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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)
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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
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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
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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
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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
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Energy loss: Energy-range relationship, protons in water
Convex shape Bragg peak
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• 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
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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 isR0 - z = Ep(z)
• E(z) = -1/p (R0 - z)1/p
• This is the energy at depth z
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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
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Energy loss: Stopping power
(Dose = Stopping power)
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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
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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
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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 approx. 1% of R0
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* = ?
Theoreticalw/o Straggling
Range StragglingDistribution
Convolution for range straggling
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What is Convolution?
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What is Convolution?
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* =
Theoreticalw/o Straggling
Range StragglingDistribution
Real Bragg Peak
Convolution for range straggling
Parabolic cylinderfunction
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Energy loss: Range straggling
With consideration ofrange 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 non-local dose deposition (neutrons!)
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• 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
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Pituitary Adenoma, PET imaging
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The Bragg curve
T. Bortfeld, Med Phys 24:2024-2033, 1997
z80=R0
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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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Jan 08
Chen, Rosenthal, et al., IJROBP 48(3):339, 2000
Proton range issues:Range uncertainties due to setup
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Jan 11
Chen, Rosenthal, et al., IJROBP 48(3):339, 2000
Proton range issues:Range uncertainties due to setup
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Proton range issues:Distal margins
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Initial Planning CTGTV 115 cc
5 weeks laterGTV 39 cc
Proton range issues:Tumor motion and shrinkage
S. Mori, G. Chen
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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
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Proton range issues:CT artifacts
gold implants
overshoot?
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 (1978)
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Tissue inhomogeneitiesBragg 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 = 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?