Page 531 - Physics Coursebook 2015 (A level)

Chapter 32: Medical imaging
For ultrasound, we are interested in the fraction of
the incident intensity of ultrasound that is reflected at the boundary. This depends on the acoustic impedance Z of each material. This quantity depends on the density ρ and the speed of sound c in the material. Acoustic impedance is defined as follows:
acoustic impedance = density × speed of sound
Z = ρc
Since the unit of density is kg m−3 and the unit of speed is m s−1, the unit of acoustic impedance Z is kg m−2 s−1.
Table 32.3 shows values of ρ, c and Z for some materials that are important in medical ultrasonography.
where Z1 and Z2 are the acoustic impedances of the two
materials (see Figure 32.24). The ratio Ir indicates the I0
fraction of the intensity of the beam that is reflected.
WORKED EXAMPLE
air
water
Biological
blood
fat
soft tissue (average)
muscle
bone (average; adult)
Transducers
barium titanate
lead zirconate titanate
quartz
polyvinylidene difluoride
1.3 330 0.0004
1000 1500 1.50
A beam of ultrasound is normally incident on the boundary between muscle and bone. Use Table 32.3 to determine the fraction of its intensity which is reflected.
Step 1 Write down the values of Z1 (for muscle) and Z2 (for bone).
Z1 =1.71×106kgm−2 s−1 Z2 =6.40×106kgm−2 s−1
Step2 SubstitutethesevaluesintheequationforIr. Ir =(Z2−Z1)2 I0 I0 (Z2 + Z1)2
Hint: We can use this equation because we know that the angle of incidence = 0°.
Ir =(6.40−1.71)2
I0 (6.40 + 1.71)2
= 0.33
Hint: We can ignore the factor of 106 in the Z values because this is a factor common to all the values, so they cancel out.
So 33% of the intensity of ultrasound will be reflected at the muscle–bone boundary.
Comparing acoustic impedances
A big change in acoustic impedance gives a large fraction of reflected intensity. Inspection of Table 32.3 shows that:
■■ averylargefraction(Ir ≈99.95%)oftheincidentultrasound I0
will be reflected at an air–tissue boundary
■■ a large fraction will be reflected at a tissue–bone boundary
(as shown in Worked example 2)
■■ very little will be reflected at a boundary between soft
tissues including fat and muscle.
This means that bone shows up well in an ultrasound scan, but it is difficult to see different soft tissues (Figure 32.25). Another problem is that the patient’s skin is in contact with air, and 99.95% of the ultrasound will be reflected before it has entered the body. To overcome this, the transducer must be ‘coupled’ to the skin using a gel whose impedance matches that of the skin. This process of impedance matching explains why the patient’s skin is smeared with gel before a scan.
2
Material
Density / kg m−3
Speed of sound / m s−1
Acoustic
impedance / 106 kg m−2 s−1
1060 1570
925 1450
1060 1540
1.66
1.34
1.63
1075 1590 1.71
1600 4000
6.40
5600 5500 30.8
7650 3790 29.0
2650 5700
1780 2360
15.1
4.20
Table 32.3 The density (ρ), speed of sound in air (c) and acoustic impedance (Z) of some materials important in medical scanning.
Calculating reflected intensities
When an ultrasound beam reaches the boundary between two materials, the greater the difference in acoustic impedances, the greater the reflected fraction of the ultrasound waves. For normal incidence (i.e. angle of incidence = 0°) the ratio of the reflected intensity Ir to the incident intensity I0 is given by:
Ir = (Z2 − Z1)2
I0 (Z2+Z1)2 or
Ir= Z2−Z1 2 I0 Z2+Z1
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