Waves & Propagation

Question 1

What is ultrasound? How is it generated?

Answer 1

Vibration of piezoelectric crystals against the skin surface, creating longitudinal waves which travel through tissue. Waves consist of oscillating pressures (compression and rarefaction).

Question 2

Define amplitude

Answer 2

The maximum change in pressure from its mean value in the tissues

Question 3

Define frequency

Answer 3

Number of cycles per second

Question 4

Define period

Answer 4

The time occupied by one cycle
= 1/f

Question 5

Define wavelength

Answer 5

The physical length of one cycle. All wavelengths for ultrasound <1mm.

Question 6

Define propagation speed and describe the determinants

Answer 6

The speed at which the ultrasound wave travels through a medium.
Depends on tissue characteristics
- Reduced density, increased speed
- Reduced elasticity, increased speed

Question 7

Define energy, work, power and intensity

Answer 7

E = The ability to do work
W = The energy transferred to or from an object via the application of force along a displacement (Joules)
P = The amount of energy transferred or converted per unit time (Watts)
I = Power transferred per unit area (power/area)

Question 8

What are the operating frequencies of diagnostic ultrasound?

Answer 8

2MHz to 20MHz

Question 9

Relate propagation speed, frequency and wavelength

Answer 9

c = f x λ
λ = c/f

Question 10

Define acoustic impedance

Answer 10

The opposition of a medium to longitudinal wave motion
It characterises the relationship between acting sound pressure and the resulting partical velocity

z (acoustic impedance) = ρ(density) x c (propagation speed)
units are in Rayls

Question 11

What are the major types of tissue interaction?

Answer 11

Attenuation, reflection, scattering, refraction

Question 12

Define attenuation + formulae for its calculation

Answer 12

Attenuation = 10 x log(I1/I2) dB

Attenuation = (α x L x f) dB
Coefficient for soft tissue is approximately 0.5dB/cm/MHz

Question 13

Define the depth of penetration and its formula + max attenuation

Answer 13

The point at which the round path attenuation exceeds the maximum the machine can tolerate (the echoes are too small to detect and are not displayed).

Attenuation = α x d x f

Max attenuation = α x (2P) x f
= 2α (P x f)

Question 14

Describe reflection and its geometry and define the formula for the reflection coefficient

Answer 14

Reflection occurs as an interaction of ultrasound with relatively large and smooth surfaces
Some of the energy is reflected and some is transmitted
The more different the acoustic impedance of the tissues, the more energy is reflected
Reflected echoes are only detected if the ultrasound beam is perpendicular to the reflecting surface
When the ultrasound strikes at an angle that is not 90 degrees (specular reflection) from the surface, the reflected energy travels away from the transducer and is lost
θi = θr

R = (z1 - z2)2 / (z1 + z2)2
This is a measure of the fraction of ultrasound energy that is reflected
When the impedance is similar, the fraction is close to 0
When the impedance is very different, the fraction is close to 1

Question 15

Describe scattering

Answer 15

The interaction of ultrasound with small structures – red blood cells, capillaries etc.
Scattered energy is distributed in all directions and is much weaker than reflected energy

Question 16

Describe speckle

Answer 16

The echo signal at any moment is the sum of many echoes, each caused by an individual scatter within the volume of tissue occupied by the ultrasound pulse
These scatters are randomly positioned relative to each other, so their echoes add together randomly, creating speckle

Question 17

Describe refraction, its geometry and define the formula describing it

Answer 17

The bending of an ultrasound wave’s path as it passes through different tissues with different propagation speeds
Geometry is determined by measuring the direction of travel of the ultrasound relative to a line drawn at right angles to the interface

Snells law - (sin θi)/c1 = (sin θt)/c2

When two tissues have the same propagation speed, there is no refraction
When the beam is perpendicular to the interface (0 deg from line), there is no refraction

Question 18

Describe the concept of the critical angle and derive its formula

Answer 18

Ultrasound cannot penetrate tissue if:
1. The propagation speed is higher in the second tissue
2. AND the incident angle is equal or larger than the critical angle

From Snells law by solving for θt = 90 degrees
θc = sin-1(c1/c2)