Week 2: Physics of waves Flashcards
What are the 3 assumptions for imaging modes?
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
What are the assumptions of a scanner?
- C is constant
- Beam axis is straight
- Attenuation is constant
- Pulse travels only to the target and back (along beam axis)
define a wave?
- Disturbance of regular repeating pattern that travel through space
Describe transverse waves
- Movement of molecules is 90 degree direction of wave
- Moving waves oscillations are perpendicular to the wave direction
Describe longitudinal waves
- 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)
…. has no net movement of medium (…. and associated….)
- transverse waves
- Disturbance
- Energy transported
Frequency (f) is
waves oscillates or crests passing a stationary observer p/sec
How is f determined?
source of the sound wave e.g. fat, soft tissue
what are mechanical waves?
a wave that travel via deformable or elastic medium, solids or liquids due to it elastic properties
Explain this picture
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.
What is frequency?
of times the ave repeats (oscillation or crests) p/sec
Anything greater than… is an US wave
> 20 Khz
define a wavelength?
The equation:
λ = c/f (mm)
length or distance between consecutive crests or similar points in the wave (single wave)
Define period? sec
T = 1/f
The time required to complete a single cycle (1 wavelength or oscillation)
What is Phase?
Phase describes the position within a cycle of oscillation and is measured in degrees (or radians, π = 180 ̊)
Describe the term pressure (Pascals)?
1 Pa= 1 N.m-2 (newtons measure of force)
- 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)
amplitude is described by peak excess … with the … value during the ….. passing
1) pressure
2) maximum
3) wave
What is power?
Energy = Joules (J)
Power = Watts (W)
—> 1 W = 1 J p/sec (s-1)
rate at which US energy is produced by the source
What is displacement amplitude?
Max distance moved by a particle from it’s rest position (measure of amplitude (strength) of the wave))
Whats the difference between actual and normal pressure?
is called excess pressure (pressure in the wave)
Describe how energy plays a role with power?
When a wave travels through a medium, it transport energy into that medium from the source.
What is intensity?
W m-2 or Wcm-2
measure of the amount of power flowing through a unit area at a 90 degree direction of propagation
What is intensity associated with?
with a wave increases with the pressure amplitude of the wave (I is proportional to pressure squared (p2))
what properties determine C?
C = √k/p
1) density/P (kg/m3)
2) stiffness/K (Pa)
What is density?
measure of weight of a standard volume of material
What is stiffness?
how well material resits being deformed
what is the normal US f in medical imaging?
2-15MHz
What is presented with low density and high stifness?
high C
What is presented with high density and low stiffness?
low C
What is Z mismatch?
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
What is the IRC equation
IRC = Ir / Ii = Pr2 / Pi2 = [Z2-Z1 / Z2 + Z1]2
Z abruptly changes at …., ratio of particle…. and particle ….. must also change
1) interface
2) pressure
3) velocity
However, the particle velocity and …. pressure cannot change abruptly at the interface with …. of medium, therefore must be continuous across interface
1) local
2) disruption
Why is US gel used?
no US would be transmitted
What is the equation for specific Z?
Z1 = Pi / Vi = Pr / Vr
particle pressure (p) & velocity (v) in incident wave i = incident r = reflected
What is RA (amplitude reflection coefficient)?
ratio of reflected to incident pressure
Why is RA important in US imaging?
determines the amplitude of echoes produced at bounderies with different tissue types
Z in the first medium will be more than Z in the second, true or false?
true
Z1 > Z2
RA is also described in terms of….. which is the ratio of intensities ….. and ……. waves
1) intensity reflection coefficient
2) reflected (Ir)
3) incident (Ii)
How would you calculate the intensity transmitted?
It = I i - I r
With I when flowing through CSA at interface, the energy flow of incident wave must be ….. and …
Conversed and split
What is this artefact? (image)
Reflection artefact
explain the principle behind reflection artefact (Law of reflection)?
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
… is determined at the interface by … at the interface
1) amplitude
2) reflection coefficient
What is specular reflection?
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)
Explain diffuse reflection?
occurs at rough surface, where target is the scale of a wavelength. The incident wave is reflected over range of angles
What is this image (a) showing?
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.
What is this image (b) showing?
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)
What is image (c) showing? gives diffuse reflection
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
Why does reflection occur?
change in acoustic properties (Z)
What is a Mirror artefact?
Image here
- 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
When does Scattering occur?
when target is greater than the wavelength
What is the correlation between change in Z values and reflection laws when talking about scattering?
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
What is the Rayleigh Scattering Equation?
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)
What is Rayleigh Scattering strongly dependent on?
- Size of d (target)
2. λ of wave
When does Rayleigh scattering occurs?
when λ»_space; diameter of scatterer
What has a major influence on US image apperance?
different tissue types scattering. Stronger backscatter can lead to to a brighter image produced.
Give an example of a substance/material property that has a influence on backscatter and why?
- 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 »_space; size than λ. Low Z mismatch between RBC and blood fluid
- -> act as Rayleigh scatters
2 important aspects of scattering: 1) US backscattered….. to transducer by small targets are small vs large….. resulting in …. echoes from parenchyma
1a) power
1b) interface
1c) weak
2) US scattered over a wide angle of …. targets, the final …. does not change with ….. of …… of the wave
2a) small
2b) appearance
2c) angle of incidence
Are contrast agents affected with scattering?
Yes.
But scatter strongly; slightly > size, high Z mismatch between the gas and blood
