The propagation of ultrasound through tissue 2
absorb, scatter and reflect ultrasound, it is possible, in principle, to predict the manner by which ultrasound propagates within, and interacts with, the body. This chapter has two parts. In the first, a general overview is given of ultrasonic wave propagation, and of the properties of body tissues that affect it. In the second, this knowledge is used to describe what may happen to a pulse of ultrasound as it travels into tissue, so setting the biophysical basis for the later discussions of ultrasound safety.
2.2 Ultrasound wave propagation Ultrasound is propagated in a manner identical to that of audible sound, through the displacements of the molecules constituting the medium in which the wave is travelling. It is thus a fundamentally different wave phenomenon from electromagnetic waves such as radio waves, infrared radiation and X-rays. The ultrasonic wave may propagate in the same direction as the displaced particles, in which case it is called a longitudinal compressional wave. Alternatively the particles may oscillate transversely, perpendicularly to the direction of propagation. Such a wave is termed a transverse or shear wave. Though shear waves can propagate in solids, and may therefore travel in calcified tissues such as bone or tooth, they are of little relevance in soft tissue, which can barely support them at ultrasonic frequencies. The longitudinal wave is therefore of primary importance for medical applications of ultrasound. In a longitudinal wave, individual molecules or particles in the medium oscillate sinusoidally about a fi xed location, moving forward and backward along the direction of propagation of the wave energy (Figure 2.1). As the particles move forward they become closer to those ahead, so increasing both the local density and the local pressure in the medium. Following their maximum forward displacement, the particles return towards and beyond their equilibrium location, resulting in a slight density reduction, and a reduction in local pressure. The difference between the ambient pressure (approximately atmospheric pressure) and the local pressure as the wave passes is called the “acoustic pressure”. This may be a compression (pressure above ambient) or a rarefaction (pressure below ambient). The greatest value of the acoustic pressure is of considerable importance when discussing aspects of safety concerning mechanical hazard. In particular, the “peak rarefaction pressure” is strongly related to cavitation events (see later). In diagnostic scanners these acoustic pressures can reach more than 2 MPa at the transducer face, or about 20 atmospheres. Referring to the rarefaction pressure, this means that the tissue is being pulled apart with a strength equal and opposite to about 20 atmospheres compression. The reason that it does not usually rupture is twofold. First, tissue, like water, can withstand this stress under many conditions. Second, the stress lasts for a very short time: at 1 MHz the rarefaction lasts only 0.5 μs, and this period becomes progressively shorter as the frequency increases. The distance between one compression (or rarefaction) and its immediate neighbour defi nes the wavelength, λ (Figure 2.1). At any particular frequency, f, the wavelength, λ, can be calculated from a knowledge of the velocity c (see below), using the expression λ = c /f. At 1 MHz the wavelength in soft tissues is typically between 1.5 mm and 1.6 mm, 0 5
Longitudinal waves are much more important than shear waves in soft tissues at diagnostic frequencies
The ultrasonic wave consists of compressions and rarefactions
Adjacent compressions are separated by one wavelength, typically 0.1–1mm in soft tissues at common diagnostic frequencies