Production and use of ultrasound
Section: Medical Physics | Syllabus: Cambridge AS Level Physics 9702
Production and Use of Ultrasound Ultrasound consists of sound waves with frequencies above the human hearing range (typically 1 MHz to 20 MHz for medical applications). It is widely used for diagnostic imaging because it is non-invasive and does not involve ionising radiation .
The Piezoelectric Effect Piezoelectric Effect A piezoelectric crystal changes shape when a potential difference (p.d.) is applied across it, and generates an electromotive force (e.m.f.) when its shape is changed by an external force.
How Ultrasound is Generated An alternating p.d. is applied across a piezoelectric crystal (e.g. quartz), causing it to expand and contract repeatedly at the frequency of the applied p.d. These rapid vibrations generate ultrasound waves in the surrounding medium.
How Ultrasound is Detected When reflected ultrasound waves return and strike the piezoelectric crystal, they cause it to change shape. This generates a small e.m.f. across the crystal, which can be amplified and processed to form an image.
A piezoelectric transducer can therefore both generate and detect ultrasound pulses, making it ideal for medical imaging. Figure: Piezoelectric Transducer Cross-section of an ultrasound transducer showing: Piezoelectric crystal (e.g., quartz or PZT) at the centre Metal electrodes on front and back faces of crystal Backing material behind crystal to damp oscillations and produce short pulses Acoustic insulating layer Plastic/rubber membrane at front (contacts patient's skin) Coaxial cable connection to electrical supply When an alternating p.d.
is applied, the crystal vibrates, emitting ultrasound pulses. When returning echoes strike the crystal, they generate an e.m.f. that is detected. Reflection at Tissue Boundaries When ultrasound travels through the body, it reflects at boundaries between different tissues .
The amount of reflection depends on the difference in specific acoustic impedance between the two media. Specific Acoustic Impedance (Z) The specific acoustic impedance of a medium is defined as the product of its density and the speed of sound in that medium.
Z = ρ c where ρ = density (kg m^-3) and c = speed of sound (m s^-1) Unit of Z: kg m^-2 s^-1 Material Speed of sound / m s^-1 Density / kg m^-3 Z / × 10^6 kg m^-2 s^-1 Air 330 1.3 0.000429 Fat 1450 952 1.38 Muscle 1580 1080 1.71 Skin 1730 1150 1.99 Bone 3500 1850 6.48 Intensity Reflection Coefficient When ultrasound is incident normally on a boundary between two media, some is reflected and some is transmitted.
The proportion reflected depends on the difference in acoustic impedances. Intensity Reflection Coefficient (α) The ratio of the reflected intensity to the incident intensity at a boundary between two media.
α = I_R/I_0 = (Z_1 - Z_2)^2/(Z_1 + Z_2)^2 where I_R = reflected intensity, I_0 = incident intensity, Z_1 and Z_2 = acoustic impedances of the two media Key Points If Z_1 Z_2: very little reflection (most ultrasound is transmitted) If Z_1 and Z_2 are very different: strong reflection The transmitted intensity: I_T = I_0 - I_R Impedance Matching with Coupling Gel Air has a very low acoustic impedance compared to skin.
At an air-skin boundary, almost all ultrasound would be reflected. A coupling gel is applied between the transducer and skin to eliminate air gaps. The gel has a similar acoustic impedance to skin, allowing ultrasound to enter the body efficiently.
Figure: Reflection at Tissue Boundaries Diagram showing an ultrasound pulse travelling through the body: Incident wave with intensity I_0 approaches boundary between Medium 1 (impedance Z_1) and Medium 2 (impedance Z_2) Part of the wave is reflected (intensity I_R) back towards transducer Part is transmitted (intensity I_T) into the second medium The proportion reflected depends on the difference between Z_1 and Z_2 If Z_1 Z_2: most energy transmitted, weak echo.
If Z_1 and Z_2 very different: strong reflection, strong echo. Attenuation of Ultrasound As ultrasound travels through tissue, its intensity decreases due to absorption (energy converted to heat) and scattering .
This reduction in intensity is called attenuation . I = I_0 e^-μ x where I = intensity at depth x, I_0 = initial intensity, μ = linear attenuation coefficient (m^-1 or cm^-1), x = distance travelled The attenuation coefficient μ depends on the tissue type and is approximately proportional to ultrasound frequency.
Higher frequencies are attenuated more rapidly. Types of Ultrasound Scans Scan Type Description Application A-scan (Amplitude) Displays echo amplitude vs time on an oscilloscope. Used to measure distances.
Ophthalmology (measuring eye dimensions) B-scan (Brightness) Echo strength controls brightness of pixels. Multiple scans build a 2D image. Foetal imaging, abdominal scans Figure: A-scan and B-scan Outputs A-scan (Amplitude scan): Oscilloscope display showing echo amplitude (y-axis) vs time (x-axis) Each peak represents a reflection from a tissue boundary Time between peaks indicates distance between…
Interactive revision notes, videos and practice questions load below.