ACCELERATORS AND MEDICAL PHYSICS 2

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1 ACCELERATORS AND MEDICAL PHYSICS 2 Ugo Amaldi University of Milano Bicocca and TERA Foundation EPFL U. Amaldi 1

2 The icone of radiation therapy Radiation beam in matter EPFL U. Amaldi 2

3 Physical phenoma in radiation therapy: 1. X ray production by electrons e accelerated electron a 10 MeV atom γ = photon 4 MeV nucleus e scattered electron 6 MeV electron e mass = 0,5 MeV EPFL U. Amaldi 3

4 Physical phenoma in radiation therapy: 2. effects produced by photons γ = photon 4 MeV PHOTOELECTRIC EFFECT e Photoelectrons 4 MeV γ = photon 4 MeV γ = photon 1 MeV e Compton electron 3 MeV COMPTON EFFECT EPFL U. Amaldi 4

5 Physical phenoma in radiation therapy: 3. ionizations and excitations caused by charged particles Electron e - stripped off by the electric force from an electron cloud. The molecules remains ionized and also excited electron = e - ion = C +6 proton = p + EPFL U. Amaldi micrometres

6 Physical phenoma in radiation therapy: 4. multiple scattering against nuclei mm depth < range in matter 3 MeV electrons m = 0.5 MeV is small w.r.t. the masses of the matter nuclei depth = range in matter 60 MeV protons M = 940 MeV 40 mm But the losses are the same EPFL U. Amaldi

7 Two quantities are relevant for the radiation effects Delivered dose = D = Energy imparted to a masse M of matter masse M in J/kg = gray (Gy) Δ E Linear Energy Transfer = LET = Δ x in kev/µm The energy is imparted to matter only by charged particles EPFL U. Amaldi 7

8 Rutherford scattering EPFL U. Amaldi 8

9 EPFL U. Amaldi 9

10 for protons Rutherford scattering E min Note: to effectively kick a swing the push has to be shorter than the period T of the oscillation EPFL U. Amaldi 10

11 Rutherford scattering EPFL U. Amaldi 11

12 Rutherford scattering Distant collisions = particle passes outside the atomic cloud Close collisions = particles passes inside the atomic cloud (The two areas are about equal ) EPFL U. Amaldi 12

13 Rutherford scattering The factor is Conference/Meeting - Date - Author 13

14 Rutherford scattering For the LET in water the particle enters only with v 2 and z 2 (protons and electrons of the same v have the same LET!) Conference/Meeting - Date - Author 14

15 The LET computed with semiclassical model is accurate! Δ E Δ x Exacte calculations In water Semiclassical model K / Mc 2 1 EPFL U. Amaldi 15

16 The LET from the semiclassical model is accurate! Δ E Δ x In water K / Mc 2 EPFL U. Amaldi 16

17 The LET from the semiclassical model is accurate! Δ E Δ x In water K / Mc 2 0 corresponds to β = 0.70 (Kinetic energy K )/ (mass energy Mc 2 ) defines uniquely the velocity v EPFL U. Amaldi 17

18 Properties of particles used in radiotherapy EPFL U. Amaldi 18

19 Before computing the range of charged hadrons p 1 cm of water C Roughly prop. to 1/ M EPFL U. Amaldi 19

20 Hadron ranges from the semiclassical LET formula Mc 2 = unit of nuclear mass = 931 MeV (MeV/u) EPFL U. Amaldi From exact calculation: 20

21 Interactions with matter in conventional The radiotherapy Bragg peak R is the residual range i.e. the range measured from the end IMPORTANT RATIO EPFL U. Amaldi 21

22 The losses seen by the water molecules Probability for the incoming particle to loose the energy E c Excitation s due to distant coll. Minimal ionization energy Absorbed energy E c in kev EPFL U. Amaldi 22

23 The losses seen by the water molecules Probability for the incoming particle to loose the energy E c Excitations Excitation s due due to to distant distant coll. coll. Ionizations due to distant coll. Minimal ionization energy Ionizations due to close coll. Absorbed energy E c in kev EPFL U. Amaldi 23

24 The losses seen by the water molecules Probability for the incoming particle to loose the energy E c Excitations Excitation s due due to to distant distant coll. coll. Ionizations due to distant coll. Minimal ionization energy Ionizations due to close coll. Absorbed energy E c in kev EPFL U. Amaldi 24

25 This ratio is almost the same for all particles and all energies EPFL U. Amaldi 25

26 Electron ranges Plural scattering multiple scattering complete scattering absorber EPFL U. Amaldi 26

27 LET of electrons in water and lead kev /µm same line as for protons electrons in water semiclassical model 0.1 electrons in Pb (exact calculation) kinetic energy in MeV Also for electrons in water the semiclassical model of LET is satisfactory. The proton line 0.12/ (K/mc 2 ) 0.82 is not perfect because the maximum electron energy is nor 2mv 2 (slide 10) but mv 2 /8. This changes by 10% the logarithm. EPFL U. Amaldi 27

28 Electron ranges Still to compute the electron ranges one can make the simplification: WATER EPFL U. Amaldi 28

29 Red points from previous table Electron ranges In this range R p (water cm) K(MeV) / 2 Total range in Al Practical range in Al Practical range in water The model is satisfactory given the experimental uncertainties in the definition of the practical range EPFL U. Amaldi 29

30 Interactions with matter in conventional radiotherapy electrons Courtesy of Elekta X X Linac for GHz 5-20 MeV 1 linac every 250,000 inhabitants tumour Multileaf collimator patients per year every 10 million inhabitants EPFL U. Amaldi 30

31 Interactions with matter in conventional radiotherapy with electrons with photons 4.5 MeV EPFL U. Amaldi 31

32 dose % of max dose Interactions with matter in conventional radiotherapy E e max E X 2K e /5 E X DOSE KERMA transition region depth depth in water EPFL U. Amaldi 32

33 % of max dose E e max E X = 2 K e / 5 R cm = K e MeV / 5 The sparing of the skin increases with the energy 20 MeV EPFL U. Amaldi depth in water 33

34 A last point: quality of a photon radiation field EPFL U. Amaldi 34

35 THE END EPFL U. Amaldi 35

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