Ultrasound Imaging (AQA A Level Physics): Revision Note

Specific acoustic impedance

• The acoustic impedance $Z$ of a medium is defined as:

The product of the speed of the ultrasound in the medium and the density of the medium

• This quantity describes how much resistance an ultrasound beam encounters as it passes through a tissue

• Acoustic impedance can be calculated using the equation:

$Z=\rho c$

• Where:

  • $Z$ = acoustic impedance (kg m^-2 s^-1)

  • $\rho$ = the density of the material (kg m^-3)

  • $c$ = the speed of sound in the material (m s^-1)

• This equation shows:

  • the higher the density of a tissue, the greater the acoustic impedance

  • the faster the ultrasound travels through the material, the greater the acoustic impedance also

• This is because sound travels faster in denser materials

  • Sound is fastest in solids and slowest in gases

  • The closer the particles in the material, the faster the vibrations can move through the material

• At the boundary between media of different acoustic impedances, some of the wave energy is reflected and some is transmitted

• The greater the difference in acoustic impedance between the two media, the greater the reflection and the smaller the transmission

  • Two materials with the same acoustic impedance would give no reflection

  • Two materials with a large difference in values would give much larger reflections

• Air has an acoustic impedance of $Z_{air}=400\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$

• Skin has an acoustic impedance of $Z_{skin}=1.7\times {10}^6\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$

  • The large difference means ultrasound would be significantly reflected, hence a coupling gel is necessary

  • The coupling gel used has a similar $Z$ value to skin, meaning that very little ultrasound is reflected

Reflection & transmission of ultrasound

• The intensity reflection coefficient $\alpha$ is defined as:

The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave

• This can be calculated using the fraction:

$\alpha =\frac{I_r}{I_i}=\frac{{\left(Z_2-Z_1\right)}^2}{{\left(Z_2+Z_1\right)}^2}$

• Where:

  • $\alpha$ = intensity reflection coefficient

  • $I_r$ = intensity of the reflected wave (W m^-2)

  • $I_i$ = intensity of the incident wave (W m^-2)

  • $Z_1$ = acoustic impedance of one material (kg m^-2 s^-1)

  • $Z_2$ = acoustic impedance of a second material (kg m^-2 s^-1)

• This ratio shows:

  • if there is a large difference between the impedance of the two materials, then most of the energy will be reflected

  • if the impedance is the same, then there will be no reflection

Coupling medium

• When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body

  • This is because the soft tissues of the body are much denser than air

• If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected

• To counter this, a coupling gel is placed between the transducer and the body

  • This is because skin and coupling gel have a similar density, so little ultrasound is reflected

• This is an example of impedance matching, which is defined as when:

Two media have a similar acoustic impedance, resulting in little to no reflection of the ultrasound wave

• In terms of intensity reflection coefficient, $\alpha$, between the two media:

  • At lower values of $\alpha$, the media are impedance matched, so less reflection occurs

  • At higher values of $\alpha$, the media are not impedance matched, so more reflection occurs