Ultrasound: Basic Physics

Question 1

What is the speed of sound in tissue assumed by most commercial ultrasound scanners?

Answer 1

1540m/s

Question 2

How is the speed of sound in a medium related to the bulk modulus (K) and the density p)?

Answer 2

c = (K/p)^0.5

Question 3

How is the acoustic impedance related to the speed of sound and the density?

Answer 3

Z = pc

Question 4

What is the equation for the depth of the far field?

Answer 4

D = (a^2)/I

a is the aperture
l is the wavelength

Question 5

What is the equation for the angle of divergence in the far-field?

Answer 5

0 = arcsin(0.61l/a)

a is the aperture
l is the wavelength

Question 6

What is another name for the near-field?

Answer 6

Fresnel zone

Question 7

What is another name for the far-field?

Answer 7

Fraunhofer zone

Question 8

For a focused lens (with speed of sound c1) with a curvature of R, what is the equation for the length of the near field (F)?

Answer 8

F = R / [(c2/c1)-1]

c2 = speed of sound in tissue

Question 9

What is the equation for the beamwidth at the focus?

Answer 9

w = IF/a

I = wavelength
F= depth to focus
a = aperture radius

Question 10

What is the equation for the amplitude reflection coefficient?

Answer 10

R = (Z2-Z1)/(Z2+Z1)

Z2 and Z1 are the acoustic impedances of the two media.

Question 11

What is the equation for the intensity reflection coefficient?

Answer 11

I = [(Z2-Z1)/(Z2+Z1)]^2

Z2 and Z1 are the acoustic impedances of the two media.

Question 12

Under what conditions is specular reflection observed?

Answer 12

When the diameter of the object is much larger than the wavelength.

Question 13

Under what conditions is Rayleigh scattering observed?

Answer 13

When the diameter of the object is much smaller than the wavelength.

Question 14

What is the scattered power proportional to?

Answer 14

(d^6) x (f^4)

Question 15

What causes ultrasonic scattering in tissue?

Answer 15

Microscopic variations in acoustic properties within tissue parenchyma.

Question 16

How does scatter appear on ultrasound images, and what is the reason for this appearances?

Answer 16

Scatter is low-power and non-directional, leading to a dark unifrom speckled appearance

Question 17

What is the equation for attenuation of an ultrasound beam through tissue?

Answer 17

I=I(0)exp(-alphaz)
alpha os the frequency dependent ultrasound coefficient (dB/cm)
z is the depth in tissue

Question 18

What is the equation for the frequency dependent ultrasound coefficient?

Answer 18

alpha = af^b
a is the frequency independent ultrasound coefficient (dB/cm/MHz)
b~1.1

Question 19

What is the value of b for liver and muscle?

Answer 19

1.1

Question 20

What is the value of b for blood and bone?

Answer 20

1.2

Question 21

What is the value of b for breast tissue?

Answer 21

1.5

Question 22

An intensity reduction of 3dB is equivalent to what fractional change in intensity?

Answer 22

1/2