Transcript Document

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
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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
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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
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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
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Energy loss: Stopping power
(Dose = Stopping power)
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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
 2me  c Tmax
Z
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
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Energy loss: Bethe Bloch equation
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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
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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?
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Convolution for range straggling
Theoretical
w/o Straggling
Range Straggling
Distribution
*
Real Bragg Peak
=
Parabolic cylinder
function
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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)
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Intensity reduction: Nuclear interactions
• Nuclear interactions lead to local and nonlocal dose deposition (neutrons!)
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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
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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
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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
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Proton range issues:
CT artifacts
gold implants
overshoot?
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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
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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
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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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