Sehgal, Chandra M.

This study deals with the relationship between the magnitude of acoustic nonlinearity, sound speed of tissues and the amount of fat present in them. A two-component model, i.e., nonfat and fat, has been assumed and equations that relate the nonlinear parameter (B/A) of a medium to the properties of its components have been derived for two cases. In the first case, the density and sound speed are the same for the two components; B/A is a linear function of fat concentration. To represent this case, mixtures of egg white and yolk were studied. Even though the differences in density and sound speed of the two egg components were within 1 percent of each other, B/A showed a deviation from linearity. In the second case, i.e., when the density and sound speed of the two components are not equal, a quadratic equation has been derived using mixture laws. Livers, fats, egg mixtures, and oil data were used to represent this case. B/A increased quadratically with fat concentration. The presence of proteins on the binary aqueous/fat mixtures modified the quadratic rule.

Scattering of ultrasound by biological tissues (continuous-inhomogeneous media) is discussed. An analytical expression for the attenuation due to scattering (α T SC ) and backscatter coefficients (σ T ) of tissues are obtained. The results explain the variation of (α T SC ) and σ T with frequency for a number of tissues. The study also provides two statistical parameters, velocity fluctuation coefficient and correlation length, in terms of which the scattering of tissues can be defined quantitatively.

On the basis of many measurements on attenuation, absorption, and speed of ultrasound in biological materials, one can make the following generalizations: (a) Biological tissues have high attenuation coefficients, about two to three orders greater than their major component, water; (b) the amplitude attenuation coefficient increases with frequency near-linearly in soft tissues and near-quadratically in fluids with frequency in the range 1 to 10 MHz, and possibly even up to 100 MHz; (c) speed dispersion is extremely small (∼0.1 to 1 m/s/ MHz); (d) absorption and attenuation coefficients either increase or decrease with an increase in temperature, depending on the nature of the tissue, and the frequency of irradiatiOn; (e) fluids containing proteins show a sharp increase in excess absorption in acidic and basic pH ranges, and finally; (f) at sufficiently high intensity of irradiation the absorption coefficient increases with intensity. Comprehensive models for the propagation of ultrasonic waves through lossy media should explain these experimental findings. We will review some of the current models and critically examine them in light of the definition of absorption in relation to attenuation and scattering. [Work supported by NIH CA 24085, CA 41324, and NSF 8310626.]

A thermodynamic method for measuring the acoustic nonlinearity parameter B/A in tissues is presented. It is based on the measurement of change in phase velocity as a function of time as the hydrostatic pressure of the sample is quickly reduced from a known value. This technique circumvents the effect of the attenuation in the medium and does not require a prior knowledge of the thermodynamic parameters of the tissues. The method is used to estimate nonlinearity parameters for normal and malignant tissues in the temperature range 20° to 37 °C. The values and the temperature dependence of these parameters are found to vary with the nature of the tissues.

An integrated approach for the absorption of ultrasound by liquids and tissues is proposed from the solution of a one-dimensional wave equation of propagation. The proposed model explains the square and linear power dependence of absorption on frequency for liquids and tissues, respectively. The study also provides a new index, specific heat ratio (γ), in terms of which the physical and the chemical state and thus possibly the pathological state of a tissue can be defined quantitatively.