Physics of particles H. Paganetti PhD Massachusetts General Hospital & Harvard Medical School
Introduction Dose The ideal dose distribution ideal Dose: Energy deposited Energy/Mass Depth [J/kg] [Gy]
Introduction Photoelectric Effect Photon ejects electron from an atom. Compton Effect Photons scattering from atomic electrons. Pair Production Photons above twice the electron rest mass energy can create a electron positron pair. g e g g q g e + f e - Z e Z
Introduction Dose deposition Electrons
Introduction Dose Photons BEAM ideal Depth
Introduction Also: Modulation of intensities INFN
Introduction Photons Charge: 0 Indirect Ionization Electrons Charge: -1 Direct Ionization Mass: 512 kev Protons Charge: +1 Direct Ionization Mass: 2,000 m e
Introduction Dose deposition Electrons Protons
Introduction The Bragg curve 120 Mono-energetic proton beam 100 Dose [%] 80 60 40 20 0 0 50 100 150 200 250 300 depth [mm]
Introduction Dose EXTRA DOSE Photons BEAM Protons ideal Beam energy controls the range Depth
Electromagnetic energy loss of protons Distal distribution p p e 120 Ionization 100 Excitation 80 Dose [%] 60 40 20 0 0 50 100 150 200 250 300 Interaction probability is proportional to proton energy depth [mm]
Bethe-Bloch equation de dx 0 2 2 nere mec 2 2 z 2 2 2 2mec T ln 2 2 I (1 - ) max - 2 2 + 2zL 1 ( ) + 2z 2 L 2 ( ) - 2 C Z - + G I : mean excitation energy, material-dependent δ : density correction C : is the shell correction, important at low energies T max : maximum energy transfer to an electron L 1 : Barkas correction (z 3 ) L 2 : Bloch (z 4 ) correction G : Mott corrections
Bethe [-Bloch] equation - de dx = 4pnk2 Z 2 e 4 é ln 2mc2 b 2 ê mc 2 b 2 I (1- b 2 ) - b 2 ë ù ú û = v/c
area A N protons Δx Dose = fluence mass stopping power
Range (cm) Protons/Ions Basic Physics Dose [%] 120 100 80 60 40 20 40 Radiography 0 0 50 100 150 200 250 300 depth [mm] 35 30 Deep seated tumors 25 20 Typical treatments 15 10 5 Eye treatments 0 0 50 100 150 200 250 300 Energy (MeV)
Protons GSI
120 100 Dose [%] 80 60 40 20 0 50 100 150 200 250 300 depth [mm] Protons lose their energy in individual collisions with electrons Protons with the same initial energy may have slightly different ranges: Range straggling 0
Beam Range 120 Dose [%] 100 80 60 40 100% 90% 80% 20 0 0 50 100 150 200 250 300 depth [mm] H. Paganetti Proton Therapy Physics Taylor & Francis / CRC Press
Electromagnetic energy loss of protons Lateral distribution p q p Multiple Coulomb scattering (small angles) Proton Pencil Beam
Multiple Coulomb Scattering Protons are deflected in the electric field of the nuclei. In general, multiple deflections will occur For treatment planning related calculations a purely Gaussian approximation is a good approximation, except at the very end of the range
Multiple Coulomb Scattering 160 MeV 200 MeV
s MCS [mm] Multiple Coulomb Scattering 4 3 Protons (148 MeV) 12 C-ions (270 MeV/A) 2 1 0 0 50 100 150 Depth [mm]
80-20 % Distance (cm) Multiple Coulomb Scattering 1.00 0.75 80/20 Penumbra Comparison 17 cm Protons 0.50 15 MV Photons 0.25 0.00 15 cm 20 cm 25 cm Norm alization Depth
Dose Protons/Ions Basic Physics 100 Ø 80 60 Ø 8 mm Ø 6 mm 40 20 Ø 4 mm Ø 2 mm Depth A. Koehler (HCL)
Nuclear interactions of protons p p p p g, n Elastic nuclear collision (large q) Nuclear interaction
Nuclear interactions of protons A certain fraction of protons have nuclear interactions in tissue, mainly with 16 O (about 1% per cm of all protons) Nuclear interactions cause a decrease in primary proton fluence Nuclear interactions lead to secondary particles and thus to local and non-local dose deposition (neutrons!) The dose from nuclear interactions is negligible in the Bragg peak
Nuclear interactions of protons Carbon (closed circles) Oxygen (open circles) H. Paganetti Proton Therapy Physics Taylor & Francis / CRC Press
Total fluence Primary fluence Nuclear build-up
total energy deposited Contribution in % primary protons secondary protons alphas & recoils
Nuclear interactions of heavy ions 12 C 12 C Elastic nuclear collision (large q) 4 He 12 C g, n Nuclear interaction (fragmentation)
Nuclear interactions of heavy ions Fragmentation tails I. Pshenischnov
Nuclear interactions of heavy ions
Nuclear interactions of heavy ions I. Pshenischnov
Clinical dose distributions Dose Photons BEAM Protons ideal Depth
Clinical dose distributions width thickness Spread-out Bragg Peak
Clinical dose distributions Multiple scattering angle and energy loss for 160 MeV protons traversing 1 g/cm2 of various materials
Clinical dose distributions H i g h - D e n s i t y S t r u c t u r e T a r g e t V o l u m e B e a m C r i t i c a l S t r u c t u r e B o d y A p e r t S u u r r e f a c e
Take Home Messages Heavy charged particles interact very differently from photons (used in conventional radiation therapy) The most important interactions are ionization, Coulomb scattering, and nonelastic nuclear interactions Heavy charged particle treatments are associated with the reduction of the total energy deposited in the patient by more than a factor of 2