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ATTENUATION OF X-RAYS IN MATTER

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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
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

**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