Production and use of ultrasound

Section: Medical Physics  |  Syllabus: Cambridge A 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:

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
Air3301.30.000429
Fat14509521.38
Muscle158010801.71
Skin173011501.99
Bone350018506.48

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 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:

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):

B-scan (Brightness scan):

Advantages of Ultrasound Imaging Limitations

Worked Examples

Worked Example: Calculating Acoustic Impedance

Question: The average density of the human brain is 1100 kg m^-3 and its specific acoustic impedance is 1.60 × 10^6 kg m^-2 s^-1. Calculate the speed of ultrasound through the brain.

Solution

Using Z = ρ c, rearranging for c:

c = (Z/ρ) = 1.60 × 10^61100 = 1450 m s^-1

Worked Example: Intensity Reflection Coefficient

Question: Calculate the intensity reflection coefficient for ultrasound incident normally on a fat-muscle boundary. (Use values from the table above.)

Solution

Z_fat = 1.38 × 10^6 kg m^-2 s^-1, Z_muscle = 1.71 × 10^6 kg m^-2 s^-1

α = ((1.38 - 1.71)^2/(1.38 + 1.71)^2) × 10^12 / 10^12 = ((-0.33)^2/(3.09)^2) = (0.1089/9.55) = 0.011

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