Week 2: Physics of waves Flashcards

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1
Q

What are the 3 assumptions for imaging modes?

A

1) Axial distance of target from the transducer - given time of arrival
2) Lateral position of target - location/direction of beam
3) Reflection/Scattering strength of target - w/ amplitude

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2
Q

What are the assumptions of a scanner?

A
  1. C is constant
  2. Beam axis is straight
  3. Attenuation is constant
  4. Pulse travels only to the target and back (along beam axis)
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3
Q

define a wave?

A
  • Disturbance of regular repeating pattern that travel through space
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4
Q

Describe transverse waves

A
  • Movement of molecules is 90 degree direction of wave

- Moving waves oscillations are perpendicular to the wave direction

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5
Q

Describe longitudinal waves

A
  • Sound waves that oscillate back and forth with the particle motion of a medium along the wave direction of propagation (parallel to the direction of wave)
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6
Q

…. has no net movement of medium (…. and associated….)

A
  1. transverse waves
  2. Disturbance
  3. Energy transported
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7
Q

Frequency (f) is

A

waves oscillates or crests passing a stationary observer p/sec

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8
Q

How is f determined?

A

source of the sound wave e.g. fat, soft tissue

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9
Q

what are mechanical waves?

A

a wave that travel via deformable or elastic medium, solids or liquids due to it elastic properties

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10
Q

Explain this picture

A

This describes compression (increased pressure) and rarefaction (decreased pressure):

1) No movement = rest position
2) Mass is displaced, stretched on one side and compressed on another (storing force & potential energy)
3) The mass is accelerated back to rest with force in the springs gaining kinetic energy while doing so. Carrying past the rest position.

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11
Q

What is frequency?

A

of times the ave repeats (oscillation or crests) p/sec

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12
Q

Anything greater than… is an US wave

A

> 20 Khz

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13
Q

define a wavelength?
The equation:
λ = c/f (mm)

A

length or distance between consecutive crests or similar points in the wave (single wave)

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14
Q

Define period? sec

T = 1/f

A

The time required to complete a single cycle (1 wavelength or oscillation)

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15
Q

What is Phase?

A

Phase describes the position within a cycle of oscillation and is measured in degrees (or radians, π = 180 ̊)

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16
Q

Describe the term pressure (Pascals)?

1 Pa= 1 N.m-2 (newtons measure of force)

A
  • pressure (p) in a medium oscillates between max & min values as a wave passes
  • Peak +ve pressure: compression (excess pressure)
  • Peak -ve pressure: rarefraction (excess pressure)
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17
Q

amplitude is described by peak excess … with the … value during the ….. passing

A

1) pressure
2) maximum
3) wave

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18
Q

What is power?
Energy = Joules (J)
Power = Watts (W)
—> 1 W = 1 J p/sec (s-1)

A

rate at which US energy is produced by the source

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19
Q

What is displacement amplitude?

A

Max distance moved by a particle from it’s rest position (measure of amplitude (strength) of the wave))

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20
Q

Whats the difference between actual and normal pressure?

A

is called excess pressure (pressure in the wave)

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21
Q

Describe how energy plays a role with power?

A

When a wave travels through a medium, it transport energy into that medium from the source.

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22
Q

What is intensity?

W m-2 or Wcm-2

A

measure of the amount of power flowing through a unit area at a 90 degree direction of propagation

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23
Q

What is intensity associated with?

A

with a wave increases with the pressure amplitude of the wave (I is proportional to pressure squared (p2))

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24
Q

what properties determine C?

C = √k/p

A

1) density/P (kg/m3)

2) stiffness/K (Pa)

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25
Q

What is density?

A

measure of weight of a standard volume of material

26
Q

What is stiffness?

A

how well material resits being deformed

27
Q

what is the normal US f in medical imaging?

A

2-15MHz

28
Q

What is presented with low density and high stifness?

A

high C

29
Q

What is presented with high density and low stiffness?

A

low C

30
Q

What is Z mismatch?

A

sound waves travels into 1 medium hitting an interface with a 2nd medium of different Z values. Some transmitted to 2nd medium, some reflected back to 1st medium

31
Q

What is the IRC equation

A

IRC = Ir / Ii = Pr2 / Pi2 = [Z2-Z1 / Z2 + Z1]2

32
Q

Z abruptly changes at …., ratio of particle…. and particle ….. must also change

A

1) interface
2) pressure
3) velocity

33
Q

However, the particle velocity and …. pressure cannot change abruptly at the interface with …. of medium, therefore must be continuous across interface

A

1) local

2) disruption

34
Q

Why is US gel used?

A

no US would be transmitted

35
Q

What is the equation for specific Z?

A

Z1 = Pi / Vi = Pr / Vr

particle pressure (p) & velocity (v) in incident wave
i = incident
r = reflected
36
Q

What is RA (amplitude reflection coefficient)?

A

ratio of reflected to incident pressure

37
Q

Why is RA important in US imaging?

A

determines the amplitude of echoes produced at bounderies with different tissue types

38
Q

Z in the first medium will be more than Z in the second, true or false?

A

true

Z1 > Z2

39
Q

RA is also described in terms of….. which is the ratio of intensities ….. and ……. waves

A

1) intensity reflection coefficient
2) reflected (Ir)
3) incident (Ii)

40
Q

How would you calculate the intensity transmitted?

A

It = I i - I r

41
Q

With I when flowing through CSA at interface, the energy flow of incident wave must be ….. and …

A

Conversed and split

42
Q

What is this artefact? (image)

A

Reflection artefact

43
Q

explain the principle behind reflection artefact (Law of reflection)?

A

Machine assumes there’s a large interface compared to the wavelength of wave approaching at 90 degrees. with the received and transmitted wave also travelling at 90 degrees

44
Q

… is determined at the interface by … at the interface

A

1) amplitude

2) reflection coefficient

45
Q

What is specular reflection?

A

occurs at a smooth large interface, w/ target greater than the wavelength and angle of reflection is equal to angle of incidence (interface extends to dimensions > than wavelength)

46
Q

Explain diffuse reflection?

A

occurs at rough surface, where target is the scale of a wavelength. The incident wave is reflected over range of angles

47
Q

What is this image (a) showing?

A

Pulse transmitted at a large and smooth interface, angle of incidence is 0 and reflected echo travel back along the same line. A strong echo is received at beam right angle to interface.

48
Q

What is this image (b) showing?

A

The angle of incidence is 10 degrees or more (not 0), therefore the echoes at the interface may not return to the transducer (t=r)

49
Q

What is image (c) showing? gives diffuse reflection

A

A pulse is sent out, reflected is received over multiple angles (pulse waves scattered) on a large, rough interface giving a diffuse reflection. Some of the reflected echos will be received back to the transducer

50
Q

Why does reflection occur?

A

change in acoustic properties (Z)

51
Q

What is a Mirror artefact?

Image here

A
  • occurs due to specular reflection at large smooth interface
  • large reflection coefficient (e.g. tissue-air interface)
  • may occurs if reflected beam encounters scattering target, and are returned along that path to the probe
52
Q

When does Scattering occur?

A

when target is greater than the wavelength

53
Q

What is the correlation between change in Z values and reflection laws when talking about scattering?

A

Parenchyma of most organs, there’s small-scale variations in Z, which can create small-scale reflections (increased scattered echoes).
- Reflections from small targets do not follow laws of reflection

54
Q

What is the Rayleigh Scattering Equation?

A

Ws∝d6f4

d = target size 
f = frequency (f proportional to 1/λ)
Ws = scattered power 

(Backscattered power (Ws) is proportional to 6th power of diameter (d) and 4th power of frequency)

55
Q

What is Rayleigh Scattering strongly dependent on?

A
  1. Size of d (target)

2. λ of wave

56
Q

When does Rayleigh scattering occurs?

A

when λ&raquo_space; diameter of scatterer

57
Q

What has a major influence on US image apperance?

A

different tissue types scattering. Stronger backscatter can lead to to a brighter image produced.

58
Q

Give an example of a substance/material property that has a influence on backscatter and why?

A
  • Collagen e.g. increased collagen content repairing post myocardial infarction
  • Blood (RBC, platelets & white blood cells) weak backscatter when compared to other tissue types. RBC &raquo_space; size than λ. Low Z mismatch between RBC and blood fluid
  • -> act as Rayleigh scatters
59
Q

2 important aspects of scattering: 1) US backscattered….. to transducer by small targets are small vs large….. resulting in …. echoes from parenchyma

A

1a) power
1b) interface
1c) weak

60
Q

2) US scattered over a wide angle of …. targets, the final …. does not change with ….. of …… of the wave

A

2a) small
2b) appearance
2c) angle of incidence

61
Q

Are contrast agents affected with scattering?

A

Yes.

But scatter strongly; slightly > size, high Z mismatch between the gas and blood