6.5.3 Using ultrasound

Humans can hear sound within the range of 20-20,000Hz. Ultrasound is longitudinal sound wave with a frequency greater than 20kHz (we can't hear this). It can be used to form images of the internal structures of the body and it is good because it is non-ionising (harmless) and non-invasive (no risk of infection) and quick. Medical imaging ultrasound has a frequency in the range of 1-15MHz. It can be refracted at a boundary between two substances and also diffracted. The wavelength of ultrasound in the human body is ,1mm so it can be used to identify features as small as a few mm. An ultrasound transducer is used to generate and to receive ultrasound. It can change electrical energy into sound and sound into electrical energy by means of the piezoelectric effect.

The piezoelectric effect
Crystals such as quartz produce an e.m.f (the energy transferred from chemical to electrical per unit charge) when compressed/stretched/twisted/distorted. This is a reversible process. When an external p.d. is applied across the opposite faces of the crystal the electric field can either compress/stretch the crystal.

To generate ultrasound a high-frequency (e.g. 5MHz) alternating p.d. is applied across the opposite faces of a crystal repeatedly compressing and expanding the crystal. The frequency chosen is the same as the natural frequency of oscillation of the crystal and the result is that the crystal resonates producing an intense ultrasound signal. As ultrasound transducer emits pulses of ultrasound (about 5,000 per second). The same transducer is used to detect ultrasound - any ultrasound incident on the crystal will make it vibrate so the crystal is compressed and expanded by tiny amounts. This generates an alternating e.m.f across the ends of the crystal which can be detected by electronic circuits. Modern ultrasound transducers use lead zirconate titanate or polyvinylidene fluorine rather than quartz.

A and B scans
A scans
This is the simplest type of ultrasound scan. A single transducer is sued to record along a straight line through the patient. Tis can be used to determine the thickness of bone/distance between the lens and retina of the eye (for example).

Each pulse sent by the transducer into the body of a patient will be partly reflected and partly transmitted at the boundary between two different tissues. The reflected pulse (known as the echo pulse) will be received at the transducer. It will have less energy than the original pulse due to energy losses within the body and because some of the energy of the original pulse is transmitted through the body. The pulsed voltage at the transducer is displayed on an oscilloscope screen/computer screen as a voltage-time graph. The amplitudes of the voltage signals are attenuated by absorption and reflection losses. The time interval is the time taken for the ultrasound pulse to travel from the (front of the) transducer to the retina and back to the transducer therefore the total distance travelled by the ultrasound pulse is 2L where L can be calculated provided the average speed of the ultrasound in the eye is known.

B scans
B scans produce a 2D image on a screen. The transducer is moved over the patients skin and the output of the transducer is connected to a high-speed computer. For each position of the transducer the computer produces a row of dots on the screen (each dot corresponds to the boundary between two tissues). The brightness of the dot is proportional to the intensity of the reflected ultrasound pulse.


Acoustic impedance
The fraction of ultrasound intensity reflected at the boundary depends on the acoustic impedance of both media. The acoustic impedance (Z) of a substance is defined as the produce of the density of the substance and the speed of the ultrasound in the substance. It has the SI unit kg m^-2 s^-1:

Z = ρc

The reflected intensity of ultrasound depends on the values of Z1 and Z2 (the acoustic impedances of two substances). For normal incidence, when the angle of incidence is 0°, the ratio of reflected intensity (Ir) to incident intensity (Io) is given by the following equation:

Ir/Io = (Z2-Z1)²/(Z2+Z1)²

Ir/Io = ((Z2-Z1)/(Z2+Z1))²

The ration fo Ir/Io is known as the intensity reflection coefficient. There is more reflection when the values of acoustic impedances are very different (e.g there will be a greater reflection at a one/muscle boundary than a blood-muscle boundary. The acoustic impedance of bone is much different to the rest of the body (the rest of the body is pretty similar) so bone is easily distinguishable in an ultrasound scan.

Coupling gel is very important. When an ultrasound transducer is placed on the skin of a patient air pockets will be trapped between the transducer and the skin. The air-skin boundary means that about 99.9% of the incident ultrasound will be reflected before it even enters the patient. To overcome this coupling gel is used. Coupling gel has a similar acoustic impedance to the skin and fills the air gaps between the transducer and the skin ensuring that almost all the ultrasound enters the patient's body. Here, we can use the term impedance/acoustic matching. This is when two substances have similar values of acoustic impedance and negligible reflection occurs at their boundary as a result.


Doppler imaging
The frequency of ultrasound changes when it is reflected off a moving object (this is known as the Doppler effect). Doppler ultrasound is a non-invasive technique that uses the reflection of ultrasound (from iron-rich blood cells) to help doctors evaluate blood flow through major arteries. It can be used to reveal blood clots/atheroma and evaluate the amount of blood flow to transplanted organs.

During Doppler ultrasound the transducer is pressed lightly over the skin above the blood vessel. It sends pulses of ultrasound and receives the reflected pulses from inside the patient.  Ultrasound reflected off tissues will return with the same frequency and wavelength but ultrasound reflected of moving objects (blood cells) will have a changed frequency. The frequency increases when blood is moving towards the transducer and decreases when blood is moving away from the transducer. The transducer is connected to a computer that produces a colour-coded image to show the direction and speed of the blood flow.

As we know ultrasound scans have a frequency of 5-15MHz. In blood flow analysis this can give a Doppler shift up to 3kHz. The frequency shift (Doppler shift in frequency) (Δf) is directly proportional to the speed (v) of approach/recession of the blood. 

The axis of the probe (ultrasound transducer) must be held at an angle θ to the blood vessel. This is because holding perpendicular would give no observed change in the frequency as cos90 = 0. The usual θ is 60°. The change in observed frequency (Δf) is given by the following equation:

Δf = (2 f v cosθ) / c

F: original ultrasound frequency
v: speed of moving blood cells
c: speed of ultrasound in the blood