X-ray Attenuation

ATTENUATION OF X-RAYS IN MATTER

ATTENUATION ■

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

Attenuation: Monochromatic X-rays

Monochromatic Attenuation (Con’t) ■

Exponential Attenuation: Nx = N0 e -µx

Where: Nx = #transmitted photons N0 = # incident photons µ = Linear Atten coeff X = Absorber thickness ■

Half-Value Layer (HVL): Nx/N0 = 0.5 = e -µ x HXL HVL = Ln(0.5)/µ = 0.693/µ

Attenuation Coefficients ■

Linear Attenuation Coefficient (µ): – – – –

Units of 1/thickness (cm-1) Fraction of x-rays removed per cm of attenuator Strictly defined for monochromatic x-rays only Can breakdown into individual components: µtot = µpe + µcompton + µcoherent – Useful for diagnostic x-ray: often want to know attenuation as a function of depth.

Mass Attenuation Coefficient

Hartford Hospital Radiology

Attenuation Coefficients ■

Mass Attenuation Coefficient (µ/ρ ): – –

Lin Atten Coeff divided by physical density, ρ Removes effect of state (ie, liquid, gas) from µ

– Units of area per gram (cm2/g): “cross-section”

Mass Attenuation Coefficient ■

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

Attenuation: Polychromatic X-rays

Polychromatic (Brems) X-ray Energy ■

“Rule of Thumb”: In general, The mean energy of a polychromatic x-ray beam (bremsstrahlung x-rays) is between one- third and one-half of its peak energy.

■

More Specific: Effective Energy µeff = 0.693/HVL

Factors Affecting Attenuation ■

For imaging, we are interested in differences in attenuation from point to point within a patient. It is this differential attenuation that produces subject contrast. Both x-ray and tissue factors affect differential attenuation

FACTORS: X-Ray Beam -- Energy

Tissue 3

-- Density (g/cm ) -- Atomic Number -- Electrons/gram

Factors Affecting Photoelectric Effect ■

Together, the x-ray beam energy and the attenuator atomic number determine how much photoelectric interactions occur PERCENT PHOTOELECTRIC INTERACTIONS

X-ray Energy

Water (Z=7.4)

Compact Bone (Z=13.8)

20 keV 60 keV 100 keV

65% 7% 2%

89% 31% 9%

Sodium Iodine (Z=49.8) 84% 95% 88%

Density and Electrons per Gram ■

The number of compton interactions depends on the number of electrons encountered in a volume, or electron density (e/cm3) e/cm3 = (e/gram) x (gram/cm3)

Electrons per Gram of Matter (con’t) No = NZ/A No = number of electrons per gram N = Avogadro’s number (6.02 x 1023) Z = Atomic Number A = Atomic Weight ■ For most Low Atomic Number elements: ■

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

No = N/2

ELECTRONS PER GRAM ELECTRONS/GRAM FOR COMMON ELEMENTS Element Hydrogen Carbon Nitrogen Oxygen Calcium

Atomic # - Z Mass # - A 1 6 7 8 20

1 7 14 16 41

Electrons/Gram 23

6.02 x 10

23

3.01 x 10

23

3.01 x 10

23

3.01 x 10

23

3.00 x 10

Density and DifferentialAttenuation Most interactions in Dx x-ray are Compton ■ Compton scatter depends on electron density ■ Differences in tissue electron density mainly due to differences in physical density (little variation in e/gram) ■ Thus: differences in tissue density is one of the primary reasons why we see an x-ray image. Density determines e/cm3 of the tissue, and thus determines its x-ray stopping power. ■

Attenuation: Summary