physics basics

1. US PHYSICS (2)
Dr. Kamal Sayed MSc US UAA
Speed of sound/amplitude /intensity/power/OK
grey scale/go return time/range equation/impedance

2. What is the principle of ultrasound?
An electric current passes through a cable to the transducer and is applied to the crystals, causing them to
deform and vibrate. This vibration produces the ultrasound beam. The frequency of the ultrasound waves
produced is predetermined by the crystals in the transducer.
•
Speed of sound (propagation speed)
•
Is the rate that sound travels through a medium measured in
meters per second, mm/microsc
•
Sp of sound is determined by only the medium (density & stiffness)
•
Density (mass per unit volume)
‫الجزيئات‬ ‫عدد‬ ‫زيادة‬ ‫او‬ ‫الكتلة‬
•
is related to weight, ie crowd of molecules which decreases speed
of sound
•
Stiffness
‫الجزيئات‬ ‫ترابط‬ ‫قوة‬
•
is related to ‘squishability’ ie ability to be compressed
•
•

3. •
sound speed = frequency (Hz) x wavelength (meters)
•
sound with a frequency of 5MHz and sound with a
•
frequency of 3MHz travel at the same propagation speed
•
if they are traveling through the same medium
•
. speed in m/s = frequency (Hz) x wavelength (meters)

4. •
Wavelength is determined by :
•
transd freq + speed
•
Speed is determined by medium
•
Period/ frequency/amplitude/power/intensity : are
determined by sound source
•
Period & freq are inversely related to each other
•
Amplitude/power/intensity are directly related to each other
•
Slide (5)

5. WAVELENGTH is the distance from the beginning of a cycle to the end of that cycle
(the distance over which one cycle occurs)

6. •
Speed of sound is very fast through stiff media & slower
through that are more compressible : 4200 m/s in bone &
1540 m/s in soft tissue & more slower through gaes
•
That is because the molecules of stiff media are tightly &
strongly bound to each other by the intermolecular elastic
bonds. When pressure is applied to medium the 1ST molecule
vibrates & affects the next molecule quickly til the last in short
time & vice versa.
•
Thus speed of sound is directly proportional to density &
inversely proportional to stiffness

7. •
Thus : speed of sound = stiffness/density ie speed of sound is
directly proportional to stiffness & inversely proportional to
Density
The denser the media (more molecules & more wt) the slower
the speed of sound because :
1- the greater mass per unit volume require more force to move
the particles (molecules) from their resting position .
2- once the molecules are vibrating the denser medium has
more inertia & it is more difficult to cause particles to change
direction with changes in the direction of the pressure wave
because particle motion is not smooth.

8. •
Some exceptions to the rule :
•
Speed of sound in water is 1480 m/s & in mercury 1450 m/s in
spite that mercury is more solid than water :
•
That is because mercury is very dense so speed of sound in
mercury is slower than in water

9. •
Speed of sound in soft tissue is 1540 m/s.
•
This figure is called calibration speed & used by the US
machine to translate time data into distance on the display :
for example students who came earlier will sit on the 1ST seats
then followed by who came after & after & so on. In that way
we translated arrival time of students into distances according
to their arrival time :
•
Thus US machine sends a pulse & starts receiving the echoes.
•
The 1ST echo to arrive is placed by the US machine on the top
of the screen then followed by the next & then followed in
turn by the next echo & so on.

10. •
How US machine performs this process of translating time
data into distances ???
•
The range equation (speed = distance/time) is used by the US
machine to arrange the processing of the image on the
display.
•
The US machine operate the pulse-echo principle by sending
a pulse the waits till 1ST echo is received.
•
This waiting time is called off time to receive the coming
echoes by the probe, assessed by the US system , then sends
another pulse.
•
This off time is just a fraction of a second.
•

11. •
When echoes return & picked by probe into the US system to
be assessed for tow factors in order to process the imagee :
•
1- amplitude (strength of the echo) to get the degree of
brightness :
•
If echo is very strong the image will be bright (echogenic).
•
If echo is medium level image will be grey (hypoechoic).
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If no echoes the image will be black (anechoic).
•
this is the so called GREY SCALE which means distribution
from absolute bright to absolute black.
•

12. •
Grey scale means distribution of image color from absolute
•
bright to absolute black
when area in the image is very bright indicates strong echoes
& more reflection.
2- Go return time
To complete the image on the display the US system assesses the
echoes for time between transmission & reception (go return
time) to calculate the depth (distance) of the (reflector) area
scanned.
The 1ST echo is placed on the top of the display & so on.
For example :

13. •
Placing the probe on the epigastric area, the 1st structure to
be seen is anterior abdominal wall then pancreas the splenic
vein then SMA then below it we see Aorta then vertebral
body below Aorta & so on.
•
To calculate the depth (distance) of the reflector scanned the
US system requires to know the time & speed.
•
As speed is calibrated already within the US system , there is
also a clock generator within the system & it automatically
calculated the GO RETURN time therefore the distance of the
reflector is also automatically calculated by the system as :
•
(Range equation) Distance = speed X time

14. •
Range equation is used to convert speed of sound & time
information into distance for the correct display of echoes in
the image.
•
Deep echoes have long go return time & placed on the
bottom of the screen while superficial echoes will have short
•
go return time & placed on the top of the screen.
•
sound will NOT always propagate with same speed
•
1540 m/s as calibrated in the system, & may pass through
some tissues (eg lipoma)which causes alteration to speed.
•
If speed decreased, location of reflector will change & will be
far away.

15. •
& if sound speed is increased within the soft tissue the
structure (reflector) will appear closer than the that calibrated
by the system
•
Thus change of the calibrated sound speed will result in the so
called SPEED ERROR ARTIFACT.
•
In soft tissue US takes (13 micro seconds per cm) i.e
•
US travels 1 cm of soft tissue (to & fro = go return time) in 13
microseconds
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Therefore to calculate reflector distance :
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Speed of sound X go return time / 2
•

16. examples :
# if reflector distance is 10 mm & Speed of sound is 1.54 mm/ms
in go return time
•
we can calculate the Go Return time : distance/speed
(range
equation) = 1.54/2= 0.77
•
10 mm/0.77=0.12987 (13) microseconds
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# if go return time in soft tissue is 104 microsec how deep is
the interface that will produce the echo ?
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104/13 = 8 cm

17. Power is the rate at which work is done
•
Intensity is concentration of power.
•
Amplitude is the maximum variation of an acoustic variable &
measured from base to peak in the positive or in the negative
direction.
•
Amplitude measures the degree of change within a medium
when sound passes through it & relate to severity of
disturbance (high 1ST pressure)so in this way the amount of
energy in a sound wave can be determined.
•
•

18. •
Amplitude is the difference between the mean resting value
when no sound is applied & maximum value of an acoustic
variable.
•
Amplitude relates to the sound wave i.e very strong sound
wave is a wave with high amplitude.
•
For audible sound amplitude is associated with loudness of
the sound
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So amplitude can be described in terms of acoustic variables
pressure, density, temperature & particle motion.
•
The most common variable to describe amplitude is pressure

19. •
Unit of amplitude depends on acoustic variable being
measured (most commonly pressure) pascal.
•
Initial amplitude of sound wave is determined by the US
system. Whenever we apply greater power (voltage) to the
transducer from US pulser the greater the initial amplitude of
US wave produced by the transducer . whenever we increase
the power voltage we increase the intensity.
•
Increasing the power will improve image quality but will be
against ALARA principle (As Low As Reasonably Achievable)
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We can improve image quality by using TGC & overall gain

20. •
Amplitude decreases as US wave propagates through tissues
& this loss in amplitude is the so called ATTENUATION which is
gradual loss of energy.
•
So increasing the amplitude of outgoing US (newer machines)
wave will increase the sensitivity & effectively increase the
depth (penetration) & allow the system to detect small
structures in most distant areas. (gain knob controls received
echoes).
•

21. •
Power, Amplitude & intensity are all related to the size &
strength of US wave : high amplitude sound wave means
strong power & high intensity.
•
Power is the rate (at which work is done) of flow of energy
through a given area.
•
in US power is the rate of work performed by production of
US wave by the transducer.
•
US wave contains mechanical energy which is used to displace
particles in the medium. The more power the greater the
capacity to displace particles tp perform this work ie to
displace particles.

22. •
So the flow of energy through the transducer to the medium
depends on power.
•
Unit of power is watt or any subunit of watt .
•
We can use also another unit called decible to compare power
or intensity level at the start & at the end.
•
Power is also controlled by US system.
•
Attenuation also causes power to decrease at a given rate.
•
Power is proportional to the amplitude of the wave squared.
•
Power = amplitude squared.
•
Power decreases as amplitude decreases

23. •
Intensity
‫الشدة‬
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Is power per unit area or concentration of power in the sound
beam .
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It also related to strength of the sound beam :
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very strong sound beam means beam with high intensity.
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Therefore intensity = power/area
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i.e intensity is directly proportional to power & inversely
related to area.
•
Increased intensity (by decreasing the area) will increase the
resolution.

24. •
Intensity is proportional both to power and to amplitude
squared
•
US beam starts wide the becomes narrow in the middle then
again becomes wide – the middle narrow area is the area of
high intensity & gives the best resolution & good image
quality & contrast.
•
Therefore we keep the the area of interest at the level of
narrowest sound beam the so called FOCAL ZONE.
•
Intensity has different values due to different attenuation that
is to say intensity in near field differs from that in the far field.

25. •
Also intensity differs as time changes ie intensity differs in the
1ST second from intensity in the 6TH second & so on.
•
Intensity also changes both spatially (with depth changes)
&
temporally (with time changes) that is to say the intensity
of
pulsed us beam is not uniform in space nor in time.
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SPATIAL INTENSITY
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Is intensity related to depth. Here intensity is not uniform in
diameter, width or area as the pulsed sound travels through
different depths from the transducer.
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SPI is measured at the center of the beam

26. •
That is, the strongest intensity is in the center of the beam
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and gradually reduces as the beam spreads out
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Pressure amplitude variations are measured with a
hydrophone (slide 29) & include peak compression &
rarefaction variations with time({A} in figure next slide 28)
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Temporal intensity variations of pulsed US vary widely from
temporal peak & temporal average values.
•
PA intensity represents the average intensity measured over
the pulse duration ({B} in slide 28)
•
•

27. •
Spatial intensity variations of pulsed ultrasound
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are described by the spatial peak value and
•
the spatial average value, measured over the ultrasound
beam( {C} in slide 28)
•
•
•
•

29. hydrophone for amplitude measurement

30. •
The changing shape of the sound beam is determined by
several factors
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The highest peak intensity is taken from the center of the
spatial beam.
•
Two spatial intensities are there :
•
1- spatial peak : the highest spatial intensity & found in the
center of the beam at the focal point
•
2- spatial average : is the average intensity across the face of
the entire beam & found in the transducer face (average of
highest intensity at the focal zone & the lowest intensity in
the periphery)

31. •
Temporal intensity (intensity over time) is not constant
there is variation due to the on off pulsed US.
•
System sends the pulse the waits to collect all the echoes.
•
It is of 3 types :
•
1- temporal peak (SP) () highest intensity recorded during the
time of transmission
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2- pulse average (SA) : the average intensity recorded during
the pulse duration (the on time) we take the average between
highest & lowest
•

32. •
3- temporal average (TA) : the lowest. It is the average
intensity recorded over all time from transmission to
reception ie during the whole on off cycle. & when it returns it
will be very weak.
•
For intensity it must be specified
•
as to where and when the sound beam was measured. The
spatial intensities,
•
spatial average (SA), and spatial peak (SP), refer to where the
•
beam was measured. The SP intensity is measured at the
center of the
•
beam.

33. •
Relationship of power and amplitude.
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P = A squared
•
Formula for intensity.
•
P (W)/AREA sq cm
=
I
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Formula for impedance
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Z = PC
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Impedance
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Any medium through which sound is traveling will offer some
amount of resistance
•
to the sound.

34. •
The resistance to the propagation of
•
sound through a medium is called impedance (z).
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The amount of impedance depends on the density (p) & the
propagation speed (c) of the medium.
•
Impedance is measured in units Called RAYLS.
•
RAYLS are the product of the density of medium &
propagation speed of medium.

35. The variations in impedance
•
help create reflections at the interface between adjacent
tissues.
•
Assuming the beam strikes the interface at a 90 angle and
there exists
•
a large impedance difference between two tissues, there will
be a strong
•
reflection and a well-defined boundary displayed on the
imaging screen.
•
If impedance difference between 2 media is subtle there will
be a weaker reflection. If impedances are the same, no
reflection occurs

36. •
Continuous Wave US (CW)
•
Sound that is continuously transmitted.
•
we cannot image with CW US though it is often employed in
Doppler studies
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A device with Continuous transmission with no off time.
•
There are Two groups of crystals. the probe divided into two
divisions. One group for transmission & the other group for
reception.

37. Review questions
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1. Which of the following is described as the ability of an object to resist
•
compression and relates to the hardness of a medium?
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a. Stiffness
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b. Density
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c. Pressure
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d. Inertia
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2. An increase in pulse repetition frequency would lead to:
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a. An increase in duty factor
•
b. An increase in pulse duration
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c. An increase in the number of cycles
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d. A decrease in resolution
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3. Which of the following would have the highest propagation speed?
•
a. Air
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b. Bone
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c. Soft tissue
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d. Water

38. •
•
4. Which of the following would have the lowest propagation
speed?
•
a. Water
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b. Soft tissue
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c. Bone
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d. Lung tissue
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5. As imaging depth increases, the pulse repetition frequency must:
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a. Not change
•
b. Increase
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c. Decrease
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d. Pulse repetition frequency does not relate to imaging depth

39. •
Lateral Resolution
A. Lateral Resolution (LR)
Ability to separate two reflectors as two reflectors
perpendicular to beam
LR (mm) = Beam diameter (mm); narrow beams provide
better resolution.
LR is best at beams focal zone or the end of the Near Field.
- Also known as L.A.T.A. (Lateral, Angular, Tranverse and
Azimuthal)
Slide (41/42)

40. Factors affecting LR : width of the beam, distance from the
transducer, frequency, side and grating lobe levels.
Side lobes and grating lobes are both unwanted parts of
the US beam emitted off axis that produce image artifacts due
to error in positioning the returning echo.
•
Now, how about when these reflectors don’t produce distinct
echoes in an image?
•
How would it affect the anatomic information?
•
What does it cause?
•
And how would it resolve?
•
•

41. normally

42. normally

43. •
Lateral Resolution Artifact occurs when two reflectors are
perpendicular to the beam’s main axis create one reflection
on the image.
It is also called point spread artifact.
Slide (43/44)
****************************************
•
Closed arrow: beamwidth is about 2mm,
•
Open arrow: beamwidth is about 10 mm,
•
Hence, the structures appear “smeared out” as the
depth increases (and anything beyond 2mm).
•
Slide (46)

44. Lateral Resolution Artifact occurs when two reflectors are perpendicular to the beam’s main
axis create one reflection on the image.
It is also called point spread artifact.

45. Lateral Resolution Artifact occurs when two reflectors are perpendicular to the beam’s main axis create one
reflection on the image.
It is also called point spread artifact.

47. •
Cause:
•
It creates one reflection on the image from two closely
spaced reflectors if the beam’s width used is wider than the
space between two reflectors.
•
What assumption:
•
Reflections arise only from structures positioned in the
beam’s main axis.
•
Description of Artifact:
•
Unresolved; it means it displays a small reflector a wide
line rather than a narrow dot.

48. •
How to prevent:
•
Use transducers with higher frequency which provides
narrower beams. Best at beams focus or the end of the Near
Zone (slides 41/42).
•
•
Hindrance, Helpful or Both- explain:
•
Hindrance, because there would be important anatomic
information that are missing.

49. •
Axial Resolution (slide 50)
•
- Ability to separate two reflectors as two reflectors
accurately along the beam axis.
•
- Also known as L.A.R.D. (Longitudinal, Axial, Range or
Radial, Depth)
•
- Associated with: a. Shorter spatial pulse length
•
b. Shorter pulse duration
•
c. Higher frequencies
•
d. Fewer cycle per pulse
•
e. Lower numerical values

50. 0.3 mm wavelength
0.9 mm pulse length