Resident Physics Lectures
03:
Attenuation
George David
Associate Professor
Medical College of Georgia
Augusta, Georgia
Attenuation
• Reduction in amplitude &
intensity as sound
travels through medium
• Causes
absorption
» sound energy converted to heat
» dominant influence in soft tissue
reflection
scattering
George David
Associate Professor
Medical College of Georgia
Augusta, Georgia
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
Logarithm Review
x = log10(y) means
10 to what power = y ?
or
10x = y
George David
Associate Professor
Medical College of Georgia
Augusta, Georgia
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
Gain & Decibels
Power In Tissue
Power Out
(attenuation)
• decibel definition
dB =10 X log10 [power out / power in]
Power Ratio = Power Out / Power In
dB =10 X log10 [power ratio]
Gain & Decibels
Power In Tissue
Power Out
(attenuation)
Power Ratio = Power Out / Power In
• Power Ratio > 1 • Power Ratio < 1
Amplifier Absorber / Attenuator
Power Out > Power In Power Out < Power In
Log [Power ratio] >0 Log [Power ratio] <0
dB =10 X log10 [power ratio]
Power Ratio
Power Ratio = Power Out / Power In
dB =10 X log10 [power ratio]
Decibel calculation
logarithms Power ratio dB
log 1 = 0 1 0
log 10 = 1 10 10
log 100 = 2
100 20
log 10n = n
log (1/10) = 10-1 = -1 1/100 -20
log (1/100) = 10-2 = -2 10 n n X 10
log (1/1000) = 10-3 = -3 2 3
dB Attenuation
• dB / 10 indicates # of powers of ten
attenuation
• Every increase of 10 dB indicates
another factor of 10 attenuation
George David
Associate Professor
Medical College of Georgia
Augusta, Georgia
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
Attenuation & Frequency
• Attenuation affected by
medium
frequency
• As frequency increases, so does
attenuation
bass sound carries farther than treble
high frequency = poorer penetration
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
Rule of Thumb
0.5 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
Attenuation Coefficient
• Attenuation Coefficient = 0.5 * Freq.
(dB/cm) (dB/cm/MHz) * (MHz)
• indicates fraction of beam
intensity lost per unit distance
of sound traval
Attenuation Coefficient
• Attenuation Coefficient = 0.5 * Freq.
(dB/cm) (dB/cm/MHz) * (MHz)
Frequency Attenuation
(MHz) Coefficient
(dB/cm)
1 0.5
2 1.0
5 2.5
10 5
Attenuation Coefficient
Comments
• 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
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
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 99.98
10.0 5.0 5.0 68 50 99.999
Attenuation
• Why dB?
dB’s can be added together
• Rule of thumb doesn’t
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
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
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
Attenuation
• half intensity depth (HID)
depth where intensity = 50% of original
corresponds to 3dB attenuation
180
HID 150
100
66
39
Practical Implications
of Attenuation
• limits maximum imaging depth
• higher frequencies result in
increased attenuation
decreased imaging depth
improved axial resolution
