# 12.7 Ultrasound  (Page 2/10)

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In some instances, you may encounter a different decibel scale, called the sound pressure level, when ultrasound travels in water or in human and other biological tissues. We shall not use the scale here, but it is notable that numbers for sound pressure levels range 60 to 70 dB higher than you would quote for $\beta$ , the sound intensity level used in this text. Should you encounter a sound pressure level of 220 decibels, then, it is not an astronomically high intensity, but equivalent to about 155 dB—high enough to destroy tissue, but not as unreasonably high as it might seem at first.

## Ultrasound in medical diagnostics

When used for imaging, ultrasonic waves are emitted from a transducer, a crystal exhibiting the piezoelectric effect (the expansion and contraction of a substance when a voltage is applied across it, causing a vibration of the crystal). These high-frequency vibrations are transmitted into any tissue in contact with the transducer. Similarly, if a pressure is applied to the crystal (in the form of a wave reflected off tissue layers), a voltage is produced which can be recorded. The crystal therefore acts as both a transmitter and a receiver of sound. Ultrasound is also partially absorbed by tissue on its path, both on its journey away from the transducer and on its return journey. From the time between when the original signal is sent and when the reflections from various boundaries between media are received, (as well as a measure of the intensity loss of the signal), the nature and position of each boundary between tissues and organs may be deduced.

Reflections at boundaries between two different media occur because of differences in a characteristic known as the acoustic impedance     $Z$ of each substance. Impedance is defined as

$Z=\text{ρv},$

where $\rho$ is the density of the medium (in ${kg/m}^{3}$ ) and $v$ is the speed of sound through the medium (in m/s). The units for $Z$ are therefore ${kg/\left(m}^{2}·\text{s)}$ .

[link] shows the density and speed of sound through various media (including various soft tissues) and the associated acoustic impedances. Note that the acoustic impedances for soft tissue do not vary much but that there is a big difference between the acoustic impedance of soft tissue and air and also between soft tissue and bone.

The ultrasound properties of various media, including soft tissue found in the body
Medium Density (kg/m 3 ) Speed of Ultrasound (m/s) Acoustic Impedance $\left(\text{kg/}\left({\text{m}}^{2}\cdot \text{s}\right)\right)$
Air 1.3 330 $429$
Water 1000 1500 $1.5×{10}^{6}$
Blood 1060 1570 $1.66×{10}^{6}$
Fat 925 1450 $1.34×{10}^{6}$
Muscle (average) 1075 1590 $1.70×{10}^{6}$
Bone (varies) 1400–1900 4080 $5.7×{10}^{6}$ to $7.8×{10}^{6}$
Barium titanate (transducer material) 5600 5500 $30.8×{10}^{6}$

At the boundary between media of different acoustic impedances, some of the wave energy is reflected and some is transmitted. The greater the difference in acoustic impedance between the two media, the greater the reflection and the smaller the transmission.

The intensity reflection coefficient     $a$ is defined as the ratio of the intensity of the reflected wave relative to the incident (transmitted) wave. This statement can be written mathematically as

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