basic radiation physics of protons - cern · photons and electrons protons • interactions of a...
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Michael Goitein, PSI teaching course January, 2010 1
Basic Radiation Physics of Protons
Michael Goitein Harvard Medical School and
Ankerstrasse 1,5210 Windisch, Switzerland [email protected]
Michael Goitein, PSI teaching course January, 2010 2
OVERVIEW
•
Interactions of individual particles with single atoms
photons and electronsprotons
•
Interactions of a proton beam in bulk matterin a water bucket
photons (briefly)protons
in simple inhomogeneitiesin complex inhomogeneities (e.g. the patient)
distal edge degradationin a moving medium
interaction between delivery dynamics and target motion
Michael Goitein, PSI teaching course January, 2010 3
INTERACTIONS OF PHOTONS
AND ELECTRONS
Michael Goitein, PSI teaching course January, 2010 4
PHOTON
INTERACTIONS
Illustrations from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
•
Compton scattering
•
Pair production
+
-
•
Photoelectric effect
dominates in the dominates in the radiotherapeutic radiotherapeutic energy rangeenergy range
Michael Goitein, PSI teaching course January, 2010 5
PHOTON
INTERACTIONS
•
Compton scattering
In the energy range of interest:In the energy range of interest:both the scattered photon and the ejected electron tend to go both the scattered photon and the ejected electron tend to go off in the nearoff in the near--forward direction (within forward direction (within ~~1010°°))the scattered photon and the ejected electron partition the the scattered photon and the ejected electron partition the incident photonincident photon’’s energy nears energy near--arbitrarilyarbitrarily
the photon is scatteredthe photon is scattered and may suffer a further and may suffer a further
interaction interaction ––
if so, almost if so, almost certainly a Compton certainly a Compton scattering interactionscattering interaction
what about the what about the electron?electron?
Illustration from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
the atom is ionized,the atom is ionized, potentially leading to potentially leading to
biological damagebiological damage
dominates in the dominates in the radiotherapeutic radiotherapeutic energy rangeenergy range
Michael Goitein, PSI teaching course January, 2010 6
ELECTRON
INTERACTIONS
•
Ionization (Coulomb effect)
•
Coulomb scattering by the atomic nucleus
•
Bremsstrahlung
•
Excitation (Coulomb effect)
dominatedominate (in the (in the
radiotherapeutic radiotherapeutic energy range)energy range)
Illustrations from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
an atomic electron is an atomic electron is knocked out of the atom, knocked out of the atom, thereby ionizing it thereby ionizing it ––
potentially leading to potentially leading to biological damage biological damage of the of the struck cellstruck cell
meanwhile, both electrons meanwhile, both electrons will go off and almost will go off and almost certainly induce further certainly induce further ionizations ionizations biological biological damage to further cellsdamage to further cells
the incident electron may be the incident electron may be scattered by the positively scattered by the positively charged nucleus charged nucleus ––
the main effect the main effect of which is to alter its directionof which is to alter its direction
Michael Goitein, PSI teaching course January, 2010 7
RELATIVE LIKELIHOODS OF INTERACTIONS (in the energy ranges of interest)
•
PhotonsBeing neutral, photons interact with atoms only weakly –
via the interactions of their
electrical/magnetic fields with atomic constituentsthe mean free path of a photon in the energy range of interest
is very approximately 20cm (i.e. a few percent chance of a single interaction per centimeter of travel)
•
ElectronsBeing charged, electrons interact with the charged constituents of atoms (orbiting electrons and the nucleus) very readily
a few-MeV electron will, together with secondary electrons that it sets loose, ionize some tens to hundreds of thousands of atoms per centimeter of travel
Michael Goitein, PSI teaching course January, 2010 8
HOW DOES RADIATION DEPOSIT ENERGY IN TISSUES?
X-ray
electronnucleus
atom within a cell
Michael Goitein, PSI teaching course January, 2010 9
HOW DOES RADIATION DEPOSIT ENERGY IN TISSUES?
X-ray
electron
nucleus
atom within a cell
scattered X-ray
Michael Goitein, PSI teaching course January, 2010 10
HOW DOES RADIATION DEPOSIT ENERGY IN TISSUES?
X-ray
nucleus
atom within a cell
scattered X-ray
X-ray energy
is lost and is
deposited locally
Michael Goitein, PSI teaching course January, 2010 11
DEPOSITED ENERGY = DOSE
•
The interactions of radiations with atoms result in the transfer of energy from the particles to the medium
•
The energy loss per unit mass is called the dose1 Joule / kilogram = 1 gray (Gy)
> 96% of energy appears as heat
•
The energy loss has two consequences:it heats up
the medium (via vibration
and rotation of molecules)it damages the molecules
of the medium
(primarily via ionization of atoms)
Michael Goitein, PSI teaching course January, 2010 12
HOW DOES RADIATION DAMAGE BIOLOGICAL TISSUES?
physicsatom within
a cell
1) ionize atoms 2) vibrate/rotate
heat
Michael Goitein, PSI teaching course January, 2010 13
HOW DOES RADIATION DAMAGE BIOLOGICAL TISSUES?
physicschemistry
H2
O H2
O+
+ e-
H2
O+
+ e-
H•
+ OH•
i.e. formation of highly reactive free radicals within cells
atom within a cell
1) ionize atoms 2) vibrate/rotate
heat
Michael Goitein, PSI teaching course January, 2010 14
HOW DOES RADIATION DAMAGE BIOLOGICAL TISSUES?
physicschemistry
H2
O H2
O+
+ e-
H2
O+
+ e-
H•
+ OH•
i.e. formation of highly reactive free radicals within cells
atom within a cell
1) ionize atoms 2) vibrate/rotate
heat
biology
free radical +
DNA
causes single- or double-strand
DNA break
DNA damage repairedcell “death”
(or direct breaking of molecular bond by ionization)
tumour
/ whole organ damage
Dose is merely a surrogate for what we care about –
namely, biological effect
Michael Goitein, PSI teaching course January, 2010 15
INTERACTIONS OF PROTONS
Michael Goitein, PSI teaching course January, 2010 16
PROTON
INTERACTIONS
Illustrations from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
•
Ionization (Coulomb effect)
•
Coulomb interactions with the atomic nucleus
•
Nuclear interactions with the atomic nucleus
An atomic electron is knocked out of the An atomic electron is knocked out of the atom, thereby ionizing it atom, thereby ionizing it ––
potentially potentially
leading to biological damage of the cell. leading to biological damage of the cell. Meanwhile, the incident proton will go off Meanwhile, the incident proton will go off and induce further ionizationsand induce further ionizations
The difference from electrons is that, The difference from electrons is that, due to the protondue to the proton’’s much greater s much greater mass, it looses very little energy, and mass, it looses very little energy, and is very little deflected.is very little deflected.
The incident proton may be scattered The incident proton may be scattered by the positively charged nucleus by the positively charged nucleus ––
thereby altering its direction, but with thereby altering its direction, but with little energy losslittle energy loss
The incident proton may interact (via The incident proton may interact (via the strong interaction force) with the the strong interaction force) with the nucleus and break it up into nucleus and break it up into fragments. Fractional energy:fragments. Fractional energy:
protonsprotons 60%60%neutronsneutrons 20%20%αα
particlesparticles 3%3%deuteronsdeuterons 1.6%1.6%othersothers 2%2%uninterestin
g
uninteresting
•
Bremsstrahlung
Michael Goitein, PSI teaching course January, 2010 17
BULK MATTER
10
Michael Goitein, PSI teaching course January, 2010 18
BULK MATTER: Dose Distribution in a Water Bucket
Michael Goitein, PSI teaching course January, 2010 19
PHOTONS
in bulk matter
most most likelylikely
(b)
next most next most likelylikely
(c)
22ndnd
most most likelylikely
(a)
Q: What is the most likely thing to happen when a photon is directed towards a bucket
of water?
A: Absolutely nothing!
Michael Goitein, PSI teaching course January, 2010 20
PHOTONS
in bulk matter
most most likelylikely
(b)
next most next most likelylikely
(c)
22ndnd
most most likelylikely
(a)
A: Absolutely nothing!
Q: What is the most likely thing to happen when a photon is directed towards a bucket
of water?
meanwhile, the incident electron will go off and almost certainly induce further ionizations
Compton collisions
reminder:
Michael Goitein, PSI teaching course January, 2010 21
PHOTONS
in bulk matter
Michael Goitein, PSI teaching course January, 2010 22schematic
Depth (cm)
0255075
100125150
0 5 10 15 20 25
Dos
e (%
)
near-exponential
fall-off (typical of uncorrelated catastrophic events)
“skin sparing”
(due to build-up
of electronic
equilibrium)
020406080100
-10 -5 0 5 10
Dos
e (%
)
Distance (cm)
~8 mm tail due to secondary X-rays
penumbra due to transport of secondary electrons
70 Gy~80 Gy
~60 Gy
Michael Goitein, PSI teaching course January, 2010 23
PROTONS
in bulk matter
depth dose
cross-field
(lateral) profile
Michael Goitein, PSI teaching course January, 2010 24
PROTONS
in bulk matter
PHOTONSPHOTONS PROTONSPROTONS
proton deflected by scattering off atomic nuclei
electron set loose by scattering of proton off atomic electron
Michael Goitein, PSI teaching course January, 2010 25
PROTONS
in bulk matter
PHOTONSPHOTONS PROTONSPROTONS
proton deflected by scattering off atomic nuclei
electron set loose by scattering of proton off atomic electron
numerous additional
electrons set loose
-
creating a local dose “splash”
100’s of thousands of “splashes”, giving rise to the:
0
20
40
6080
100
0 10 155Depth (cm)
Dos
e (%
)
Bragg peak(named after Sir William Henry Bragg –
not his
son, Sir William
Lawrence
Bragg)
Michael Goitein, PSI teaching course January, 2010 26
CONSTRUCTION OF THE BRAGG PEAK principal effect: Coulomb interactions of protons with atomic electrons
Δx
Ε−ΔEΕ
Ζ,Α
vz E0
zAZ
xE
v1 22
⎟⎠
⎞⎜⎝
⎛∝ΔΔ
Illustration from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
depthR0
NUMBER vs
DEPTHnumber of
protons (%)
= dose
ΔEΔx
depth
(increasing)
R0
energy and
velocity
(decreasing)
E0 0
●
●A
B
vA
vB
DOSE vs
DEPTH
Michael Goitein, PSI teaching course January, 2010 27
depth (gm.cm-2)
R0
DOSE vs
DEPTHdose
(rel.)
CONSTRUCTION OF THE BRAGG PEAK: 3 components
1
Coulomb interactions of protons with atomic electrons
depth (gm.cm-2)
R0
NUMBER vs
DEPTH# of protons
100%
50%
0%
2
Near-Gaussian blurring of the Bragg peak due to energy loss fluctuations and
beam energy spread
3
Nuclear interactions with atomic nuclei -
including build-up of interaction products
Michael Goitein, PSI teaching course January, 2010 28
IMPORTANCE OF THE INGREDIENTS OF THE PROTON DEPTH-DOSE DISTRIBUTION
1
Ionizations produced primarily by electrons set loose by Coulomb interactions of protons with orbiting electrons of the atoms in the medium
Bethe-Bloch formula
3
Nuclear interactions of the protons with the nuclei of atoms in the medium
typically ~1%/cm
2
Near-Gaussian blurring of the Bragg peakstatistical fluctuations in the interactions
σ
typically ~1% of the proton rangeenergy distribution of protons
σ
also typically ~1% of the proton range
σ
typically ~1.5% overall
Michael Goitein, PSI teaching course January, 2010 29
WIDTH OF BRAGG PEAK vs.
BEAM ENERGY SPREAD
Fluence and dose as a function of depth for proton beams of a given range and different energy spreads, illustrating r0
= d80
.
50%
80%
20%
dd8080--2020
typically typically about 2.5% about 2.5% times rangetimes rangei.e. ~
4 mm at 15
cm depth
Figure courtesy of Bernie Gottschalk
N.B. range is stable at the 50% level while dose is stable at the 80% level.The 80% dose level is important!
Michael Goitein, PSI teaching course January, 2010 30
RANGE SHIFTING: by altering residual range or
beam energy
depth0
dose
(rel.)
69
MeV
231
MeV
When primary energy changed
graph courtesy
of Gottschalk
rangerange
EE1.81.8∝∝
ΔΔR R ≈≈
1.1% . R1.1% . R
When residual penetration changed by adding material upstream
When primary beam energy changed
The penetration of protons in the patient can be very accurately adjusted using either one of these methods.
Michael Goitein, PSI teaching course January, 2010 31
AREAL DENSITY (brief interlude)
•
It is common to express the thickness of a piece of material, not in terms of its physical thickness, l, but in terms of what is called its areal density, given by ρ•
l where ρ
is the density of the material.
•
If l
is expressed in cm, and ρ
in units of gm.cm-3, then areal density has the units of gm.cm-2.
E E-ΔE
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
18% thinner
i.e. 0.85 cm
areal density
= 1.18•
0.85 = 1.0 gm.cm-2plastic
ρ=1.18
gm/cm3
H2
O
ρ=1.0
gm/cm3
1.0 cm……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
……
15%
1.15
Michael Goitein, PSI teaching course January, 2010 32
SPREAD-OUT BRAGG PEAK (SOBP)
~10 MeV photonsTarget volume
Michael Goitein, PSI teaching course January, 2010 33
LATERAL DOSE DISTRIBUTION
Dominated by multiple Coulomb scattering
20
Michael Goitein, PSI teaching course January, 2010 34
protons protons protons
5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Michael Goitein, PSI teaching course January, 2010 35
PROTON SCATTERING IN A THIN
SCATTERER
protons
Illustration from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
Molière theory
plural/single
Coulomb scattering
proton halo from inelastic nuclear scattering
dose
multiple
Coulomb scattering
distance
0
20
2.21Xl
pcMeVzβ
θ ⋅≈
where X0
is the radiation length of the scattering medium and varies approximately as:
( )1+ZZA
Michael Goitein, PSI teaching course January, 2010 36
PROTON SCATTERING IN A THICK
SCATTERER
Image courtesy of Eros Pedroni
protons
σσ ≈≈
2% of range2% of range
fwhm = fwhm = 2.35 2.35 σσ ≈≈
4.7% of range4.7% of range
i.e. ~7mm at 15cm depth
infinitesimal pencil beam (scattering only)
Minimum penumbra (80-
20%) due to scattering
within the patient:uniform beam
penumbra ≥
1.68 σ
i.e. ≥
5 mm at 15 cm depthintensity modulated beam
(using edge enhancement)
penumbra ≥
1.12 σ
i.e. ≥
3.3 mm at 15 cm depth
Figure courtesy of B. Gottschalk
variation of σ
along the proton path
Michael Goitein, PSI teaching course January, 2010 37
PROTON SCATTERING IN A THICK
SCATTERER: very narrow pencil beams → depressed Bragg peak
Image courtesy of Eros Pedroni
protons
“low”
doseis augmented by neighbors
40 mm diameter20 mm
20, 40
Hong et al. Phys Med Biol
41: 1305, 1996
40 mm diameter20 mm10 mm5 mm3 mm2 mm
2 3 510
20, 40
Hong et al. Phys Med Biol
41: 1305, 1996
but, this does not mean that a broad beam made up of many pencil beams has a degraded Bragg peak:
Michael Goitein, PSI teaching course January, 2010 38
BROAD BEAM OF PROTONS
protons
-1.0 0 1.0-2.0 2.0
distance (cm)
dose
(rel
ativ
e) at distal end of SOBP
at entrance
5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Image courtesy of Radhe Mohan
80%
20%
dd8080--2020
≈≈
1.68 1.68 σσ
≈≈
3.3% of range3.3% of rangei.e. ~5 mm at 15cm depth (~ 6mm in practice)
Michael Goitein, PSI teaching course January, 2010 39
SUMMARY
11
plateau protons plateau protons –– excitation/ionization; & excitation/ionization; &
nuclear interactionsnuclear interactions22
excitation/ionization excitation/ionization (Bragg peaks);(Bragg peaks);
& nuclear interactions& nuclear interactions33
range straggling and range straggling and energy spreadenergy spread
44
multiple Coulomb multiple Coulomb scattering off nucleiscattering off nuclei
55
wide angle Coulomb wide angle Coulomb scattering off nucleiscattering off nuclei
66
protons and neutrons protons and neutrons from nuclear interactionsfrom nuclear interactions
77
neutrons from nuclear neutrons from nuclear interactionsinteractions
dose
distancepenumbra
(80%-20%)
R80
dose
depth
distal fall-off
(80%-20%)
1
1
2
2
3
7
5
4
5
6
4
7 2
6
3
4
Illustration from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
30
Michael Goitein, PSI teaching course January, 2010 40
INHOMOGENEITIES
infinite slab
proton beam
sliver
proton beam
semi-infinite slab
proton beam
patient:
Michael Goitein, PSI teaching course January, 2010 41
INFINITE SLAB
Andy Koehler’s “proof”
Lamb chop in H2
O tank
Michael Goitein, PSI teaching course January, 2010 42
overlying material
SEMI-INFINITE SLAB
A B
Goitein et al. Med Phys. 1978; 5; 265-273.
Michael Goitein, PSI teaching course January, 2010 43
SLIVER
Goitein and Sisterton
Radiation Research 1978; 74:217-230
Michael Goitein, PSI teaching course January, 2010 44
IN THE PATIENT
Urie et al. Phys Med Biol
1986; 31: 1
Michael Goitein, PSI teaching course January, 2010 45
pristine Bragg Peak
spread-out Bragg Peak
THE PATIENT: RANGE DEGRADATION
Urie et al. Phys Med Biol
1986; 31: 1
pristine Bragg Peak
spread-out Bragg Peak
Irradiation of a water-filled human skull
Michael Goitein, PSI teaching course January, 2010 46
Dose (%)
Depth (cm)15
20
8090
100
50
0 5 100
Dose (%)
Depth (cm)15
20
8090
100
50
0 5 100
distal edge degradation
Michael Goitein, PSI teaching course January, 2010 48
and in the Lung…
protonsprotons
average density
= 0.2 gm/cm3
density
= 1.0 gm/cm3
3x3x3 mm3
Images courtesy of Uwe Titt, MDACC
80 mm
50 mm
20 mm
in lung
Michael Goitein, PSI teaching course January, 2010 49
WHAT CAN ONE DO ABOUT DISTAL DOSE DEGRADATION?
•
Be aware of it!
•
When possible, avoid beam directions which pass through regions of complex inhomogeneity
especially when pointed at a critical OAR just beyond the target
volume
•
Allow an adequate safety margin distal to the target volume
dose
distance
target
volume
•
Perform uncertainty analysisto assess uncertainty in dose and hence the size of safety margin needed
•
Improve calculational method to further reduce uncertaintyuse fine image and calculational grids (≤
1mm)
Monte carlo
•
Possibly “fill in”
dose with another beam
Michael Goitein, PSI teaching course January, 2010 50
BEAM DELIVERY
38
Michael Goitein, PSI teaching course January, 2010 51
SCATTERED BEAM GENERATION
patient
aperture
protons
first
scatterer
range modulator
Illustration from M. Goitein “Radiation Oncology:
A Physicist’s-Eye View”
©
Springer, 2007
second
scatterer
compensator
full dose
region
tumor
(i.e. target volume)
compensated
range modulator
Wilson, Koehler
Gottschalk
Koehler, Gottschalk
Wagner
Michael Goitein, PSI teaching course January, 2010 52
Scanned beams are needed for IMPT
gantry “nozzle”
-
can rotate around patient
control system
scanning magnets
Pretty much the only way to implement IMRT with protons (IMPT) is to deliver the protons by scanning a pencil beam of protons throughout the target volume
Scanned beams are the wave of the future
pioneered at PSI
Michael Goitein, PSI teaching course January, 2010 53
SHARP PEMUMBRAS ARE NEEDED CLINICALLY!
•
Scattering systemsdouble scattering degrades the penumbra
because it increases the effective source sizethe aperture needs to be close to patient
but not too close because of edge scattering
•
Scanning systemsa narrow pencil beam (fwhm < 10mm σ < 4 mm)is essential for close work at medium and small depthsscattering in the patient dominates edge sharpness –
but only
for deep-seated targets
Inadequate attention in current commercial systems is being given to achieving good edge sharpness
(i.e. to getting a sharp penumbra)
Michael Goitein, PSI teaching course January, 2010 54
THE FLY IN THE IMPT OINTMENT: motion
scan
scancell
cell has received ~5 times intended dose
scancell
cell has received ~0 times intended dose
Michael Goitein, PSI teaching course January, 2010 55
Intestinal Crypt Regeneration in Mice in PSI’s Scanned Proton Beam (contd.)
dose(GyE)
# regenerated crypts
/ circumference
Scatter in results interpreted as due to ±
14% (SD) dose mottle
as a consequence of about 1 to 2 mm motion of the intestine during scan
Michael Goitein, PSI teaching course January, 2010 56
and the simplest solution presently is:
1.
reduce motion as much as possible –
e.g. bypatient immobilizationrepiration
gating / breath hold
abdominal compression, etc.
2.
apply the treatment multiple times (repaint) thereby averaging out the dose mottle
the more repaintings, the lesser the dose mottle ( )about 10 repaintings (reducing dose mottle by about a factor of 3)
seems a reasonable goal
The timing of the repainting is critical. The period of respiration, tρ
, (~4s) sets the scale.•
ideally, the entire dose delivery would occur in much less than tρ
,
–
but this is impractical.•
alternatively, the each repainting should take place on the order of, or more than, tρ
–
i.e. roughly every few secondsand each repainting should be given either randomly in time, or at progressive phases of the repiratory cycle.
nDD 1
∝Δ
Michael Goitein, PSI teaching course January, 2010 57
DOSE HOMOGENEITY vs.
# REPAINTINGS
Grözinger
et al. Phys. Med. Biol. 51 (2006) 3517–3531and thesis: http://elib.tu-
darmstadt.de/diss/000407/
motion: periodic with amplitude of 13.5 mm and period of 3.3 seconds
scanned beam: fwhm = 6.5 mm
scan vs.
motion not “de-synchronized”
in this simulation
Michael Goitein, PSI teaching course January, 2010 59
The commercial realization of beam scanning (and, hence, IMPT)
is immature and the currently implemented solutions appear to be inadequate for general clinical use.
Michael Goitein, PSI teaching course January, 2010 60
RECENT TEXTS
•
Gottschalk B (2004) “Passive Beam Spreading in Proton Radiation Therapy”
http://huhepl.harvard.edu/~gottschalk/
File named “pbs.pdf”
can be extracted from BGdocs.zip See, also, PowerPoint lectures in BGtalks.zip
•
ICRU report 78 “Prescribing, Recording and Reporting Proton Beam Therapy”
Oxford U. Press. Journal of the ICRU 7(2); 2007
•
T.F. Delaney and H.M. Kooy (eds) “Proton and Charged Particle
Radiotherapy”
Lippincott
Williams and Wilkins, 2008
•
M. Goitein “Radiation Oncology: A Physicist’s-Eye View”
Springer, 2008
Michael Goitein, PSI teaching course January, 2010 61
the end