X-Ray Attenuation

ATTENUATION OF X-RAYS ATTENUATION OF X-RAYS IN MATTERIN MATTER

ATTENUATIONATTENUATION

Attenuation is the reduction in the Attenuation is the reduction in the intensity of an x-ray beam as it intensity of an x-ray beam as it traverses matter, either by the traverses matter, either by the absorptionabsorption of photons or of photons or deflection deflection (scattering)(scattering) of photons from the of photons from the beam.beam.

Attenuation: Monochromatic X-raysAttenuation: Monochromatic X-rays

Monochromatic Attenuation (Con’t)Monochromatic Attenuation (Con’t) Exponential AttenuationExponential Attenuation::

NNxx = N = N00 e e -µx-µx

Where:Where:NNxx = #transmitted = #transmitted

photonsphotonsNN00 = # incident photons = # incident photonsµ = Linear Atten coeffµ = Linear Atten coeffX = Absorber thicknessX = Absorber thickness

Half-Value Layer (HVL):Half-Value Layer (HVL):

NNx/x/NN0 0 == 0.5 = e 0.5 = e -µ x HXL-µ x HXL

HVL = Ln(0.5)/µ = 0.693/µHVL = Ln(0.5)/µ = 0.693/µ

Attenuation CoefficientsAttenuation Coefficients Linear Attenuation Coefficient (µ):Linear Attenuation Coefficient (µ):

– Units of 1/thickness (cm-1)Units of 1/thickness (cm-1)– Fraction of x-rays removed per cm of Fraction of x-rays removed per cm of

attenuatorattenuator– Strictly defined for monochromatic x-rays Strictly defined for monochromatic x-rays

onlyonly– Can breakdown into individual components:Can breakdown into individual components:

µµtottot = µ = µpepe + µ + µcomptoncompton + µ + µcoherentcoherent

– Useful for diagnostic x-ray: often want to Useful for diagnostic x-ray: often want to know attenuation as a function of know attenuation as a function of depthdepth. .

Hartford Hospital Radiology

Mass Attenuation CoefficientMass Attenuation Coefficient

Attenuation CoefficientsAttenuation Coefficients

Mass Attenuation Coefficient (µ/Mass Attenuation Coefficient (µ/):):– Lin Atten Coeff divided by physical Lin Atten Coeff divided by physical

density, density, – Removes effect of state (ie, liquid, gas) Removes effect of state (ie, liquid, gas)

from µfrom µ– Units of area per gram (cmUnits of area per gram (cm22/g): “cross-/g): “cross-

section”section”

Mass Attenuation CoefficientMass Attenuation Coefficient

Over most of the Over most of the diagnostic x-ray diagnostic x-ray energies, tin is a energies, tin is a better x-ray better x-ray absorber gram for absorber gram for gram than lead. gram than lead.

Attenuation: Polychromatic X-raysAttenuation: Polychromatic X-rays

Polychromatic (Brems) X-ray EnergyPolychromatic (Brems) X-ray Energy ““Rule of Thumb”:Rule of Thumb”: In general, In general,

The mean energy of a polychromatic x-The mean energy of a polychromatic x-ray beam (bremsstrahlung x-ray beam (bremsstrahlung x-rays) is between one- third and one-half rays) is between one- third and one-half of its peak energy.of its peak energy.

More Specific: Effective EnergyMore Specific: Effective Energy

µµeffeff = 0.693/HVL = 0.693/HVL

Factors Affecting AttenuationFactors Affecting Attenuation For imaging, we are interested in For imaging, we are interested in differences in differences in

attenuationattenuation from point to point within a patient. It from point to point within a patient. It is this is this differential attenuationdifferential attenuation that produces that produces subject contrast. subject contrast. Both x-ray and tissue factors Both x-ray and tissue factors affect differential attenuationaffect differential attenuation

FACTORS: X-Ray Beam Tissue

-- Energy -- Density (g/cm3)-- Atomic Number-- Electrons/gram

Factors Affecting Photoelectric EffectFactors Affecting Photoelectric Effect Together, the x-ray Together, the x-ray beam energybeam energy and the and the

attenuator attenuator atomic numberatomic number determine how determine how much photoelectric interactions occur much photoelectric interactions occur

PERCENT PHOTOELECTRIC INTERACTIONS

Compact SodiumX-ray Water Bone IodineEnergy (Z=7.4) (Z=13.8) (Z=49.8)

20 keV 65% 89% 84%60 keV 7% 31% 95%100 keV 2% 9% 88%

Density and Electrons per GramDensity and Electrons per Gram The number of compton interactions The number of compton interactions

depends on the number of electrons depends on the number of electrons encountered in a volume, or electron encountered in a volume, or electron density (e/cmdensity (e/cm33))

e/cme/cm33 = (e/gram) x (gram/cm = (e/gram) x (gram/cm3)3)

Electrons per Gram of Matter (con’t)Electrons per Gram of Matter (con’t) NNoo = NZ/A = NZ/A

NNoo = number of electrons per gram = number of electrons per gram

N = Avogadro’s number (6.02 x 10N = Avogadro’s number (6.02 x 102323))

Z = Atomic NumberZ = Atomic Number

A = Atomic WeightA = Atomic Weight For most Low Atomic Number elements:For most Low Atomic Number elements:

Z/A = ½ (since # of neutrons = # Z/A = ½ (since # of neutrons = # protons), soprotons), so

NNoo = N/2 = N/2

ELECTRONS PER GRAMELECTRONS PER GRAM

ELECTRONS/GRAM FOR COMMON ELEMENTS

Element Atomic # - Z Mass # - A Electrons/Gram

Hydrogen 1 1 6.02 x 1023

Carbon 6 7 3.01 x 1023

Nitrogen 7 14 3.01 x 1023

Oxygen 8 16 3.01 x 1023

Calcium 20 41 3.00 x 1023

Density and DifferentialAttenuationDensity and DifferentialAttenuation Most interactions in Dx x-ray are Compton Most interactions in Dx x-ray are Compton Compton scatter depends on electron densityCompton scatter depends on electron density Differences in tissue electron density mainly Differences in tissue electron density mainly

due to differences in physical density (little due to differences in physical density (little variation in e/gram)variation in e/gram)

Thus: Thus: differences in tissue density is one of differences in tissue density is one of the primary reasons why we see an x-ray the primary reasons why we see an x-ray image. Density determines e/cmimage. Density determines e/cm33 of the of the tissue, and thus determines its x-ray stopping tissue, and thus determines its x-ray stopping power.power.

Attenuation:Attenuation:SummarySummary