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1. ATTENUATION OF X-RAYS IN MATTER
2. 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.
3. Attenuation: Monochromatic X-rays
4. Monochromatic Attenuation (Con’t) Exponential Attenuation:
Nx = N0 e -µx
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
5. 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.
6. Mass Attenuation Coefficient
7. Attenuation Coefficients Mass Attenuation Coefficient (µ/?):
Lin Atten Coeff divided by physical density, ?
Removes effect of state (ie, liquid, gas) from µ
Units of area per gram (cm2/g): “cross-section”
8. Mass Attenuation Coefficient Over most of the diagnostic x-ray energies, tin is a better x-ray absorber gram for gram than lead.
9. Attenuation: Polychromatic X-rays
10. 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
11. 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
12. Factors Affecting Photoelectric Effect Together, the x-ray beam energy and the attenuator atomic number determine how much photoelectric interactions occur
13. 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)
14. 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 = ˝ (since # of neutrons = # protons), so
No = N/2
15. ELECTRONS PER GRAM
16. 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.
17. Attenuation: Summary