ACCELERATORS AND MEDICAL PHYSICS 2 Ugo Amaldi University of Milano Bicocca and TERA Foundation EPFL 2-28.10.10 - U. Amaldi 1
The icone of radiation therapy Radiation beam in matter EPFL 2-28.10.10 - U. Amaldi 2
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 2-28.10.10 - U. Amaldi 3
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 2-28.10.10 - U. Amaldi 4
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 2-28.10.10 - U. Amaldi 0.0005 micrometres
Physical phenoma in radiation therapy: 4. multiple scattering against nuclei 10-20 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 2-28.10.10 - U. Amaldi
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 2-28.10.10 - U. Amaldi 7
Rutherford scattering EPFL 2-28.10.10 - U. Amaldi 8
EPFL 2-28.10.10 - U. Amaldi 9
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 2-28.10.10 - U. Amaldi 10
Rutherford scattering EPFL 2-28.10.10 - U. Amaldi 11
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 2-28.10.10 - U. Amaldi 12
Rutherford scattering The factor 0.0076 is Conference/Meeting - Date - Author 13
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
The LET computed with semiclassical model is accurate! Δ E Δ x Exacte calculations In water Semiclassical model K / Mc 2 1 EPFL 2-28.10.10 - U. Amaldi 15
The LET from the semiclassical model is accurate! Δ E Δ x In water K / Mc 2 EPFL 2-28.10.10 - U. Amaldi 16
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 2-28.10.10 - U. Amaldi 17
Properties of particles used in radiotherapy EPFL 2-28.10.10 - U. Amaldi 18
Before computing the range of charged hadrons p 1 cm of water C Roughly prop. to 1/ M EPFL 2-28.10.10 - U. Amaldi 19
Hadron ranges from the semiclassical LET formula Mc 2 = unit of nuclear mass = 931 MeV (MeV/u) EPFL 2-28.10.10 - U. Amaldi From exact calculation: 20
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 2-28.10.10 - U. Amaldi 21
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 2-28.10.10 - U. Amaldi 22
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 2-28.10.10 - U. Amaldi 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 2-28.10.10 - U. Amaldi 24
This ratio is almost the same for all particles and all energies EPFL 2-28.10.10 - U. Amaldi 25
Electron ranges Plural scattering multiple scattering complete scattering absorber EPFL 2-28.10.10 - U. Amaldi 26
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 2-28.10.10 - U. Amaldi 27
Electron ranges Still to compute the electron ranges one can make the simplification: WATER EPFL 2-28.10.10 - U. Amaldi 28
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 2-28.10.10 - U. Amaldi 29
Interactions with matter in conventional radiotherapy electrons Courtesy of Elekta X X Linac for electrons @3 GHz 5-20 MeV 1 linac every 250,000 inhabitants tumour Multileaf collimator 20 000 patients per year every 10 million inhabitants EPFL 2-28.10.10 - U. Amaldi 30
Interactions with matter in conventional radiotherapy with electrons with photons 4.5 MeV EPFL 2-28.10.10 - U. Amaldi 31
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 2-28.10.10 - U. Amaldi 32
% 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 2-28.10.10 - U. Amaldi depth in water 33
A last point: quality of a photon radiation field EPFL 2-28.10.10 - U. Amaldi 34
THE END EPFL 1-28.10.10 - U. Amaldi 35