Resident Physics Lectures

1
Resident Physics Lectures

• 03
• Attenuation

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Attenuation

• Reduction in amplitude intensity as sound
  travels through medium
• Causes
• absorption
• sound energy converted to heat
• dominant influence in soft tissue
• reflection
• scattering

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Absorption

• Units
• decibels (dB)
• dB indicates signal gain
• indicates signal gets larger
• - indicates signal gets smaller
• ultrasound absorption is always negative dB
• sound always loses intensity
• negative sometimes implied
• dB indicates fraction of intensity lost

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Logarithm Review

• x log10(y) means10 to what power y
  ?or10x y

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Logarithms Review

• log 1 0
• log 10 1
• log 100 2
• log 10n n
• log (1/10) 10-1 -1
• log (1/100) 10-2 -2
• log (1/1000) 10-3 -3

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Gain Decibels
Power In
Tissue (attenuation)
Power Out

• decibel definition
• dB 10 X log10 power out / power in

Power Ratio Power Out / Power In
dB 10 X log10 power ratio
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Gain Decibels
Power In
Tissue (attenuation)
Power Out
Power Ratio Power Out / Power In

• Power Ratio gt 1
• Amplifier
• Power Out gt Power In
• Log Power ratio gt0

• Power Ratio lt 1
• Absorber / Attenuator
• Power Out lt Power In
• Log Power ratio lt0

dB 10 X log10 power ratio
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Power Ratio
Power Ratio Power Out / Power In
dB 10 X log10 power ratio
Decibel calculation Power ratio dB 1
0 10 10
100 20 1/100 -20
10 n n X 10 2
3

• logarithms
• log 1 0
• log 10 1
• log 100 2
• log 10n n
• log (1/10) 10-1 -1
• log (1/100) 10-2 -2
• log (1/1000) 10-3 -3

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dB Attenuation

• dB / 10 indicates of powers of ten attenuation
• Every increase of 10 dB indicates another factor
  of 10 attenuation

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dB Try Again
10 dB 1 factor of 10 or 10 you morons
60 dB 6 factors of 10 or 1,000,000, nyuk, nyuk,
nyuk
20 dB 2 factors of 10 or 10 X 10 or 100
10 dB 1 power of 10 10 20 dB 2 powers of 10
100 60 dB 6 powers of 10 1,000,000
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Attenuation Frequency

• Attenuation affected by
• medium
• frequency
• As frequency increases, so does attenuation
• bass sound carries farther than treble
• high frequency poorer penetration

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Attenuation In Soft Tissue Rule of Thumb

• 0.5 dB / cm attenuation for each MHz frequency
• cm refers to distance of sound travel
• other texts may say 1 dB / cm depth / MHz
• 1 cm depth equivalent to 2 cm sound travel

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Rule of Thumb0.5 dB/cm/MHz

• To calculate attenuation (dB) simply multiply
  rule of thumb by round trip distance by
  frequency
• 5 MHz sound 10 cm sound travel
• attenuation 0.5 dB/cm/MHz X 10 cm X 5 MHz 25
  dB
• 3.5 MHz sound 4 cm sound travel
• attenuation 0.5 dB/cm/MHz X 4 cm X 3.5 MHz 7
  dB

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Attenuation Coefficient

• Attenuation Coefficient 0.5
  Freq. (dB/cm) (dB/cm/MHz) (MHz)
• indicates fraction of beamintensity lost per
  unit distanceof sound traval

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Attenuation Coefficient

• Attenuation Coefficient 0.5
  Freq. (dB/cm) (dB/cm/MHz) (MHz)

Frequency (MHz) Attenuation Coefficient (dB/cm)
1 0.5
2 1.0
5 2.5
10 5
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Attenuation CoefficientComments

• Attenuation Coefficient 0.5
  Freq. (dB/cm) (dB/cm/MHz) (MHz)
• Longer path results in increased attenuation
• Higher frequency results in increased attenuation
  coefficient
• Higher attenuation coefficient results in more
  attenuation

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dB vs. Intensity Ratio
dB attenuation 10 X log10 intensity ratio
Fraction attenuated 1 - intensity ratio

• dB Intensity Fraction
• atten. Ratio atten.
• 1 .79 .21
• 2 .63 .37
• 3 .50 .50
• 4 .40 .60
• 5 .32 .68
• 10 .1 .90
• 20 .01 .99
• 30 .001 .999

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Soft Tissue Attenuation Calculation

• Attenuation Attenuation Coefficient X Path
  Length

Freq. Atten Coef. Atten(dB). Int. Red.
Atten(dB) Int. Red. dB /
cm 1 cm 1 cm 10 cm 10 cm
2.0 1.0 1 21 10 90 3.5 1.8 1.8 34 18 98
5.0 2.5 2.5 44 25 99.7 7.5 3.8 3.8 58 38 9
9.98 10.0 5.0 5.0 68 50 99.999
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Attenuation

• Why dB?
• dBs can be added together
• Rule of thumb doesnt always work
• Attenuation higher in lung bone than in soft
  tissue
• Attenuation in lung and bone not proportional to
  frequency

Class during lecture on attenuation
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Attenuation Coefficients
0.5 dB/cm/MHz is soft tissue average assumed by
scanner
Tissue Attenuation Coefficient
(dB/cm/MHz)

• Fat 0.6
• Brain 0.6
• Liver 0.5
• Kidney 0.9
• Muscle 1.0
• Heart 1.1

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Half Intensity Depth

• Decreases with increasing frequency

HID 3 dB / Attenuation Coefficient
HID 3 dB / Freq (MHz) 2
Frequency Atten Coef. HID (MHz) dB/cm cm -------
-----------------------------------------------
1 0.5 6.0 2 1.0 3.0 5 2.5 1.2 10 5.0 0.
6
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Attenuation

• half intensity depth (HID)
• depth where intensity 50 of original
• corresponds to 3dB attenuation

180
150
HID
100
66
39
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Practical Implications of Attenuation

• limits maximum imaging depth
• higher frequencies result in
• increased attenuation
• decreased imaging depth
• improved axial resolution