Acoustic impedance

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Acoustic impedance (Z) is a physical property of tissue. It describes how much resistance an ultrasound beam encounters as it passes through a tissue.

Acoustic impedance depends on:

  • the density of the tissue (d, in kg/m)
  • the speed of the sound wave (c, in m/s)

and they are related by:

  • Z = d x c 

So, if the density of a tissue increases, impedance increases. Similarly, but less intuitively, if the speed of sound increases, then impedance also increases.

The effect of acoustic impedance in medical ultrasound becomes noticeable at interfaces between different tissue types. The ability of an ultrasound wave to transfer from one tissue type to another depends on the difference in impedance of the two tissues. If the difference is large, then the sound is reflected. We grasp this intuitively at a macroscopic level. If you were to yell into a canyon, you would expect an echo to return to you. The sound wave in air meets the dense rocky canyon wall and reverberates off it back to you; the sound wave does not just pass into the rock. This is due to the difference in impedance.

Similarly, when an ultrasound beam passes through muscle tissue and encounters bone, it reflects off of it due to the difference in density between the tissues.

The amount of reflection that occurs in a perpendicular direction is expressed by:

Reflection fraction = [(Z2 - Z1) / (Z2 + Z1)]

Where Z1 and Z2 represent the impedance in tissue 1 and tissue 2, respectively. The signs in this equation are easy to remember because you can't reflect more sound than you originally sent, so the (Z2 - Z1) term must be the numerator.

Examples of impedance for bodily tissues (in kg/(ms)):

  • air  0.0004 × 10 
  • lung  0.18 × 10
  • fat  1.34 × 10
  • water  1.48 × 10
  • kidney  1.63 × 10
  • blood  1.65 × 10
  • liver  1.65 × 10
  • muscle  1.71 × 10
  • bone  7.8 × 10

Using these values with the equation above, you would see that less than 1% of sound is reflected at a fat-liver interface.

If the sound wave is not perpendicular to a surface, some of the sound wave will be reflected away from the transducer.

The SI unit for acoustic impedance is the Rayl, kg/(ms), after J W Strutt, 3rd Baron Rayleigh.