indeed, Hueter (1958) included these mechanisms as possibly contributing to a viscoelastic model of tissue. The contribution (a„) to the absorption coefficient by a single mechanism of the viscous relative motion type (see Dunn et al. 1969, p. 235) is given by:

4 An alternative interpretation of these phenomena will be provided in Section 4.3.7.

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