Summary
- ultrasound; longitudinal wave with frequency greater than 20 kHz
- piezoelectric effect; ultrasound transducer as a device that emits and receives ultrasound
- ultrasound A-scan and B-scan
- acoustic impedance of a medium
- reflection of ultrasound at a boundary
Ultrasound scans:
Ultrasound waves are sound waves which are above the limit of human hearing, with frequencies higher than 20000Hz. Ultrasound scans are non-invasive and do not expose patients to ionising radiation. The scans are used for viewing an unborn foetus in pregnancy and also to detect kidney stones and gallstones.
The scans use pulses of ultrasound from a transducer which are reflected at boundaries between different mediums. The amount reflected and the time taken for the signals to return are used to produce images of the body.
Piezoelectric effect:
The ultrasound transducer is made of piezoelectric material, which allows it to transmit and detect ultrasound signals. The piezoelectric effect is the change in volume of a material when a p.d. is applied. It is also induced emf when crystals are under stress.
A potential difference across the transducer causes it to contract. If a high-frequency alternating potential difference is applied, the crystals oscillate at this frequency and produce ultrasound waves. When the ultrasound waves are detected, the oscillations produce an alternating potential difference. This allows the transducer to act as a transmitter and receiver.
A-scans and B-scans:
There are two types of ultrasound scan; an A-scan and a B-scan.
A-scan:
An A-scan is an amplitude scan, a pulse of ultrasound is sent to the body and at the same time an electron beam travels across a cathode-ray oscilloscope. Each time a pulse is received by the transducer a spike is produced on the oscilloscope. The x-axis shows the time taken and the y-axis is signal strength.
We can use the time between the spikes to determine the thickness and depths at which the ultrasound is reflected. The strength of the signal shows how much ultrasound is reflected. No image is produced with this method but measurements can be made of dimensions.
B-scan:
A B-scan is a brightness scan, it is most commonly used and can produce a real-time 2D or 3D image. This requires multiple transducers or one transducer moved around the body. If the amplitude of the reflection is greater, the brighter that region will show up. The scan therefore will show where bone, liquid and soft tissue reflect.
Acoustic impedance:
For an ultrasound to work, the waves must be reflected at the boundaries between materials. If all of the wave is reflected at the first boundary, the scan will not work because there will be no more ultrasound at the next boundary. The ultrasound is reflected when there is a change in density of the material, it will be completely reflected by dense materials such as bone so it cannot be used for fractures.
Acoustic impedance can be used to find what fraction of the signal’s intensity is reflected at each boundary, acoustic impedance, Z, is defined as:
Where is the density
is the speed of sound in the material
The following equation can be used to determine the intensity of the reflected wave at a boundary:
Where is the reflected intensity, is the incident (initial) intensity
is the acoustic impedance of the material the sound waves are leaving.
is the acoustic impedance of the material the sound waves are entering
Example: Find the percentage of ultrasound reflected when it travels from muscle to fat. Muscle has an acoustic impedance of and fat has an impedance of
Put values into the equation:
Percentage reflected: 0.44%
Impedance matching:
When an ultrasound scan is carried out, a gel is put onto the skin. If the gel was not used, all the ultrasound would be reflected at the boundary between the air and the skin, meaning none enters the body. The gel has a similar impedance to the skin, the transducer is submerged in the gel so only a small amount of reflection occurs at the gel/skin boundary.
Doppler effect:
The doppler effect can be used to measure the blood flow in the blood vessels. The diagram below shows how this is set up. We know the doppler equation is:
For blood moving at speed v, the equation linking the frequency of emitted and reflected waves to the speed is:
Example: Ultrasound is transmitted through the skin to a blood vessel, the transducer makes and angle of 50 with the vessel. The initial frequency is 5MHz but the frequency reflected is 4.98MHz, what is the speed of the blood flow? Sound has a velocity of in blood.
Rearrange for v:
Find :
Put values into equation:
The ultrasound scans can be colour-coded. The blood flowing towards the scanner is coloured red and blood moving away is coloured blue. On the screen, this makes oxygenated blood red and deoxygenated blood blue. Note that these colours are artificial and different to what we would observe in the doppler effect.
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