1. RTT 425 Radiation Therapy Physics Radiation Quality, Chapter 4 From Stanton and Stinson: Applied physics for Radiation Oncology

2. Intensity Amount of energy per unit time per unit area. Depends on original energy of the beam, divergence of the beam and attenuation.

3. Beam divergence (inverse square law)

4. Beam divergence Intensity is inversely proportional to the square of the distance from the source. This is due to the fact that the beam spreads out. I 1 /I 2 = (D 2 ) 2 / (D 1 ) 2

5. Attenuation The removal of energy from the beam. This happens when a beam passes through matter.

6. Attenuation If matter (a filter) is placed in the beam’s path, some of the photons will be absorbed, some will be scattered and some will pass through (be transmitted) to the other side. The reduction in the number of photons is proportional to the number of incident photons and to the thickness of the absorber The ratio of the beam intensity on one side of the matter to the other is called the transmission. T = I/I 0

7. Attenuation For a photon source with one energy, the attenuation is given by: I = I 0 e -μx e is the natural log or 2.718, x is the thickness of the filter and μ is the linear attenuation coefficient. Linear attenuation coefficient represents the probability per unit thickness that any one photon will be attenuated.

8. Mathematics of attenuation μ is the constant of proportionality called the attenuation coefficient. If the thickness is expressed in length, then μ is called the linear attenuation coefficient. The units of μ are 1/cm, or cm -1

9. Attenuation If the beam is heterogeneous, like an x-ray beam made up of Bremstrahlung, this exponential attenuation cannot occur, as each photon energy will have its own linear attenuation coefficient.

10. Attenuation Homogeneous beam Heterogeneous beam

11. Attenuation Why does this happen? As more layers of filter are added, the lower energy photons are removed and so the emerging beam is “harder”, or more penetrating.

12. Half value layer The thickness of an absorber of specified composition required to attenuate the intensity of the beam to half its original value. All beams can be described in terms of its HVL, but the quality is usually stated in terms of its energy. Quality of gamma beam is stated as energy of gamma ray OR its nuclide of origin.

13. HVL HVL is mostly used to describe the quality of low energy x-ray beams, together with kVp. An important fact about HVL is that for a heterogeneous beam, each consecutive layer has to be larger ie: 2 nd HVL is larger than the first, 3 rd is larger than the 2 nd.

14. Quality of an x-ray beam Penetrating ability of the beam. How much of the beam goes into the patient?

15. Filters An x-ray beam has a distribution of energies of bremsstrahlung photons on which is superimposed lines of characteristic radiation. Inherent filtration occurs because of the glass envelope, oil, and exit window of the tube.

16. Thoreaus filters Tube – tin – copper – aluminum – air – patient. Highest atomic number nearest the x-ray target.

17. HVL mathematics Attenuation equation: I = I 0 e -μx When x = HVL, I 0 is ½ therefore from the above equation, we get HVL = 0.693/μ

18. HVL If you increase the filtration, you reduce the exposure rate, so a filter is carefully chosen to give a suitable HVL and an acceptable exposure rate.

19. Energies and HVL’s