Ultrasound is a sound wave with a frequency above 20 kHz. In medicine it usually has a range of 2 - 10 MHz

 

How are the waves produced?

The most common material (crystal) used in ultrasound transducers is Lead Zirconate Titanate (PZT)[1]. The crystals used are ones which exhibit the “Piezoelectric Effect”, which  means that when a potential difference is applied across the material it expands, and when the material contracts a potential difference is created.

When the crystal expands and vibrates due to an alternating current an ultrasound wave is given off at the same frequency of the vibration of the crystal, and because of this the crystal transducer allows for electrical energy to be converted into sound energy, and vice versa.

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How are the waves used?

The transducer sends waves into the body, towards the organ you want to investigate, then the waves reflect off boundaries between different tissues and come back to the transducer.

The distance between the boundary and the transducer can be found by using the equation, d = vt/2 , where v (in m/s) is the speed of the wave, t (in s) is the time taken to travel to the boundary and back, and d (in m) is the distance from the transducer to the boundary . There is a division by 2 because in the time measured the wave has actually travelled double the distance between the transducer and the boundary (as shown in Fig.2 on the right.)

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Acoustic impedance:

The reason the waves are reflected at a boundary between tissues is because the tissues have different “acoustic impedances.” Acoustic impedance is defined by the equation [2],     Z = ρv   , where Z is the acoustic impedance (in Kg/m^2s), ρ is the density of the tissue (in Kg/m^3  ), and v is the acoustic velocity (speed of sound in the tissue, in m/s).

 

Not all the ultrasound wave that is incident on a boundary will reflect, some is refracted due to the acoustic impedance of the new medium.

The fraction of the original wave sent from the transducer can be found using the equation [2],

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where I_r is the reflected intensity, I_0 is the incident (original) intensity, Z_1 is the acoustic impedance of the first material in the boundary, and Z_0 is the acoustic impedance of the second material being entered in the boundary. Overall, (I_r/I_0) is the fraction of the incident wave coming back after being reflected at a boundary.

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It is important to know how much is being reflected back as it allows the scientists reading and analysing the data to know how far away the boundary is, and what tissues the boundary is between.

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A gel has to be used between the transducer and the skin, because air has an acoustic impedance (Z value) of 400 Kg/m^2s and skin has a Z value of 1.7 x 10^6 Kg/m^2s [3], so without a gel to assists, 99.9% of the ultrasound would be reflected and very little would enter the body, therefore not allowing the desired tissues to be viewed.

Impedance matching is used, a technique where the gel placed on the skin, removing the air to flesh boundary, has a similar Z value to the skin, allowing the maximum fraction of waves from the transducer to enter the body.

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References:

[1] Brief Overview of the Physics of Ultrasound: Dr Emma J Helm: https://www.ers-education.org/lrmedia/2016/pdf/298677.pdf  (accessed 05/02/19)
[2] NDT Resource Centre: https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/reflectiontransmission.htm (accessed 07/02/19)
[3] Basics of Biomedical Ultrasound for Engineers, by Haim AzhariCopyright © 2010 John Wiley & Sons, Inc
[4] Tech FAQ: http://www.tech-faq.com/piezoelectric-effect.html (accessed 22/02/19)