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Interactions of charged particles
with the patient
I.
II.
The depth-dose distribution
- How the Bragg Peak comes about (Thomas Bortfeld)
The lateral dose distribution
- Dose calculation issues (Bernard Gottschalk)
Course Outline
Feb 5
Feb 12
Feb 19
Feb 26
Mar 4
Mar 11
Mar 18
Mar 25
Apr 1
Apr 8
Apr 15
Apr 22
Apr 29
May 6
May 13
Introduction: Physical, biological and clinical rationale
 Bragg Peak, LET, OER, RBE
Acceleration of charged particles
 Standard techniques (with demonstration)
 Laser acceleration
 Dielectric wall acceleration
Making a useful treatment beam
 beam line and “gantry”
 scattering system, collimation
 magnetic beam scanning
Interactions of charged particles with the patient
Neutrons in particle therapy
 Neutrons as a by-product of charged particle therapy
 Biological effects
 Neutron therapy
Biological aspects of particle therapy
Spring break (HMS)
Spring break (MIT)
Imaging for charged particle therapy
 Image guided procedures
 In-vivo dose localization through imaging
Treatment planning for charged particle therapy
 Dose computation
 Issue of motion
 Practical demonstrations at MGH
Clinical treatments
Dosimetry and quality assurance
Intensity-modulated particle therapy
Treatment with heavier charged particles
Special topics and wrap-up
T. Bortfeld
J. Flanz
B. Gottschalk
B. Gottschalk,
T. Bortfeld
H. Paganetti
H. Paganetti
H.-M. Lu
M. Engelsman
M. Engelsman
T. Bortfeld
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
3
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
4
Energy loss:
Energy-range relationship, protons in water
200 MeV, 26.0 cm
150 MeV, 15.6 cm
100 MeV, 7.6 cm
50 MeV, 2.2 cm
10 cm
20 cm
30 cm
5
Depth
Energy loss:
Energy-range relationship, protons in water
Convex shape  Bragg peak
6
Energy loss:
Energy-range relationhip
• General approximate relationship:
R0 = a E0p
• For energies below 10 MeV:
p = 1.5
(Geiger’s rule)
• Between 10 and 250 MeV:
p = 1.8
• Bragg-Kleeman rule: a = c (Aeff)0.5/r
7
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 is
R0 - z = a Ep(z)
• E(z) = a-1/p (R0 - z)1/p
• This is the energy at depth z
8
Energy loss: Stopping power
• Stopping power:
dE
1
1/ p 1
R0  z 
S ( z)  

1/ p
dz pa
• The stopping power is (within certain
approximations) proportional to the dose
9
Energy loss: Stopping power
(Dose = Stopping power)
10
Energy loss: Stopping power
• Stopping power:
dE
1
1/ p 1
R0  z 
S ( z)  

1/ p
dz pa
• Expressed as a function of the energy:
1 1 p
S ( z) 
E ( z)
pa
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Energy loss: Stopping power
• Bethe-Bloch equation:
charge of projectile
2 2

z

Z
2me  c Tmax
S ( z )  Kr
ln  2
2
A    I (1   )
2
p
2
electron density
of target
2
v
2
  2 E
c


2
  2    


ionization potential
12
Energy loss: Bethe Bloch equation
13
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
s approx. 1% of R0
14
Convolution for range straggling
Theoretical
w/o Straggling
Range Straggling
Distribution
*
= ?
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What is Convolution?
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What is Convolution?
17
Convolution for range straggling
Theoretical
w/o Straggling
Range Straggling
Distribution
*
Real Bragg Peak
=
Parabolic cylinder
function
18
Energy loss: Range straggling
With consideration of
range straggling
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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
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Intensity reduction: Nuclear interactions
Rule of thumb: 1% loss of intensity per cm (in water)
21
Intensity reduction: Nuclear interactions
• Nuclear interactions lead to local and nonlocal dose deposition (neutrons!)
22
PET isotope activation by protons
• 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
Mainly 11C (T1/2 = 20.3 min)
Proton
and 15O (T1/2 = 121.8 s)
Proton
16
15O
O
Atomic nucleus
of tissue
Neutron
E=110 MeV
Target fragment
Dose proportionality:
15O, 11C,
...
A(r) ≠ D(r)
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Pituitary Adenoma, PET imaging
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The Bragg curve
z80=R0
T. Bortfeld, Med Phys 24:2024-2033,25 1997
Protons vs. carbon ions (physical dose)
Wilkens & Oelfke, IJROBP 70:262-266, 2008
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Tissue inhomogeneities:
A lamb chop experiment
© A.M. Koehler, Harvard Cyclotron
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Proton range issues:
Range uncertainties due to setup
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:
Distal margins
30
Proton range issues:
Tumor motion and shrinkage
Initial Planning CT
GTV 115 cc
5 weeks later
GTV 39 cc
S. Mori, G. Chen
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Proton range issues:
Tumor motion and shrinkage
What you see in the plan…
Beam stops at distal edge
Is not always what you get
Beam overshoot
S. Mori, G. Chen
32
Proton range issues:
CT artifacts
gold implants
overshoot?
33
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
34
Tissue inhomogeneities
Goitein & Sisterson, Rad Res 74:217-230 35(1978)
Tissue inhomogeneities
Bragg Peak degradation in the patient
M. Urie et al., Phys Med Biol 31:1-15, 1986
36
Problems
• Consider the proton treatment of a lung tumor
(density r = 1) with a diameter of 2 cm. The tumor
is surrounded by healthy lung tissue (r = 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?
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