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2.4.6 Medical ultrasonics
Applications of ultrasound in medicine mainly utilise the frequency range 0.5 to 10 MHz. Measurements of ultrasound related to these medical uses generally involve the determination of acoustic pressure, intensity and power in water, although the use of tissue-mimicking materials and reference acoustical attenuators is of growing interest. As there are no widely accepted standard tissue-mimicking materials for ultrasound, the reference data given below have been limited to the properties of fluids currently used as reference standards and the typical range of properties of tissues.
Hydrophones are used to measure the acoustic pressure in medical ultrasonic fields propagating in water. Hydrophones with active elements of diameter between 0.1 and 1 mm are usually calibrated by placing the hydrophone which is to be calibrated in an ultrasonic field of known total power or local pressure. The techniques of free-field reciprocity (see IEC Standard 866: 1987) and planar scanning (see IEC Standard 1101: 1991) are widely used to achieve accuracies of between ± 7% and ± 15% (95% confidence) and laser interferometry (see Bacon 1988) has been developed to achieve higher accuracies, typically ± 3%. Intensity may be derived from measurement of acoustic pressure under the assumption of plane progressive wave propagation, a situation in which the particle velocity and acoustic pressure are in phase. In this case, the peak intensity, I, is derived from peak acoustic pressure, p, using the relationship:
where ρ is the density of water and c is the velocity of sound in water. The product ρc is known as the characteristic acoustic impedance of the propagating medium, usually water.
When ultrasound propagates through an absorbing medium, the initial intensity, I0 is reduced to Id at a distance d according to the expression:
where α is the amplitude attenuation coefficient. The attenuation coefficient includes all mechanisms which remove energy from the ultrasound beam and it is important to distinguish between absorption coefficient and attenuation coefficient. Absorption coefficient, αa, is used to predict the heating in tissue as it relates to the dissipation of sound at the point of interest. Attenuation coefficient, α, relates to the total loss of sound by any means, including scattering, and is more relevant to the prediction of the overall transmission of ultrasound as it propagates through tissue. For a homogeneous medium, attenuation and absorption coefficients are equal.
The pressure–density relationship for an acoustic wave propagating in a medium is expressed by the Taylor expansion:
where P, P0 are the
instantaneous and hydrostatic pressures, ρ, ρ0
are the instantaneous and equilibrium densities and A, B are
parameters whose values depend on the properties of the medium. In linear
acoustics, only the first term is significant, in which case the particle
pressure (P − P0) and density (ρ
− ρ0) are linearly related. At the high pressures
and frequencies encountered in medical ultrasonics, the degree of non-linearity
in a medium can be characterised by the ratio, B/A, known as the
non-linearity parameter. B/A is used to predict the degree of
distortion occurring in a pulse, and the loss of energy occurring in an
ultrasound beam, as a result of the effects of non-linear propagation in the
The velocity of sound and absorption (here attenuation and absorption can be considered the same) in castor oil and Dow–Corning 710 phenylated silicone oil (DC-710) are given in the table below in the range 0 to 40 °C. The frequency dependent absorption coefficient for castor oil at 30 °C is 5.8 f1.667 neper m−1 over the range 400 kHz to 500 MHz (see Dunn et al. 1969) where f is the frequency in MHz. For DC-710 silicone oil, the absorption coefficient at 20 °C is 7.3 f1.79 neper m−1 over the frequency range 2 to 10 MHz (see Zeqiri 1989).
Density, velocity of sound, attenuation coefficients and nonlinearity parameter for typical human fluids and tissues are given in the table below. Data corresponding to a temperature of 37 °C (body temperature) have been selected from the compilation prepared by Duck (1990). Although the majority of the data originates from measurements made on human organs, where information is not available, the results of measurements on equivalent animal organs have been used. For density and velocity of sound, ranges of values are given where this information is available. Values marked + have been taken from Report No. 74, Biological effects of ultrasound: mechanisms and clinical implications, National Council on Radiation Protection and Measurements, Bethesda, USA, 1983. For attenuation, where sufficient data are available to enable the frequency dependence to be given in the form af b the two coefficients a and b are given. In other cases, the attenuation in neper m−1 is given at a specific frequency and to determine the attenuation at other frequencies, it is reasonable to assume that the attenuation is proportional to frequency. It should be noted that, in all cases, a range of values would be expected for human tissue properties as a result of natural variation between humans and of the difficulties inherent in making these measurements.
D. R. Bacon (1988) IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,
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