1. Title

2. 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

3. Production of sound
“Clink”
“Clink”
“Clink”

4. Particle vibrations

5. Talking
Air vibrations
Voice box
Ear drum

6. 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.

7. Bell Jar Experiment

8. Generation of ultrasound
Piezoelectric ‘element’

9. Generation of ultrasound
Piezoelectric ‘element’
(vibrates when driven with an electrical signal)

10. 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

12. Two Types of Waves Mechanical ocean waves seismic waves sound waves
Electromagnetic
radio waves
x-rays
light waves

13. Mechanical Waves:
characterized by physical motion of particles in the medium
cannot travel through a vacuum
(Electromagnetic waves CAN travel through a vacuum.)

14. Longitudinal
Particle motion (vibration) parallel to direction of wave travel
Particle motion (vibration) perpendicular to direction of wave travel

15. 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

16. 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).

17. 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

18. Compression and rarefaction
Continuous Transmission

19. 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.

20. Compression and rarefaction
Compression: density is higher than normal
Rarefaction: density is lower than normal

21. Compression and rarefaction
Pulsed Transmission

22. Pressure amplitude Amplitude
Amplitude: measure of the amount of change of a time varying quantity.

23. Pressure amplitude pascals (Pa) megapascals (MPa) (mega = 1,000,000)
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

24. PSI
kPa 30
207 35
240 40
280 45
310

25. 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 25

26. Ways we describe amplitude
High vs. low
Loud vs. soft
Strong echoes vs. weak echoes
Bright dots vs. dim dots

27. Ways we describe amplitude
High vs. low
Loud vs. soft
Strong echoes vs. weak echoes
Bright dots vs. dim dots

28. 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

29. 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

30. Frequency

31. Supersonic vs. Ultrasonic
Supersonic = faster that sound
Ultrasonic = sound whose frequency is above the audible (greater than 20 kHz)

32. Pressure amplitude Amplitude
Amplitude: measure of the amount of change of a time varying quantity.

34. Wave Period T 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.

35. Period vs. frequency
period
period

36. Wave Period Amount of time for 1 cycle
Equal to the inverse of the frequency
What is the period for a 10 Hz wave?

37. Wave Period Amount of time for 1 cycle
Equal to the inverse of the frequency
What is the period for a 10 Hz wave? 37

38. 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? 38

39. Dividing fractions To divide 1 fraction (1/2) by another (1/4)
Invert the denominator
Multiply the numerator by the inverted denominator

40. Wave Period Amount of time for 1 cycle
Equal to the inverse of the frequency
Frequency
Period
1,000 Hz
1 ms
1 MHz
10 MHz
0.1 ms

41. Metric System Unit Prefixes
Meaning
Symbol
Example
micro
10-6 m
mm (micrograms)
milli
10-3
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!

42. Wave Period Amount of time for 1 cycle
Equal to the inverse of the frequency
Frequency
Period
Period expressed as a fraction
1,000 Hz
1 ms
1/1,000 s
1 MHz
1/1,000,000 s
10 MHz
0.1 ms
1/10,000,000 s

43. Pressure fluctuations
Wavelength l
Wavelength is the distance between any two corresponding points on the waveform.

44. 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.

45. Wavelength depends on speed of sound and 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.)

46. Suppose the speed of sound is 330 m/s
Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength?

47. Suppose the speed of sound is 330 m/s
Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength? 47

48. Suppose the speed of sound is 330 m/s
Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength? 48

49. The average speed of sound in soft tissue is 1,540 m/s
The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam?

50. 1 meter=1,000 millimeters; 1 mm = 0.001 m
The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam?
1 meter=1,000 millimeters; 1 mm = m 50

51. When the speed of sound is 1,540 m/s, and frequency is expressed in MHz:
The frequency is “F” MHz = F,000,000 /s where F may be 3, 5, 7.5, etc,
then

52. 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.

53. 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

54. 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

55. Intensity
Units are mW/cm2
W/m2

56. 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

57. 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 57

58. Propagation Of Ultrasound Through Tissue
Speed, attenuation, reflection, refraction, scatter

59. Speed of Sound Determined by properties of the medium
Stiffness
Density
Not determined by the source of sound
B=“Bulk modulus” (stiffness)
r=“density” (grams/cm3) (kilograms/m3)
c=speed of sound (m/s)

60. Relative Speed of Sound
Solids fast
Liquids intermediate
Gases (ie, air) slow

61. Speed of Sound Tissue Air Fat Water Liver Blood Muscle Skull bone
Speed of sound (m/s)
330
1460
1480
1555
1560
1600
4080

62. 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. 62

63. 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

64. 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

65. Suppose the density of liver is 1. 061g/cm3
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?

66. 1 g/cm3 = 1,000g/1,000cm3 = 1,000kg/1,000,000cm3 = 1,000kg/m3
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?
1 g/cm3 = 1,000g/1,000cm3 = 1,000kg/1,000,000cm3 = 1,000kg/m3
1cm
1m=100cm
1m x 1m x 1m = 100cm x 100cm x 100cm =1,000,000cm3 1m 66

67. Suppose the density of liver is 1. 061g/cm3
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? 67

68. Unit is the rayl, 1 rayl = 1 kg/m2s
John William Strutt
“Lord Rayleigh”
( )
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

69. 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
1.71 x 106
7.8 x 106 69

70. 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
1.71 x 106
7.8 x 106
Note, the range of impedances of soft tissues (that do not contain air) is relatively narrow.

71. Ways we describe amplitude
High vs. low
Loud vs. soft
Strong echoes vs. weak echoes
Bright dots vs. dim dots

72. 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

73. Reflection

74. Types of Reflectors Specular Diffuse reflecting interface Scatter
Large
Smooth
Diffuse reflecting interface
Echoes travel in all directions
Scatter
Small interfaces
Scattered echoes travel in different directions.

75. 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.

76. 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

77. Compute the reflection coefficient for an interface formed by muscle and air. (Sound is traveling through muscle and encounters an air interface)

78. 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%.

79. Tissue-to-air interface
This is why we have to use coupling gel on the patient!

80. Nonperpendicular beam incidence
Reflected beam does not travel back to transducer
For a perfectly smooth interface, qr = qi

81. 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!

82. 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.

83. Signal Effects Specular reflector Diffuse reflector
The transducer serves both as the transmitter and echo detector.
Specular reflector
Diffuse reflector

84. Fetal skull only partially outlined because of unfavorable incident angle.
“Specular Highlight” is a term being coined to describe this situation.

85. Refraction in water

87. Conditions for Refraction
Beam is incident obliquely
Sound speeds are different

88. Snell’s Law

89. Sine of an angle
angle A

90. So, the angle whose sin is 0.45626 is found using
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. qi
So, the angle whose sin is is found using
Change (2.9 degrees) qt

91. 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.

92. Scatter can be called multi-directional reflection.
Diffuse Reflector
Scatterer

93. Scattering of ultrasound
Scatter can be called multi-directional reflection.
Diffuse Reflector
Scatterer

94. Gray Scale Image
Lung/liver easily differentiated because of differences in scattering levels

95. “Echogenic”
Tendency of a tissue to produce echoes, usually from scattering
Terms
Echogenic
Hypoechoic
Hyperechoic
Anechoic
isoechoic

99. Angle Effects
Diffuse Reflector

100. 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.

101. 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!

102. 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

103. Attenuation

104. Causes of Attenuation Reflection and scatter at interfaces Absorption
Very small contribution within organs
Can be significant at calcifications, stones
Absorption
Beam energy converted to heat
Diagnostic beams usually cause negligible heating

105. Attenuation
The Attenuation Coefficient (Amount of attenuation per unit distance)
Units are dB/cm

106. 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.)

107. 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

108. Decibels Example, let I2 be 100 I1 dB = 10 log(I2 / I1)
dB = 10 log(100) = 10 x 2 = 20
When the intensity is increased by 20 dB, it is increased by 100 times!

109. Amplitude ratio Intensity ratio
A2/A1 Log A2/A1 dB I2/I1 Log I2/I1
,000 4
,000,000 6
1/ /4 -0.6
1/ /100 -2
1/ /10,000 -4

110. Attenuation
The Attenuation Coefficient (Amount of attenuation per unit distance)
Units are dB/cm

111. 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

112. Adult Liver
4 MHz
7 MHz

113. Dependence on Frequency

114. 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.

115. Calculate attenuation

116. 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

117. Attenuation terms: “attenuating”

118. Attenuation terms: Enhancement

119. Attenuation terms: Shadowing

120. 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

121. 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