Ultrasound: Wave interactions

Question 1

If the relative pressure level of two ultrasonic pulses is −32 dB, what is the ratio of their acoustic pressures?

Answer 1

1/40

Question 2

If the relative intensity level of two ultrasonic pulses is +26 dB, what is the ratio of their acoustic intensities?

Answer 2

400

Question 3

What is the definition of acoustic impedance?

Answer 3

The ratio of acoustic pressure to particle velocity

Question 4

If the acoustic impedance on the far side of an interface is twice that on the near side, what is the amplitude reflection coefficient?

Answer 4

+0.33

Question 5

If the acoustic impedance on the far side of an interface is twice that on the near side, what is the amplitude transmission coefficient?

Answer 5

+1.33

Question 6

How does the acoustic impedance of liver compare with that of water?

Answer 6

Much higher

Question 7

What proportion of the incident intensity is usually reflected at the interface between two soft tissues?

Answer 7

Less than 2%

Question 8

What proportion of the incident intensity is usually reflected at the interface between soft tissue and bone?

Answer 8

Between 20-60%

Question 9

When does refraction occur at the interface between two soft tissues?

Answer 9

The sound speeds are different and the beam is incident obliquely

Question 10

How does the amplitude attenuation coefficient vary in most soft tissues as the frequency is increased?

Answer 10

Increases roughly linearly with frequency

Question 11

If the amplitude attenuation coefficient in liver is given by afb, what are typical values for a and b?

Answer 11

a = 0.4 dB cm−1 MHz−b and b = 1.2

Question 12

Roughly what proportion of the attenuation in most soft tissues occurs as a result of absorption?

Answer 12

Between 80 and 90 %

Question 13

Calculate the acoustic impedance of a soft tissue with a density of 1050 kg/m3, a bulk modulus of 2.5 GPa, and a shear modulus 5.0 kPa. (Answer in megarayls)

Answer 13

1.62
The acoustic impedance is simply Z0 = (Kρ0)1/2 where K is the bulk modulus and ρ0 is the density, giving a value of 1.62 megarayls.

Question 14

If a tissue-mimicking phantom has an ‘attenuation’ of 0.8 dB cm−1 MHz−1, what is the amplitude of a 4 MHz plane wave at a depth of 10 cm? Assume that the initial amplitude of the wave is 1 MPa. (Answer in kPa)

Answer 14

25
The attenuation loss, afbz = 0.8 × 41.0 × 10 = 32 dB = 20 + 6 + 6 dB

Now, 20 dB corresponds to an acoustic pressure ratio of 10, and 6 dB corresponds to an acoustic pressure ratio of 2, so that 32 dB corresponds to an acoustic pressure ratio of 10 × 2 × 2 = 40

Hence, the amplitude of the wave is p = 1.0/40 MPa = 0.025 MPa = 25 kPa