1. Interactions of charged particles with the patient I.The depth-dose distribution - How the Bragg Peak comes about - (Thomas Bortfeld) II.The lateral dose distribution - Dose calculation issues - (Bernard Gottschalk)

2. Course Outline

3. 3 How the Bragg peak comes about 1) Energy loss –collisions with atomic electrons 2) Intensity reduction –nuclear interactions W.R. Leo: Techniques for Nuclear & Particle Physics Experiments 2nd ed. Springer, 1994 T. Bortfeld: An Analytical Approximation of the Bragg Curve for Therapeutic Proton Beams, Med. Phys. 24:2024-2033, 1997

4. 4 Energy loss Protons are directly ionizing radiation (as opposed to photons) Protons suffer some 100,000s of interactions per cm They will eventually lose all their energy and come to rest

5. 5 Energy loss: Energy-range relationship, protons in water 10 cm20 cm30 cm Depth 50 MeV, 2.2 cm100 MeV, 7.6 cm150 MeV, 15.6 cm200 MeV, 26.0 cm

6. 6 Energy loss: Energy-range relationship, protons in water Convex shape  Bragg peak

7. 7 General approximate relationship: R 0 =  E 0 p For energies below 10 MeV: p = 1.5(Geiger’s rule) Between 10 and 250 MeV: p = 1.8 Bragg-Kleeman rule:  = c (A eff ) 0.5 /  Energy loss: Energy-range relationhip

8. 8 Energy loss: Depth dependence of the energy Protons lose energy between z = 0 and z = R 0 in the medium At a depth z the residual range is R 0 - z =  E p (z) E(z) =  -1/p (R 0 - z) 1/p This is the energy at depth z

9. 9 Energy loss: Stopping power Stopping power: The stopping power is (within certain approximations) proportional to the dose

10. 10 Energy loss: Stopping power (Dose = Stopping power)

11. 11 Energy loss: Stopping power Stopping power: Expressed as a function of the energy:

12. 12 Energy loss: Stopping power Bethe-Bloch equation: electron density of target charge of projectile ionization potential

13. 13 Energy loss: Bethe Bloch equation

14. 14 Energy loss: Range straggling So far we used the continuously slowing down approximation (CSDA) In reality, protons lose their energy in individual collisions with electrons Protons with the same initial energy E 0 may have slightly different ranges: “Range straggling” Range straggling is Gaussian  approx. 1% of R 0

15. 15 * = ? Theoretical w/o Straggling Range Straggling Distribution Convolution for range straggling

16. 16 What is Convolution?

17. 17 What is Convolution?

18. 18 * = Theoretical w/o Straggling Range Straggling Distribution Real Bragg Peak Convolution for range straggling Parabolic cylinder function

19. 19 Energy loss: Range straggling With consideration of range straggling

20. 20 Intensity reduction: Nuclear interactions A certain fraction of protons have nuclear interactions with the absorbing matter (tissue), mainly with 16 O Those protons are “lost” from the beam

21. 21 Intensity reduction: Nuclear interactions Rule of thumb: 1% loss of intensity per cm (in water)

22. 22 Intensity reduction: Nuclear interactions Nuclear interactions lead to local and non- local dose deposition (neutrons!)

23. 23 Positron Emission Tomography (PET) is potentially a unique tool for in vivo monitoring of the precision of the treatment in ion therapy In-situ, non-invasive detection of  + -activity induced by irradiation Before collisionAfter collision Proton Target fragment Proton Atomic nucleus of tissue 16 O 15 O Neutron Mainly 11 C ( T 1/2 = 20.3 min) and 15 O ( T 1/2 = 121.8 s) Dose proportionality: A ( r ) ≠ D ( r ) 15 O, 11 C,... E =110 MeV PET isotope activation by protons

24. 24 Pituitary Adenoma, PET imaging

25. 25 The Bragg curve T. Bortfeld, Med Phys 24:2024-2033, 1997 z 80 =R 0

26. 26 Protons vs. carbon ions (physical dose) Wilkens & Oelfke, IJROBP 70:262-266, 2008

27. 27 Tissue inhomogeneities: A lamb chop experiment © A.M. Koehler, Harvard Cyclotron

28. Jan 08 Chen, Rosenthal, et al., IJROBP 48(3):339, 2000 Proton range issues: Range uncertainties due to setup

29. Jan 11 Chen, Rosenthal, et al., IJROBP 48(3):339, 2000 Proton range issues: Range uncertainties due to setup

30. 30 Proton range issues: Distal margins

31. 31 Initial Planning CT GTV 115 cc 5 weeks later GTV 39 cc Proton range issues: Tumor motion and shrinkage S. Mori, G. Chen

32. 32 What you see in the plan… Beam stops at distal edge Is not always what you get Beam overshoot Proton range issues: Tumor motion and shrinkage S. Mori, G. Chen

33. 33 Proton range issues: CT artifacts

34. 34 Proton range issues: Reasons for range uncertainties Differences between treatment preparation and treatment delivery (~ 1 cm) –Daily setup variations –Internal organ motion –Anatomical/ physiological changes during treatment Dose calculation errors (~ 5 mm) –Conversion of CT number to stopping power –Inhomogeneities, metallic implants –CT artifacts

35. 35 Tissue inhomogeneities Goitein & Sisterson, Rad Res 74:217-230 (1978)

36. 36 Tissue inhomogeneities Bragg Peak degradation in the patient M. Urie et al., Phys Med Biol 31:1-15, 1986

37. 37 Problems Consider the proton treatment of a lung tumor (density  = 1) with a diameter of 2 cm. The tumor is surrounded by healthy lung tissue (  = 0.2). The treatment beam is designed to stop right on the edge of the tumor. After a couple of weeks the tumor shrinks down to 1.5 cm. By how much does the beam extend into the healthy lung now? Consider a hypothetical world in which the proton energy is proportional to the proton range. How would that affect the shape of the Bragg peak?