The propagation of ultrasound through tissue 2
when considering mechanical effects which might result from the interaction of a single pulse with tissue, rather than a series of pulses. The most fundamental of these is the peak rarefaction pressure, pr. The two other quantities, which are also used to describe the magnitude of the pulse, are the mechanical index, which is calculated directly from the peak rarefaction pressure (see Chapter 10), and the pulse-average intensity which describes the “brightness” of each pulse.
Rarefaction pressure, mechanical index and pulse-average intensity all describe the size of the ultrasound pulse itself
2.2.6 Estimates of in situ exposure It is not generally possible to measure the acoustic field within the body directly. This difficulty has meant that alternative methods have been developed to give estimates of acoustic quantities such as power, acoustic pressure and intensity within the tissue during scanning, so-called “estimated in situ exposure”. Ideally, a numerical model would be used to predict pulse wave propagation through body tissues, taking account of all absorption, scattering, refraction and non-linear processes, and recognizing that the body tissues form a three-dimensional distribution of varying acoustic properties. The extreme complexity of this approach has led to a practical simplification, which is used at present whenever “estimated in situ exposure” is required.
Very simple models are generally used to estimate in situ exposure
All calculations are based upon measurements of the acoustic pressure in water. The tissue is modelled with uniform, homogeneous attenuating properties, with an attenuation coefficient of 0.3 dB cm⁻1 MHz⁻1. The selection of this value for attenuation coefficient, which is lower than the average for soft tissues alone (see Table 2.1), is justifi ed by the view that it safely takes account of propagation through both soft tissue (with a slightly higher loss) and fluids (with lower loss). On average this method should overestimate the local exposure. Whilst this may be generally true, it must also be emphasized that in situ exposures estimated using this very simple model can only be taken as gross approximations to actual exposures.
0.3 dB cm−1 MHz−1 allows a safety margin for estimated in situ exposure for many situations
2.3 Non-linear propagation effects Thus far the discussion has assumed that the ultrasonic wave is governed by linear laws of acoustic propagation. This may be a poor approximation to what actually happens when ultrasonic pulses travel through tissue. So-called “fi nite-amplitude” eff ects occur, the terminology coming from the need to describe theoretically waves apart from those with vanishingly small amplitudes. These effects are of practical importance when considering exposure measurement, and the biophysical effe cts of ultrasound (Duck, 2002). An initially sinusoidal pressure wave of fi nite amplitude does not retain its sinusoidal waveform as it propagates. The compressions in the wave travel forward faster than the associated rarefactions partly because the speed of sound depends on density. This results in a distortion of the wave, in which the compressions catch up on the preceding rarefactions, ultimately forming a pressure discontinuity or shock. A comparison between the pulsepressure waveform at two distances from a transducer is shown in Figure 2.4. This shows the distortion in wave shape, which has been caused by several centimetres travel through water, with its accompanying acoustic shock separating the highest amplitude rarefaction and compression. The amount of non-linear distortion increases with several factors: the 11
Non-linear propagation causes waveform distortion and acoustic shock formation