href="#fb3_img_img_ace89036-cec4-59be-88c5-eb2177051cf4.gif" alt="wavelength_speed_frequency"/>
Table 2.1 lists a number of typical ultrasound frequencies and wavelengths in soft tissue (assuming c = 1540 m/sec).
Table 2.1 Typical frequencies used in diagnostic ultrasound and the corresponding wavelengths in soft tissue.
| Frequency (MHz) | Wavelength (mm) |
|---|---|
| 2 | 0.77 |
| 3 | 0.51 |
| 5 | 0.31 |
| 8 | 0.19 |
| 10 | 0.15 |
| 15 | 0.10 |
Notice that for all frequencies the wavelength is less than 1 mm. Also notice that the wavelength becomes smaller as the frequency increases.
It will become clear that the resolution of an ultrasound image is directly related to the wavelength – the smaller the wavelength the better the resolution. Given the inverse relationship between frequency and wavelength this means that:
The higher the frequency the better the resolution.
Unfortunately we will shortly see that it is not possible to keep increasing the frequency to achieve ever better resolution. The physics of ultrasound places a limit on the frequency that can be used in a given clinical situation.
Frequency analysis
In this chapter we have implicitly assumed that the ultrasound wave is continuous (i.e. it goes on for ever). This is referred to as "continuous wave" ultrasound. Later we will see that diagnostic ultrasound actually uses short "pulses" of ultrasound (although there is one situation where continuous wave ultrasound is used – "continuous wave Doppler").
A continuous wave is the purest form of oscillation. It is often found in nature, e.g. in the motion of a plucked guitar string or of a clock pendulum. Mathematically it is referred to as a "sinusoidal" wave because it can be described by the sine function. For example, the mathematical expression for the pressure at a point as a function of time (as shown in Figure 2.2) is:
pressure = A × sin(2πft)
where f is the frequency of the wave and t is time.
The sinusoidal wave is also useful as the building block for more complex waveforms. Any form of repetitive function can be broken up into the sum of a number of sinusoidal waves of different frequencies. This process is referred to as "frequency analysis". Thus, for example, a continuous triangular wave can be broken up into the sum of a number of sinusoidal waves of different frequencies, as shown in Figure 2.4.
Figure 2.4 A non-sinusoidal waveform (like this triangle waveform) with frequency f can be broken up into the sum of sinusoidal waves of different amplitudes and with frequencies f, 2f, 3f, .... etc.
Note that there are frequency components at the repetition frequency of the wave and at integer multiples of it ("harmonics"). We will return to this concept in chapter 12 when we discuss Harmonic Imaging.
Similarly a pulse (i.e. a wave that lasts just a short time) can be broken up into the sum of many different waves with different frequencies. This will be discussed further in chapter 3.
Suggested activities
1 Look at ripples travelling in water and think about the similarities and differences to ultrasound waves.
2 Calculate the wavelength for ultrasound frequencies of 5 MHz and 10 MHz. Check your answers against Table 2.1.
3 Calculate what frequency would give a wavelength of 0.51 mm and make sure you get the same answer as in the table above.
Attenuation
Diagnostic ultrasound gives useful information precisely because it interacts strongly with soft tissue. In this and the following two sections the major types of interaction will be discussed. These are:
attenuation
reflection
scattering
refraction
We will start with attenuation. As an ultrasound wave travels through tissue it becomes progressively weaker. This is referred to as attenuation (see Figure 2.5).
Figure 2.5 Attenuation of ultrasound as it travels through tissue. The amount of attenuation depends on the type of tissue, the frequency and the total distance travelled (L).
The attenuation is calculated as the ratio of the input ultrasound intensity to the output intensity (I1/I2). Since it is a ratio, it is usually measured in decibels (see Mathematics Review in chapter 1 for further discussion of decibels).
It is calculated as follows:
In soft tissue, the primary mechanism causing attenuation is heating of the tissue due to absorption of some of the wave's energy as it passes through.
Why does this happen? Since tissue is not perfectly elastic there is friction as it moves back and forth in response to the pressure variations in the wave and this means that heat is generated. Energy cannot be created or destroyed and so this process of heating removes energy from the ultrasound wave.
Other factors can contribute to attenuation.
As discussed in the next section, reflection and scattering from structures in the body cause some of the ultrasound energy to be deflected in other directions. This energy is therefore lost from the wave, resulting in weakening, i.e. attenuation, of the ongoing ultrasound.
If the ultrasound beam diverges (due to defocussing or other mechanisms) the energy in the beam is spread over a greater area, and so the intensity of the ultrasound decreases. (Think of a torch being focussed and defocussed and how this affects its intensity).
The use of decibels makes it particularly easy to calculate the attenuation for a given situation:
where α is the "attenuation coefficient" for the specific tissue involved (in dB/cm/MHz), f is the ultrasound frequency (in MHz) and L is the total distance travelled by the ultrasound (in cm).
For
