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ACCELERATORS AND MEDICAL PHYSICS

2 Ugo Amaldi University of Milano Bicocca and TERA Foundation

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The icone of radiation therapy

Radiation beam in matter EPFL 2 - 28.10.10 - U. Amaldi

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Physical phenoma in radiation therapy: 1. X ray production by electrons

γ = photon 4 MeV

e

electron “e” mass = 0,5 MeV

accelerated electron a 10 MeV nucleus atom

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e scattered electron 6 MeV

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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

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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 = eion = C+6 proton = p+

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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

in J/kg = gray (Gy)

masse M

ΔE Linear Energy Transfer = LET =

Δx

in

keV/µm

The energy is imparted to matter only by charged particles EPFL 2 - 28.10.10 - U. Amaldi

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Rutherford scattering

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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

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Rutherford scattering

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Rutherford scattering

Distant collisions =

particle passes outside the atomic cloud

Close collisions =

particles passes inside the atomic cloud

(The two areas are about equal )

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Rutherford scattering

The factor 0.0076 is

Conference/Meeting - Date - Author

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Rutherford scattering

For the LET in water the particle enters only with v2 and z2 (protons and electrons of the same v have the same LET!)

Conference/Meeting - Date - Author

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The LET computed with semiclassical model is accurate !

ΔE Δx

Exacte calculations

In water

K/ EPFL 2 - 28.10.10 - U. Amaldi

Semiclassical model

Mc2

1

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The LET from the semiclassical model is accurate !

ΔE Δx

In water

K / Mc2 EPFL 2 - 28.10.10 - U. Amaldi

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The LET from the semiclassical model is accurate !

ΔE Δx

In water

K / Mc2

0 corresponds to β = 0.70

(Kinetic energy K )/ (mass energy Mc2) defines uniquely the velocity v 17

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Properties of particles used in radiotherapy

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Before computing the range of charged hadrons

1 cm of water p

C

Roughly prop. to 1/√ M

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Hadron ranges from the semiclassical LET formula

Mc2 = unit of nuclear mass = 931 MeV

(MeV/u)

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From exact calculation:

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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

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Probability for the incoming particle to loose the energy Ec

The losses seen by the water molecules

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Excitation s due to distant coll.

Minimal ionization energy

Absorbed energy Ec in keV

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Probability for the incoming particle to loose the energy Ec

The losses seen by the water molecules

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Ionizations due to distant coll.

Excitation Excitations sdue duetoto distant distant coll. coll.

Minimal ionization energy

Ionizations due to close coll.

Absorbed energy Ec in keV

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Probability for the incoming particle to loose the energy Ec

The losses seen by the water molecules

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Ionizations due to distant coll.

Excitation Excitations sdue duetoto distant distant coll. coll.

Minimal ionization energy

Ionizations due to close coll.

Absorbed energy Ec in keV

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This ratio is almost the same for all particles and all energies

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Electron ranges

Plural scattering multiple scattering

complete scattering

absorber

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LET of electrons in water and lead

same line as for protons keV /µm

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/mc2)0.82 is not perfect because the maximum electron energy is nor 2mv2 (slide 10) but mv2/8. This changes by 10% the logarithm. EPFL 2 - 28.10.10 - U. Amaldi

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Electron ranges Still to compute the electron ranges one can make the simplification:

WATER EPFL 2 - 28.10.10 - U. Amaldi

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Red points from previous table

Electron ranges In this range Rp (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

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Interactions with matter in conventional radiotherapy Courtesy of Elekta

electrons

X

X

Linac for electrons @3 GHz 5-20 MeV

tumour

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Multileaf collimator

1 linac every 250,000 inhabitants

20 000 patients per year every 10 million inhabitants 30

Interactions with matter in conventional radiotherapy with electrons

with photons

4.5 MeV

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Interactions with matter in conventional radiotherapy Ee max ≈ EX≈ 2Ke/5

dose

% of max dose

EX

transition region

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depth

DOSE

KERMA

depth in water

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The sparing of the skin increases with the energy Ee max ≈ EX = 2 Ke / 5 Rcm = Ke MeV / 5

% of max dose

20 MeV

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depth in water

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A last point: quality of a photon radiation field

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THE END

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