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)

Feb 5 Introduction: Physical, biological and clinical rationale Bragg Peak, LET, OER, RBE

T. Bortfeld

Feb 12 Acceleration of charged particles Standard techniques (with demonstration) Laser acceleration Dielectric wall acceleration

J. Flanz

Feb 19 Making a useful treatment beam beam line and “gantry” scattering system, collimation magnetic beam scanning

B. Gottschalk

Feb 26 Interactions of charged particles with the patient B. Gottschalk, T. Bortfeld

Mar 4 Neutrons in particle therapy Neutrons as a by-product of charged particle therapy Biological effects Neutron therapy

H. Paganetti

Mar 11 Biological aspects of particle therapy H. Paganetti Mar 18 Spring break (HMS) Mar 25 Spring break (MIT) Apr 1 Imaging for charged particle therapy

Image guided procedures In-vivo dose localization through imaging

H.-M. Lu

Apr 8 Treatment planning for charged particle therapy Dose computation Issue of motion Practical demonstrations at MGH

M. Engelsman

Apr 15 Clinical treatments Apr 22 Dosimetry and quality assurance M. Engelsman Apr 29 Intensity-modulated particle therapy T. Bortfeld May 6 Treatment with heavier charged particles May 13 Special topics and wrap-up

Course Outline

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 Experiments2nd ed. Springer, 1994

T. Bortfeld: An Analytical Approximation of the Bragg Curve for Therapeutic Proton Beams, Med. Phys. 24:2024-2033, 1997

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

Energy loss: Energy-range relationship, protons in water

10 cm 20 cm 30 cmDepth

50 MeV, 2.2 cm

100 MeV, 7.6 cm

150 MeV, 15.6 cm

200 MeV, 26.0 cm

6

Energy loss: Energy-range relationship, protons in water

Convex shape Bragg peak

7

• General approximate relationship:R0 = E0

p

• For energies below 10 MeV:p = 1.5 (Geiger’s rule)

• Between 10 and 250 MeV:p = 1.8

• Bragg-Kleeman rule: = c (Aeff)0.5/

Energy loss: Energy-range relationhip

8

Energy loss: Depth dependence of the energy

• Protons lose energy between z = 0 and z = R0 in the medium

• At a depth z the residual range isR0 - z = Ep(z)

• E(z) = -1/p (R0 - z)1/p

• This is the energy at depth z

9

Energy loss: Stopping power

• Stopping power:

• The stopping power is (within certain approximations) proportional to the dose

1/10/1

1)( p

pzR

pdz

dEzS

10

Energy loss: Stopping power

(Dose = Stopping power)

11

Energy loss: Stopping power

• Stopping power:

• Expressed as a function of the energy:

1/10/1

1)( p

pzR

pdz

dEzS

)(1

)( 1 zEp

zS p

12

Energy loss: Stopping power

• Bethe-Bloch equation:

222max

22e

2

2

2)1(

2ln)(

I

Tcmz

A

ZKzS p

Ec

v

2

22

electron densityof target

charge of projectile

ionization potential

13

Energy loss: Bethe Bloch equation

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 E0 may have slightly different ranges:“Range straggling”

• Range straggling is Gaussian approx. 1% of R0

15

* = ?

Theoreticalw/o Straggling

Range StragglingDistribution

Convolution for range straggling

16

What is Convolution?

17

What is Convolution?

18

* =

Theoreticalw/o Straggling

Range StragglingDistribution

Real Bragg Peak

Convolution for range straggling

Parabolic cylinderfunction

19

Energy loss: Range straggling

With consideration ofrange straggling

20

Intensity reduction: Nuclear interactions

• A certain fraction of protons have nuclear interactions with the absorbing matter (tissue), mainly with 16O

• Those protons are “lost” from the beam

21

Intensity reduction: Nuclear interactions

Rule of thumb: 1% loss of intensity per cm (in water)

22

Intensity reduction: Nuclear interactions

• Nuclear interactions lead to local and non-local dose deposition (neutrons!)

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 collision After collision

Proton

Target fragment

Proton

Atomic nucleusof tissue

16O 15ONeutron

Mainly 11C (T1/2 = 20.3 min) and 15O (T1/2 = 121.8 s)

Dose proportionality:

A(r) ≠ D(r)

15O, 11C, ...

E=110 MeV

PET isotope activation by protons

24

Pituitary Adenoma, PET imaging

25

The Bragg curve

T. Bortfeld, Med Phys 24:2024-2033, 1997

z80=R0

26

Protons vs. carbon ions (physical dose)

Wilkens & Oelfke, IJROBP 70:262-266, 2008

27

Tissue inhomogeneities:A lamb chop experiment

© A.M. Koehler, Harvard Cyclotron

Jan 08

Chen, Rosenthal, et al., IJROBP 48(3):339, 2000

Proton range issues:Range uncertainties due to setup

Jan 11

Chen, Rosenthal, et al., IJROBP 48(3):339, 2000

Proton range issues:Range uncertainties due to setup

30

Proton range issues:Distal margins

31

Initial Planning CTGTV 115 cc

5 weeks laterGTV 39 cc

Proton range issues:Tumor motion and shrinkage

S. Mori, G. Chen

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

Proton range issues:CT artifacts

gold implants

overshoot?

gold implants

overshoot?

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

Tissue inhomogeneities

Goitein & Sisterson, Rad Res 74:217-230 (1978)

36

Tissue inhomogeneitiesBragg Peak degradation in the patient

M. Urie et al., Phys Med Biol 31:1-15, 1986

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?