Title
Elementary Principles
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What is sound and how is it produced?
Audible sound vs. ultrasound
Waves, “wavelength”
Pressure, intensity, power
Frequency and period
Acoustic impedance
Reflection
Review metrics
Production of sound
“Clink”
“Clink”
“Clink”
Particle vibrations
Talking
Air vibrations
Voice box
Ear drum
Sound
• A mechanical disturbance
propagating through a medium
– Mechanical: particle motion is involved
– Particle vibrations
– Energy is transmitted through the
medium
– Particles themselves do not propagate
through the medium.
Bell Jar Experiment
Generation of ultrasound
Piezoelectric ‘element’
Generation of ultrasound
Piezoelectric ‘element’
(vibrates when driven with an electrical signal)
Sound travels in “waves”
• A wave is an oscillating
disturbance that travels
through a medium
• Many forms of energy
travel in waves
• Sound travels as a wave
Two Types of Waves
Mechanical
Electromagnetic
ocean waves
radio waves
seismic waves
x-rays
sound waves
light waves
Mechanical Waves:
• characterized by physical motion
of particles in the medium
• cannot travel through a vacuum
• (Electromagnetic waves CAN
travel through a vacuum.)
Longitudinal
Particle motion (vibration) parallel to direction of wave travel
Particle motion (vibration) perpendicular to direction of wave trav
Picture of slinky
• “Compressional (or
longitudinal) wave
traveling along a
slinky
• Simply snap one end
back and forth
• Transverse wave
obtained by jerking
up and down
Ultrasound waves in tissue
• Sound waves used for
medical diagnosis are
LONGITUDINAL.
• Transverse waves are not
involved at all (at least not
until recently … “supersonic
imaging” and ARFI imaging
involve transverse waves,
though these are not
produced by the
transducer).
Other types of elasticity
imaging
• Acoustic radiation force imaging (ARFI)
– Tissue displacement created by energetic acoustic pulses
from the transducer
• SuperSonic Shear wave Imaging
– Energetic pulse
• =>shear wave
• Create shock front
– High speed imaging
• Tracks shear wave
– Reconstruct speed
• Related to elasticity
US Innovations,
Advances RSNA
2008
(Supersonic Imagine white paper, Jeremy Bercoff
www.supersonicimagine.fr)
Compression and rarefaction
Continuous Transmission
Schlieren Photography
Water
Light beam
This is a way to view sound waves. The compressions and
rarefactions disturb light propagating through the beam. One
can view these disturbances.
Compression and rarefaction
Compression: density is higher than normal
Rarefaction: density is lower than normal
Compression and rarefaction
Pulsed Transmission
Pressure amplitude
Amplitude
Amplitude: measure of the amount of change of
a time varying quantity.
Pressure amplitude
• pascals (Pa)
– 1 Pa = 1N/m2
• megapascals (MPa) (mega =
1,000,000)
• Other units
– Pounds/square inch (32 lb/in2 ~ 220 kPa)
(kilo = 1,000)
– mm of mercury (blood pressure)
– cm of water
PSI
kPa
30
207
35
240
40
280
45
310
Pressure of the atmosphere
• pascals (Pa)
• megapascals (MPa) (mega =
1,000,000)
• Other units
– Pounds/square inch (32 lb/in2 ~ 250 kPa)
(kilo = 1,000)
– mm of mercury (blood pressure)
– cm of water
Ways we describe amplitude
• High vs. low
• Loud vs. soft
• Strong echoes vs.
weak echoes
• Bright dots vs. dim
dots
Ways we describe amplitude
• High vs. low
• Loud vs. soft
• Strong echoes vs.
weak echoes
• Bright dots vs. dim
dots
Frequency
• Number of oscillations per
second
– By the source
– By the particles
• Called “pitch” for audible
sounds
• Expressed in hertz (Hz)
– 1 Hz = 1 cycle/s
– 1 kHz = 1,000 cycles/s
– 1 MHz = 1,000,000 cycles/s
Frequency
• Number of oscillations per second
– By the source
– By the particles
• Called “pitch” for audible sounds
• Expressed in hertz (Hz)
– 1 Hz = 1 cycle/s
– 1 kHz = 1,000 cycles/s = 103 cycles/s
– 1 MHz = 1,000,000 cycles/s = 106
cycles/s
– 2.5 MHz = 2,500,000 cycles/s = 2.5 x
106 cycles/s
– 7.5 MHz = 7,500,000 cycles/s = 7.5 x
106 cycles/s
Frequency
Supersonic vs. Ultrasonic
• Supersonic = faster that sound
• Ultrasonic = sound whose frequency
is above the audible (greater than
20 kHz)
Pressure amplitude
Amplitude
Amplitude: measure of the amount of change of
a time varying quantity.
WaveT Period
Distance
Pressure vs. distance at two
different times.
Wave motion at a specific point
in space. The wave variable
(pressure in this case) varies
over time. Period = time for 1
cycle.
Period vs. frequency
period
period
Wave Period
T
• Amount of time for 1 cycle
• Equal to the inverse of the
frequency
1
T
f
• What is the period for a 10 Hz wave?
Wave Period
T
• Amount of time for 1 cycle
• Equal to the inverse of the
frequency
1
1
1
T 
 s
f 10 / s 10
• What is the period for a 10 Hz wave?
Wave Period
T
• Amount of time for 1 cycle
• Equal to the inverse of the frequency
1
T
f
1
1
1
f  

 100/ s  100Hz
T 0.01s 1 / 100s
• If the period is 0.01 s, what is the
frequency?
Dividing fractions
• To divide 1 fraction (1/2) by another
(1/4)
– Invert the denominator
– Multiply the numerator by the inverted
denominator
1
2  1 4  4  2
2 1
2
1
4
Wave Period
T
• Amount of time for 1 cycle
• Equal to the inverse of the
frequency
1
T
f
Frequency
Period
1,000 Hz
1 ms
1 MHz
1 ms
10 MHz
0.1 ms
Metric System Unit Prefixes
Prefix Meaning Symbol
Example
micro
10-6
m
mm (micrograms)
milli
10-3
m
mm (millimeters)
centi
10-2
c
cm (centimeters)
deci
10-1
d
dB (decibel)
kilo
103
k
km (kilograms)
Mega
106
M
MHz
Please note: the sound emitted from your 3.5 MHz transducer is
3.5 MHz, not 3.5 mHz or 3.5 mhz!
Wave Period
T
• Amount of time for 1 cycle
• Equal to the inverse of the
frequency
1
T
f
Frequency
Period
1,000 Hz 1 ms
Period expressed as a fraction
1/1,000 s
1 MHz
1 ms
1/1,000,000 s
10 MHz
0.1 ms
1/10,000,000 s
Wavelength
Pressure fluctuations
l
• Wavelength is the distance between
any two corresponding points on
the waveform.
Wavelength vs. frequency
• As frequency increases, wavelength
decreases.
• Wavelength is inversely proportional
to frequency.
• If you double the frequency, the
wavelength is halved.
• If you triple the frequency,
wavelength is cut to 1/3 of the
original.
Wavelength depends on speed
of sound and Frequency
c sound speed
l 
f
frequency
Wavelength is “directly proportional” to sound speed.
(For a given frequency, if 1 medium’s sound speed is 2
times that of another, the wavelength for any frequency
will also be two times that of the other.)
Suppose the speed of sound is 330 m/s. For a 1 kHz
sound wave, what is the wavelength?
c
330m/s 330m/s
l 

s/c  .33 m
f 1,000c/s 1,000
Suppose the speed of sound is 330 m/s. For a 1 kHz
sound wave, what is the wavelength?
c 330m/s 330m/s
l 

s  .33 m
f 1,000/s 1,000
Suppose the speed of sound is 330 m/s. For a 1 kHz
sound wave, what is the wavelength?
c 330m/s 330m/s
l 

s  .33 m
f 1,000/s 1,000
The average speed of sound in soft tissue is 1,540
m/s. What is the wavelength for a 3 MHz sound
beam?
c
1540m/s
l 
 0.000513m 0.513mm
f 3,000,000/s
The average speed of sound in soft tissue is 1,540
m/s. What is the wavelength for a 3 MHz sound
beam?
c
1540m/s
l 
 0.000513m 0.513mm
f 3,000,000/s
1 meter=1,000 millimeters; 1 mm = 0.001 m
c
1540m/s 1,540,000m
m/s
l 

 .513mm
f 3,000,000/s
3,000,000/
s
When the speed of sound is 1,540 m/s, and
frequency is expressed in MHz:
1,540m/s  1,540,000mm/s
The frequency is “F” MHz = F,000,000 /s where F may
be 3, 5, 7.5, etc,
then
c 1,540,000mm/s 1.54mm
l 

f
F,000,000/s
F (MHz)
Wavelength vs. Frequency
For soft tissue, c=1,540 m/s
lsoft tissue
1.54mm

F(MHz)
1 MHz has a 1.54 mm wavelength
2 MHz has a ? mm wavelength.
Typical Wavelengths
F
2 MHz
2.5 MHz
5 MHz
7.5 MHz
10 MHz
Wavelength (l)
0.72 mm
0.62 mm
0.31 mm
0.21 mm
0.15 mm
In medical ultrasound, wavelengths usually are
less than a mm
Power
• Rate at which energy
comes out of the
transducer
• Includes energy
throughout the beam
• Units are in watts (W)
• Typical values
– 10 mW
– 80 mW
Intensity
Units are mW/cm2
W/m2
Relationship Between Intensity
and Amplitude
• Intensity, I is proportional to the
amplitude squared
I
A2
– if A is “1” I is 1
– if A is “2” I is 4
– if A is “3” I is 9, etc
Relationship Between Intensity
and Acoustic Pressure Amplitude
• Under “ideal” conditions (large distance from the source;
no reflectors around) Intensity, I is given by:
2
P
I
2 rc
–
P is the pressure amplitude (Pascals)
–
–
–
r is the density in the medium (kg/m3)
c is the speed of sound (m/s)
I is expressed in W/m2
Propagation Of Ultrasound
Through Tissue
Speed, attenuation, reflection,
refraction, scatter
Speed of Sound
• Determined by properties of the medium
– Stiffness
– Density
• Not determined by the source of sound
c
B
r
B=“Bulk modulus” (stiffness)
r=“density” (grams/cm3) (kilograms/m3)
c=speed of sound (m/s)
Relative Speed of Sound
• Solids
• Liquids
• Gases (ie, air)
fast
intermediate
slow
Speed of Sound
Tissue
Air
Fat
Water
Liver
Blood
Muscle
Skull bone
Speed of sound (m/s)
330
1460
1480
1555
1560
1600
4080
Speed of Sound
Tissue
Air
Fat
Water
Liver
Blood
Muscle
Skull bone
Speed of sound (m/s)
330
1460
1480
1555
1560
1600
4080
Note, the range of speeds at which sound travels in various soft tissues
(that do not contain air) is narrow.
Speed of Sound
• The average speed of sound
in soft tissue is taken to be
1540 m/s.
• This value is assumed in the
calibration of scanners.
• Scanners now have controls
that allow the sonographer
to select alternative values
Acoustic Impedance (Z)
• Important in reflection
• A property of the tissue
• Given by the speed of sound (c)
times the density r
Z  rc
• Unit is the rayl, 1 rayl = 1 kg/m2s
Suppose the density of liver is 1.061g/cm3. If the
speed of sound is 1,555 m/s, what is the acoustical
impedance of liver?
z  rc  1.061g / cm  1,555m/s
3
z  1,061kg/ m  1,555m/s
3
kg m
z  1649 10 3   (or kg / m 2s)
m
s
z  1649 106 kg / m 2s
6
Suppose the density of liver is 1.061g/cm3. If the
speed of sound is 1,555 m/s, what is the acoustical
impedance of liver?
z  rc  1.061g / cm  1,555m/s
3
z  1,061kg/ m  1,555m/s
3
kg m
2
z1 g/cm
1649

10


(or
kg
/
m
s)
3 = 1,000g/1,000cm
3 3 = 1,000kg/1,000,000cm3 = 1,000kg/m3
m
s
6
2
z  1649

10
kg
/
m
s
1cm
6
1m=100cm
1m x 1m x 1m = 100cm x 100cm x 100cm =1,000,000cm3
1m
Suppose the density of liver is 1.061g/cm3. If the
speed of sound is 1,555 m/s, what is the acoustical
impedance of liver?
z  rc  1.061g / cm 1,555m/s
3
z  1,061kg/ m 1,555m/s
3
kg m
z  1.64910 3   (or kg / m 2s)
m
s
z  1.649106 kg / m 2s
6
John William Strutt
“Lord Rayleigh”
(1842-1919)
• Unit is the rayl, 1 rayl = 1 kg/m2s
• If the density doubles, the impedance
doubles
• If the Speed of sound doubles, the
impedance doubles
Acoustic Impedance
Tissue
Air
Fat
Water
Liver
Blood
Muscle
Skull bone
Impedance (Rayls))
0.004 x 106
1.34 x 106
1.48 x 106
1.65 x 106
1.65 x 106
1.71 x 106
7.8 x 106
Acoustic Impedance
Tissue
Air
Fat
Water
Liver
Blood
Muscle
Skull bone
Impedance (Rayls))
0.004 x 106
1.34 x 106
1.48 x 106
1.65 x 106
1.65 x 106
1.71 x 106
7.8 x 106
Note, the range of impedances of soft tissues (that do not contain air) is
relatively narrow.
Ways we describe amplitude
• High vs. low
• Loud vs. soft
• Strong echoes vs.
weak echoes
• Bright dots vs. dim
dots
Reflection
• Partial reflection of a sound
beam occurs at tissue
interfaces.
• Interfaces are formed by
tissues that have different
impedances.
• Examples:
– Muscle-to-fat
– Bone-to muscle
– Red blood cell-to-plasma
Reflection
Types of Reflectors
•
Specular
– Large
– Smooth
•
Diffuse reflecting interface
– Echoes travel in all directions
•
Scatter
– Small interfaces
– Scattered echoes travel in different
directions.
Reflection Coefficient, R
R is the ratio of the amplitude reflected to the incident amplitude. The
greater R is, the more sound gets reflected, and the higher is the
amplitude. Also, the greater R is, the less gets transmitted to deeper
tissues.
Z 2  Z1
R
Z 2  Z1
Impedance Mismatch
Another way to express “Z2 – Z1”
• Small mismatch
– Weak echo
– Most sound gets
transmitted through
• Large mismatch
– Strong echo
– Less sound gets
transmitted through
Compute the reflection coefficient for an interface
formed by muscle and air. (Sound is traveling
through muscle and encounters an air interface)
Z 2  Z1 0.0004106  1.7 106 0.0004 1.7
R


 .99
6
6
Z 2  Z1 0.000410  1.7 10 0.0004 1.7
Amplitude Reflection
Coefficients
Muscle-liver
Fat-muscle
Muscle-bone
Muscle-air
.02
.1
.64
.99
Note, the reflection coefficient between soft tissues is relatively weak;
reflection at interfaces between soft tissue and bone is much stronger.
Reflection at interfaces between tissue and air approaches 100%.
Tissue-to-air interface
This is why we have to use coupling gel on the patient!
Nonperpendicular beam
incidence
Reflected beam does not
travel back to transducer
For a perfectly smooth
interface, qr = qi
Nonperpendicular beam
incidence
Reflected beam does not
travel back to transducer
Echo amplitude depends
strongly on the orientation
of the beam with respect to
the interface!
Nonperpendicular beam
incidence
Reflected beam does not
travel back to transducer
Echo amplitude depends
strongly on the oprientation
of the beam with respect to
the interface!
Assignment: bring in
examples of echo
amplitudes that vary with
angle of incidence.
Signal Effects
The transducer
serves both as the
transmitter and
echo detector.
Specular reflector
Diffuse reflector
Fetal skull only
partially outlined
because of
unfavorable incident
angle.
“Specular Highlight”
is a term being coined
to describe this
situation.
Refraction in water
Conditions for Refraction
•Beam is incident
obliquely
•Sound speeds are
different
Snell’s Law
Sine of an angle
angle A
Compute the refracted angle if the incident beam is
propagating through muscle and the transmitted beam is
through fat. The incident beam angle is 30 degrees.
c2
1460m / s
sin(q t )  sin(q i )  sin(30)
c1
1600m / s1
1460m / s
sin(q t )  0.5
 0.45625
1600m / s1
qi
So, the angle whose sin is 0.45626 is
found using
qt  arcsin(0.45625)  27.1degrees
qt
Change
(2.9
degrees)
Change in Beam Direction for 30o angle
of incidence at a tissue interface
•
•
•
•
Bone-soft tissue
Muscle-fat
Muscle-fluid
Muscle-blood
19.1o
2.9o
1.2o
0.8o
Refraction is strongest at interfaces where
there are large changes in the speed of sound.
Scatter can be called multi-directional reflection.
Diffuse Reflector
Scatterer
Scattering of ultrasound
Scatter can be called multi-directional reflection.
Diffuse Reflector
Scatterer
Gray Scale Image
Lung/liver easily
differentiated because of
differences in scattering
levels
“Echogenic”
• Tendency of a tissue to produce echoes,
usually from scattering
• Terms
– Echogenic
– Hypoechoic
– Hyperechoic
– Anechoic
– isoechoic
Angle Effects
Diffuse
Reflector
Image contrasting specular vs
scattering
Diffuse reflector?
Likely, most
interfaces have
some degree of
surface
roughness.
Presents a bit of a
diffuse surface.
Echoes from diaphragm highly dependent on orientation
Echoes from liver are not.
Rayleigh Scattering
• Objects much smaller than the
wavelength
• Scattering varies with the fourth
power of the frequency (I a f4)
– Doubling the frequency increases the
scattered signal intensity by 24 = 2 x 2 x
2 x 2 = 16!
Rayleigh Scattering (blood)
• Objects much smaller
than the wavelength
• RBC’s are about 8
micrometers in
diameter
• They are considered
Rayleigh scatterers in
medical ultrasound
10 mm
100 mm; wavelength for 15.4 MHz ultrasound
Attenuation
Causes of Attenuation
•
Reflection and scatter at
interfaces
– Very small contribution within organs
– Can be significant at calcifications,
stones
•
Absorption
– Beam energy converted to heat
– Diagnostic beams usually cause
negligible heating
Attenuation
The Attenuation Coefficient
(Amount of attenuation per unit distance)
Units are dB/cm
Decibels
• Units that allow one to compare the
intensity or amplitude of one signal
relative to that of another.
• (The loudness level of audible
sounds often is given in decibels.)
Decibels
• To express the relationship between two
intensities, I2 and I1, in dB,
dB = 10 log(I2 /I1 )
– Take ratio
– Take the log of the ratio
– Multiply by 10
Decibels
• Example, let I2 be 100 I1
• dB = 10 log(I2 / I1)
• dB = 10 log(100/1)
• dB = 10 log(100) = 10 x 2 = 20
• When the intensity is increased by 20 dB, it
is increased by 100 times!
Amplitude ratio
A2/A1
1
1.414
2
4
10
100
1000
1/
2
1/
10
1/
100
Log A2/A1 dB
0
0.15
0.3
0.6
1
2
3
0.3
1
2
0
3
6
12
20
40
60
6
20
40
Intensity ratio
I2/I1
Log I2/I1
1
0
2
0.3
4
0.6
16
1.2
100
2
10,000 4
1,000,000 6
1/
0.6
4
1/
2
100
1/
4
10,000
Attenuation
The Attenuation Coefficient
(Amount of attenuation per unit distance)
Units are dB/cm
Typical attenuation coefficients
(dB/cm)
•
•
•
•
•
•
Water
Blood
Liver
Muscle
Skull bone
Lung
0.002 dB/cm
0.18
0.5
1.2
20
41
Values are at 1 MHz
Adult Liver
4 MHz
7 MHz
Dependence on Frequency
Frequency Dependence
(liver)
•1 MHz
•2 MHz
•4 MHz
0.5 dB/cm
1.0 dB/cm
2.0 dB/cm
To find the attenuation at a given
frequency, use simple ratios.
Calculate attenuation
Calculate attenuation
•
•
•
•
If a 3 MHz ultrasound beam travels through 5
cm of muscle, how much is the beam
attenuated? (The AC of muscle at 1 MHz is 1.2
dB/cm)
First, determine the attenuation coefficient at
3 MHz. It is 3/1 x 1.2 dB/cm, or 3.6 dB/cm.
Then, the total attenuation is just the AC times
the distance, or
Attenuation = 3.6 dB/cm x 5 cm = 18 dB
Attenuation terms:
“attenuating”
Attenuation terms:
Enhancement
Attenuation terms: Shadowing
Units commonly used in
ultrasound
Quantity
Unit
Abbreviation
Length
Area
meter,
m, cm
centimeter
square meters m2
Volume
cubic meters
m3
Time
seconds
s
period
seconds
s
Units commonly used in
ultrasound
Quantity
Unit
Abbreviation
mass
gram
g
speed
meter per second m/s
frequency
cycles per second s-1 (Hz)
power
watts
intensity
Watts per square W/cm2
centimeter
W