title elementary principles what is sound and how is it produced? audible sound vs. ultrasound...
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Title
Elementary Principles
• 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
Voice box
Air vibrations
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
ocean waves
seismic waves
sound waves
Electromagnetic
radio waves
x-rays
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.)
LongitudinalParticle motion (vibration) parallel to direction of wave travel
Particle motion (vibration) perpendicular to direction of wave travel
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).
US Innovations, Advances RSNA 2008
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
(Supersonic Imagine white paper, Jeremy Bercoffwww.supersonicimagine.fr)
Compression and rarefactionContinuous Transmission
Schlieren Photography
Water
This is a way to view sound waves. The compressions and rarefactions disturb light propagating through the beam. One can view these disturbances.
Light beam
Compression and rarefaction
Compression: density is higher than normalRarefaction: density is lower than normal
Compression and rarefactionPulsed 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.
Wave PeriodT
Wave motion at a specific point in space. The wave variable (pressure in this case) varies over time. Period = time for 1 cycle.
Pressure vs. distance at two different times.
Distance
Period vs. frequency
period
period
Wave Period
• Amount of time for 1 cycle• Equal to the inverse of the
frequency
• What is the period for a 10 Hz wave?
fT
1
T
Wave Period
• Amount of time for 1 cycle• Equal to the inverse of the
frequency
• What is the period for a 10 Hz wave?
T
ssf
T10
1
/10
11
Wave Period
• Amount of time for 1 cycle• Equal to the inverse of the frequency
• If the period is 0.01 s, what is the frequency?
T
Hz100s/100s100/1
1
01.0
11
1
sTf
fT
Dividing fractions
• To divide 1 fraction (1/2) by another (1/4)– Invert the denominator– Multiply the numerator by the inverted
denominator
224
14
21
41
21
Wave Period
• Amount of time for 1 cycle• Equal to the inverse of the
frequency
fT
1
Frequency Period
1,000 Hz 1 ms
1 MHz 1 ms
10 MHz 0.1 ms
T
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
• Amount of time for 1 cycle• Equal to the inverse of the
frequency
fT
1
Frequency Period Period expressed as a fraction
1,000 Hz 1 ms 1/1,000 s
1 MHz 1 ms 1/1,000,000 s
10 MHz 0.1 ms 1/10,000,000 s
T
Pressure fluctuationsWavelength
• Wavelength is the distance between any two corresponding points on the waveform.
l
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
frequency
speed sound
f
c
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?
m .33s/c 1,000
330m/s
c/s 1,000
330m/s
f
c
Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength?
m .33s 1,000
330m/s
/s1,000
330m/s
f
c
Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength?
m .33s 1,000
330m/s
/s1,000
330m/s
f
c
The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam?
0.513mm513m000.0 /s3,000,000
1540m/s
f
c
The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam?
0.513mm513m000.0 /s3,000,000
1540m/s
f
c
.513mm s3,000,000/
m/s1,540,000m
/s3,000,000
1540m/s
f
c
1 meter=1,000 millimeters; 1 mm = 0.001 m
When the speed of sound is 1,540 m/s, and frequency is expressed in MHz:
mm/s000,540,1m/s540,1
The frequency is “F” MHz = F,000,000 /s where F may be 3, 5, 7.5, etc, then
(MHz) F
mm 1.54
/sF,000,000
mm/s 1,540,000
f
c
Wavelength vs. Frequency
For soft tissue, c=1,540 m/s
1 MHz has a 1.54 mm wavelength
2 MHz has a ? mm wavelength.
F(MHz)
1.54mmesoft tissu
Typical Wavelengths
F2 MHz
2.5 MHz5 MHz
7.5 MHz10 MHz
Wavelength ( )l0.72 mm0.62 mm0.31 mm0.21 mm0.15 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
– if A is “1” I is 1– if A is “2” I is 4– if A is “3” I is 9, etc
I A2
Relationship Between Intensity and Acoustic Pressure Amplitude
• Under “ideal” conditions (large distance from the source; no reflectors around) Intensity, I is given by:
– 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
c2I
2
P
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
B
c B=“Bulk modulus” (stiffness)r=“density” (grams/cm3) (kilograms/m3)c=speed of sound (m/s)
Relative Speed of Sound
• Solids fast• Liquids intermediate• Gases (ie, air) slow
Speed of Sound
TissueAirFat
WaterLiverBlood
MuscleSkull bone
Speed of sound (m/s)
330146014801555156016004080
Speed of Sound
TissueAirFat
WaterLiverBloodMuscle
Skull bone
Speed of sound (m/s)330146014801555156016004080
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
• Unit is the rayl, 1 rayl = 1 kg/m2s
cZ
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?
sm/kg 101649z
s)m/kg(or s
m
m
kg101649z
m/s555,1m/1,061kgz
m/s555,1cm/g061.1
26
23
6
3
3
cz
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?
sm/kg 101649z
s)m/kg(or s
m
m
kg101649z
m/s555,1m/1,061kgz
m/s555,1cm/g061.1
26
23
6
3
3
cz
1 g/cm3 = 1,000g/1,000cm3 = 1,000kg/1,000,000cm3 = 1,000kg/m3
1m=100cm1m x 1m x 1m = 100cm x 100cm x 100cm =1,000,000cm3
1m
1cm
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?
sm/kg 10649.1z
s)m/kg(or s
m
m
kg10649.1z
m/s555,1m/1,061kgz
m/s555,1cm/g061.1
26
23
6
3
3
cz
• 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
John William Strutt“Lord Rayleigh”(1842-1919)
Acoustic Impedance
TissueAirFat
WaterLiverBloodMuscle
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
TissueAirFat
WaterLiverBlood
MuscleSkull 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 106Note, 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
12
12
ZZ
ZZR
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.
Impedance MismatchAnother 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)
99.7.10004.0
7.10004.0
107.1100004.0
107.1100004.066
66
12
12
ZZ
ZZR
Amplitude Reflection Coefficients
Muscle-liverFat-muscleMuscle-
boneMuscle-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 EffectsThe transducer serves both as the transmitter and echo detector.
Diffuse reflectorSpecular 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
angle A
Sine of an angle
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.
45625.0/1600
/14605.0)sin(
/1600
/1460)30sin()sin()sin(
1
11
2
sm
sm
sm
sm
c
c
t
it
degrees1.27)45625.0arcsin( t
So, the angle whose sin is 0.45626 is found using
qt
qi
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 ultrasoundScatter 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
Echoes from diaphragm highly dependent on orientationEchoes from liver are not.
Diffuse reflector?Likely, most interfaces have some degree of surface roughness. Presents a bit of a diffuse surface.
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
Units are dB/cm
The Attenuation Coefficient (Amount of attenuation per unit distance)
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 Intensity ratioA2/A1 Log A2/A1 dB I2/I1 Log I2/I1
1 0 0 1 01.414 0.15 3 2 0.32 0.3 6 4 0.64 0.6 12 16 1.210 1 20 100 2100 2 40 10,000 41000 3 60 1,000,000 61/2 -0.3 -6 1/4 -0.61/10 -1 -20 1/100 -21/100 -2 -40 1/10,000 -4
Attenuation
Units are dB/cm
The Attenuation Coefficient (Amount of attenuation per unit distance)
Typical attenuation coefficients (dB/cm)
• Water• Blood• Liver• Muscle• Skull bone• Lung
0.002 dB/cm0.180.51.22041
Values are at 1 MHz
Adult Liver
7 MHz4 MHz
Dependence on Frequency
Frequency Dependence (liver)
•1 MHz 0.5 dB/cm•2 MHz 1.0 dB/cm•4 MHz 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 meter, centimeter
m, cm
Area 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 W
intensity Watts per square centimeter
W/cm2