Radiation Quality Chapter 4

X-ray Intensity Intensity: the amount of energy present per unit time per unit area perpendicular to the beam direction at the location of interest.  The number of photons reaching the detector per second is a measure of beam intensity (photons/cm 2 ).  Exposure Rate: (mR/hr); dose rate: (cGy/min) Intensity of photon beam at the tumor  Depends primarily on the original strength of the beam.  Reduced by beam divergence and attenuation.

Beam Divergence The area over which radiation spreads, is proportional to the square of the distance from the source. Inverse square law: intensity is inversely proportional to the square of the distance from the source. I 1 / I 2 = D 2 2 / D 1 2 Or I 2 = I 1 (D 1 /D 2 ) 2

Beam attenuation Attenuation: the removal of energy from the beam. X-rays interact with charged particles through the electromagnetic fields associated with the electric and magnetic fields of electrons and nuclei.  When a beam passes through matter, energy is removed from the beam. Photons will either…  Interact with the filter/attenuator  Be absorbed by the material  They deposit all their energy in the filter  Direction changed or scattered  Unaffected by the filter

Transmission Transmission: the ratio of beam intensity I to I O. As the filter thickness increases, the intensity of the attenuated beam drops. Transmission = I/ I O  I O : initial intensity at the detector before filtration  I: the final beam intensity after filtration

Transmission Photon source with single energy- attenuation of the beam:  I = I O e -μx x = thickness of the filter μ = linear attenuation coefficient, (length -1 ) e = base of natural logarithm (2.718) Each millimeter of thickness added to the filter reduces the beam by a constant percent

Transmission Example Attenuation coefficient (μ) = 0.2 mm -1 Thickness (x) = 3mm I O = 2000 photons I = I O e -μx I = 2000 * e (-0.2 *3) I = 2000 * I = 1098 photons

Linear Attenuation Coefficient Linear attenuation coefficient (μ ): a function of the filter material and the energy of the photon beam.  Represents a probability per unit thickness that any one photon will be attenuated. Half-Value Layer determined by μ

Monoenergetic / Homogenous Monoenergetic/homogenous: all photons in the beam have the same energy  μ: remains unchanged for all filter thicknesses or number of photons removed (number of photons change)  Higher μ  higher probability of interaction  smaller HVL More easily reduced in intensity An exponential function produces a straight line on semi-log graph paper.

Polyenergetic / Heterogenous Polyenergetic/heterogenous: broad range of photon energies (bremsstrahlung).  μ: each energy has a different value. On semi-log graph paper, the slope changes as filter is added due to beam hardening. Beam Hardening: the effective energy of the beam increases as it passes through the filter.  Only occurs in a polyenergetic/heterogeneous beam.

Half-Value Layer Half-value layer (HVL): the thickness required for a particular material to cut the beam’s intensity in half.  HVL = 0.693/ μ  Used to describe the beam’s penetrability  Convenient to characterize different bremsstrahlung beams using their attenuation characteristics. Materials used to specify beams HVL changes with energy range  Diagnostic/superficial: mm Al  Orthovoltage: mm Cu  MeV: mmPb

Homogeneity Coefficient Homogeneity Coefficient:  HC = 1 st HVL/2 nd HVL As HC  1: the more alike individual beam energy are. 1 st HVL = 2 nd HVL = 3 rd HVL…  monoenergetic beam

Equivalent Energy Equivalent Energy: represents the average energy of the beam  The energy of the monoenergetic beam that would have an HVL equal to the first HVL of the bremmsstrahlung beam in question.

Attenuation Coefficients Linear attenuation coefficient (μ): gives the probability that a given photon will be attenuated in a unit thickness of a particular attenuator. –Photon energy & material dependant Mass attenuation coefficient (μ/ρ): probability of interaction per unit mass length when μ/ρ << 1, (cm 2 /g) –Decreasing the density of the material will cause much less attenuation.