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Resident Physics Lectures

Resident Physics Lectures. Attenuation Math. Attenuation. Reduction in amplitude & intensity as sound travels through medium Causes absorption sound energy converted to heat dominant influence in soft tissue reflection scattering. Absorption. Units decibels (dB)

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Resident Physics Lectures

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  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 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. Logarithm Review x = log10(y) means10 to what power = y ?or10x = 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 Power In Tissue (attenuation) • decibel definition dB =10 X log10 [power out / power in] Power Out Power Ratio = Power Out / Power In • dB =10 X log10 [power ratio]

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

  8. Power Ratio Power Ratio = Power Out / Power In • dB =10 X log10 [power ratio] 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 • Decibel calculation • Power ratio dB • 1 0 • 10 10 • 100 20 • 1/100 -20 • 10 n n X 10 • 2 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 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 = 10 dB + 3 dB + 3 dB X10 X2 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 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

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

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

  18. Attenuation CoefficientComments • 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 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

  20. 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

  21. 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

  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. 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

  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

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