Physics of particles. H. Paganetti PhD Massachusetts General Hospital & Harvard Medical School

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1 Physics of particles H. Paganetti PhD Massachusetts General Hospital & Harvard Medical School

2 Introduction Dose The ideal dose distribution ideal Dose: Energy deposited Energy/Mass Depth [J/kg] [Gy]

3 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

4 Introduction Dose deposition Electrons

5 Introduction Dose Photons BEAM ideal Depth

6 Introduction Also: Modulation of intensities INFN

7 Introduction Photons Charge: 0 Indirect Ionization Electrons Charge: -1 Direct Ionization Mass: 512 kev Protons Charge: +1 Direct Ionization Mass: 2,000 m e

8 Introduction Dose deposition Electrons Protons

9 Introduction The Bragg curve 120 Mono-energetic proton beam 100 Dose [%] depth [mm]

10 Introduction Dose EXTRA DOSE Photons BEAM Protons ideal Beam energy controls the range Depth

11 Electromagnetic energy loss of protons Distal distribution p p e 120 Ionization 100 Excitation 80 Dose [%] Interaction probability is proportional to proton energy depth [mm]

12 Bethe-Bloch equation de dx nere mec 2 2 z mec T ln 2 2 I (1 - ) max zL 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

13 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

14 area A N protons Δx Dose = fluence mass stopping power

15 Range (cm) Protons/Ions Basic Physics Dose [%] Radiography depth [mm] Deep seated tumors Typical treatments Eye treatments Energy (MeV)

16 Protons GSI

17 Dose [%] 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

18 Beam Range 120 Dose [%] % 90% 80% depth [mm] H. Paganetti Proton Therapy Physics Taylor & Francis / CRC Press

19 Electromagnetic energy loss of protons Lateral distribution p q p Multiple Coulomb scattering (small angles) Proton Pencil Beam

20 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

21 Multiple Coulomb Scattering 160 MeV 200 MeV

22 s MCS [mm] Multiple Coulomb Scattering 4 3 Protons (148 MeV) 12 C-ions (270 MeV/A) Depth [mm]

23 80-20 % Distance (cm) Multiple Coulomb Scattering /20 Penumbra Comparison 17 cm Protons MV Photons cm 20 cm 25 cm Norm alization Depth

24 Dose Protons/Ions Basic Physics 100 Ø Ø 8 mm Ø 6 mm Ø 4 mm Ø 2 mm Depth A. Koehler (HCL)

25 Nuclear interactions of protons p p p p g, n Elastic nuclear collision (large q) Nuclear interaction

26 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

27 Nuclear interactions of protons Carbon (closed circles) Oxygen (open circles) H. Paganetti Proton Therapy Physics Taylor & Francis / CRC Press

28 Total fluence Primary fluence Nuclear build-up

29 total energy deposited Contribution in % primary protons secondary protons alphas & recoils

30 Nuclear interactions of heavy ions 12 C 12 C Elastic nuclear collision (large q) 4 He 12 C g, n Nuclear interaction (fragmentation)

31 Nuclear interactions of heavy ions Fragmentation tails I. Pshenischnov

32 Nuclear interactions of heavy ions

33 Nuclear interactions of heavy ions I. Pshenischnov

34 Clinical dose distributions Dose Photons BEAM Protons ideal Depth

35 Clinical dose distributions width thickness Spread-out Bragg Peak

36 Clinical dose distributions Multiple scattering angle and energy loss for 160 MeV protons traversing 1 g/cm2 of various materials

37 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

38 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

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