1. Resident Physics Lectures
Attenuation Math

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

3. Absorption Units dB indicates signal gain
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

4. x = log10(y) means 10 to what power = y ? or 10x = y
Logarithm Review
x = log10(y) means 10 to what power = y ? or 10x = y

5. 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

6. Gain & Decibels dB =10 X log10 [power out / 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]

7. Gain & Decibels Power Ratio < 1 Power Ratio = Power Out / Power In
Tissue
(attenuation)
Power Out
Power Ratio = Power Out / Power In
                
Power Ratio > 1
Amplifier
Power Out > Power In
Log [Power ratio] >0
Power Ratio < 1
Absorber / Attenuator
Power Out < Power In
Log [Power ratio] <0
dB =10 X log10 [power ratio]

8. Power Ratio Decibel calculation Power Ratio = Power Out / Power In
dB =10 X log10 [power ratio]
Decibel calculation
Power ratio dB 1/
10 n n X 10
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

9. dB Attenuation dB / 10 indicates # of powers of ten attenuation
Every increase of 10 dB indicates another factor of 10 attenuation

10. dB: Try Again 10 dB = 1 power of 10 = 10 20 dB = 2 powers of 10 = 100
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

11. Logarithm Law
Log(A x B) = Log(A) + Log(B)
Log(20) = Log(10) + Log(2)

12. Logarithm Law - 16 dB means signal is reduced by a factor of 40
16 dB = 10 dB + 3 dB + 3 dB X X X2 = X40
- 16 dB means signal is reduced by a factor of 40

13. Attenuation & Frequency
Attenuation affected by
medium
frequency
As frequency increases, so does attenuation
bass sound carries farther than treble
high frequency = poorer penetration

14. 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

15. 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

16. 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

17. 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

18. Attenuation Coefficient Comments
Attenuation Coefficient = 0.5 * Freq. (dB/cm) (dB/cm/MHz) (MHz)
Longer path increased attenuation
Higher frequency  increased attenuation coefficient
Higher attenuation coefficient  more attenuation

19. dB vs. Intensity Ratio dB Intensity Fraction atten. Ratio atten.
dB attenuation =10 X log10 [intensity ratio]
Fraction attenuated = 1 - intensity ratio
dB Intensity Fraction
atten Ratio atten.

20. Soft Tissue Attenuation Calculation
Attenuation = Attenuation Coefficient X Path Length
Freq. Atten Coef. Atten(dB). % Int. Red. Atten(dB) % Int. Red dB / cm cm cm 10 cm cm

21. Attenuation Why dB? Rule of thumb doesn’t always work
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

22. 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

23. HID = 3 dB / Attenuation Coefficient
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

24. Attenuation half intensity depth (HID)
depth where intensity = 50% of original
corresponds to 3dB attenuation
180
150
HID
100 66 39

25. Practical Implications of Attenuation
limits maximum imaging depth
higher frequencies result in
increased attenuation
decreased imaging depth
improved axial resolution