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Introduction to Medical Imaging > Ultrasound 1 > Flashcards

Ultrasound 1 Flashcards

1
Q

what is acoustic pressure?

A

also called excess pressure
Pressure_Tube = pressure from the ambient level + acoustic pressure

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2
Q

When is there an increase in pressure in a longitudinal wave?

A

compression (positive pressure)

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3
Q

When is there a decrease in pressure in a longitudinal wave?

A

rarefaction (negative pressure)

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4
Q

When is the acoustic pressure at a maximum?

A

When the particles are moving towards to each other

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5
Q

How are pressure and particle velocity related?

A

related by the bulk speed of sound value and the ambient value of density
pressure of the particle in a plane wave = pressure of the ambient * bulk sound speed value * particle velocity

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6
Q

For waves with a small amplitude, how are pressure and density related?

A

By the sound speed:
p = c^2 * density

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7
Q

what is the equation that describes the wave with a small amplitude, in time and space?

A

p(x,t) = p_0 * sin(kx + wt)

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8
Q

What does the constant k represent in the equation describing the wave in time and space?

A

2*pi/ wavelength also known as the wavenumber (i.e number of waves that fit in one full oscillation)

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9
Q

what does the constant w represent in the equation of a small amplitude wave?

A

w = 2*pi * frequency of the wave

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10
Q

How is angular frequency and wavenumber related?

A

w = c* k
given that k = 2pi/ wavelength
and w = 2pif
where c = fwavelength
so that f = c/wavelength
substituting into the equation for angular frequency
w = 2* pi* c/wavelength
wavelength = k/2*pi
substituting again
w = ck

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11
Q

what is the constant c equal to in the equation describing the wave in space and time w = ck

A

c = sqrt (K/density)

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12
Q

What is the constant K in the equation of wave speed derived from the wave in time and space equation?

A

The Bulk modulus

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13
Q

What does the bulk modulus describe?

A

The stiffness of the medium
The relative change in density of a material induced by an applied pressure (the higher the change, the lower the resistance)
density, applied pressure are inversely proportional

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14
Q

What is the density of water?

A

1000kg/m^3

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15
Q

How can the transfer of energy through the medium in acoustic waves be described?

A

Acoustic energy density
Kinetic energy
Kinetic energy density
Potential energy density

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16
Q

What is the word definition of acoustic energy

A

The sum of time averaged kinetic and potential energy density

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17
Q

What is the mathematical definition of kinetic energy?

A

1/2 * m* v^2

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18
Q

What is the mathematic definition of kinetic energy density?

A

1/2 * density * speed of particle^2

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19
Q

What is the mathematical definition of potential energy density?

A

1/2 * (pressure ^2) * (1/ambient pressure * speed of sound ^2)

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20
Q

How to describe the energy flow of acoustic waves?

A

Energy/energy density, intensity, Power

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21
Q

What is the word definition of intensity?

A

the energy flowing through unit area per second.

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22
Q

What is the definition of power?

A

The rate of energy production by a source, or the rate at which energy flows across a surface- the sum or integral of intensity over a surface

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23
Q

Mathematical definition of instantaneous intensity (a function of space and time)

A

I(x,t) = pu
pressure of the wave * speed of the wave

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24
Q

Mathematical definition of the time averaged intensity (a function of space)

A

I(x) = <pu>
The pressure and particle velocity are averaged over a whole number of wave cycles</pu>

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25
Q

How are echoes created?

A

By reflections and scattering from objects, structures or small scatterers in the tissues of the body.

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26
Q

What must there be for an echo to be generated?

A

A difference in the sound speed and/or the density of the structure for this to happen - i.e the acoustic impedance must vary

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27
Q

What does the impedance describe?

A

How particles in a medium respond to a pressure wave.

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28
Q

What type of quantity is specifci acoustic impedance?

A

A local quantity

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29
Q

How to mathematically define the specific acoustic impedance?

A

The ratio of pressure to the particle velocity z = p/u

30
Q

What does the impedance depend on?

A

The density and stiffness of the medium (i.e the bulk modulus)

31
Q

What kind of quantity is charactersitic acoustic impedance?

A

A bulk property

32
Q

for a plane wave, what is the characteristic acoustic impedance equal to?

A

z = ambient density * speed of sound = ambient density * sqrt( bulk modulus/density of the material )

33
Q

What happens to a wave incident on a boundary?

A

It will be partly reflected and partly transmitted

34
Q

What do the amplitudes of the reflected and transmitted waves relative to the amplitude of the incident wave depend on?

A

The impedance of the materials on either side of the boundary

35
Q

What constant defines the factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave? (reflection)

A

The factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave is the amplitude reflection coefficient

36
Q

What constant defines the factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave? (transmission)

A

The factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave is the amplitude transmission coefficient

37
Q

what is the amplitude reflection coefficient equal to?

A

the ratio between the reflection pressure amplitude/ incident pressure amplitude

38
Q

what is the amplitude transmission coefficient equal to?

A

the ratio between the transmission pressure amplitude and the incident pressure amplitude

39
Q

How can the ratio of reflected pressure amplitude and incident pressure amplitude be calculated?

A

From the properties (impedances) of the 2 materials on either sides of the boundary
i.e
amplitude reflection coefficient = (z_2 - z_1)/(z_2 + z_1)

40
Q

How can the ratio of transmission pressure amplitude and incident pressure amplitude be calculated?

A

From the properties (impedances) of the 2 materials on either sides of the boundary
i.e
2*z_2 / (z_2 + z_1)

41
Q

How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (1)

A

at the boundary: pressure must be continuous, so pressure at one side of the boundary = pressure at other side
incident pressure + reflected pressure = transmitted pressure

42
Q

How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (2)

A

The particle velocity at either side of the boundary must also be continuous - particles at one side are moving at the same velocity as particles on the other side
u_i + u_r = u_t
(incident particle velocity+ reflected particle velocity = transmitted particle velocity)

43
Q

How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (3)

A

The specific impedances of the 2 materials are given by the ratio of the pressure to the particle velocity

44
Q

How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (4)

A

The specific impedances for the incident, reflected and transmitted waves are:
- u_i = P_i / z_1
- u_r = -P_r /z_1
- u_t = P_t / z_2

substitue these into the equation for velocities and rearrange for the form p_r / p_i = amplitude reflection coefficient

45
Q

How are the intensity reflection and transmission coefficient sderived?

A

There must be conservation of energy at the boundary so the intensity reflection coefficient + intensity transmission reflection coefficient = 1

46
Q

what is the intensity of the wave proportional to ?

A

the square of the pressure

47
Q

how can the intensity reflection coefficient be rewritten?

A

the ratio of the reflected intensity coefficient / incident intensity coefficient = pressure of the reflected wave ^ 2/ pressure of the incident wave ^ 2 = amplitude reflection coefficient ^ 2

48
Q

How can the intensity transmission coefficient be written as?

A

1 - intensity reflection coefficient = 1 - ratio of intensity reflected coefficient / intensity incident coefficient = 1 - amplitude reflection coefficient ^ 2
T_1 = 4z_1z_2 / (z_2 + z_1)^2

49
Q

What is snell’s law in terms of velocity of the wave in medium 1/2?

A

sintheta 1/ c_1 = sintheta 2 / c_2

50
Q

When does TIR occur?

A

when the velocity of the wave in the first material < wave in the second material (i.e impedance of first is higher than impedance of second material)

51
Q

what is the equation for the critical angle?

A

sin(critical angle) = c_1/ c_2

52
Q

On what types of boundaries does specular reflection occur?

A

At large, flat and smooth boundaries

53
Q

What is the dependency of power and frequency of sound during specular reflection?

A

NO dependency

54
Q

How does the type of interaction with structures on a range of scales depend on in specular reflection?

A

depends on the size of the structure relative to the wavelength of sound

55
Q

When does Rayleigh scattering occur?

A

When the size a of the scatterer is much less than the wavelength a&laquo_space;wavelength

56
Q

What is the dependency of power of the scattered sound, W, on the frequency of the sound?

A

W is proportional to the a^6 * f^4

57
Q

When the sound is scattered over a large angle in Rayleigh scattering, what will be the appearance on an ultrasound image?

A

The same when imaged from different angles

58
Q

When does diffraction occur?

A

when the size of the scatterer is similar to the wavelength

59
Q

What happens to sound as it passes through a medium?

A

Some of the energy is lost, and the wave amplitude decreases with distance

60
Q

What are the mechanism of energy loss of a wave as it travels?

A

absorption, scattering and diffraction

61
Q

What is the overall loss in energy from a beam called?

A

attenuation
Absorption, scattering and diffraction(divergence of the beam)

62
Q

How does pressure decay with distance?

A

Exponentially

p(z) = ambient pressure * e^(-attenuation coefficient * specific acoustic impedance)

63
Q

In exponential form, what are the units of the attenuation coefficient?

A

Nepers/m or m^-1. Nepers is dimensionless

64
Q

How to convert from nepers/m to dB/m

A

20log10((p_0 * e^-a)/p_0) = -a20log10(e) = -8.686a

65
Q

How can the attenuation over some distance be calculated for a graph in the units of db/m vs m?

A

Adding together the reduction over each cm

66
Q

In tissues, how does the attenuation coefficient change with frequency?

A

It increases with frequency

67
Q

for many tissues, the value of the attenuation coefficient doesn’t vary linearly with frequency so what is the actual equation?

A

a = a_0 * f^y

68
Q

What is the equation for attenuation?

A

the sum of the absorption attenuation coefficient and scattering attenuation coefficient

69
Q

What forces resist the movement of the particles in the medium (oscillation)?

A

Viscous drag

70
Q

What are the main forms of energy loss in oscillating wave?

A

viscous drag (friction)
processes on the molecular level

71
Q

What is the energy transfer from being removed from the oscillation of the wave and the molecular level energy?

A

absorbed by the medium and turned into thermal energy

72
Q

What does the energy transfer due to attenuation effects lead to?

A

A temperature rise as it is turned into thermal energy

Introduction to Medical Imaging (16 decks)

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