basic radiation physics of protons - cern · photons and electrons protons • interactions of a...

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]


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


INTERACTIONS OF PHOTONS

AND ELECTRONS


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


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:


©

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


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)



©

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


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


HOW DOES RADIATION DEPOSIT ENERGY IN TISSUES?

X-ray

electronnucleus

atom within a cell



X-ray

electron

nucleus

atom within a cell

scattered X-ray



X-ray

nucleus

atom within a cell

scattered X-ray

X-ray energy

is lost and is

deposited locally


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)


HOW DOES RADIATION DAMAGE BIOLOGICAL TISSUES?

physicsatom within

a cell

1) ionize atoms 2) vibrate/rotate

heat



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


heat



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


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


INTERACTIONS OF PROTONS


PROTON

INTERACTIONS



©

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


BULK MATTER

10


BULK MATTER: Dose Distribution in a Water Bucket


PHOTONS

in bulk matter

most most likelylikely

(b)

next most next most likelylikely

(c)

22ndnd


(a)

Q: What is the most likely thing to happen when a photon is directed towards a bucket

of water?

A: Absolutely nothing!


PHOTONS

in bulk matter


(b)

next most next most likelylikely

(c)

22ndnd


(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:


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


PROTONS

in bulk matter

depth dose

cross-field

(lateral) profile


PROTONS

in bulk matter

PHOTONSPHOTONS PROTONSPROTONS

proton deflected by scattering off atomic nuclei

electron set loose by scattering of proton off atomic electron


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)


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



©

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


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


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


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!


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.


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


SPREAD-OUT BRAGG PEAK (SOBP)

~10 MeV photonsTarget volume


LATERAL DOSE DISTRIBUTION

Dominated by multiple Coulomb scattering

20


protons protons protons

5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


PROTON SCATTERING IN A THIN

SCATTERER

protons



©

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


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


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:


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)


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



©

Springer, 2007

30


INHOMOGENEITIES

infinite slab

proton beam

sliver

proton beam

semi-infinite slab

proton beam

patient:


INFINITE SLAB

Andy Koehler’s “proof”

Lamb chop in H2

O tank


overlying material

SEMI-INFINITE SLAB

A B

Goitein et al. Med Phys. 1978; 5; 265-273.


SLIVER

Goitein and Sisterton

Radiation Research 1978; 74:217-230


IN THE PATIENT

Urie et al. Phys Med Biol

1986; 31: 1


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


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


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


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


BEAM DELIVERY

38


SCATTERED BEAM GENERATION

patient

aperture

protons

first

scatterer

range modulator



©

Springer, 2007

second

scatterer

compensator

full dose

region

tumor

(i.e. target volume)

compensated

range modulator

Wilson, Koehler

Gottschalk

Koehler, Gottschalk

Wagner


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


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)


THE FLY IN THE IMPT OINTMENT: motion

scan

scancell

cell has received ~5 times intended dose

scancell

cell has received ~0 times intended dose


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


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


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


The commercial realization of beam scanning (and, hence, IMPT)

is immature and the currently implemented solutions appear to be inadequate for general clinical use.


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


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basic radiation physics of protons - cern · photons and electrons protons • interactions of a...

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